Using factor theorem, show that g(x) is a factor of p(x), when
p(x) = 2x⁴ + 9x³ + 6x² – 11x – 6, g(x) = x – 1

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Solution

Let:
p(x) = 2x⁴ + 9x³ + 6x² – 11x – 6
Here,
$x - 1 = 0 \Rightarrow x = 1$
By the factor theorem, (x $-$ 1) is a factor of the given polynomial if p(1) = 0.
Thus, we have:
$p (1) = (2 \times 1^{4} + 9 \times 1^{3} + 6 \times 1^{2} - 11 \times 1 - 6) = (2 + 9 + 6 - 11 - 6) = 0$
Hence, (x $-$ 1) is a factor of the given polynomial.

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