Chapter 6: Q. 376 (page 635)

n the following exercise, factor.
$8 a^{2} + 32 a + 24$

Short Answer

Expert verified

Factorisation of the given polynomial is:

$8 a^{2} + 32 a + 24 = 8 (a + 3) (a + 1)$

Step by step solution

Step 1. Given information

The given expression is

$8 a^{2} + 32 a + 24$

Step 2. Use ac method for factorisation

To factorise the polynomial $a x^{2} + b x + c$ by $a c$ method, we need to think of two numbers whose product is equal to $a c$ and the sum is equal to $b$ .

For polynomial $8 a^{2} + 32 a + 24$ we have:

$a c = 24 \times 8 = 192$

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

Then,

$24 \times 8 = 192 24 + 8 = 32$

So, the two required numbers are $24 & 8$

Step 3. Perform factorisation

Now,

$8 a^{2} + 32 a + 24 8 a^{2} + 24 a + 8 a + 24 8 a (a + 3) + 8 a (a + 3) [t a k i n g 8 a o u t a s a c o m m o n] (a + 3) (8 a + 8) [t a k i n g (a + 3) o u t a s a c o m m o n] 8 (a + 3) (a + 1) [t a k i n g 8 o u t a c o m m o n]$

The factorisation of the given polynomial is:

localid="1644681470435" $8 a^{2} + 32 a + 24 = 8 (a + 3) (a + 1)$

Step 4. Check the answer

Multiplying the factors, we get:

$8 a^{2} + 32 a + 24 = 8 (a + 3) (a + 1) 8 a^{2} + 32 a + 24 = 8 (a^{2} + 4 a + 3) 8 a^{2} + 32 a + 24 = 8 a^{2} + 32 a + 24$

This is true

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n the following exercise, factor.
$8 a^{2} + 32 a + 24$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use ac method for factorisation

Step 3. Perform factorisation

Step 4. Check the answer

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n the following exercise, factor.8a2+32a+24

Short Answer

Step by step solution

Step 1. Given information

Step 2. Use ac method for factorisation

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

Discrete Mathematics

Calculus

Logic and Functions

Decision Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

n the following exercise, factor.
$8 a^{2} + 32 a + 24$