Advertisements
Advertisements
Question
If the quotient obtained on dividing (8x4 – 2x2 + 6x – 7) by (2x + 1) is (4x3 + px2 – qx + 3), then find p, q and also the remainder
Advertisements
Solution
p(x) = 8x4 – 2x2 + 6x – 7
d(x) = 2x + 1
2x + 1 = 0
2x = – 1
x = `-1/2`
The quotient = `1/2` [8x3 – 4x2 + 6]
= 4x3 – 2x2 + 3
= 4x3 – 2x2 + 0x + 3
The given quotient is = 4x3 + px2 – qx + 3 .........(compared with the given quotient)
The value of p = – 2 and q = 0
Remainder = – 10
APPEARS IN
RELATED QUESTIONS
Divide the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.
(2m2 − 3m + 10) ÷ (m − 5)
Divide the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.
`(y^3 - 216) ÷ (y - 6)`
Divide the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.
`(2x^4 + 3x^3 + 4x - 2x^2) ÷ (x + 3)`
Divide polynomial 3x3 - 8x2 + x + 7 by x - 3 using synthetic method and write the quotient and remainder.
Find the quotient and remainder for the following using synthetic division:
(x3 + x2 – 7x – 3) ÷ (x – 3)
Find the quotient and remainder for the following using synthetic division:
(3x3 – 2x2 + 7x – 5) ÷ (x + 3)
Find the quotient and remainder for the following using synthetic division:
(8x4 – 2x2 + 6x + 5) ÷ (4x + 1)
Factorise the following polynomials using synthetic division:
x3 – 3x2 – 10x + 24
Factorise the following polynomials using synthetic division:
2x3 – 3x2 – 3x + 2
Factorise the following polynomials using synthetic division:
– 7x + 3 + 4x3
