Chapter 11: Q. 382 (page 1069)

In the following exercise, factor using substitution.
${(x - 3)}^{2} - 5 (x - 3) - 36$

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

Step 1. Given information

The given polynomial is:

${(x - 3)}^{2} - 5 (x - 3) - 36$

Step 2. substitute x-3=u

Substituting $x - 3 = u$ in the given polynomial, we get:

$u^{2} - 5 u - 36$

Step 3. Perform factorisation

Factorising the polynomial, we get:

$u^{2} - 5 u - 36 u^{2} - 9 u + 4 u - 36 u (u - 9) + 4 (u - 9) [t a k i n g o u t u a n d 4 a s c o m m o n] (u + 4) (u - 9) [t a k i n g (u - 9) a s c o m m o n]$

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

localid="1644654402554" $u^{2} - 5 u - 36 = (u + 4) (u - 9) {(x - 3)}^{2} - 5 (x - 3) - 36 = (x - 3 + 4) (x - 3 - 9) {(x - 3)}^{2} - 5 (x - 3) - 3 = (x + 1) (x - 12)$

Thus, the factorisation of the given polynomial is:

localid="1644654442697" ${(x - 3)}^{2} - 5 (x - 3) - 3 = (x + 1) (x - 12)$

Step 4. Check the answer

Multiplying the factors, we get:

${(x - 3)}^{2} - 5 (x - 3) - 36 = (x + 1) (x - 12) x^{2} - 6 x + 9 - 5 x + 15 - 36 = x^{2} - 12 x + x - 12 x^{2} - 11 x - 12 = x^{2} - 11 x - 12$

This is true.

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In the following exercise, factor using substitution.
${(x - 3)}^{2} - 5 (x - 3) - 36$

Short Answer

Step by step solution

Step 1. Given information

Step 2. substitute x-3=u

Step 3. Perform factorisation

Step 4. Check the answer

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In the following exercise, factor using substitution.(x−3)2−5(x−3)−36

Short Answer

Step by step solution

Step 1. Given information

Step 2. substitute x-3=u

Step 3. Perform factorisation

Step 4. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercise, factor using substitution.
${(x - 3)}^{2} - 5 (x - 3) - 36$