Question

Common Factors of Polynomials

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Which statements are true?

Select each correct answer.​

Answer 1

9g³ + 12 = 3(3g³ + 4)

35g⁵ – 25g² = 5g²(7g³ – 5)

Explanation:

To know which statement is true, we shall facotrise each expression.

This is illustrated below:

4g² – g = g²(4 – g)

g(4g – 1) ≠ g²(4 – g)

Thus,

4g² – g = g²(4 – g) is not true.

9g³ + 12 = 3(3g³ + 4)

3(3g³ + 4) = 3(3g³ + 4)

Thus,

9g³ + 12 = 3(3g³ + 4) is true

24g⁴ + 18g² = 6g²(4g² + 3g)

6g²(4g² + 3) ≠ 6g²(4g² + 3g)

Thus,

24g⁴ + 18g² = 6g²(4g² + 3g) is not true

35g⁵ – 25g² = 5g²(7g³ – 5)

5g²(7g³ – 5) = 5g²(7g³ – 5)

Thus,

35g⁵ – 25g² = 5g²(7g³ – 5) is true

From the illustrations above,

9g³ + 12 = 3(3g³ + 4) is true

35g⁵ – 25g² = 5g²(7g³ – 5) is true