The <em><u>correct answers</u></em> 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)
