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

Question

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

Answer 1

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`