Question

5.7 divide polynomials: problem 1
(1 point)
perform the indicated division of a polynomial by a monomial.
\\( \frac { 16 x ^ { 4 } + 24 x ^ { 3 } - 20 x ^ { 2 } + 16 x } { 4 x } \\)
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Explanation:

Step1: Divide each term by \(4x\)

$$\frac{16x^{4}}{4x}+\frac{24x^{3}}{4x}-\frac{20x^{2}}{4x}+\frac{16x}{4x}$$

Step2: Simplify each term using \(\frac{a^{m}}{a^{n}}=a^{m - n}\)

For \(\frac{16x^{4}}{4x}\): \(\frac{16}{4}x^{4-1}=4x^{3}\)
For \(\frac{24x^{3}}{4x}\): \(\frac{24}{4}x^{3 - 1}=6x^{2}\)
For \(\frac{20x^{2}}{4x}\): \(\frac{20}{4}x^{2-1}=5x\)
For \(\frac{16x}{4x}\): \(\frac{16}{4}x^{1 - 1}=4\)

Answer:

\(4x^{3}+6x^{2}-5x + 4\)