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?

Question

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DelcieRiveria DelcieRiveria · Answer 1 · 2018-11-19T08:54:15+01:00

Answer: The correct option is c.

Explanation:

Reason for correct option:

[tex]3x(9x^2+1)[/tex]

This expression cannot be factored further because [tex](9x^2+1)[/tex] is the complete factor. Therefore the option c is correct.

Reason for incorrect option:

[tex]5x^2-17x+14=5x^2-10x-7x+14=5x(x-2)-7(x-2)=(x-2)(5x-7)[/tex]

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

[tex]4(4x^4-1)=4((2x)^2-1)=4(2x^2-1)(2x^2+1)[/tex]

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

[tex]2x(y^3-4y^2+5y)=2xy(y^2-4y+5)[/tex]

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

ahirohit963 ahirohit963 · Answer 2 · 2021-10-18T15:30:37+02:00

The correct option is c).

Step-by-step explanation:

a) [tex]4(4x^4-1) = 4(2x^2-1)(2x^2+1)[/tex]

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

b) [tex]2x(y^3-4y^2+5y)=2xy(y^2-4y+5)[/tex]

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

c) [tex]3x(9x^2+1)[/tex]

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

d) [tex]5x^2-17x+14=5x^2-10x-7x+14=5x(x-2)-7(x-2)= (x-2)(5x-7)[/tex]

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

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https://brainly.com/question/20293447?referrer=searchResults