Question

Select one of the factors of x3y2 8xy2 − 5x2 − 40. (xy2 5) (x2 4) (xy2 − 5) (x2 − 8) 4. select one of the factors of 5x2 7x 2. (5x − 2) (x 2) (5x 1) none of the above 5. select one of the factors of 4x2 5x − 6. (x − 3) (4x − 3) (4x 2) (x 6)

Answer 1

The correct answers are:

(xy² − 5); none of the above; and (4x − 3)

Explanation:

To factor the first one, we will use factoring by grouping.  First group the first two together and the second two together:

(x³y²+8xy²)+(-5x²-40)

Find the GCF of each group.  The  GCF of the first one is xy² and the GCF of the second is -5.  Factor these out of each group:

xy²(x²+8)-5(x²+8)

We now have a GCF of the terms as we have rewritten them.  Factoring out (x²+8), we have:

(x²+8)(xy²-5)

To factor the second question, we want factors of 10 that sum to 7.  5 and 2 work for this, so this is how we will split up the x term in our polynomial:

5x²+5x+2x+2

Group together the first two and the last two:

(5x²+5x)+(2x+2)

Find the GCF of each group.  The first one has a GCF of 5x and the second has a GCF of 2.  Factor these out:

5x(x+1)+2(x+1)

The GCF of the rewritten terms is (x+1).  Factoring this out, we have

(x+1)(5x+2)

To factor the third question, we want factors of -24 that sum to 5.  -3 and 8 will do this, and this is how we will split up the x term:

4x²+8x-3x-6

Group together the first two and the last two:

(4x²+8x)+(-3x-6)

Find the GCF of each group.  The GCF of the first group is 4x and the GCF of the second group is -3.  Factor these out:

4x(x+2)-3(x+2)

The GCF of the rewritten polynomial is (x+2).  Factor this out:

(x+2)(4x-3)

Answer 2

Select one of the factors of x3y2 8xy2 − 5x2 − 40
x^3y^2 + 8xy^2 – 5x^2 – 40 

xy^2 ( x^2 + 8) - 5 ( x^2 + 8) 

( xy^2 - 5) ( x^2 + 8) 

ANSWER( xy^2 -5) 

Select one of the factors of 5x2 7x 2. 
3x^2 +6x -2x -4 
3x ( x + 2) -2( x + 2) 

( 3x - 2) ( x+2) 

ANSWER = (3x – 2)