Factorise- x-3-3x-2-3x-7- Maths Q-A

We need to factorise x^3 3x^2+3x+7:x^3 3x^2+3x+70ex0ex=x^3+x^2 4x^2 4x+7x+70ex0ex=x^2(x+1) 4x(x+1)+7(x+1)0ex0ex=(x+1)(x^2 4x+7)Hence, the factors of x^3 3x^2+3x ...

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Standard XIII

Mathematics

Higher Order Equations

Factorise: x^...

Question

Factorise: $x^{3} - 3 x^{2} + 3 x + 7$

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Solution

We need to factorise $x^{3} - 3 x^{2} + 3 x + 7$ :
$x^{3} - 3 x^{2} + 3 x + 7 = x^{3} + x^{2} - 4 x^{2} - 4 x + 7 x + 7 = x^{2} (x + 1) - 4 x (x + 1) + 7 (x + 1) = (x + 1) (x^{2} - 4 x + 7)$
Hence, the factors of $x^{3} - 3 x^{2} + 3 x + 7$ are $(x + 1)$ and $(x^{2} - 4 x + 7)$ .

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Factorise :

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

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

(a) x³ − 3x² + 3x − 5
(b) −x³ − 3x² − 3x − 5
(c) −x³ + 3x² − 3x + 5
(d) x³ − 3x² − 3x + 5

Q. Factorise:

x^{3} - 3 x^{2} + 3 x + 7

Factorise

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

Q. Factorize:

(i)

x^{3} + 3 x^{2} + 3 x - 7

(ii)

x^{3} - 3 x^{2} + 3 x + 7

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Factorise: x3-3x2+3x+7

We need to factorise x3-3x2+3x+7:x3-3x2+3x+7=x3+x2-4x2-4x+7x+7=x2(x+1)-4x(x+1)+7(x+1)=(x+1)(x2-4x+7)Hence, the factors of x3-3x2+3x+7 are x+1 and x2-4x+7.

Factorise: $x^{3} - 3 x^{2} + 3 x + 7$

We need to factorise $x^{3} - 3 x^{2} + 3 x + 7$ :
$x^{3} - 3 x^{2} + 3 x + 7 = x^{3} + x^{2} - 4 x^{2} - 4 x + 7 x + 7 = x^{2} (x + 1) - 4 x (x + 1) + 7 (x + 1) = (x + 1) (x^{2} - 4 x + 7)$
Hence, the factors of $x^{3} - 3 x^{2} + 3 x + 7$ are $(x + 1)$ and $(x^{2} - 4 x + 7)$ .