Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
6001	Find the Roots (Zeros)	f(x)=5(x+7)^2(x-7)^3	$f (x) = 5 {(x + 7)}^{2} {(x - 7)}^{3}$
6002	Find the Roots (Zeros)	f(x)=50x^4-150x^3-450x^2+1350x	$f (x) = 50 x^{4} - 150 x^{3} - 450 x^{2} + 1350 x$
6003	Find the Roots (Zeros)	f(x)=6(x-7)(x-9)^2	$f (x) = 6 (x - 7) {(x - 9)}^{2}$
6004	Find the Roots (Zeros)	P(x)=x^4+3x^2-4	$P (x) = x^{4} + 3 x^{2} - 4$
6005	Find the Roots (Zeros)	P(x)=x^4-4x^2	$P (x) = x^{4} - 4 x^{2}$
6006	Find the Roots (Zeros)	P(x)=2x^4-13x^3+6x^2+64x-32	$P (x) = 2 x^{4} - 13 x^{3} + 6 x^{2} + 64 x - 32$
6007	Find the Roots (Zeros)	q(x)=x^4-7x^3-5x+10	$q (x) = x^{4} - 7 x^{3} - 5 x + 10$
6008	Find the Roots (Zeros)	f(x)=3x^3-21x^2+36x	$f (x) = 3 x^{3} - 21 x^{2} + 36 x$
6009	Find the Roots (Zeros)	P(x)=12x^3-20x^2+x+3	$P (x) = 12 x^{3} - 20 x^{2} + x + 3$
6010	Find the Roots (Zeros)	P(x)=-2x^4-x^3+3x^2	$P (x) = - 2 x^{4} - x^{3} + 3 x^{2}$
6011	Find the Roots (Zeros)	f(x)=9x^4+28x^3+48x^2+140x+15	$f (x) = 9 x^{4} + 28 x^{3} + 48 x^{2} + 140 x + 15$
6012	Find the Roots (Zeros)	f(x)=(9x-1)/(x-1)	$f (x) = \frac{9 x - 1}{x - 1}$
6013	Find the Roots (Zeros)	f(x)=2^x+3	$f (x) = 2^{x} + 3$
6014	Find the Roots (Zeros)	f(x)=4x^3-12x^2-40x	$f (x) = 4 x^{3} - 12 x^{2} - 40 x$
6015	Find the Domain and Range	r(x)=(8x-8)/(x+2)	$r (x) = \frac{8 x - 8}{x + 2}$
6016	Find the Domain and Range	r(x)=(2x^2+2x-4)/(x^2+x)	$r (x) = \frac{2 x^{2} + 2 x - 4}{x^{2} + x}$
6017	Find the Domain and Range	r(x)=(2x+4)/(x-1)	$r (x) = \frac{2 x + 4}{x - 1}$
6018	Find the Domain and Range	r(x)=(x^2-4x-5)/(x-3)	$r (x) = \frac{x^{2} - 4 x - 5}{x - 3}$
6019	Find the Domain and Range	p(x)=(2x-1)(x+1)(x-3)	$p (x) = (2 x - 1) (x + 1) (x - 3)$
6020	Find the Domain and Range	q(x)=(x-2)^2-6	$q (x) = {(x - 2)}^{2} - 6$
6021	Find the Domain and Range	r(x)=(x^2+3x)/(x^2-x-6)	$r (x) = \frac{x^{2} + 3 x}{x^{2} - x - 6}$
6022	Find the Domain and Range	s(x)=(x^3-x^2)/(x^3-3x-2)	$s (x) = \frac{x^{3} - x^{2}}{x^{3} - 3 x - 2}$
6023	Find the Domain and Range	r(x)=(4x^2+16x-180)/(x^2+4x)	$r (x) = \frac{4 x^{2} + 16 x - 180}{x^{2} + 4 x}$
6024	Find the Domain and Range	r(x)=(x-1)/(x^2-4)	$r (x) = \frac{x - 1}{x^{2} - 4}$
6025	Find the Roots (Zeros)	f(x)=(x-1)^2-9	$f (x) = {(x - 1)}^{2} - 9$
6026	Find the Roots (Zeros)	f(x)=\|x\|+9	$f (x) = \| x \| + 9$
6027	Find the Roots (Zeros)	f(x) = square root of 49-x^2	$f (x) = \sqrt{49 - x^{2}}$
6028	Find the Roots (Zeros)	f(x)=x^2-6x+8	$f (x) = x^{2} - 6 x + 8$
6029	Find the Roots (Zeros)	f(x)=x^2-7	$f (x) = x^{2} - 7$
6030	Find the Roots (Zeros)	f(x)=-x^2+4x-5	$f (x) = - x^{2} + 4 x - 5$
6031	Find the Roots (Zeros)	f(x)=-x^2-4	$f (x) = - x^{2} - 4$
6032	Find the Roots (Zeros)	f(x)=(6x-6)/(x+2)	$f (x) = \frac{6 x - 6}{x + 2}$
6033	Find the Roots (Zeros)	f(x) = square root of 4x-x^2	$f (x) = \sqrt{4 x - x^{2}}$
6034	Find the Roots (Zeros)	f(x) = square root of x-6	$f (x) = \sqrt{x - 6}$
6035	Find the Roots (Zeros)	f(x) = cube root of x+4	$f (x) = \sqrt[3]{x} + 4$
6036	Find the Roots (Zeros)	f(x) = fifth root of x-4+2	$f (x) = \sqrt[5]{x - 4} + 2$
6037	Find the Roots (Zeros)	f(x)=-2 square root of x-1+3	$f (x) = - 2 \sqrt{x - 1} + 3$
6038	Use the Factor Theorem to Determine if +x=0 is a Factor	f(x)=4x^2-2x-3 , x=0	$f (x) = 4 x^{2} - 2 x - 3$ , $x = 0$
6039	Find the Roots (Zeros)	f(x)=16-(x-1)^2	$f (x) = 16 - {(x - 1)}^{2}$
6040	Find the Roots (Zeros)	f(x)=2(x-1)^2-2	$f (x) = 2 {(x - 1)}^{2} - 2$
6041	Find the Roots (Zeros)	f(x)=2x-3	$f (x) = 2 x - 3$
6042	Find the Roots (Zeros)	f(x)=3+(1/10)^x	$f (x) = 3 + {(\frac{1}{10})}^{x}$
6043	Find the Roots (Zeros)	f(x)=x^3-4	$f (x) = x^{3} - 4$
6044	Find the Roots (Zeros)	f(x)=4x^2-2x+1	$f (x) = 4 x^{2} - 2 x + 1$
6045	Use the Factor Theorem to Determine if x>=0 is a Factor	f(x)=x^2-4 , x=0	$f (x) = x^{2} - 4$ , $x = 0$
6046	Find the Roots (Zeros)	f(x)=x^3-2x^2-21x-18	$f (x) = x^{3} - 2 x^{2} - 21 x - 18$
6047	Find the Roots (Zeros)	f(x)=(2/3)^(5x)	$f (x) = {(\frac{2}{3})}^{5 x}$
6048	Find the Roots (Zeros)	f(x)=5/6x-25	$f (x) = \frac{5}{6} x - 25$
6049	Find the Roots (Zeros)	f(x)=x^3-2x^2-36x+72	$f (x) = x^{3} - 2 x^{2} - 36 x + 72$
6050	Graph	(x^2)/400+(y^2)/625=1	$\frac{x^{2}}{400} + \frac{y^{2}}{625} = 1$
6051	Find the Roots (Zeros)	f(x)=x^3-13x^2-x-182	$f (x) = x^{3} - 13 x^{2} - x - 182$
6052	Find the Roots (Zeros)	f(x)=x^3+6x^2-9x-14	$f (x) = x^{3} + 6 x^{2} - 9 x - 14$
6053	Use the Rational Roots Test to Find All Possible Roots	x^3-5x^2-4x+20	$x^{3} - 5 x^{2} - 4 x + 20$
6054	Find the Roots (Zeros)	f(x)=3(x-7)(x+5)^4	$f (x) = 3 (x - 7) {(x + 5)}^{4}$
6055	Find the Roots (Zeros)	f(x)=3x^3+39x^2+39x+27	$f (x) = 3 x^{3} + 39 x^{2} + 39 x + 27$
6056	Find the Roots (Zeros)	f(x)=2x^3-13x^2+26x-10	$f (x) = 2 x^{3} - 13 x^{2} + 26 x - 10$
6057	Find the Roots (Zeros)	f(x)=25x^4+126x^3+180x^2+882x+35	$f (x) = 25 x^{4} + 126 x^{3} + 180 x^{2} + 882 x + 35$
6058	Find the Roots (Zeros)	f(x)=25x^4+26x^3+51x^2+52x+2	$f (x) = 25 x^{4} + 26 x^{3} + 51 x^{2} + 52 x + 2$
6059	Find the Roots (Zeros)	f(x)=3x^3-13x^2-59x+21	$f (x) = 3 x^{3} - 13 x^{2} - 59 x + 21$
6060	Find the Roots (Zeros)	f(x)=3x^5+6x^4-x-3	$f (x) = 3 x^{5} + 6 x^{4} - x - 3$
6061	Find the Roots (Zeros)	f(x)=4x^2+8x^3+2	$f (x) = 4 x^{2} + 8 x^{3} + 2$
6062	Find the Roots (Zeros)	f(x)=5x^3-17x^2-14x+8	$f (x) = 5 x^{3} - 17 x^{2} - 14 x + 8$
6063	Find the Roots (Zeros)	f(x)=15x^3+14x^2-3x-2	$f (x) = 15 x^{3} + 14 x^{2} - 3 x - 2$
6064	Find the Roots (Zeros)	f(x)=x^4-8x^3+17x^2-8x+16	$f (x) = x^{4} - 8 x^{3} + 17 x^{2} - 8 x + 16$
6065	Find the Roots (Zeros)	f(x)=-x^6+3x^4+4x^2	$f (x) = - x^{6} + 3 x^{4} + 4 x^{2}$
6066	Find the Roots (Zeros)	f(x)=(x-4)/(x^2-16)	$f (x) = \frac{x - 4}{x^{2} - 16}$
6067	Find the Roots (Zeros)	f(x)=x^4-12x^2-64	$f (x) = x^{4} - 12 x^{2} - 64$
6068	Find the Roots (Zeros)	f(x)=x^4-14x^2-40x-75	$f (x) = x^{4} - 14 x^{2} - 40 x - 75$
6069	Find the Roots (Zeros)	f(x)=x^4-15x^2-16	$f (x) = x^{4} - 15 x^{2} - 16$
6070	Find the Roots (Zeros)	f(x)=x^4-3x^2-x+2	$f (x) = x^{4} - 3 x^{2} - x + 2$
6071	Evaluate Using the Given Value	f(0)=0^2+2(0)	$f (0) = 0^{2} + 2 (0)$
6072	Evaluate Using the Given Value	f(-2)=2^(1-(-2))	$f (- 2) = 2^{1 - (- 2)}$
6073	Evaluate Using the Given Value	f(-2)=1	$f (- 2) = 1$
6074	Evaluate Using the Given Value	f(-2)=2(-2)+3	$f (- 2) = 2 (- 2) + 3$
6075	Evaluate Using the Given Value	f(-1)=34	$f (- 1) = 34$
6076	Evaluate Using the Given Value	3=pi/2+2pin , (3pi)/2+2pin	$3 = \frac{π}{2} + 2 π n$ , $\frac{3 π}{2} + 2 π n$
6077	Evaluate Using the Given Value	square root of x^2-9 , x=3sec(x)	$\sqrt{x^{2} - 9}$ , $x = 3 \sec (x)$
6078	Evaluate Using the Given Value	2/5 , y=5	$\frac{2}{5}$ , $y = 5$
6079	Evaluate Using the Given Value	10=f(-4)	$10 = f (- 4)$
6080	Factor by Grouping	30uv+30u+36u^2+25v	$30 u v + 30 u + 36 u^{2} + 25 v$
6081	Factor by Grouping	4x^2+19x-5	$4 x^{2} + 19 x - 5$
6082	Factor by Grouping	4tan(x)^2-4	$4 \tan^{2} (x) - 4$
6083	Factor by Grouping	5x^3-10x^2+3x-6	$5 x^{3} - 10 x^{2} + 3 x - 6$
6084	Factor by Grouping	5x^2-12x+7	$5 x^{2} - 12 x + 7$
6085	Factor by Grouping	ax-5bx+5ay-25 by	$a x - 5 b x + 5 a y - 25$ by
6086	Factor by Grouping	4x-10	$4 x - 10$
6087	Factor by Grouping	7ax-7bx-2ay+2 by	$7 a x - 7 b x - 2 a y + 2$ by
6088	Factor by Grouping	5ax-5bx-2ay+2 by	$5 a x - 5 b x - 2 a y + 2$ by
6089	Factor by Grouping	tan(x/2)	$\tan (\frac{x}{2})$
6090	Factor by Grouping	y^3-4y^2+3y-12	$y^{3} - 4 y^{2} + 3 y - 12$
6091	Evaluate Using the Given Value	tan(x)=1/5 , csc(x)	$\tan (x) = \frac{1}{5}$ , $\csc (x)$
6092	Evaluate Using the Given Value	sin(-t)=3/8 , csc(t)	$\sin (- t) = \frac{3}{8}$ , $\csc (t)$
6093	Evaluate Using the Given Value	y=10 , 0(1+0.055/4)^(0.055(4))	$y = 10$ , $0 {(1 + \frac{0.055}{4})}^{0.055 (4)}$
6094	Find the GCF	14x^3+3x^2-19x-34	$14 x^{3} + 3 x^{2} - 19 x - 34$
6095	Find the GCF	20x^3-16x^2+12	$20 x^{3} - 16 x^{2} + 12$
6096	Find the GCF	5x^4-35x^3+15x^2	$5 x^{4} - 35 x^{3} + 15 x^{2}$
6097	Find the GCF	cos(77)cos(103)-sin(77sin(103))	$\cos (77) \cos (103) - \sin (77 \sin (103))$
6098	Find the GCF	sin(54)cos(9)-cos(54)sin(9)	$\sin (54) \cos (9) - \cos (54) \sin (9)$
6099	Find the GCF	a^3-27	$a^{3} - 27$
6100	Find the GCF	5y^7+5y^6-10y^5+2y^8+8y^7+8y^6	$5 y^{7} + 5 y^{6} - 10 y^{5} + 2 y^{8} + 8 y^{7} + 8 y^{6}$