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Basic Math Examples
3c2-5c-26c2⋅4c2-8cc2-4c+43c2−5c−26c2⋅4c2−8cc2−4c+4
Step 1
Step 1.1
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅-2=-6 and whose sum is b=-5.
Step 1.1.1
Factor -5 out of -5c.
3c2-5(c)-26c2⋅4c2-8cc2-4c+4
Step 1.1.2
Rewrite -5 as 1 plus -6
3c2+(1-6)c-26c2⋅4c2-8cc2-4c+4
Step 1.1.3
Apply the distributive property.
3c2+1c-6c-26c2⋅4c2-8cc2-4c+4
Step 1.1.4
Multiply c by 1.
3c2+c-6c-26c2⋅4c2-8cc2-4c+4
3c2+c-6c-26c2⋅4c2-8cc2-4c+4
Step 1.2
Factor out the greatest common factor from each group.
Step 1.2.1
Group the first two terms and the last two terms.
(3c2+c)-6c-26c2⋅4c2-8cc2-4c+4
Step 1.2.2
Factor out the greatest common factor (GCF) from each group.
c(3c+1)-2(3c+1)6c2⋅4c2-8cc2-4c+4
c(3c+1)-2(3c+1)6c2⋅4c2-8cc2-4c+4
Step 1.3
Factor the polynomial by factoring out the greatest common factor, 3c+1.
(3c+1)(c-2)6c2⋅4c2-8cc2-4c+4
(3c+1)(c-2)6c2⋅4c2-8cc2-4c+4
Step 2
Step 2.1
Factor 4c out of 4c2.
(3c+1)(c-2)6c2⋅4c(c)-8cc2-4c+4
Step 2.2
Factor 4c out of -8c.
(3c+1)(c-2)6c2⋅4c(c)+4c(-2)c2-4c+4
Step 2.3
Factor 4c out of 4c(c)+4c(-2).
(3c+1)(c-2)6c2⋅4c(c-2)c2-4c+4
(3c+1)(c-2)6c2⋅4c(c-2)c2-4c+4
Step 3
Step 3.1
Rewrite 4 as 22.
(3c+1)(c-2)6c2⋅4c(c-2)c2-4c+22
Step 3.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
4c=2⋅c⋅2
Step 3.3
Rewrite the polynomial.
(3c+1)(c-2)6c2⋅4c(c-2)c2-2⋅c⋅2+22
Step 3.4
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=c and b=2.
(3c+1)(c-2)6c2⋅4c(c-2)(c-2)2
(3c+1)(c-2)6c2⋅4c(c-2)(c-2)2
Step 4
Step 4.1
Combine.
(3c+1)(c-2)(4c(c-2))6c2(c-2)2
Step 4.2
Cancel the common factor of c-2 and (c-2)2.
Step 4.2.1
Factor c-2 out of (3c+1)(c-2)(4c(c-2)).
(c-2)((3c+1)(4c(c-2)))6c2(c-2)2
Step 4.2.2
Cancel the common factors.
Step 4.2.2.1
Factor c-2 out of 6c2(c-2)2.
(c-2)((3c+1)(4c(c-2)))(c-2)(6c2(c-2))
Step 4.2.2.2
Cancel the common factor.
(c-2)((3c+1)(4c(c-2)))(c-2)(6c2(c-2))
Step 4.2.2.3
Rewrite the expression.
(3c+1)(4c(c-2))6c2(c-2)
(3c+1)(4c(c-2))6c2(c-2)
(3c+1)(4c(c-2))6c2(c-2)
Step 4.3
Cancel the common factor of 4 and 6.
Step 4.3.1
Factor 2 out of (3c+1)(4c(c-2)).
2((3c+1)(2c(c-2)))6c2(c-2)
Step 4.3.2
Cancel the common factors.
Step 4.3.2.1
Factor 2 out of 6c2(c-2).
2((3c+1)(2c(c-2)))2(3c2(c-2))
Step 4.3.2.2
Cancel the common factor.
2((3c+1)(2c(c-2)))2(3c2(c-2))
Step 4.3.2.3
Rewrite the expression.
(3c+1)(2c(c-2))3c2(c-2)
(3c+1)(2c(c-2))3c2(c-2)
(3c+1)(2c(c-2))3c2(c-2)
Step 4.4
Cancel the common factor of c and c2.
Step 4.4.1
Factor c out of (3c+1)(2c(c-2)).
c((3c+1)(2(c-2)))3c2(c-2)
Step 4.4.2
Cancel the common factors.
Step 4.4.2.1
Factor c out of 3c2(c-2).
c((3c+1)(2(c-2)))c(3c(c-2))
Step 4.4.2.2
Cancel the common factor.
c((3c+1)(2(c-2)))c(3c(c-2))
Step 4.4.2.3
Rewrite the expression.
(3c+1)(2(c-2))3c(c-2)
(3c+1)(2(c-2))3c(c-2)
(3c+1)(2(c-2))3c(c-2)
Step 4.5
Cancel the common factor of c-2.
Step 4.5.1
Cancel the common factor.
(3c+1)(2(c-2))3c(c-2)
Step 4.5.2
Rewrite the expression.
(3c+1)⋅(2)3c
(3c+1)⋅(2)3c
Step 4.6
Move 2 to the left of 3c+1.
2(3c+1)3c
2(3c+1)3c