Find the critical values of P(x)
p(x)= (28+x)(8-x/4)
the answer was p=244-7x+8x-x^2/4
p=-x^2/4 + x + 244
p'= -x/2 +1 = 0
X=2
My question is, I do not understand how they got -7x + 8x at the beginning. I know (28)(8)=244 but I do not get the rest.
Use FOIL:
(28+x)(8-x/4)
=28*8 -28*x/4 + 8*x -x*x/4
=244 -7x + 8x -x²/4
=244 + x -x²/4
and the rest follows.
Oh I see. I made a mistake with the 28 (x/4). Thanks!
To determine how the expression of p(x) simplifies to p = 244 - 7x + 8x - x^2/4, let's expand the given expression step by step.
p(x) = (28 + x)(8 - x/4)
To multiply the two binomials, you can use the distributive property or the FOIL method (First, Outer, Inner, Last). We will use the distributive property in this case.
p(x) = 28(8) - 28(x/4) + x(8) - x(x/4)
First, let's simplify the 28(8) term:
p(x) = 224 - 28(x/4) + x(8) - x(x/4)
Next, let's simplify the -28(x/4) term:
p(x) = 224 - (28/4)(x) + x(8) - x(x/4)
Then, let's simplify the (28/4)(x) term:
p(x) = 224 - 7x + x(8) - x(x/4)
Now, let's simplify the x(8) term:
p(x) = 224 - 7x + 8x - x(x/4)
Lastly, let's simplify the -x(x/4) term:
p(x) = 224 - 7x + 8x - (x^2/4)
So, the final simplified expression is p(x) = 244 - 7x + 8x - x^2/4.
If you arrange the terms, it becomes p = -x^2/4 + x + 244, which is equivalent to the previous expression.