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Chapter 11: Q. 382 (page 1069)

In the following exercise, factor using substitution.

(x鈭�3)2鈭�5(x鈭�3)鈭�36

Short Answer

Expert verified

Thus, the factorisation of the given polynomial is:

(x-3)2-5(x-3)-3=(x+1)(x-12)

Step by step solution

01

Step 1. Given information  

The given polynomial is:

(x鈭�3)2鈭�5(x鈭�3)鈭�36

02

Step 2.  substitute x-3=u 

Substituting x-3=uin the given polynomial, we get:

u2-5u-36

03

Step 3. Perform factorisation 

Factorising the polynomial, we get:

u2-5u-36u2-9u+4u-36u(u-9)+4(u-9)[takingoutuand4ascommon](u+4)(u-9)[taking(u-9)ascommon]

Again, substituting u=x-3,we get:

localid="1644654402554" u2-5u-36=u+4)(u-9(x-3)2-5(x-3)-36=(x-3+4)(x-3-9)(x-3)2-5(x-3)-3=(x+1)(x-12)

Thus, the factorisation of the given polynomial is:

localid="1644654442697" (x-3)2-5(x-3)-3=(x+1)(x-12)

04

Step 4. Check the answer

Multiplying the factors, we get:

(x-3)2-5(x-3)-36=(x+1)(x-12)x2-6x+9-5x+15-36=x2-12x+x-12x2-11x-12=x2-11x-12

This is true.

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