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Chapter 6: Q. 376 (page 635)

n the following exercise, factor.

8a2+32a+24

Short Answer

Expert verified

Factorisation of the given polynomial is:

8a2+32a+24=8(a+3)(a+1)

Step by step solution

01

Step 1. Given information  

The given expression is

8a2+32a+24

02

Step 2.  Use ac method for factorisation 

To factorise the polynomial ax2+bx+cby acmethod, we need to think of two numbers whose product is equal to acand the sum is equal to b.

For polynomial 8a2+32a+24we have:

ac=24脳8=192

And we have to think of two numbers whose sum is equal to 32and product is equal to 192.

Then,

24脳8=19224+8=32

So, the two required numbers are24&8

03

Step 3. Perform factorisation  

Now,

8a2+32a+248a2+24a+8a+248a(a+3)+8a(a+3)[taking8aoutasacommon](a+3)(8a+8)[taking(a+3)outasacommon]8(a+3)(a+1)[taking8outacommon]

The factorisation of the given polynomial is:

localid="1644681470435" 8a2+32a+24=8(a+3)(a+1)

04

Step 4. Check the answer

Multiplying the factors, we get:

8a2+32a+24=8(a+3)(a+1)8a2+32a+24=8(a2+4a+3)8a2+32a+24=8a2+32a+24

This is true

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