I need help on factoring monomials in quadratic form.
The problem is:
a² + 17a + 16
I know that the first step is to multiply 16 times the coefficient of "a", which is 1. I get 16.
Now I have to fill in factors that when multiplied, equal 16, but when added, equal 17.
So now I have 16 x 1 = 16
and 16 + 1 = 17.
And now I have to fill in the addition factors to make a² + 16a + 1a + 16.
I am just confused as to what to do next to solve the problem.
from your
a² + 16a + 1a + 16 use grouping
a(a+16) + 1(a+16)
=(a+16)(a+1)
you could also have arranged your terms this way
a² + 1a + 16a + 16
=a(a+1) + 16(a+1)
=(a+1)(a+16)
Oh, okay! I understand now. Thank you!
To factor the quadratic expression a² + 17a + 16, you're on the right track with multiplying 16 (the coefficient of the constant term) by 1 (the coefficient of the linear term).
Now that you have determined 16 x 1 = 16 and 16 + 1 = 17, you need to rewrite the expression a² + 16a + 1a + 16 as a sum of two groups that can be factored separately.
First, group the terms:
(a² + 16a) + (1a + 16)
Now, factor out the common factors from each group:
a(a + 16) + 1(a + 16)
As you can see, both groups share a common factor, which is (a + 16). Now, you can factor out (a + 16) from both terms:
(a + 16)(a + 1)
So, the factored form of the quadratic expression a² + 17a + 16 is (a + 16)(a + 1).
To check your answer, you can expand the factored form to see if it simplifies back to the original expression. In this case, you would multiply (a + 16)(a + 1) to verify that it gives you a² + 17a + 16.