Question

Which of the following is one of the factors of 3x2 − 14x + 8?

Answer 1

Given the expression

`3x^2-14x+8`

The factors of the above expression are evaluated by the factorization of the expression.

Thus,

Step 1:

Replace the middle term of the expression with two factors in terms of x, such that the sum of the terms gives the middle term, and the product of the terms gives the product of the first and the last term.

`\begin{gathered} \text{the factors are -12x and -2x} \\ \text{this is because} \\ -12x\text{ + (-2x) = -14x, which is the middle term} \\ -12x\text{ }*\text{ -2x =24x}^2,\text{ which gives the same result as (3x}^2\text{ }*8) \end{gathered}`

Thus,

`\begin{gathered} 3x^2-14x+8 \\ 3x^2-12x-2x+8 \end{gathered}`

Step 2:

Factorize out the common factors.

`\begin{gathered} (3x^2-12x)(-2x+8) \\ 3x(x-4)-2(x-4) \\ (3x-2)(x-4) \end{gathered}`

Hence, (3x-2) is one of the factors of 3x²-14x+8.

The second option is the correct answer.