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Chapter 6: Q. 374 (page 635)

In the following exercise, factor.

15p2+2p鈭�8

Short Answer

Expert verified

Factorisation of the given polynomial is:

15p2+2p鈭�8=(5p+4)(3p-2)

Step by step solution

01

Step 1. Given information 

The given expression is

15p2+2p鈭�8

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 15p2+2p鈭�8we have:

ac=15脳(-8)=-120

And we have to think of two numbers whose sum is equal to 2and product is equal to -120.

Then,

12-10=212脳(-10)=-120

So the required numbers are12&-10

03

Step 3. Perform factorisation 

Now,

15p2+2p鈭�815p2+12p-10p-83p(5p+4)-2(5p+4)[takingout3pand-2ascommon](5p+4)(3p-2)[takingout5p+4ascommon]

The factorisation of the given polynomial is:

(5p+4)(3p-2)

04

Step 4. Check the answer 

Multiplying the factors, we get:

15p2+2p鈭�8=5p+4(3p-2)15p2+2p鈭�8=5p2-10p+12p-815p2+2p鈭�8=15p2+2p鈭�8

This is true.

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