Question

Find the quotient and remainder when 16x + 40x’ - 270 is divided by 4r +1 Quotient = Remainder =

Answer 1

SOLUTION

Therefore,

16x340x27x f (x) 4x 1

Step 1

16x340x2 27x 4x 1

Divide the leading term of the dividend by the leading term of the divisor:

16x3 = 4x2 4x

Write down the calculated result in the upper part

Multiply it by the divisor

4x2 (4x1) 16x34x4

Subtract the dividend from the obtained result:

(16x 40x 27x) - (16x34x2)=36x 27x

Therefore,

36x2 27x 4x2 16x340x2 27x 4x 1 4x1

Step 2

36x2 27x 4x 1 X

Divide the leading term of the obtained remainder by the leading term of the divisor:

36x2 = 9x 4x

Write down the calculated result in the upper part

Multiply it by the divisor

9x (4x 1)36x9x

Subtract the dividend from the obtained result:

36х - 27х)- (36х + 9х) —36х

Therefore,

27x 36x2 -36x 9x 4x 1 4x 1

so,

-36x 16x340x2 27x 4x29x 4х + 1 4x1

Step 3

$\frac{-36x}{4x+1}$

Divide the leading term of the obtained remainder by the leading term of the divisor:

$\frac{- 36 x}{4 x}=-9$

Write down the calculated result in the upper part

Multiply it by the divisor

$-9\left(4 x+1\right)=- 36 x-9$

Subtract the dividend from the obtained result:

$\left(- 36 x\right)-\left(- 36 x-9\right)=9$

Therefore,

$\frac{-36x}{4x+1}=-9+\frac{9}{4x+1}$

so,

$\frac{16x^3+40x^2-27x}{4x+1}=4x^2+9x-9+\frac{9}{4x+1}$

Step 4

Therefore,

Quotient

$=4x^2+9x-9$

Remainder

$=9$