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polet [3.4K]
4 years ago
13

Help please I don't know how to do this

Mathematics
1 answer:
d1i1m1o1n [39]4 years ago
7 0
The answer is D not C

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What is the product of the polynomial 2x^3 + 8x^2 + x + 3 times the<br> monomial x?
Elis [28]

Answer:

\huge\boxed{2x^4 + 8x^3 + x^2 + 3x}

Step-by-step explanation:

When we multiply a polynomial by a specific monomial, all terms in the polynomial get multiplied by the monomial.

So we can do this by term.

2x^3 \cdot x

Multiplying x by x to the something power will just increase the exponent on the x term by one (since powers are just x multiplied by itself). This means the exponent here will increase by 1, so this becomes 2x^4.

Same logic applies to the second term: 8x^2, raise the exponent by one, 8x^3.

For the third term, if there is no exponent on a term you can assume it's exponent is 1 (so x^1 in this case - as x^1=x). Again, using the same logic, this turns into x^2.

For the last term, when we multiply a constant by a variable, we get a term with a variable and a coefficient - the constant becomes the coefficient and the variable stays the variable. Therefore, 3 \cdot x = 3x.

Adding these terms all together gets us 2x^4 + 8x^3 + x^2 + 3x.

Hope this helped!

8 0
4 years ago
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