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Help ! It's A Math Problem I don't know What to do I am confused

Help ! It's A Math Problem I don't know What to do I am confused-example-1
User Marcel Popescu
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2 Answers

25 votes
25 votes

Answer:

The answer would be the first option or the last option: x + 5 or x - 3

Explanation:

Simplify:

x2 - 25

Trying to factor by splitting the middle term

1.1 Factoring x2 - 8x + 15

The first term is, x2 its coefficient is 1 .

The middle term is, -8x its coefficient is -8 .

The last term, "the constant", is +15

Step-1 : Multiply the coefficient of the first term by the constant 1 • 15 = 15

Step-2 : Find two factors of 15 whose sum equals the coefficient of the middle term, which is -8 .

-15 + -1 = -16

-5 + -3 = -8 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -3

x2 - 5x - 3x - 15

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-5)

Add up the last 2 terms, pulling out common factors :

3 • (x-5)

Step-5 : Add up the four terms of step 4 :

(x-3) • (x-5)

Which is the desired factorization

Trying to factor as a Difference of Squares:

1.2 Factoring: x2-25

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 25 is the square of 5

Check : x2 is the square of x1

Factorization is : (x + 5) • (x - 5)

Canceling Out :

1.3 Cancel out (x - 5) which appears on both sides of the fraction line.

Final result :

x - 3 / x + 5

HOPE THIS HELPS! HAVE A WONDERFUL DAY!!! :)

User Salandur
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2.7k points
22 votes
22 votes
The common factor would be -5
The factors for x^2 - 25 are -5 and 5 (they add up to zero and multiply to -25)
The factors for x^2 - 8x -15 are 3 and -5 (add up to -8 and multiply to -15)
User Mosbah
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3.1k points