Question

which polynomial is not equivalent to (5x - 2)(-2x + 4)?
-10x + 20x + 4x - 8
4x + 20x - 10x² - 8
-8 + 24x - 10x²
-10x² + 24x - 8

Explanation:

Step1: Expand the original polynomial

Using the distributive property (FOIL method) to expand \((5x - 2)(-2x + 4)\):
\[

$$\begin{align*} (5x)(-2x)+(5x)(4)+(-2)(-2x)+(-2)(4)&=-10x^{2}+20x + 4x-8\\ &=-10x^{2}+24x - 8 \end{align*}$$

\]

Step2: Analyze each option

• Option 1: \(-10x + 20x + 4x - 8\) has a mistake in the first term (should be \(-10x^{2}\) instead of \(-10x\)), so this polynomial is not equivalent.
• Option 2: Rearranging \(4x + 20x - 10x^{2}-8\) gives \(-10x^{2}+24x - 8\), which is equivalent.
• Option 3: \(-8 + 24x - 10x^{2}\) is the same as \(-10x^{2}+24x - 8\) (just reordered), so it is equivalent.
• Option 4: \(-10x^{2}+24x - 8\) is the expanded form, so it is equivalent.

Answer:

\(-10x + 20x + 4x - 8\) (the first option)