Given the function f(x)=x2+10x+24, the factors are...

Question

This is the full question: Given the function f(x)=x2+10x+24, the factors are _____ and _____, which means that the zeroes of the function occur at _____ and ___.

 

I just have no clue how to go about this..

Answer 1

This question is asking for the value(s) of X when F(X) = 0
Given that F(X) = X2 + 10X + 24
We can factorize F(X) = X2 + 4X + 6X + 24
= X (X + 4) + 6 (X+ 4)
= (X + 4) (X + 6)
We need to evaluate X in F (X) = 0
Thus, (X + 4) (X + 6) = 0
X = -4 or -6
So,
Given the function f(x)=x2+10x+24,
the factors are (X + 4) and (X + 6), which means that the zeroes of the function occur at -4 and -6.

Answer 2

f(x) is a 2nd order polynomial.

 

I can see from my experience that the factors are (x+4) and (x+6). Using the FOIL method to multiply these together:

• F stands for FIRSTS: x*x = x^2
• O stands for OUTERS and I stands for INNERS: 6*x + 4*x = 10x
• L stands for LASTS: 4*6 = 24

 

The zeroes of a function are defined as where that function is equal to...... wait for it.......   ZERO! Remember that any number times zero is zero. The zeroes of a factor-able function can be determined by finding where its factors are each equal to zero. in this case, at -4 and at -6.

 

Jeff