Question
Asked Nov 11, 2019
1 views

Use polynomial long division to rewrite f as f = g · q + r for each of the following:

(a) Divide f(x) = 6x3 − 12x2 + 8x − 16 by the linear polynomial g(x) = 2x − 4.
(b) Dividef(x)=3x3 −8x2 +x−5 by the linear polynomial g(x)=3x−2.

check_circle

Expert Answer

Step 1

Given:

help_outline

Image Transcriptionclose

(a).f(x)6x-12x +8x-16, g(x)= 2x-4 (b).f(x) 3x-8x +x-5, g(x)3x-2

fullscreen
Step 2

Solve (a) by long division:

Here,

help_outline

Image Transcriptionclose

f(x)= 6x3 -12x2 +8x -16 g(x) 2x -4 So, (x) 3x24 2x 46x12x2 +8x -16 6x3 -12x2 1 f(x) 8х —16 g(x) 8х -16 0 r(x)

fullscreen
Step 3

Now, substitute the value of f(...

help_outline

Image Transcriptionclose

f (x)g(x) q(x)+r(x) 6x3 -12x2+8x-16= (2x - 4)- (3x2 +4)+0

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Algebra

Other