Question

What is the completely factored form of x4 + 8x2 – 9?

Answer 1

The answer is B:
${x}^{4} + 8 {x}^{2} - 9$
$= ( {x}^{2} + 9)( {x}^{2} - 1)$
$= (x + 1)(x - 1)( {x}^{2} + 9)$
Hope this helped

Answer 2

ANSWER

The correct answer is B


EXPLANATION

We want to factor completely,
${x}^{4} + 8 {x}^{2} - 9$


We can rewrite the above expression in the form.


${( {x}^{2}) }^{2} + 8( {x}^{2} ) - 9$


We can think of this expression as a quadratic trinomial in
${x}^{2}$


We need to split the middle term with factors of -9 that adds up to 8.



${( {x}^{2}) }^{2} - {x}^{2} + 9{x}^{2} - 9$


We factorize to obtain,

${x}^{2} ( {x}^{2} - 1) + 9( {x}^{2} - 1)$



We factor further to obtain,

$({x}^{2} - 1)( {x}^{2} + 9)$


We apply difference of two squares on the leftmost factor to obtain,


$(x - 1)(x + 1)( {x}^{2} + 9)$