Question

question
factor completely.
4x² + 9x + 2

Explanation:

Step1: Multiply leading - coefficient and constant

For the quadratic $ax^{2}+bx + c=4x^{2}+9x + 2$, where $a = 4$, $b = 9$, $c = 2$. Calculate $a\times c=4\times2 = 8$.

Step2: Find two numbers that multiply to 8 and add to 9

The numbers are 8 and 1 since $8\times1=8$ and $8 + 1=9$.

Step3: Rewrite the middle term

Rewrite $4x^{2}+9x + 2$ as $4x^{2}+8x+x + 2$.

Step4: Group the terms

Group the terms: $(4x^{2}+8x)+(x + 2)$.

Step5: Factor out the greatest - common factor from each group

From the first group $4x^{2}+8x$, the GCF is $4x$, so $4x^{2}+8x=4x(x + 2)$. The second group is $x + 2$. So we have $4x(x + 2)+1(x + 2)$.

Step6: Factor out the common binomial factor

Factor out $(x + 2)$ to get $(4x + 1)(x + 2)$.

Answer:

$(4x + 1)(x+2)$