What is the product of 6,x^(2)-3x, and x-10 ? Choose 1 answer: (A) -42 x+180 (B) 6x^(2)-78 x+180 (C) 6x^(3)-42x^(2)+180 x (D) 6x^(3)-78x^(2)+180 x

Identify Terms: Identify the terms to be multiplied. We need to multiply the polynomial (6x^2 - 3x) by the binomial (x - 10).Use Distributive Property: Use the distributive property to multiply each term in the first polynomial by each term in the binomial. First, multiply 6x^2 by x to get 6x^3. Then, multiply 6x^2 by -10 to get -60x^2. Next, multiply -3x by x to get -3x^2. Finally, multiply -3x by -10 to get 30x.Combine Like Terms: Combine like terms. We have 6x^3 from the first multiplication. From the second and third multiplications, we combine -60x^2 and -3x^2 to get -63x^2. From the last multiplication, we have 30x. So, the expression becomes 6x^3 - 63x^2 + 30x.Match with Choices: Match the resulting expression with the given choices. The expression we found is 6x^3 - 63x^2 + 30x, which is not exactly listed in the choices. However, we can see that there is a mistake in the combination of like terms. The correct combination should be -60x^2 and -3x^2 to get -63x^2, which is not one of the choices. We need to re-evaluate our calculations.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the product of
6,x^(2)-3x, and
x-10 ?
Choose 1 answer:
(A)
-42 x+180
(B)
6x^(2)-78 x+180
(C)
6x^(3)-42x^(2)+180 x
(D)
6x^(3)-78x^(2)+180 x

What is the product of $6, x^{2}-3 x$ , and $x-10$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-42 x+180$ $\newline$ (B) $6 x^{2}-78 x+180$ $\newline$ (C) $6 x^{3}-42 x^{2}+180 x$ $\newline$ (D) $6 x^{3}-78 x^{2}+180 x$

View step-by-step help

Home

Math Problems

Algebra 1

Unions and intersections of sets

Full solution

Q. What is the product of

6, x^{2}-3 x

, and

x-10

\newline

Choose

1

answer:

\newline

(A)

-42 x+180

\newline

(B)

6 x^{2}-78 x+180

\newline

(C)

6 x^{3}-42 x^{2}+180 x

\newline

(D)

6 x^{3}-78 x^{2}+180 x

Identify Terms: Identify the terms to be multiplied. $\newline$ We need to multiply the polynomial $(6x^2 - 3x)$ by the binomial $(x - 10)$ .
Use Distributive Property: Use the distributive property to multiply each term in the first polynomial by each term in the binomial. $\newline$ First, multiply $6x^2$ by $x$ to get $6x^3$ . $\newline$ Then, multiply $6x^2$ by $-10$ to get $-60x^2$ . $\newline$ Next, multiply $-3x$ by $x$ to get $-3x^2$ . $\newline$ Finally, multiply $-3x$ by $-10$ to get $x$ $1$ .
Combine Like Terms: Combine like terms. $\newline$ We have $6x^3$ from the first multiplication. $\newline$ From the second and third multiplications, we combine $-60x^2$ and $-3x^2$ to get $-63x^2$ . $\newline$ From the last multiplication, we have $30x$ . $\newline$ So, the expression becomes $6x^3 - 63x^2 + 30x$ .
Match with Choices: Match the resulting expression with the given choices. $\newline$ The expression we found is $6x^3 - 63x^2 + 30x$ , which is not exactly listed in the choices. However, we can see that there is a mistake in the combination of like terms. The correct combination should be $-60x^2$ and $-3x^2$ to get $-63x^2$ , which is not one of the choices. We need to re-evaluate our calculations.