What is the sum of (4x^(5)-8x^(3)+(1)/(3)x^(2)) and ((1)/(2)x^(3)-4x^(2)) ? Choose 1 answer: (A) 4x^(5)-12x^(3)+(5)/(6)x^(2) (B) 4x^(5)-(15)/(2)x^(3)-(11)/(3)x^(2) (c) 4x^(5)-(7)/(2)x^(3)-x^(2) (D) 4x^(5)-(17)/(2)x^(3)+(11)/(3)x^(2)

Write down polynomials: Write down the given polynomials and prepare to combine like terms. We have: First polynomial: 4x^5 - 8x^3 + (1/3)x^2 Second polynomial: (1/2)x^3 - 4x^2 To find the sum, we will add the coefficients of the like terms.Combine x^5 terms: Combine the coefficients of the x^5 terms. Since there is only one x^5 term in the first polynomial and none in the second, the x^5 term in the sum is 4x^5.Combine x^3 terms: Combine the coefficients of the x^3 terms. The first polynomial has -8x^3 and the second polynomial has (1/2)x^3. Adding these gives us -8x^3 + (1/2)x^3 = -8x^3 + 0.5x^3 = -7.5x^3.Combine x^2 terms: Combine the coefficients of the x^2 terms. The first polynomial has (1/3)x^2 and the second polynomial has -4x^2. Adding these gives us (1/3)x^2 - 4x^2 = (1/3)x^2 - (12/3)x^2 = -(11/3)x^2.Write down final sum: Write down the final sum of the polynomials. Combining the results from the previous steps, we get: 4x^5 - 7.5x^3 - (11/3)x^2 However, we need to express -7.5x^3 as a fraction to match the answer choices. -7.5 is the same as -(15/2), so the term becomes -(15/2)x^3.Match with answer choices: Match the final expression with the given answer choices. The final expression is 4x^5 - (15/2)x^3 - (11/3)x^2, which corresponds to answer choice (B).

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What is the sum of
(4x^(5)-8x^(3)+(1)/(3)x^(2)) and
((1)/(2)x^(3)-4x^(2)) ?
Choose 1 answer:
(A)
4x^(5)-12x^(3)+(5)/(6)x^(2)
(B)
4x^(5)-(15)/(2)x^(3)-(11)/(3)x^(2)
(c)
4x^(5)-(7)/(2)x^(3)-x^(2)
(D)
4x^(5)-(17)/(2)x^(3)+(11)/(3)x^(2)

What is the sum of $\left(4 x^{5}-8 x^{3}+\frac{1}{3} x^{2}\right)$ and $\left(\frac{1}{2} x^{3}-4 x^{2}\right) ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $4 x^{5}-12 x^{3}+\frac{5}{6} x^{2}$ $\newline$ (B) $4 x^{5}-\frac{15}{2} x^{3}-\frac{11}{3} x^{2}$ $\newline$ (C) $4 x^{5}-\frac{7}{2} x^{3}-x^{2}$ $\newline$ (D) $4 x^{5}-\frac{17}{2} x^{3}+\frac{11}{3} x^{2}$

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Algebra 1

Compare linear, exponential, and quadratic growth

Full solution

Q. What is the sum of

\left(4 x^{5}-8 x^{3}+\frac{1}{3} x^{2}\right)

and

\left(\frac{1}{2} x^{3}-4 x^{2}\right) ?

\newline

Choose

1

answer:

\newline

(A)

4 x^{5}-12 x^{3}+\frac{5}{6} x^{2}

\newline

(B)

4 x^{5}-\frac{15}{2} x^{3}-\frac{11}{3} x^{2}

\newline

(C)

4 x^{5}-\frac{7}{2} x^{3}-x^{2}

\newline

(D)

4 x^{5}-\frac{17}{2} x^{3}+\frac{11}{3} x^{2}

Write down polynomials: Write down the given polynomials and prepare to combine like terms. $\newline$ We have: $\newline$ First polynomial: $4x^5 - 8x^3 + \left(\frac{1}{3}\right)x^2$ $\newline$ Second polynomial: $\left(\frac{1}{2}\right)x^3 - 4x^2$ $\newline$ To find the sum, we will add the coefficients of the like terms.
Combine $x^5$ terms: Combine the coefficients of the $x^5$ terms. $\newline$ Since there is only one $x^5$ term in the first polynomial and none in the second, the $x^5$ term in the sum is $4x^5$ .
Combine $x^3$ terms: Combine the coefficients of the $x^3$ terms. $\newline$ The first polynomial has $-8x^3$ and the second polynomial has $(1/2)x^3$ . Adding these gives us $-8x^3 + (1/2)x^3 = -8x^3 + 0.5x^3 = -7.5x^3$ .
Combine $x^2$ terms: Combine the coefficients of the $x^2$ terms. $\newline$ The first polynomial has $(1/3)x^2$ and the second polynomial has $-4x^2$ . Adding these gives us $(1/3)x^2 - 4x^2 = (1/3)x^2 - (12/3)x^2 = -(11/3)x^2$ .
Write down final sum: Write down the final sum of the polynomials. $\newline$ Combining the results from the previous steps, we get: $\newline$ $4x^5 - 7.5x^3 - \left(\frac{11}{3}\right)x^2$ $\newline$ However, we need to express $-7.5x^3$ as a fraction to match the answer choices. $-7.5$ is the same as $-\left(\frac{15}{2}\right)$ , so the term becomes $-\left(\frac{15}{2}\right)x^3$ .
Match with answer choices: Match the final expression with the given answer choices. $\newline$ The final expression is $4x^5 - \left(\frac{15}{2}\right)x^3 - \left(\frac{11}{3}\right)x^2$ , which corresponds to answer choice (B).