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8 votes
8 votes
What is
(2 {x}^(2) - 7x + 6)divided by
(x - 2)

User TexasEngineer
by
2.2k points

1 Answer

22 votes
22 votes
Step-by-step explanation

Factoring by grouping the numerator

Step 1: We rewrite the middle terms as a sum of two terms whose product is a·c = 2·6 = 12 and whose sum is b = -7.


2x^2-7x+6=2x^2-3x-4x+6

Step 2 We group the first two terms and last two terms.


2x^2-7x+6=(2x^2-3x)-4x+6

Step 3: We factor out the greatest common factor from each group.


2x^2-7x+6=x(2x-3)-2(2x-3)

Step 4: We factor the polynomial by factoring out the greatest common factor, 2x - 3.


2x^2-7x+6=(2x-3)(x-2)

Simplifying the expression

We cancel the common factor.


\begin{gathered} (2x^2-7x+6)/(x-2)=((2x-3)(x-2))/(x-2) \\ (2x^2-7x+6)/(x-2)=2x-3 \end{gathered}Answer
2x-3

User Cosjav
by
3.0k points