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2 votes
Factor the expression by grouping

x \sqrt + 8x 15

User Daxnitro
by
8.8k points

1 Answer

2 votes

Answer:

The Completing the Square Method basically "forces" the existence of a perfect square trinomial in order to easily factor an equation where factoring by grouping is impossible.

For

x

2

8

x

15

, the first step would be to make the equation equal to zero and add 15 to both sides.

x

2

8

x

=

15

Next, we need to turn the binomial on the left side of the equation into a perfect trinomial. We can do this by dividing the coefficient of the "middle x-term", which would be

8

, in half then squaring it.

8

2

=

4

and

(

4

)

2

=

16

We then add the result to both sides of the equation.

x

2

8

x

+

16

=

15

+

16

Now, we can factor the perfect square trinomial and simplify

15

+

16

.

(

x

+

4

)

2

=

31

Now, we subtract

31

from both sides of the equation.

(

x

+

4

)

2

31

In order to factor these terms, both of them need to be the "squared version of their square rooted form" so that the terms stay the same when factoring.

(

x

+

4

)

2

31

2

Now, we can factor them. Since the expression follows the case

a

2

b

2

, where, in this case,

a

=

(

x

+

4

)

and

b

=

31

, we can factor them by following the Difference of Squares Formula:

a

2

b

2

=

(

a

+

b

)

(

a

b

)

.

Your final answer would be:

(

(

x

+

4

)

+

31

)

(

(

x

+

4

)

3

User Hau
by
7.8k points

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