8p3+12/5p2+6/25p+1/125
Answers
Answer:
(10p−1) 3
125
Step-by-step explanation:
1000p3 - 300p2 + 30p - 1
can be divided with 10p - 1
Polynomial Long Division :
10.10 Polynomial Long Division
Dividing : 1000p3 - 300p2 + 30p - 1
("Dividend")
By : 10p - 1 ("Divisor")
dividend 1000p3 - 300p2 + 30p - 1
- divisor * 100p2 1000p3 - 100p2
remainder - 200p2 + 30p - 1
- divisor * -20p1 - 200p2 + 20p
remainder 10p - 1
- divisor * p0 10p - 1
remainder 0
Quotient : 100p2-20p+1 Remainder: 0
Trying to factor by splitting the middle term
10.11 Factoring 100p2-20p+1
The first term is, 100p2 its coefficient is 100 .
The middle term is, -20p its coefficient is -20 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 100 • 1 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is -20 .
-100 + -1 = -101
-50 + -2 = -52
-25 + -4 = -29
-20 + -5 = -25
-10 + -10 = -20 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -10
100p2 - 10p - 10p - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
10p • (10p-1)
Add up the last 2 terms, pulling out common factors :
1 • (10p-1)
Step-5 : Add up the four terms of step 4 :
(10p-1) • (10p-1)
Which is the desired factorization
Multiplying Exponential Expressions:
10.12 Multiply (10p-1) by (10p-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (10p-1) and the exponents are :
1 , as (10p-1) is the same number as (10p-1)1
and 1 , as (10p-1) is the same number as (10p-1)1
In our case, the common base is (10p-1) and the exponents are :
2
and 1 , as (10p-1) is the same number as (10p-1)1
The product is therefore, (10p-1)(2+1) = (10p-1)3
Final result :
(10p - 1)3
——————————
125