Question
Points: 0 of 1 Decide whether the following statement is true or false. \[ \begin{array}{cccc} - 2 \longdiv { 5 } \begin{array} { c c c } { 4 } & { 3 } & { 1 } \\ { } & { - 1 0 } & { 1 2 } \end{array} - 3 0 \\ \hline 5 & -6 & 15 & -29 \end{array} \text { means } \frac{5 x^{3}+4 x^{2}+3 x+1}{x+2}=5 x^{2}-6 x+15+\frac{-29}{x+2} \] Choose the correct answer below. True False
Ask by Curry Matthews. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The statement is true.
Solution
The statement is true.
The division shown is equivalent to writing
(5x³ + 4x² + 3x + 1) / (x + 2) = 5x² – 6x + 15 + (–29)/(x + 2)
which means that when (5x³ + 4x² + 3x + 1) is divided by (x + 2), the quotient is 5x² – 6x + 15 and the remainder is –29. This is consistent with the result given, so the answer is True.
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Simplify this solution Beyond the Answer
The statement is true! What you’re looking at is the process of polynomial long division. When dividing the polynomial \(5x^3 + 4x^2 + 3x + 1\) by \(x + 2\), the result can be expressed as a polynomial quotient (in this case \(5x^2 - 6x + 15\)) plus a remainder term \(\frac{-29}{x + 2}\), making it a proper division representation. Now, the next time you're handling polynomials, remember to always double-check your long division steps. Keeping your terms lined up neatly helps avoid common pitfalls, like misplaced coefficients or incorrect signs. If you get confused, just go slow and do it step by step!
