Using synthetic division- solve x4 - 2x3 - 3x2 - 4x - 5 - x - 2-Write the quotient and the remainder-

Synthetic division: (x^4 + 2x^3 + 3x^2 + 4x + 5) ÷ (x + 2) nbsp;Dividend = x^4 + 2x^3 + 3x^2 + 4x + 5 ∴ nbsp;Coefficient form of dividend = (1, 2, 3, 4, 5) n ...

You visited us 8 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Long Division of Polynomials

Using synthet...

Question

Using synthetic division, solve $(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)$ .
Write the quotient and the remainder.

Open in App

Solution

Synthetic division:
$(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)$
$Dividend = x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5$
$∴ Coefficient form of dividend = (1, 2, 3, 4, 5)$
$Divisor = x + 2$
$∴ Opposite of + 2 is -2$

$Coefficient form of quotient = (1, 0, 3, - 2)$
$∴ Quotient = x^{3} + 3 x - 2,$
$Remainder = 9$

Suggest Corrections

Similar questions

Use synthetic division method for performing the following division. Write the result in the form
Dividend = Divisor x Quotient + Remainder.

(2 x^{3} - 3 x^{2} + 4 x + 2) \div (x - 1)

Q. Divide the following polynomials by linear division method. Write the quotient and the remainder.

(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)

Divide each of the following polynomials by synthetic division method and also by

linear division method. Write the quotient and the remainder.

(i)

(2 m^{2} - 3 m + 10) \div (m - 5)

(ii)

(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)

(iii)

(y^{3} - 216) \div (y - 6)

(iv)

(2 x^{4} + 3 x^{3} + 4 x - 2 x^{2}) \div (x + 3)

(v)

(x^{4} - 3 x^{2} - 8) \div (x + 4)

(vi)

(y^{3} - 3 y^{2} + 5 y - 1) \div (y - 1)

Use synthetic division method for performing the following division. Write the result in the form
Dividend = Divisor x Quotient + Remainder.

(x^{3} - 3 x^{2} - 12 x + 4) \div (x - 2)

Q. Find the quotient and remainder using synthetic division.

(8 x^{4} - 2 x^{2} + 6 x - 5) \div (4 x + 1)

Join BYJU'S Learning Program

Using synthetic division, solve (x4+2x3+3x2+4x+5)÷(x+2). Write the quotient and the remainder.

Synthetic division: (x4+2x3+3x2+4x+5)÷(x+2) Dividend=x4+2x3+3x2+4x+5 ∴Coefficient form of dividend =(1,2,3,4,5) Divisor=x+2 ∴Opposite of + 2 is -2 Coefficient form of quotient=(1,0,3,−2) ∴ Quotient=x3+3x–2, Remainder = 9

Using synthetic division, solve $(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)$ .
Write the quotient and the remainder.