factor the following trinomial. 2x² - 7x + 6 (?x - 3)(x - )

Answer

Explanation:

Step1: Multiply leading - coefficient and constant

For the trinomial (2x^{2}-7x + 6), the leading - coefficient (a = 2) and the constant (c=6). So (ac=2\times6 = 12).

Step2: Find two numbers that multiply to (ac) and add to (b)

We need two numbers that multiply to (12) and add to (-7). The numbers are (-3) and (-4) since ((-3)\times(-4)=12) and (-3+( - 4)=-7).

Step3: Rewrite the middle term

Rewrite (-7x) as (-3x-4x). So (2x^{2}-7x + 6=2x^{2}-3x-4x + 6).

Step4: Group the terms

((2x^{2}-3x)+(-4x + 6)).

Step5: Factor out the greatest common factor from each group

From (2x^{2}-3x), the GCF is (x), so (2x^{2}-3x=x(2x - 3)). From (-4x + 6), the GCF is (-2), so (-4x + 6=-2(2x - 3)). Then (x(2x - 3)-2(2x - 3)=(2x - 3)(x - 2)).

Answer:

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