Question
Divide. \[ \left(28 x^{3}+16 x^{2}+24 x\right) \div(-4 x) \] Simplify your answer as much as possible.
Ask by Clarke Stuart. in the United States
Dec 02,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The result is \(-7x^{2}-4x-6\).
Solution
Using long division to calculate \( (28x^3+16x^2+24x) \div (-4x) \).
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
\(\left(28x^{3}+16x^{2}+24x\right)\div \left(-4x\right)\)
- step1: Calculate:
\(\left(-7x^{2}-4x-6\right)\text{ }\textrm{remainder}\text{ }0\)
The division of \(28x^{3}+16x^{2}+24x\) by \(-4x\) results in \(-7x^{2}-4x-6\) with a remainder of 0.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To divide \( 28x^3 + 16x^2 + 24x \) by \(-4x\), we can rewrite the expression as follows: \[ \frac{28x^3 + 16x^2 + 24x}{-4x} \] Now, we can split the division across each term in the numerator: \[ \frac{28x^3}{-4x} + \frac{16x^2}{-4x} + \frac{24x}{-4x} \] Now we simplify each term: 1. For the first term: \[ \frac{28x^3}{-4x} = -7x^{3-1} = -7x^2 \] 2. For the second term: \[ \frac{16x^2}{-4x} = -4x^{2-1} = -4x \] 3. For the third term: \[ \frac{24x}{-4x} = -6 \] Now, combining all the simplified terms, we have: \[ -7x^2 - 4x - 6 \] Thus, the simplified answer is: \[ \boxed{-7x^2 - 4x - 6} \]
