Question

6.4 trinomials where a does not equal
(1 point)
factor:
$4x^2 - 9x - 9 = \square$
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Explanation:

Step1: Multiply the coefficient of \(x^{2}\) and the constant term

For the trinomial \(4x^{2}-9x - 9\), \(a = 4\), \(b=-9\), \(c=-9\). Calculate \(a\times c=4\times(-9)=- 36\)

Step2: Find two numbers that multiply to \(a\times c\) and add up to \(b\)

We need two numbers \(m\) and \(n\) such that \(m\times n=-36\) and \(m + n=-9\). The numbers are \(m = 3\) and \(n=-12\) since \(3\times(-12)=-36\) and \(3+(-12)=-9\)

Step3: Rewrite the middle term

Rewrite \(-9x\) as \(3x-12x\). So, \(4x^{2}-9x - 9=4x^{2}+3x-12x - 9\)

Step4: Group the terms

Group the terms as \((4x^{2}+3x)-(12x + 9)\)

Step5: Factor out the greatest common factor from each group

Factor out \(x\) from the first group and \(3\) from the second group: \(x(4x + 3)-3(4x + 3)\)

Step6: Factor out the common binomial factor

Factor out \((4x + 3)\), we get \((4x + 3)(x-3)\)

Answer:

\((4x + 3)(x - 3)\)