Answer:
x^2-16 goes with (x+4)(x-4)
x^2+10x+16 goes with (x+8)(x+2)
Step-by-step explanation:
The first one you got wrong is known as a difference of squares.
To factor a difference of squares, a^2-b^2, you just write it as (a-b)(a+b) or (a+b)(a-b) would work too.
So x^2-16=(x-4)(x+4) or (x+4)(x-4).
Let's check (x+4)(x-4) using foil!
First: x(x)=x^2
Outer: x(-4)=-4x
Inner: 4(x)=4x
Last: 4(-4)=-16
----------------------Add
x^2-16
Bingo! (x+4)(x-4) definitely corresponds to x^2-16.
Here are more examples of factoring a difference of squares:
Example 1: x^2-25 = (x+5)(x-5)
Example 2: x^2-81 = (x+9)(x-9)
Example 3: x^2-100 =(x+10)(x-10)
Onward to the next problem:
x^2+10x+16
When the coefficient of the leading term of a quadratic is 1, all you have to do is find two numbers that multiply to be c=16 and add up be b=10.
Those numbers would be 8 and 2
because 8(2)=16 and 8+2=10.
So the factored form of x^2+10x+16 is (x+2)(x+8) or (x+8)(x+2).
Here is another example of when the leading coefficient of a quadratic is 1:
Example 1: x^2+5x+6=(x+2)(x+3) since 3(2)=6 and 3+2=5.
Example 2: x^2-x-6=(x-3)(x+2) since -3(2)=-6 and -3+2=-1.
