# Factor completely each polynomial, and indicate any that are not

Factor completely each polynomial, and indicate any that are not factorable using integers. $6{x}^{4}-5{x}^{2}-21$
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redhotdevil13l3
Step 1
Given: $6{x}^{4}-5{x}^{2}-21$
To factor the given trinomial?
Using the fact that by letting ${x}^{2}=y$ (substitution method)
Step 2
$6{x}^{4}-5{x}^{2}-21$
Put ${x}^{2}=y⇒6{y}^{2}-5y-21$
=(3y-7)(2y+3)
$=\left(3{x}^{2}-7\right)\left(2{x}^{2}+3\right)$ (by replacing y as ${x}^{2}$)
Therefore, $6{x}^{4}-5{x}^{2}-21=\left(3{x}^{2}-7\right)\left(2{x}^{2}+3\right)$
but still it is not factored interms of linear expressionie., the expression $\left(2{x}^{2}+3\right)$ can be factored into twopairs of complex number $\left(x+i\sqrt{\frac{3}{2}}\right)\left(x-i\sqrt{\frac{3}{2}}$ which is absqrt in real number system here.

Matthew Rodriguez