Question

Select the factors of x2 − 16x + 64.

I know that it is between these two, but I can't figure out which one it is. Please help?

(x + 4)(x + 16)

(x − 4)(x − 16)

Answer 1

\[x^2-16x+64 \]
Final result :

\[ (x - 8)^2\]

Answer 2

Step by step solution :
Step 1 :

Simplify x2-16x + 64

Trying to factor by splitting the middle term

1.1 Factoring x2-16x+64

The first term is, x2 its coefficient is 1 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is +64

Step-1 : Multiply the coefficient of the first term by the constant 1 • 64 = 64

Step-2 : Find two factors of 64 whose sum equals the coefficient of the middle term, which is -16 .
-64 + -1 = -65
-32 + -2 = -34
-16 + -4 = -20
-8 + -8 = -16 That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -8
x2 - 8x - 8x - 64

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-8)
Add up the last 2 terms, pulling out common factors :
8 • (x-8)
Now add up the four terms of step 3 :
(x-8) • (x-8)
Which is the desired factorization
Multiplying Exponential Expressions :

1.2 Multiply (x-8) by (x-8)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x-8) and the exponents are :
1 , as (x-8) is the same number as (x-8)1
and 1 , as (x-8) is the same number as (x-8)1
The product is therefore, (x-8)(1+1) = (x-8)2

Answer 3

its the second one

Answer 4

Thank you both for all your help. @Muzzack I really appreciate the step by step, it really cleared things up for me and help me understand how to find the answer. Thank you both again!

Answer 5

np