Answer:
( x + 4 ) ( x + 5 )
Step-by-step explanation:
For this polynomial, we will factor the coefficient of the x^2 term and the constant.
The coefficient of x^2 is 1, which just factors to 1.
The constant 20 factors into 2 * 2 * 5.
Note, that our middle term coefficient is 9 and thus we want a pairing of 1 with either 2, 4, or 5 to make 9. 4 + 5 = 9, so we will choose that.
Using the standard binomials, we will factor the polynomial:
( x^2 + 9x + 20 )
= ( x + 4 ) ( x + 5)
We can check by performing foil:
= ( x + 4 ) ( x + 5 )
= ( x * x + x * 5) + ( 4 * x + 4 * 5)
= ( x^2 + 5x ) + ( 4x + 20 )
= ( x^2 + 9x + 20 )
Thus, we have successfully factored our polynomial.
Cheers.
