SOLUTION: Find the product of (2x2 + 7x - 4) with the quotient of (36x5 + 9x4 + 18x3) ÷ 3x3.
How i would go back about setting the problem up? Please don't give me the answer. I just wan
Algebra ->
Polynomials-and-rational-expressions
-> SOLUTION: Find the product of (2x2 + 7x - 4) with the quotient of (36x5 + 9x4 + 18x3) ÷ 3x3.
How i would go back about setting the problem up? Please don't give me the answer. I just wan
Log On
Question 149806This question is from textbook
: Find the product of (2x2 + 7x - 4) with the quotient of (36x5 + 9x4 + 18x3) ÷ 3x3.
How i would go back about setting the problem up? Please don't give me the answer. I just want to understand how to set the problem up. Thank you This question is from textbook
You can put this solution on YOUR website! Think of it this way, there are two parts:
Part 1: "product" (multiplication)
Part 2: "quotient" (division)
.
Concentrate on Part 2 FIRST!
(36x^5 + 9x^4 + 18x^3) ÷ 3x^3
We can "distribute" the division to EACH term inside the parenthesis:
= (36x^5 ÷ 3x^3) + (9x^4 ÷ 3x^3) + (18x^3 ÷ 3x^3)
Now, looking at just the numbers, we can reduce thus:
= (13x^5 ÷ x^3) + (3x^4 ÷ x^3) + (6x^3 ÷ x^3)
Now, looking at the x's, we can reduce thus:
= (13x^2) + (3x) + (6)
Resulting in:
= 13x^2 + 3x + 6
.
Finally, we do Part 1:
(2x^2 + 7x - 4)(13x^2 + 3x + 6)
Multiply each term inside the first parenthesis with each term in the second:
= (26x^4 + 6x^3 + 12x^2) + (91x^3 + 21x^2 - 24) + (-52x^2 - 12x - 24)
Now, group like-terms:
= 26x^4 + (6x^3 + 91x^3) + (12x^2 + 21x^2 - 52x^2) + (- 24- 24)
= 26x^4 + (97x^3) + (-19x^2) + (-48)
= 26x^4 + 97x^3 - 19x^2 - 48
