Question

Will reward brainless! Evaluate (10x^4-4x^3+14x^2-14x-16)/(2x-2)

Answer 1

Answer:

(10x^4–4x^3+14x^2–14x–16)/(2x–2) =

$5x³+3x²+10x+3–\frac{10}{2x–2}$

Explanation:

Given the quotient of two polynomials, you can use synthetic division to quickly divide the two.

First find the root of the denominator.

2x - 2 → 2x - 2 = 0 → 2x = 2 → x = 1.

Now since the denominator has a greatest common factor of 2 because 2x -2 = 2(x-1) this is what we will divide the result by at the end.

Synthetic division is a quicker method relative to polynomial long division.

It is in the format of:

R(Root of denominator) | a b. c .........

+aR +R(b+aR)...

|__________

a b+aR c + R(b+aR) .... ..

Since the denominator has a degree of 1

The results on the bottom are the coefficients of the divided polynomial minus 1 degree respectively.

The letters are the coefficients of the polynomial from a → z.

For this particular expression of two polynomials that are being divided.

Here is it's format in synthetic division:

The coefficient of the highest term is an exception and is just dropped down.

(10x^4-4x^3+14x^2-14x-16)/(2x-2)

= 1 | (10) (-4) (14) (-14) (-16)

↓ +10 +6 +20. +6

↓ ↓ ↓ ↓

|___________

10 6 20 6 -10