Question

Which polynomial is factored completely

Answer 1

$a.\ 4(4x^4-1)=4[(2x^2)^2-1^2]=4(2x^2-1)(2x^2+1)-NOT\\\\b.\ 2x(y^3-4y^2+5y)=2xy(y^2-4y+5)-NOT\\\\c.\ 3x(9x^2+1)-YES\\\\d.\ 5x^2-17x+14=5x^2-10x-7x+14\\=5x(x-2)-7(x-2)=(x-2)(5x-7)-NOT$
Answer: c.

Answer 2

Answer: The correct option is c.

Explanation:

Reason for correct option:

$3x(9x^2+1)$

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

Reason for incorrect option:

$5x^2-17x+14=5x^2-10x-7x+14=5x(x-2)-7(x-2)=(x-2)(5x-7)$

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

$4(4x^4-1)=4((2x)^2-1)=4(2x^2-1)(2x^2+1)$

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

$2x(y^3-4y^2+5y)=2xy(y^2-4y+5)$

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