Using a table, What is the product of the two polynomials shown?
(2x^2+3x) (4x^2-2x-1)
To find the product of the two polynomials, we will multiply each term of the first polynomial by each term of the second polynomial and combine like terms.
First, let's write out the two polynomials as shown:
2x^2 + 3x
× (4x^2 - 2x - 1)
Now, let's multiply each term:
2x^2 * (4x^2 - 2x - 1) = 8x^4 - 4x^3 - 2x^2
3x * (4x^2 - 2x - 1) = 12x^3 - 6x^2 - 3x
Now, let's combine the like terms:
8x^4 + (-4x^3 + 12x^3) + (-2x^2 - 6x^2) + (-3x) = 8x^4 + 8x^3 - 8x^2 - 3x
Therefore, the product of the two polynomials (2x^2 + 3x)(4x^2 - 2x - 1) is:
8x^4 + 8x^3 - 8x^2 - 3x
To find the product of these two polynomials, we can use the distributive property and multiply each term of the first polynomial by each term of the second polynomial.
First, let's write down the polynomials:
First Polynomial: 2x^2 + 3x
Second Polynomial: 4x^2 - 2x - 1
Now we will multiply each term in the first polynomial by each term in the second polynomial:
2x^2 * (4x^2 - 2x - 1) = 8x^4 - 4x^3 - 2x^2
3x * (4x^2 - 2x - 1) = 12x^3 - 6x^2 - 3x
Now we can combine the like terms:
(8x^4 - 4x^3 - 2x^2) + (12x^3 - 6x^2 - 3x) = 8x^4 + 8x^3 - 8x^2 - 3x
So, the product of the two polynomials (2x^2 + 3x) and (4x^2 - 2x - 1) is 8x^4 + 8x^3 - 8x^2 - 3x.
To find the product of two polynomials, we need to perform the distributive property, multiplying every term in the first polynomial by every term in the second polynomial. To make it easier, you can use a table where you write down all the terms and their products.
Here's how to set up the table:
1. Write down the two polynomials horizontally across the top rows of the table:
(2x^2 + 3x) and (4x^2 - 2x - 1)
2. Draw a grid-like structure below the polynomials. The grid will have rows and columns.
3. Label the vertical column headings with the terms from the first polynomial:
2x^2 and 3x.
4. Label the horizontal row headings with the terms from the second polynomial:
4x^2, -2x, and -1.
Now, fill in the grid by multiplying each term in the first polynomial by each term in the second polynomial. For example, the first cell in the grid will be the product of 2x^2 and 4x^2, which is 8x^4.
Once you complete the grid, add up all the products within each row. This will give you the final polynomial.
Let me know if you would like me to show you the completed table or explain further.