Question

3 mark for review which expression is equivalent to $5x^5 - 6x^4 + 8x^3$? a $x^4(5x - 6)$ b $x^3(5x^2 - 6x + 8)$ c $8x^3(5x^2 - 6x + 1)$ d $6x^5(-6x^4 + 8x^3 + 1)$

Explanation:

Step1: Identify greatest common factor

The terms are $5x^5$, $-6x^4$, $8x^3$. The greatest common factor (GCF) of the coefficients $5, -6, 8$ is $1$, and the GCF of the variable parts $x^5, x^4, x^3$ is $x^3$. So the overall GCF is $x^3$.

Step2: Factor out the GCF

Divide each term in $5x^5 - 6x^4 + 8x^3$ by $x^3$:
$\frac{5x^5}{x^3} = 5x^2$, $\frac{-6x^4}{x^3} = -6x$, $\frac{8x^3}{x^3} = 8$
Write the factored form: $x^3(5x^2 - 6x + 8)$

Step3: Match with options

Compare the factored expression to the given options.

Answer:

B. $x^3(5x^2 - 6x + 8)$