Q. 148E

In the following exercises, factor each expression using any method $18 m^{2} + 15 m + 3$

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Answer

The factors are $3 (2 m + 1) (3 m + 1)$

1Step 1. Given Information

The trinomial is $18 m^{2} + 15 m + 3$

Find factors using 'ac' method.

2Step 2. Find GCF

Find GCF and factor it

GCF is 3

So, $3 (6 m^{2} + 5 m + 1)$

3Step 3. Find 'ac'

Compare the trinomial inside the parenthesis with $a x^{2} + b x + c$

So, $a = 6, b = 5, c = 1$

So, $a c = 6$

Find two number such as their product is 6 and sum is 5

So numbers are 2,3.

4Step 4. Split the middle and factor trinomial by grouping

Split the middle term

$3 (6 m^{2} + 3 m + 2 m + 1)$

Factor it

$3 (3 (2 m + 1) + 1 (2 m + 1)) 3 (2 m + 1) (3 m + 1)$

5Step 5. Check

Multiply the factors $3 (2 m + 1) (3 m + 1)$

$3 (6 m^{2} + 2 m + 3 m + 1) 3 (6 m^{2} + 5 m + 1) 18 m^{2} + 15 m + 3$