Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
6401	Use the Rational Roots Test to Find All Possible Roots	x^3-2x	$x^{3} - 2 x$
6402	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3-5x^2+8x-24	$f (x) = x^{3} - 5 x^{2} + 8 x - 24$
6403	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^4+x^3+2x^3+4x-8	$f (x) = x^{4} + x^{3} + 2 x^{3} + 4 x - 8$
6404	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^4-2x^3-8x^2+18x-9	$f (x) = x^{4} - 2 x^{3} - 8 x^{2} + 18 x - 9$
6405	Rationalize the Denominator	( square root of 10+ square root of 3)/( square root of 10- square root of 3)	$\frac{\sqrt{10} + \sqrt{3}}{\sqrt{10} - \sqrt{3}}$
6406	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3-20x^2+123x-216	$f (x) = x^{3} - 20 x^{2} + 123 x - 216$
6407	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3-10x^2-4x+40	$f (x) = x^{3} - 10 x^{2} - 4 x + 40$
6408	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3+3x^2-13x-15	$f (x) = x^{3} + 3 x^{2} - 13 x - 15$
6409	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^4-81	$f (x) = x^{4} - 81$
6410	Use the Rational Roots Test to Find All Possible Roots	f(x)=2x^5+4x^3-7x^3-4x^2+6x+12	$f (x) = 2 x^{5} + 4 x^{3} - 7 x^{3} - 4 x^{2} + 6 x + 12$
6411	Use the Rational Roots Test to Find All Possible Roots	f(x)=3x^4-11x^3-3x^2-6x+8	$f (x) = 3 x^{4} - 11 x^{3} - 3 x^{2} - 6 x + 8$
6412	Use the Rational Roots Test to Find All Possible Roots	f(x)=5x^6+7x^4-58x^3-24x	$f (x) = 5 x^{6} + 7 x^{4} - 58 x^{3} - 24 x$
6413	Use the Rational Roots Test to Find All Possible Roots	f(x)=6x^4+7x^3-12x^2-3x+2	$f (x) = 6 x^{4} + 7 x^{3} - 12 x^{2} - 3 x + 2$
6414	Use the Rational Roots Test to Find All Possible Roots	f(x)=-49x^5-x^4+x+7	$f (x) = - 49 x^{5} - x^{4} + x + 7$
6415	Use the Rational Roots Test to Find All Possible Roots	f(x)=10x^3+17x^2-97x-20	$f (x) = 10 x^{3} + 17 x^{2} - 97 x - 20$
6416	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^4-4x^3+9x^2-20x+20	$f (x) = x^{4} - 4 x^{3} + 9 x^{2} - 20 x + 20$
6417	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^4-6x^3-31x^2+216x-180	$f (x) = x^{4} - 6 x^{3} - 31 x^{2} + 216 x - 180$
6418	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^4-8x^3+15x^2+58x+34	$f (x) = x^{4} - 8 x^{3} + 15 x^{2} + 58 x + 34$
6419	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3-3x^2-4x+12	$f (x) = x^{3} - 3 x^{2} - 4 x + 12$
6420	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^4-x^3-20x^2	$f (x) = x^{4} - x^{3} - 20 x^{2}$
6421	Use the Rational Roots Test to Find All Possible Roots	3x^3-7x^2+6x-14	$3 x^{3} - 7 x^{2} + 6 x - 14$
6422	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3-10x^2+44x-69	$f (x) = x^{3} - 10 x^{2} + 44 x - 69$
6423	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3+8x^2+11x-20	$f (x) = x^{3} + 8 x^{2} + 11 x - 20$
6424	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3+9x^2-135x-143	$f (x) = x^{3} + 9 x^{2} - 135 x - 143$
6425	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3-10x^2+9x-24	$f (x) = x^{3} - 10 x^{2} + 9 x - 24$
6426	Use the Rational Roots Test to Find All Possible Roots	f(x)=12x^3+73x^2+5x-6	$f (x) = 12 x^{3} + 73 x^{2} + 5 x - 6$
6427	Use the Rational Roots Test to Find All Possible Roots	f(x)=3x^3+4x^2-7x+2	$f (x) = 3 x^{3} + 4 x^{2} - 7 x + 2$
6428	Use the Rational Roots Test to Find All Possible Roots	f(x)=3x^3+43x^2+43x+27	$f (x) = 3 x^{3} + 43 x^{2} + 43 x + 27$
6429	Use the Rational Roots Test to Find All Possible Roots	f(x)=3x^3-3x^2-10x+6	$f (x) = 3 x^{3} - 3 x^{2} - 10 x + 6$
6430	Use the Rational Roots Test to Find All Possible Roots	f(x)=3x^4-4x^3-12x^2-20x-6	$f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} - 20 x - 6$
6431	Use the Rational Roots Test to Find All Possible Roots	f(x)=2x^3-7x^2-17x+10	$f (x) = 2 x^{3} - 7 x^{2} - 17 x + 10$
6432	Use the Rational Roots Test to Find All Possible Roots	f(x)=4x^3-x+5	$f (x) = 4 x^{3} - x + 5$
6433	Use the Rational Roots Test to Find All Possible Roots	f(x)=5x^3-3x^2-7x-2	$f (x) = 5 x^{3} - 3 x^{2} - 7 x - 2$
6434	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3+5x^2-28x-32	$f (x) = x^{3} + 5 x^{2} - 28 x - 32$
6435	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^2-2x-3	$f (x) = x^{2} - 2 x - 3$
6436	Use the Rational Roots Test to Find All Possible Roots	f(x)=(2x-1)(x+1)(x-5)	$f (x) = (2 x - 1) (x + 1) (x - 5)$
6437	Use the Rational Roots Test to Find All Possible Roots	f(x)=1/7x^2+1/7x-2/7	$f (x) = \frac{1}{7} x^{2} + \frac{1}{7} x - \frac{2}{7}$
6438	Use the Rational Roots Test to Find All Possible Roots	3x^4-10x^3-9x^2+40x-12	$3 x^{4} - 10 x^{3} - 9 x^{2} + 40 x - 12$
6439	Use the Rational Roots Test to Find All Possible Roots	11x^3+17x^2-21x+5	$11 x^{3} + 17 x^{2} - 21 x + 5$
6440	Use the Rational Roots Test to Find All Possible Roots	-2x^4+x^3-19x^2+9	$- 2 x^{4} + x^{3} - 19 x^{2} + 9$
6441	Use the Rational Roots Test to Find All Possible Roots	2x^4+x^3-35x^2-113x+65	$2 x^{4} + x^{3} - 35 x^{2} - 113 x + 65$
6442	Use the Rational Roots Test to Find All Possible Roots	-2x^4+13x^3-21x^2+2x+8	$- 2 x^{4} + 13 x^{3} - 21 x^{2} + 2 x + 8$
6443	Use the Rational Roots Test to Find All Possible Roots	2x^3-3x^2-4x+6	$2 x^{3} - 3 x^{2} - 4 x + 6$
6444	Use the Rational Roots Test to Find All Possible Roots	2x^3-7x^2-17x+10	$2 x^{3} - 7 x^{2} - 17 x + 10$
6445	Use the Rational Roots Test to Find All Possible Roots	22x^4+9x^3+30x^2+63x+28	$22 x^{4} + 9 x^{3} + 30 x^{2} + 63 x + 28$
6446	Combine	(8x)/(yz)+(4y)/(xz)	$\frac{8 x}{y z} + \frac{4 y}{x z}$
6447	Find the LCD	1-(cos(x)^2)/(sin(x)^2)	$1 - \frac{\cos^{2} (x)}{\sin^{2} (x)}$
6448	Find the LCD	(cos(x))/(sin(x))+(sin(x))/(cos(x))	$\frac{\cos (x)}{\sin (x)} + \frac{\sin (x)}{\cos (x)}$
6449	Find the LCD	(sin(x))/(1+cos(x))*(1-cos(x))/(1-cos(x))	$\frac{\sin (x)}{1 + \cos (x)} \cdot \frac{1 - \cos (x)}{1 - \cos (x)}$
6450	Combine	1/(1-cos(x))+1/(1+cos(x))	$\frac{1}{1 - \cos (x)} + \frac{1}{1 + \cos (x)}$
6451	Find the LCD	(2+tan(x)^2)/(sec(x)^2)-1	$\frac{2 + \tan^{2} (x)}{\sec^{2} (x)} - 1$
6452	Find the GCF	cos(x)-cos(x)sin(x)^2	$\cos (x) - \cos (x) \sin^{2} (x)$
6453	Find the GCF	5x^2-18x+9	$5 x^{2} - 18 x + 9$
6454	Find the GCF	cos((13pi)/15)cos(-pi/5)-sin((13pi)/15)sin(-pi/5)	$\cos (\frac{13 π}{15}) \cos (- \frac{π}{5}) - \sin (\frac{13 π}{15}) \sin (- \frac{π}{5})$
6455	Find the LCD	7/(6p)-3/(2p^2)	$\frac{7}{6 p} - \frac{3}{2 p^{2}}$
6456	Find the LCD	(cos(x))/(1+sin(x))+(1+sin(x))/(cos(x))	$\frac{\cos (x)}{1 + \sin (x)} + \frac{1 + \sin (x)}{\cos (x)}$
6457	Find the LCD	(sin(x))/(cos(x))+sin(x)	$\frac{\sin (x)}{\cos (x)} + \sin (x)$
6458	Combine	cos(pi/12)cos((-pi)/6)+sin(pi/12)sin((-pi)/6)	$\cos (\frac{π}{12}) \cos (\frac{- π}{6}) + \sin (\frac{π}{12}) \sin (\frac{- π}{6})$
6459	Combine	cos(112)cos(45)+sin(112)sin(45)	$\cos (112) \cos (45) + \sin (112) \sin (45)$
6460	Combine	cos(2x)+2sin(x)^2	$\cos (2 x) + 2 \sin^{2} (x)$
6461	Combine	cos(x)+cos(x+2pi)+cos(x+4pi)	$\cos (x) + \cos (x + 2 π) + \cos (x + 4 π)$
6462	Combine	cos((5pi)/7)cos(pi/21)+sin((5pi)/7)sin(pi/21)	$\cos (\frac{5 π}{7}) \cos (\frac{π}{21}) + \sin (\frac{5 π}{7}) \sin (\frac{π}{21})$
6463	Combine	sin(32)cos(42)+cos(32)sin(42)	$\sin (32) \cos (42) + \cos (32) \sin (42)$
6464	Combine	cos((5pi)/12)+cos(pi/12)	$\cos (\frac{5 π}{12}) + \cos (\frac{π}{12})$
6465	Combine	sin(pi/6)+cos(pi/6)	$\sin (\frac{π}{6}) + \cos (\frac{π}{6})$
6466	Find the LCD	(sin(x)-cos(x))/(cos(x))+(sin(x)+cos(x))/(sin(x))	$\frac{\sin (x) - \cos (x)}{\cos (x)} + \frac{\sin (x) + \cos (x)}{\sin (x)}$
6467	Combine	(6x)/(7x^2-6x-16)-(5x)/(7x^2-15x+2)	$\frac{6 x}{7 x^{2} - 6 x - 16} - \frac{5 x}{7 x^{2} - 15 x + 2}$
6468	Combine	cube root of 3z- square root of 3z	$\sqrt[3]{3 z} - \sqrt{3 z}$
6469	Combine	3a(-a+5)-4(2a-3)^2-a(a-1)	$3 a (- a + 5) - 4 {(2 a - 3)}^{2} - a (a - 1)$
6470	Solve for x	log base 4 of 7x-6=3	$\log_{4} (7 x - 6) = 3$
6471	Find the LCM	7/(6x^2) , 9/(14x^3)	$\frac{7}{6 x^{2}}$ , $\frac{9}{14 x^{3}}$
6472	Find the LCM	x^2+11x , x^2	$x^{2} + 11 x$ , $x^{2}$
6473	Combine	sin(pi/12)cos((7pi)/12)+cos(pi/12)sin((7pi)/12)	$\sin (\frac{π}{12}) \cos (\frac{7 π}{12}) + \cos (\frac{π}{12}) \sin (\frac{7 π}{12})$
6474	Combine	3-x^3-7	$3 - x^{3} - 7$
6475	Find the LCM	(12a+2) , (7a+7)	$(12 a + 2)$ , $(7 a + 7)$
6476	Combine	sin(5)cos(40)+cos(5)sin(40)	$\sin (5) \cos (40) + \cos (5) \sin (40)$
6477	Combine	square root of 8z^3+10z square root of 2z	$\sqrt{8 z^{3}} + 10 z \sqrt{2 z}$
6478	Find the LCM	x , ( square root of 3)/3	$x$ , $\frac{\sqrt{3}}{3}$
6479	Find the LCM	2 , 3i , -3i	$2$ , $3 i$ , $- 3 i$
6480	Find the LCD	(69) , (68)	$(69)$ , $(68)$
6481	Find the LCD	7/6 , 5/3 , 13/6	$\frac{7}{6}$ , $\frac{5}{3}$ , $\frac{13}{6}$
6482	Find the LCD	2 , 3 , square root of 2i	$2$ , $3$ , $\sqrt{2 i}$
6483	Determine the Possible Number of Real Roots	x^3-3x+12	$x^{3} - 3 x + 12$
6484	Determine the Possible Number of Real Roots	x^2-2x-3	$x^{2} - 2 x - 3$
6485	Determine the Possible Number of Real Roots	f(x)=4x^3+23x^2-14x-5	$f (x) = 4 x^{3} + 23 x^{2} - 14 x - 5$
6486	Determine the Possible Number of Real Roots	x^3-3x^2-4x+12	$x^{3} - 3 x^{2} - 4 x + 12$
6487	Determine the Possible Number of Real Roots	x^3-3x^2-6x+8	$x^{3} - 3 x^{2} - 6 x + 8$
6488	Determine the Possible Number of Real Roots	3x^4-x^2+1	$3 x^{4} - x^{2} + 1$
6489	Determine the Possible Number of Real Roots	4x^10+20x^9+35x^8+127x^7+35x^6-533x^5+433x^4-487x^3+321x^2+153x-108	$4 x^{10} + 20 x^{9} + 35 x^{8} + 127 x^{7} + 35 x^{6} - 533 x^{5} + 433 x^{4} - 487 x^{3} + 321 x^{2} + 153 x - 108$
6490	Determine the Possible Number of Real Roots	4x^4-3x^3+3x^2+x+3	$4 x^{4} - 3 x^{3} + 3 x^{2} + x + 3$
6491	Determine the Possible Number of Real Roots	x^3+5x	$x^{3} + 5 x$
6492	Determine the Possible Number of Real Roots	2x^3-14x^2+9x+24	$2 x^{3} - 14 x^{2} + 9 x + 24$
6493	Determine the Possible Number of Real Roots	x^3-x+13	$x^{3} - x + 13$
6494	Determine the Possible Number of Real Roots	2x^4-7x^3+x^2-18x+3	$2 x^{4} - 7 x^{3} + x^{2} - 18 x + 3$
6495	Determine the Possible Number of Real Roots	x^4-4x^3+8x^2-16x+16	$x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16$
6496	Determine the Possible Number of Real Roots	3x^5-13x^4+13x^3+9x^2-16x+4	$3 x^{5} - 13 x^{4} + 13 x^{3} + 9 x^{2} - 16 x + 4$
6497	Determine the Possible Number of Real Roots	4x^3-12x^2+15	$4 x^{3} - 12 x^{2} + 15$
6498	Determine the Possible Number of Real Roots	-9x^2+2x+2	$- 9 x^{2} + 2 x + 2$
6499	Determine the Possible Number of Real Roots	7x^3+11x^2-13x+3	$7 x^{3} + 11 x^{2} - 13 x + 3$
6500	Use the Rational Roots Test to Find All Possible Roots	2(x)^5-10x^4+18x^3-18x^2+16x-8	$2 {(x)}^{5} - 10 x^{4} + 18 x^{3} - 18 x^{2} + 16 x - 8$