SOLUTION: Factor out the GCF of the polynomial (x^2-3x)(x^2+4x+5)+(6x+2)(x^2+4x+5)

Question 268710: Factor out the GCF of the polynomial
(x^2-3x)(x^2+4x+5)+(6x+2)(x^2+4x+5)
Answer by persian52(161) (Show Source): You can put this solution on YOUR website!
here you go my friend, hope it helps!
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(x^(2)-3x)(x^(2)+4x+5)+(6x+2)(x^(2)+4x+5)
Arrange the variables alphabetically within the expression (6x+2)(x^(2)+4x+5). This is the standard way of writing an expression.
(x^(2)-3x)(x^(2)+4x+5)+(x^(2)+4x+5)(6x+2)

Factor out the GCF of (x^(2)+4x+5) from each term in the polynomial.
(x^(2)+4x+5)((x^(2)-3x))+(x^(2)+4x+5)((6x+2))

Factor out the GCF of (x^(2)+4x+5) from (x^(2)-3x)(x^(2)+4x+5)+(x^(2)+4x+5)(6x+2).
(x^(2)+4x+5)((x^(2)-3x)+(6x+2))

Remove the parentheses that are not needed from the expression.
(x^(2)+4x+5)(x^(2)-3x+6x+2)

Since -3x and 6x are like terms, subtract 6x from -3x to get 3x.
(x^(2)+4x+5)(x^(2)+3x+2)

For a polynomial of the form x^(2)+bx+c, find two factors of c (2) that add up to b (3). In this problem 2*1=2 and 2+1=3, so insert 2 as the right hand term of one factor and 1 as the right-hand term of the other factor.
(x^(2)+4x+5)(x+2)(x+1)

The GCF (Greatest Common Factor) is the polynomial that was factored from each expression.
Answer: (x^(2)+4x+5)
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