What is the product of the two polynomials shown?
(3x^3+2x^2+x)(x-2)
To find the product of the two polynomials, we can apply the distributive property.
(3x^3 + 2x^2 + x)(x - 2) = 3x^3(x) + 2x^2(x) + x(x) - 3x^3(2) - 2x^2(2) - x(2)
Simplifying this expression, we get:
= 3x^4 + 2x^3 + x^2 - 6x^3 - 4x^2 - 2x
Combining like terms, we have:
= 3x^4 - 4x^3 - 3x^2 - 2x
To find the product of two polynomials, we can use the distributive property. Here are the step-by-step calculations:
Step 1: Multiply each term of the first polynomial by the second polynomial.
(3x^3 + 2x^2 + x) * (x - 2) = 3x^3*(x) + 3x^3*(-2) + 2x^2*(x) + 2x^2*(-2) + x*(x) + x*(-2)
Step 2: Simplify each term.
= 3x^4 - 6x^3 + 2x^3 - 4x^2 + x^2 - 2x
Step 3: Combine like terms.
= 3x^4 - 4x^3 - 3x^2 - 2x
Therefore, the product of the two polynomials (3x^3+2x^2+x)(x-2) is 3x^4 - 4x^3 - 3x^2 - 2x.
To find the product of the two polynomials, we can use the distributive property. We need to multiply each term of the first polynomial by each term of the second polynomial and then add the resulting terms.
Let's start by multiplying each term of the first polynomial (3x^3+2x^2+x) by the first term of the second polynomial (x).
(3x^3+2x^2+x) * (x-2)
= 3x^3 * x + 2x^2 * x + x * x
When we multiply monomials together, we add their exponents.
= 3x^4 + 2x^3 + x^2
Next, let's multiply each term of the first polynomial by the second term of the second polynomial (-2).
= 3x^4 + 2x^3 + x^2 + (-2)(3x^3) + (-2)(2x^2) + (-2)(x)
Multiplying each term by -2:
= 3x^4 + 2x^3 + x^2 - 6x^3 - 4x^2 - 2x
Finally, let's combine like terms:
= 3x^4 + (2x^3 - 6x^3) + (x^2 - 4x^2) + (-2x)
= 3x^4 - 4x^3 - 3x^2 - 2x
Therefore, the product of the two polynomials (3x^3+2x^2+x)(x-2) is equal to 3x^4 - 4x^3 - 3x^2 - 2x.