Advertisements
Advertisements
प्रश्न
Divide the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.
`(x^4 - 3x^2 - 8) ÷ (x + 4)`
Advertisements
उत्तर
Synthetic Division:
Dividend = `x^4 - 3x^2 - 8 = x^4 +0x^3 - 3x^2 + 0x - 8`
Divisor = x + 4
Opposite of 4 = −4
The coefficient form of the quotient is (1, −4, 13, −52).
∴ Quotient = x3 − 4x2 + 13x − 52 and Remainder = 200
Linear Method:
`x^4 - 3x^2 - 8`
`= x^3 (x + 4) - 4x^3 - 3x^2 - 8`
`= x^3 (x + 4) - 4x^2 (x +4) + 16x^2 -3x^2 - 8`
`= x^3 (x + 4) - 4x^2 (x + 4) + 13x (x +4) - 52x - 8`
`= x^3 (x + 4) - 4x^2 (x + 4) + 13x (x +4) - 52(x + 4) + 208 - 8`
`= (x + 4) (x^3 - 4x^2 + 13 x - 52) + 200`
APPEARS IN
संबंधित प्रश्न
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 of the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.
`(x^4 + 2x^3 +3x^2 + 4x + 5) ÷ (x + 2)`
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 the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.
`(y^3 - 3y^2 + 5y - 1) ÷ (y - 1)`
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 + 2x2 – x – 4) ÷ (x + 2)
Find the quotient and remainder for the following using synthetic division:
(8x4 – 2x2 + 6x + 5) ÷ (4x + 1)
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
If the quotient obtained on dividing 3x3 + 11x2 + 34x + 106 by x – 3 is 3x2 + ax + b, then find a, b and also the remainder
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:
x3 + x2 – 14x – 24
Factorise the following polynomials using synthetic division:
x3 – 7x + 6
Factorise the following polynomials using synthetic division:
x3 – 10x2 – x + 10
