Question

How to factor 2x^2 - 7x +6

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

$2x^2-7x+6$

STEP 2: Multiply the constant with the leading term

$6\times2x^2=12x^2$

STEP 3: Write the possible factors of the result in product form

$\begin{gathered} 12x^2 \\ x\cdot12x,-x\cdot-12x \\ 2x\cdot6x,-2x\cdot-6x \\ 3x\cdot4x,-3x\cdot-4x \end{gathered}$

STEP 4: Find the factors that will give the second term (-7x) when added

$\begin{gathered} -7x \\ -3x+(-4x)=-3x-4x=-7x \end{gathered}$

STEP 5: Substitute these factors for -7x in the expression in step 1

$2x^2-4x-3x+6$

STEP 6: Factorize by grouping

$\begin{gathered} 2x(x-2)-3(x-2) \\ (2x-3)(x-2) \end{gathered}$

Hence, the factors of the given expression are:

$(2x-3)(x-2)$