Question

factor the trinomial completely. if the polynomial cannot be factored, say it is prime. 9x^{2}+18x + 8 select the correct choice below and fill in any answer boxes within your choice. a. 9x^{2}+18x + 8= b. the polynomial is prime.

Explanation:

Step1: Multiply leading - coefficient and constant

For the trinomial \(9x^{2}+18x + 8\), the leading - coefficient \(a = 9\) and the constant \(c = 8\). So \(ac=9\times8 = 72\).

Step2: Find two numbers that multiply to \(ac\) and add to the middle - coefficient

We need to find two numbers that multiply to \(72\) and add to \(18\). The numbers are \(6\) and \(12\) since \(6\times12=72\) and \(6 + 12=18\).

Step3: Rewrite the middle term

Rewrite \(18x\) as \(6x+12x\). So \(9x^{2}+18x + 8=9x^{2}+6x+12x + 8\).

Step4: Group the terms

\((9x^{2}+6x)+(12x + 8)\).

Step5: Factor out the greatest common factor from each group

From \(9x^{2}+6x\), the GCF is \(3x\), so \(9x^{2}+6x=3x(3x + 2)\). From \(12x + 8\), the GCF is \(4\), so \(12x + 8=4(3x + 2)\).

Step6: Factor out the common binomial factor

\(3x(3x + 2)+4(3x + 2)=(3x + 2)(3x+4)\).

Answer:

A. \(9x^{2}+18x + 8=(3x + 2)(3x + 4)\)