Using factor theorem- show that-x-2 is a factor of x4-x2-12

Let: fx=x4 x2 12 Here, nbsp; #160;x+2=0 #8658;x= 2 By the factor theorem, (x + 2) is a factor of nbsp;the given polynomial if nbsp;f nbsp;( 2) = 0. ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Factor Theorem

Using factor ...

Question

Using factor theorem, show that:
(x + 2) is a factor of (x⁴ − x² − 12)

Open in App

Solution

Let:
$f (x) = x^{4} - x^{2} - 12$
Here,
$x + 2 = 0 \Rightarrow x = - 2$
By the factor theorem, (x + 2) is a factor of the given polynomial if f ( $-$ 2) = 0.
Thus, we have:
$f (- 2) = [{(- 2)}^{4} - {(- 2)}^{2} - 12] = (16 - 4 - 12) = 0$
Hence, (x + 2) is a factor of the given polynomial.

Suggest Corrections

Similar questions

Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = x^{4} - x^{2} - 12, g (x) = x + 2$

Q. Using factor theorem, show that:
(x − 3) is a factor of (2x³ + 7x² − 24x − 45)

Q. Using factor theorem, show that:

(x + \sqrt{2})

is a factor of

(2 \sqrt{2} x^{2} + 5 x + \sqrt{2})

Q. Using factor theorem, show that

x^{2} + 5 x + 6

is a factor of

x^{4} + 5 x^{3} + 9 x^{2} + 15 x + 18

Q. Using factor theorem show

x - 2

is a factor of

x^{6} - 64

Join BYJU'S Learning Program

Using factor theorem, show that: (x + 2) is a factor of (x4 − x2 − 12)

Let: fx=x4-x2-12 Here, x+2=0⇒x=-2 By the factor theorem, (x + 2) is a factor of the given polynomial if f (-2) = 0. Thus, we have: f-2=-24--22-12 =16-4-12 =0 Hence, (x + 2) is a factor of the given polynomial.

Using factor theorem, show that:
(x + 2) is a factor of (x⁴ − x² − 12)

Let:
$f (x) = x^{4} - x^{2} - 12$
Here,
$x + 2 = 0 \Rightarrow x = - 2$
By the factor theorem, (x + 2) is a factor of the given polynomial if f ( $-$ 2) = 0.
Thus, we have:
$f (- 2) = [{(- 2)}^{4} - {(- 2)}^{2} - 12] = (16 - 4 - 12) = 0$
Hence, (x + 2) is a factor of the given polynomial.