Question

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

Polynomial factorization
ANSWERED
asked 2021-05-25
Which of the following is the correct factorization of \(6x^{2} + x - 12\)?

Answers (1)

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 \((2x+3)\)

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