(m+8) is a factor of (m²– 16)
Answers
Answer:
The product is therefore, (m-4)(1+1) = (m-4)2
Step-by-step explanation:
1.1 Factoring m2-8m+16
The first term is, m2 its coefficient is 1 .
The middle term is, -8m its coefficient is -8 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 1 • 16 = 16
Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is -8 .
-16 + -1 = -17
-8 + -2 = -10
-4 + -4 = -8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -4
m2 - 4m - 4m - 16
Step-4 : Add up the first 2 terms, pulling out like factors :
m • (m-4)
Add up the last 2 terms, pulling out common factors :
4 • (m-4)
Step-5 : Add up the four terms of step 4 :
(m-4) • (m-4)
Which is the desired factorization
Multiplying Exponential Expressions:
1.2 Multiply (m-4) by (m-4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (m-4) and the exponents are :
1 , as (m-4) is the same number as (m-4)1
and 1 , as (m-4) is the same number as (m-4)1