Factorize x-3 - x - 3x-2 - 3 - Maths Q-A

Factorize the given polynomialx^3+ x–3x^2–30ex0ex=x^3 3x^2+x 30ex0ex=x^2(x 3)+1(x 3)0ex0ex=(x^2+1)(x 3)Hence the factors of the polynomial x^3+ x–3x^2–3 are x^2 ...

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Standard X

Mathematics

Division Algorithm for a Polynomial

Factorize x^3...

Question

Factorise $x^{3} + x - 3 x^{2} - 3$ .

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Solution

Factorize the given polynomial
$x^{3} + x - 3 x^{2} - 3 = x^{3} - 3 x^{2} + x - 3 = x^{2} (x - 3) + 1 (x - 3) = (x^{2} + 1) (x - 3)$
Hence the factors of the polynomial $x^{3} + x - 3 x^{2} - 3$ are $x^{2} + 1$ and $x - 3$ .

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Q. The polynomial which when divided by −x² + x − 1 gives a quotient x − 2 and remainder 3, is

(a) x³ − 3x² + 3x − 5
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Q. Factorize:

1.

x^{3} + x - 3 x^{2} - 3

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Factorise x3+x–3x2–3.

Factorize the given polynomialx3+x–3x2–3=x3-3x2+x-3=x2(x-3)+1(x-3)=(x2+1)(x-3)Hence the factors of the polynomial x3+x–3x2–3 are x2+1 andx-3.

Factorise $x^{3} + x - 3 x^{2} - 3$ .

Factorize the given polynomial
$x^{3} + x - 3 x^{2} - 3 = x^{3} - 3 x^{2} + x - 3 = x^{2} (x - 3) + 1 (x - 3) = (x^{2} + 1) (x - 3)$
Hence the factors of the polynomial $x^{3} + x - 3 x^{2} - 3$ are $x^{2} + 1$ and $x - 3$ .