Question 389735: If x+2 is a factor of x^2+bx+10, what is the value of b?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! First of all, by inspection, we see that the other factor has to be (x+5) because there's no other factor that will give us 10 as the third term
(x+2)(x+5)=x^2+7x+10; therefore b=7
Here's another way:
Let x+a be the other factor, so:
(x+2)(x+a)=x^2+bx+10
Expand the left side using FOIL (First, Outer, Inner, Last)
x^2+ax+2x+2a=x^2+bx+10 simplifying
x^2+(a+2)x+2a=x^2+bx+10
Now we know that the left side is identical to the right side. That means that the two expressions are identical term for term, so:
1=1
a+2=b
2a=10 or a=5
a+2=b or 5+2=b; so b=7
Hope this helps-----ptaylor
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