Which polynomial is factored completely a. 4 (4x^4-1) b. 2x (y^3-4y^2+5y) c. 3x (9×^2+1) d. 5x^2-17x+14?

The correct option is c.

Explanation:

Reason for correct option:

This expression cannot be factored further because is the complete factor. Therefore the option c is correct.

Reason for incorrect option:

Since the given expression can be factored further therefore the option d is incorrect.

Since the given expression can be factored further. Therefore the option a is incorrect.

Since the given expression can be factored further. Therefore the option b is incorrect.

The correct option is c).

Step-by-step explanation:

a)

Therefore, option a) is incorrect because it can be further factorised.

b)

Therefore, option b) is incorrect because it can be further factorised.

c)

This cannot be further factorised. Therefore, option c) is correct.

d)

Therefore, option d) is incorrect because it can be factorised completely.

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step-by-step explanation:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)