Question

Divide the polynomial p(x)- 4x'- 8x?+ 8x - 1
by the polynomial g(x) = 2x - 3x + 2. Find
the quotient and the remainder.​

Answer 1

Answer:

Step-by-step explanation:

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

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Answer 2

Let f(x)=4x3−8x2+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)=ax2+bx+c

4x3−8x2+8x+1=(ax2+bx+c)(2x−1)+x+3

=2ax3+2bx2+2cx−ax2−bx+c+x+3

=2ax3+(2b−a)x2+(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⇒

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