Question

# Which of the following is the correct factorization of 6x^{2} + x - 12?

Polynomial factorization
Which of the following is the correct factorization of $$6x^{2} + x - 12$$?

2021-05-26

Step 1
Consider the given expression.
$$f(x)=6x^{2}+x−12$$
Multiplication of 6 and 12 is 72.
$$72=9\times 8$$
Split the middle term x as $$9x −8x$$.
We get
$$f(x)=6x^{2}+9x-8x-12$$
$$=3x(2x+3)-4(2x+3)$$
$$=(3x-4)(2x+3)$$
Step 2
Hence, the factor of the function $$f(x)=6x^{2}+x-12$$ are $$(3x-4)$$ and $$(2x+3)$$