Question

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Determine inhether a CC) is a factor of Plac)
In this Call Ploc) 2x² + x² - 2x - 1 g ex axtla​

Answer 1

$\huge{\underline{\underline{\bf{Solution}}}}$

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$\tt Given\begin{cases} \sf{P(x) = 2x^3 + x^2 - 2x - 1} \\ \sf{g(x) = x + 1} \end{cases}$

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$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to determine whether g(x) is a factor of p(x).

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$\Large{\underline{\underline{\bf{Explanation :}}}}$

As, it is given that x + 1 is g(x).

So, x = -1

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Putting value of x as -1.

$\sf{\mapsto 2(-1)^3 + (-1)^2 - 2(-1) - 1} \\ \\ \sf{\mapsto 2(-1) + 1 + 2 - 1} \\ \\ \sf{\mapsto -2 + 3 - 1} \\ \\ \sf{\mapsto 3 - 3} \\ \\ \sf{\mapsto 0}$

$\therefore$ It is a factor of polynomial.

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$\Large{\underline{\underline{\bf{Verification :}}}}$

For verification put value of x as - 1 and put it equal to zero.

$\sf{\mapsto 2(-1)^3 + (-1)^2 - 2(-1) - 1 = 0} \\ \\ \sf{\mapsto 2(-1) + 1 + 2 - 1 = 0} \\ \\ \sf{\mapsto -2 + 3 - 1 = 0} \\ \\ \sf{\mapsto 3 - 3 = 0} \\ \\ \sf{\mapsto 0 = 0}$

★ Hence Verified