Question
Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(-2 z^{3}+8 z^{2}+47 z-35\right) \div(z-7) \) Submit
Ask by Montgomery Stewart. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The result of dividing \( -2z^{3}+8z^{2}+47z-35 \) by \( z-7 \) is \( -2z^{2}-6z+5 \).
Solution
Calculate or simplify the expression \( (-2*z^3+8*z^2+47*z-35)/(z-7) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(-2z^{3}+8z^{2}+47z-35\right)}{\left(z-7\right)}\)
- step1: Remove the parentheses:
\(\frac{-2z^{3}+8z^{2}+47z-35}{z-7}\)
- step2: Factor the expression:
\(\frac{\left(z-7\right)\left(-2z^{2}-6z+5\right)}{z-7}\)
- step3: Reduce the fraction:
\(-2z^{2}-6z+5\)
The result of dividing the polynomial \( -2z^{3}+8z^{2}+47z-35 \) by \( z-7 \) is \( -2z^{2}-6z+5 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To divide the polynomial \(-2z^{3}+8z^{2}+47z-35\) by \(z-7\), we can use synthetic division or polynomial long division. We'll proceed with synthetic division, using \(7\) (the zero of \(z-7\)). Setting up synthetic division: ``` 7 | -2 8 47 -35 | -14 -42 35 ----------------------- -2 -6 5 0 ``` The coefficients represent the result of the division, where the quotient is \(-2z^2 - 6z + 5\) with a remainder of \(0\). Thus, the division results in: \[ -2z^{2} - 6z + 5 \] Since the remainder is \(0\), the polynomial divides evenly.
