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Answer:

To find the remainder when a polynomial is divided by a linear factor, we can use the remainder theorem. According to the remainder theorem, if we divide a polynomial f(x) by x - a, the remainder will be equal to f(a).

Let's apply the remainder theorem to the given polynomials:

For the polynomial x³ + 2x² + 2x - 4 divided by x - 2, the remainder R₁ will be:

R₁ = (2)³ + 2(2)² + 2(2) - 4

= 8 + 8 + 4 - 4

= 16

For the polynomial x³ + 2x² - 3x + 6 divided by x - 2, the remainder R₂ will be:

R₂ = (2)³ + 2(2)² - 3(2) + 6

= 8 + 8 - 6 + 6

= 16

Therefore, the remainder R₁ is equal to the remainder R₂, and the true statement is that R₁ = R₂ = 16.

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