Factorise 3x-3 - x-2 - 3x - 1- - Maths Q-A

Factories the polynomial3x^3 x^2 3x+10ex0ex=x^2(3x 1) 1(3x 1)0ex0ex=(x^2 1)(3x 1)0ex0ex=(x+1)(x 1)(3x 1) [x^2 1=(x+1)(x 1)]Hence, the factors of 3x^3 x^2 3 ...

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Standard X

Mathematics

Division Algorithm for a Polynomial

Factorise 3x^...

Question

Factorise $3 x^{3} - x^{2} - 3 x + 1$ .

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Solution

Factories the polynomial
$3 x^{3} - x^{2} - 3 x + 1 = x^{2} (3 x - 1) - 1 (3 x - 1) = (x^{2} - 1) (3 x - 1) = (x + 1) (x - 1) (3 x - 1) [x^{2} - 1 = (x + 1) (x - 1)]$
Hence, the factors of $3 x^{3} - x^{2} - 3 x + 1$ are $(x + 1)$ , $(x - 1)$ and $(3 x - 1)$ .

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Similar questions

Q. 3x³ − x² − 3x + 1

Q. Question 31

The value of

(3 x^{3} + 9 x^{2} + 27 x) \div 3 x

is
a)

x^{2} + 9 + 27 x

3 x^{3} + 3 x^{2} + 27 x

3 x^{3} + 9 x^{2} + 9

x^{2} + 3 x + 9

Factorise :

$(x^{2} - 3 x) (x^{2} - 3 x - 1) - 20$

Using the remainder Theorem, factorise each of the following completely:
(i) $3 x^{3} + 2 x^{2} - 19 x + 6$
(ii) $2 x^{3} + x^{2} - 13 x + 6$
(iii) $3 x^{3} + 2 x^{2} - 23 x - 30$
(iv) $4 x^{3} + 7 x^{2} - 36 x - 63$
(v) $x^{3} + x^{2} - 4 x - 4.$

Q. f(x) = 3x³ + x² − 20x +12, g(x) = 3x − 2

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Factorise 3x3-x2-3x+1.

Factories the polynomial3x3-x2-3x+1=x2(3x-1)-1(3x-1)=x2-13x-1=x+1x-13x-1x2-1=x+1x-1Hence, the factors of 3x3-x2-3x+1are (x+1) , (x-1)and (3x-1).

Factorise $3 x^{3} - x^{2} - 3 x + 1$ .

Factories the polynomial
$3 x^{3} - x^{2} - 3 x + 1 = x^{2} (3 x - 1) - 1 (3 x - 1) = (x^{2} - 1) (3 x - 1) = (x + 1) (x - 1) (3 x - 1) [x^{2} - 1 = (x + 1) (x - 1)]$
Hence, the factors of $3 x^{3} - x^{2} - 3 x + 1$ are $(x + 1)$ , $(x - 1)$ and $(3 x - 1)$ .