Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping? x2(4x + 1) – 2(4x + 1) x2(4x – 1) + 2(4x – 1) 4x2(x + 2) – 1(x + 2) 4x2(x – 2) – 1(x – 2)

Looking at 4x3 + x2 – 8x – 2, I see immediately that x^2 can be factored out of the first 2 terms => 4x^2(x+1)
and -2 out of the last 2 terms => -2(4x+1).

Notice how the factor (4x+1) shows up twice.

We can factor this (4x+1) out, obtaining (x^2 - 2) (4x+1). These are the desired factors, found "by grouping."

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shubhamchouhanvrVT shubhamchouhanvrVT · Answer 2 · 2022-06-10T14:02:50+02:00

The factors of the given expression will be (x ²- 2) (4x+1).

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Looking at 4x³ + x² – 8x – 2, I see immediately that x² can be factored out of the first 2 terms 4x²(x+1) and -2 out of the last 2 terms -2(4x+1).

Notice how the factor ( 4x + 1 ) shows up twice.

We can factor this (4x+1) out, obtaining (x² - 2) (4x+1). These are the desired factors, found "by grouping.

Therefore the factors of the given expression will be (x ²- 2) (4x+1).

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