Question

Divide (2x^4 + x^3 - 14x^2 - 19x - 6 ) by( 2x^2 - 5x - 3) Find the quotient and remainder.









pls fas

Answer 1

Answer:

Let p(x)=2x

4

+x

3

−14x

2

−19x+6.

Given that the divisor is 2x+1. Write 2x+1=0. Then x=−

2

1

therefore The zero of the divisor is x=−

2

1

.

So, 2x

4

+x

3

−14x

2

−19x+6=(x+

2

1

){2x

3

−14x−12}+12

=(2x+1)

2

1

(2x

3

−14x−12)+12

Thus, the quotient is

2

1

(2x

2

−14x−12)=x

3

−7x−6 and the remainder is 12.

But, given quotient is x

3

+ax

2

−bx−6. Comparing this with the quotient obtained we get, a = 0 and b = 7.

Thus, a=0, b=7 and the remainder is 12.

Step-by-step explanation:

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