Question

factor the trinomial completely.
14y^2 - 23y + 9
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. 14y^2 - 23y + 9 = (factor completely.)
b. the polynomial is prime.

Explanation:

Step1: Multiply leading - coefficient and constant

Multiply 14 and 9, we get $14\times9 = 126$.

Step2: Find two numbers

We need to find two numbers that multiply to 126 and add up to - 23. After considering factors of 126: $1\times126,2\times63,3\times42,6\times21,7\times18,9\times14$. The pair of numbers is - 14 and - 9 since $(-14)\times(-9)=126$ and $-14+( - 9)=-23$.

Step3: Rewrite the middle term

Rewrite $-23y$ as $-14y-9y$. So, $14y^{2}-23y + 9=14y^{2}-14y-9y + 9$.

Step4: Group the terms

Group the terms: $(14y^{2}-14y)+(-9y + 9)$.

Step5: Factor out the GCF from each group

From the first group $14y^{2}-14y$, the GCF is $14y$, so $14y^{2}-14y=14y(y - 1)$. From the second group $-9y + 9$, the GCF is - 9, so $-9y + 9=-9(y - 1)$.

Step6: Factor out the common binomial factor

We have $14y(y - 1)-9(y - 1)=(y - 1)(14y-9)$.

Answer:

A. $14y^{2}-23y + 9=(y - 1)(14y-9)$