Using factor theorem- show that-x-1 is a factor of 2 x4-9 x3-6 x2-11 x-6

Let: fx=2x4+9x3+6x2 11x 6 Here, nbsp; x 1=0 #8658;x=1 By the factor theorem, (x nbsp; 1) is a factor of nbsp;the given polynomial if nbsp;f(1) = 0. ...

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Standard IX

Mathematics

Factor Theorem

Using factor ...

Question

Using factor theorem, show that:
(x − 1) is a factor of (2x⁴ + 9x³ + 6x² − 11x − 6)

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Solution

Let:
$f (x) = 2 x^{4} + 9 x^{3} + 6 x^{2} - 11 x - 6$
Here,
$x - 1 = 0 \Rightarrow x = 1$
By the factor theorem, (x $-$ 1) is a factor of the given polynomial if f(1) = 0.
Thus, we have:
$f (1) = (2 \times 1^{4} + 9 \times 1^{3} + 6 \times 1^{2} - 11 \times 1 - 6) = (2 + 9 + 6 - 11 - 6) = 0$
Hence, (x $-$ 1) is a factor of the given polynomial.

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Using factor theorem, show that: (x − 1) is a factor of (2x4 + 9x3 + 6x2 − 11x − 6)

Let: fx=2x4+9x3+6x2-11x-6 Here, x-1=0⇒x=1​ By the factor theorem, (x - 1) is a factor of the given polynomial if f(1) = 0. Thus, we have: f1=2×14+9×13+6×12-11×1-6 =2+9+6-11-6 =0 Hence, (x - 1) is a factor of the given polynomial.

Using factor theorem, show that:
(x − 1) is a factor of (2x⁴ + 9x³ + 6x² − 11x − 6)