Question

Please explain why. Thanks

Answer 1

Question :-

Is (x-2) is a factor of x³-3x²-x +7 –

• Yes
• No ☑

Explanation :-

We are given –

• Polynomial function, P(x) = x³-3x²-x +7

• In order to check if x - 2 is a factor of x³-3x²-x +7 or not, we must show that P(2) = 0.

• Let's find value of x!

$\qquad$ $\twoheadrightarrow\bf P(x) = x³-3x²-x +7$

$\qquad$ $\twoheadrightarrow\bf Q(x) =x - 2$

$\qquad$ $\twoheadrightarrow\bf If \:Q(x) = 0$

$\qquad$ $\twoheadrightarrow\bf x - 2 = 0$

$\qquad$ $\twoheadrightarrow\bf x = 2$

Now Put x = 2 into the polynomial –

$\qquad$ $\purple{\twoheadrightarrow\bf P(2) = 2³-3(2)²-2+7}$

$\qquad$ $\twoheadrightarrow\sf P(2) = 8 - 3 \times 4 +5$

$\qquad$ $\twoheadrightarrow\sf P(2) = 8 -12 +5$

$\qquad$ $\twoheadrightarrow\sf P(2) = 13-12$

$\qquad$ $\purple{\twoheadrightarrow\bf P(2) =1 }$

• Since the value of the polynomial function st x = 2 is not Zero (0). Henceforth, ( x - 2) is a factor of  x³-3x²-x +7.

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