Which polynomial is NOT equivalent to (5x – 2)(-2x + 4)?
– -10x + 20x + 4x – 8
– -8 + 24x – 10x²
– 4x + 20x – 10x² – 8
– -10x² + 24x – 8
Which polynomial is NOT equivalent to (5x – 2)(-2x + 4)
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Which polynomial is NOT equivalent to (5x – 2)(-2x + 4)?
– -10x + 20x + 4x – 8
– -8 + 24x – 10x²
– 4x + 20x – 10x² – 8
– -10x² + 24x – 8
To determine which polynomial is NOT equivalent to ( (5x – 2)(-2x + 4) ), we first need to expand this expression.
1. Use the distributive property (FOIL method):
[
(5x)(-2x) + (5x)(4) + (-2)(-2x) + (-2)(4)
]
This simplifies to:
[
-10x^2 + 20x + 4x – 8
]
Combine like terms:
[
-10x^2 + 24x – 8
]
Now, let’s compare this result with the provided options:
1. (-10x + 20x + 4x – 8 = 14x – 8) (not equivalent)
2. (-8 + 24x – 10x^2) (equivalent)
3. (4x + 20x – 10x^2 – 8 = -10x^2 + 24x – 8) (equivalent)
4. (-10x^2 + 24x – 8) (equivalent)
The polynomial that is NOT equivalent to ( (5x – 2)(-2x + 4) ) is:
-10x + 20x + 4x – 8.
This