Question

(x - 2) is a factor of 2x^3 - 7x² + x + 10,

which means there is some other factor A
where 2x³ - 7x² + x + 10 = (x − 2)(A).
Finish the division started here to find the
value of A.

Answer 1

Hi,

Explanation:

An other is:

`2x^3-7x^2+x+10\\=2x^3-4x^2-3x^2+6x-5x+10\\=2x^2(x-2)-3x(x-2)-5(x-2)\\=(x-2)(2x^2-3x-5)\\\\A=2x^2-3x-5\\`

With a synthetic division:

`\begin{array}c&x^3&x^2&x&1\\---&--&--&--&--\\&2&-7&1&10\\x=2&&4&-6&-10\\---&--&--&--&--\\&2&-3&-5&0\\\end {array}`