(3xsquared-2x-1)(xsquared+x+5)
(3x^2 - 2x - 1)(x^2 + x + 5)
= 3x^4 + 3x^3 + 15x^2 + -2x^3 - 2x^2 ..... etc
(you should have 9 terms in this line)
can you see what I am doing?
it is just an expanded version of the old FOIL concept
I am sure you can finish it
There will be all kinds of like terms, make sure to simplify.
compare your answer with
http://www.wolframalpha.com/input/?i=expand+%283x%5E2+-+2x+-+1%29%28x%5E2+%2B+x+%2B+5%29
To multiply the two polynomials (3x^2 - 2x - 1) and (x^2 + x + 5), we can use the distributive property and multiply each term of the first polynomial by each term of the second polynomial.
Let's break down the steps:
1. Start with the first polynomial: (3x^2 - 2x - 1).
2. Multiply the first term of the first polynomial (3x^2) by each term of the second polynomial: (3x^2)*(x^2) + (3x^2)*(x) + (3x^2)*(5) = 3x^4 + 3x^3 + 15x^2.
3. Multiply the second term of the first polynomial (-2x) by each term of the second polynomial: (-2x)*(x^2) + (-2x)*(x) + (-2x)*(5) = -2x^3 - 2x^2 - 10x.
4. Multiply the third term of the first polynomial (-1) by each term of the second polynomial: (-1)*(x^2) + (-1)*(x) + (-1)*(5) = -x^2 - x - 5.
5. Combine like terms by adding or subtracting them:
(3x^4 + 3x^3 + 15x^2) + (-2x^3 - 2x^2 - 10x) + (-x^2 - x - 5) = 3x^4 + 3x^3 - 2x^3 + 15x^2 - 2x^2 - x^2 - 10x - x - 5.
6. Simplify the expression:
3x^4 + (3x^3 - 2x^3) + (15x^2 - 2x^2 - x^2) + (-10x - x) - 5.
Combine like terms:
3x^4 + x^3 + 12x^2 - 11x - 5.
So, the product of (3x^2 - 2x - 1) and (x^2 + x + 5) is 3x^4 + x^3 + 12x^2 - 11x - 5.