Download App

Factorisation of Polynomials — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsFactorisation of Polynomials2 Marks
Question
Factorise:
$x^3 - 3x^2+ 3x + 7$
✓

Answer

$x^3 - 3x^2+ 3x + 7$
$= x^3 - 3x^2+ 3x - 1 + 8$
$= (x^3 - 3x^2+ 3x - 1) + 8$
$= (x - 1)^3 + 2^3$
$= (x - 1 + 2)[(x - 1)^2 - (x - 1)(2) + 2^2]$
$= (x + 1)(x^2 - 2x + 1 - 2x + 2 + 4)$
$= (x + 1)(x^2 - 4x + 7)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Mark Question" from Factorisation of Polynomials→Factorisation of Polynomials — all question types→Maths STD 9 question papers→Maharashtra Board STD 9 question papers→Maharashtra Board question paper generator→

Similar questions

Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
$f(x)=x^2, x=0$
→
Factorise:
$15 x^2-x-28$
→
The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the excluded number.
→
Write the ratio of first quantity to second quantity in the reduced form : 4 sq.m, 800 sq.cm
→
In the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
$f(x) = x^3 - 6x^2 - 19x + 84, g(x) = x - 7$
→
Retionalise the denominator of each of the following:$\frac{\sqrt2}{\sqrt5}$
→
Factorize the following expressions:
$27x^3 - y^3 - z^3 - 9xyz$
→
Classify the following polynomials as linear, quadratic and cubic polynomial.
i. $2 x^2+3 x+1$
ii. $5 p$
iii. $\sqrt{ } 2-\frac{1}{2}$
iv. $m^3+7 m^2+\sqrt[5]{2} m-\sqrt{7}$
V. $a^2$
vi. $3 r^3$
→
Factorise:$1+\frac{27}{125}\text{a}^3+\frac{9\text{a}}{5}+\frac{27\text{a}^2}{25}$
→
Write the ratio of first quantity to second quantity in the reduced form : ₹ 17, ₹ 25 and 60 paise
→