Question

6.03 dividing polynomials by a monomial

1. fill in the missing values to make the statement true.

$\frac{8x^{5} - 6x^{7}}{2x^{square}} = 4x^{3} - 3x^{5}$

Explanation:

Step1: Find missing exponent (denominator)

Use $\frac{x^m}{x^n}=x^{m-n}$. For $4x^3$:
$5 - n = 3 \implies n=2$

Step2: Verify with second term

For $-3x^5$:
$7 - n = 5 \implies n=2$

Step3: Confirm coefficient order

Rewrite the numerator to match quotient order:
$-6x^7 + 8x^5 = -(6x^7 - 8x^5)$, so numerator is $-6x^7 + 8x^5$ (or $8x^5 - 6x^7$ matches quotient order when dividing)

Answer:

Missing value in numerator coefficient: $6$
Missing value in denominator exponent: $2$

Full true statement: $\frac{8x^5 - 6x^7}{2x^2}=4x^3 - 3x^5$