Question

divide the polynomial p(X)=4x^3-8x^2+8x-1 by the polynomial g(X)=2x^2-3x+2. find the quotient and the remainder. pls answer this question step by step.​

Answer 1

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p(x) = 4x^3-8x^2+8x-1

q(x) =2x-1

r(x) =x+3

f(x) -g(x) ×q(x) +r(x)

degree of g(x) is 2 ....

f(x) = 4x3 + 8x2 + 8x + 7, g(x)= 2x2 – x + 1

f(x) = 4x3 + 8x2 + 8x + 7 and g(x)= 2x^2-x+1...

2x^2-x+1√4x^3+8x^2+8x+7= 2x+5

_

4x^2-2x^2+2x

_______________

10x^2+6x+7

_

10x^2-5x+5

_______________

11x+12

_________________

Thus q(x) = 15x +10 and r(x) = 3x-32

Hope I help you❤❤......

Answer 2

Here is Your answer...❤

Let f(x)=4x 3

−8x 2 +8x+1

q(x)=2x−1

r(x)=x+3

f(x)=g(x)×q(x)+r(x)

Degree of g(x) be 2. as degree of f(x) is 3.

∴g(x)=ax

2 +bx+c

4x 3 −8x

2 +8x+1=(ax

2 +bx+c)(2x−1)+x+3

=2ax 3 +2bx 2 +2cx−ax 2

−bx+c+x+3

=2ax 3 +(2b−a)x 2

+(2c−b+1)+(3−c)

Equating coefficient of power of x,

2a=4⇒a= 24

=2

2b−a=−8⇒b=−3

2c−b+1=8

⇒2c+3=7

⇒c=2

∴g(x)=2x

2

−3x+2

Hope it helps..

Please Mark branilest Answer...❤