Julia White

2021-12-16

Factor completely each polynomial, and indicate any that are not factorable using integers. $6{x}^{4}-5{x}^{2}-21$

redhotdevil13l3

Beginner2021-12-17Added 30 answers

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${x}^{2}=y\Rightarrow 6{y}^{2}-5y-21$

=(3y-7)(2y+3)

$=(3{x}^{2}-7)(2{x}^{2}+3)$ (by replacing y as $x}^{2$ )

Therefore,$6{x}^{4}-5{x}^{2}-21=(3{x}^{2}-7)(2{x}^{2}+3)$

but still it is not factored interms of linear expressionie., the expression$(2{x}^{2}+3)$ can be factored into twopairs of complex number $(x+i\sqrt{\frac{3}{2}})(x-i\sqrt{\frac{3}{2}}$ which is absqrt in real number system here.

Given:

To factor the given trinomial?

Using the fact that by letting

Step 2

Put

=(3y-7)(2y+3)

Therefore,

but still it is not factored interms of linear expressionie., the expression

Matthew Rodriguez

Beginner2021-12-18Added 32 answers

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