# RS Aggarwal Solutions Class 9 Mathematics Solutions for Factorization of Polynomials Exercise 3F in Chapter 3 - Factorization of Polynomials

Question 31 Factorization of Polynomials Exercise 3F

𝑥^3 − 3𝑥^2 + 3𝑥 + 7

𝑥^3 − 3𝑥^2 + 3𝑥 + 7

We can write the given question as

= 𝑥^3 − 3𝑥^2 + 3𝑥 − 1 + 8

By grouping the terms

= (𝑥^3 − 3𝑥^2 + 3𝑥 − 1) + 8

We know that (𝑎 − 𝑏)^3 = 𝑎^3 − 3𝑎^2𝑏 + 3𝑎𝑏^2 − 𝑏^3

So we get,

= (𝑥 − 1)^3 + 2^3

According to the equation

𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)

We get,

= ((𝑥 − 1) + 2)((𝑥 − 1)^2 − 2(𝑥 − 1) + 2^2)

According to the equation

(𝑎 − 𝑏)^2 = 𝑎^2 − 2𝑎𝑏 + 𝑏^2

= (𝑥 − 1 + 2)( 𝑥^2 − 2𝑥(1) + 1^2 − 2𝑥 + 2 + 4)

On further simplification

= (𝑥 + 1)( 𝑥^2 − 2𝑥 + 1 − 2𝑥 + 6)

= (𝑥 + 1)( 𝑥^2 − 4𝑥 + 7)

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