1) x^2 + 7x + 10
First, you find the factors of 10 that can be added or subtracted together to equal 7.
10: 1, 2, 5, 10.
5 + 2 = 7
Now we have this set up since both numbers are positive added together to equal 7:
(x + 5)(x + 2)
To check this, we use the distributive property.
(x + 5)(x + 2)
x times x = x^2
x times 2 = 2x
5 times x = 5x
5 times 2 = 10
x^2 + 2x + 5x + 10
Now we combine like terms:
x^2 + 2x + 5x + 10
x^2
2x + 5x = 7x
10
x^2 + 7x + 10