Question

show what you know : factor trinomials
1 of 4
factor : $2x^2 - 13x + 6$ select all that apply.
$\square$ $(2x - 1)$
$\square$ $(2x + 1)$
$\square$ $(x - 6)$
$\square$ $(x + 6)$

Explanation:

Step1: Try factoring the trinomial

We need to factor \(2x^2 - 13x + 6\). We look for two numbers that multiply to \(2\times6 = 12\) and add up to \(-13\). The numbers are \(-12\) and \(-1\).
So we rewrite the middle term: \(2x^2 - 12x - x + 6\).

Step2: Group and factor

Group the terms: \((2x^2 - 12x) + (-x + 6)\).
Factor out common factors from each group: \(2x(x - 6) - 1( x - 6)\).
Now factor out \((x - 6)\): \((2x - 1)(x - 6)\).

Step3: Identify the factors

From the factored form \((2x - 1)(x - 6)\), the factors are \((2x - 1)\) and \((x - 6)\).

Answer:

(2x - 1), (x - 6)