Write the polynomial as the product of factors that are irreducible over the rationals. ? F(x)= x⁴ + 6x² - 27 ? A) $\left( x ^ { 2 } + 9 \right) \left( x ^ { 4 } - 3 \right)$ B) $\left( x ^ { 2 } + 9 \right) \left( x ^ { 2 } - 3 \right)$ C) $( x + 9 ) \left( x ^ { 2 } - 3 \right)$ D) $( x + 6 ) \left( x ^ { 2 } - 3 \right)$ E) $\left( x ^ { 2 } + 9 \right) ( x + \sqrt { 3 } ) ( x + \sqrt { 3 } )$

Question

Quizplus · Accepted Answer

The polynomial $F(x) = x^4 + 6x^2 - 27$ can be factored as $(x^2 + 9)(x^2 - 3)$, both of which are irreducible over the rationals.

Write the Polynomial as the Product of Factors That Are (x2+9)(x4−3)\left( x ^ { 2 } + 9 \right) \left( x ^ { 4 } - 3 \right)(x2+9)(x4−3)

Write the Polynomial as the Product of Factors That Are $\left( x ^ { 2 } + 9 \right) \left( x ^ { 4 } - 3 \right)$