Dividend=x3 3x2 12x+4Index nbsp;form=x3 3x2 12x+4Coefficient nbsp;form=1, nbsp; 3, nbsp; 12, nbsp;4Comparing nbsp;the nbsp;divisor nbsp;x 2 nb ...

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Byju's Answer

Standard VII

Mathematics

Addition and Subtraction of like Terms

x3-3 x2-12 x+...

Question

(x³ $-$ 3x² $-$ 12x + 4) $\div$ (x $-$ 2)

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Solution

$Dividend = x^{3} - 3 x^{2} - 12 x + 4 Index form = x^{3} - 3 x^{2} - 12 x + 4 Coefficient form = (1, - 3, - 12, 4) Comparing the divisor x - 2 with x - a, we get a = 2$

$Now, quotient in coefficient form = (1, - 1, - 14) ∴ Quotient = x^{2} - x - 14 in the variable x Remainder = - 24 ∴ x^{3} - 3 x^{2} - 12 x + 4 = (x - 2) (x^{2} - x - 14) - 24$

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Similar questions

Q. Find the equation whose roots are the cubes of the roots of

x^{3} + 3 x^{2} + 2 = 0

Find in each case, the remainder when
(i) $x^{4} - 3 x^{2} + 2 x + 1$ is divided by x - 1
(ii) $x^{3} + 3 x^{2} - 12 x + 4 i s d i v i d e d b y x - 2$
(iii) $x^{4} + 1 i s d i v i d e d b y x + 1.$

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. Perform the division:

3 x^{2} + x^{3} + 4

x + 2

Q. If

f (x) = x^{3} + 3 x^{2} + 12 x - 2 sin x

such that

f : R \to R

then

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(x3 - 3x2 - 12x + 4) ÷ (x - 2)

Dividend=x3-3x2-12x+4Index form=x3-3x2-12x+4Coefficient form=1, -3, -12, 4Comparing the divisor x-2 with x-a, we get a=2 Now, quotient in coefficient form=1, -1, -14∴ Quotient = x2-x-14 in the variable xRemainder = -24∴ x3-3x2-12x+4 = x-2x2-x-14 -24

(x³ $-$ 3x² $-$ 12x + 4) $\div$ (x $-$ 2)