Question

factor trinomials (a≠1) level 2
question
factor completely.
5x^{2}+14x + 9

Explanation:

Step1: Multiply a and c

For the trinomial $5x^{2}+14x + 9$, where $a = 5$, $b=14$, $c = 9$, $a\times c=5\times9 = 45$.

Step2: Find two numbers

We need to find two numbers that multiply to 45 and add up to 14. The numbers are 9 and 5 since $9\times5=45$ and $9 + 5=14$.

Step3: Rewrite the middle - term

Rewrite $14x$ as $9x+5x$. So, $5x^{2}+14x + 9=5x^{2}+9x+5x + 9$.

Step4: Group the terms

Group the terms: $(5x^{2}+9x)+(5x + 9)$.

Step5: Factor out the GCF from each group

From the first group $5x^{2}+9x$, the GCF is $x$, so $5x^{2}+9x=x(5x + 9)$. The second group is $5x + 9$.

Step6: Factor out the common binomial

We have $x(5x + 9)+1(5x + 9)=(5x + 9)(x + 1)$.

Answer:

$(5x + 9)(x + 1)$