what is the factored form of $6x^{2}+13x + 6$?\n$(x + 4)(x + 9)$\n$(2x + 3)(3x + 2)$\n$(2x + 6)(3x +…
what is the factored form of $6x^{2}+13x + 6$?\n$(x + 4)(x + 9)$\n$(2x + 3)(3x + 2)$\n$(2x + 6)(3x + 1)$\n$(6x + 1)(6x + 1)$
Answer
Explanation:
Step1: Identify a, b and c
For the quadratic expression $6x^{2}+13x + 6$, we have $a = 6$, $b=13$, $c = 6$. Then $ac=6\times6 = 36$.
Step2: Find two numbers that multiply to ac and add to b
We need two numbers that multiply to 36 and add up to 13. The numbers are 4 and 9 since $4\times9=36$ and $4 + 9=13$.
Step3: Rewrite the middle - term
Rewrite $13x$ as $4x+9x$. So, $6x^{2}+13x + 6=6x^{2}+4x+9x + 6$.
Step4: Group the terms
Group the terms: $(6x^{2}+4x)+(9x + 6)$.
Step5: Factor out the greatest common factor from each group
From the first group $6x^{2}+4x$, the GCF is $2x$, so $6x^{2}+4x=2x(3x + 2)$. From the second group $9x + 6$, the GCF is 3, so $9x + 6=3(3x + 2)$.
Step6: Factor out the common binomial factor
$2x(3x + 2)+3(3x + 2)=(2x + 3)(3x + 2)$.
Answer:
B. $(2x + 3)(3x + 2)$