Factorise : x^{3}+x^{2}-26 x+24

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2. Polynomials

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Factorise $: x^{3}+x^{2}-26 x+24$

Option A

Option B

Option C

Option D

Solution

Sum of all the coefficients of terms of the polynomial

$=1+1-26+24$

$=26-26=0$

So, $(x-1)$ is a factor of $p(x)$

$x^{3}+x^{2}-26 x+24$

$=\underline{x^{3}}-x^{2}+\underline{2 x^{2}-2 x}-\underline{24 x+24}$

[Splitting the terms to get $x-1$ as a factor.]

$=x^{2}(x-1)+2 x(x-1)-24(x-1)$

$=(x-1)\left(x^{2}+2 x-24\right)$

$=(x-1)\left(x^{2}+6 x-4 x-24\right)$

[By splitting the middle term]

$=(x-1)[x(x+6)-4(x+6)]$

$=(x-1)(x+6)(x-4)$

Standard 9

Mathematics

With the help of the remainder theorem, find the remainder when the polynomial $x^{3}+x^{2}-26 x+24$ is divided by each of the following divisors

$x+4$

easy

Factorise each of the following

$8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$

easy

Classify the following as a constant, linear,quadratic and cubic polynomials:

$1+x+x^{2}$

easy

Expand the following:

$(3 a-5 b-c)^{2}$

hard

Evaluate the following products without multiplying directly

$78 \times 84$

hard

Factorise $: x^{3}+x^{2}-26 x+24$

Solution

Similar Questions

With the help of the remainder theorem, find the remainder when the polynomial $x^{3}+x^{2}-26 x+24$ is divided by each of the following divisors $x+4$

Factorise each of the following $8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$

Classify the following as a constant, linear,quadratic and cubic polynomials: $1+x+x^{2}$

Expand the following: $(3 a-5 b-c)^{2}$

Evaluate the following products without multiplying directly $78 \times 84$

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With the help of the remainder theorem, find the remainder when the polynomial $x^{3}+x^{2}-26 x+24$ is divided by each of the following divisors

$x+4$

Factorise each of the following

$8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$

Classify the following as a constant, linear,quadratic and cubic polynomials:

$1+x+x^{2}$

Expand the following:

$(3 a-5 b-c)^{2}$

Evaluate the following products without multiplying directly

$78 \times 84$