Question

Verify that -1 is the zero of the cubic polynomial p(x)=3x^3-5x^2-11x-3

Answer 1

$\huge{ \mathbb{SOLUTION:-}}$

$\bold{\mathsf{Method\: of \: Solution}}$

Required Polynomial:-

3x³-5x²-11x-3

Factor of Polynomial=-1




f(x)=x=1

Hence, Factor=-1

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Substitute the value of Factor in Required Polynomial:-

3x³-5x²-11x-3

f(1)=3(-1)³-5(-1)²-11(-1)-3

-3-5+11-3

-3-5-3)+11

-11+11

0

Here, 0 Shows it is Factor of the Polynomial.

Answer 2

Hey mate, here is your answer -:)

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$p(x) = {3x}^{3} - {5x}^{2} - 11x - 3 \\ \\ on \: putting \: x = - 1 \\ \\ p(1) = 3 {( - 1)}^{3} - 5 {( - 1) }^{2} - 11( - 1) - 3 \\ \: \: \: \: \: \: \: \: \: = 3( - 1) - 5(1) - 11( - 1) - 3 \\ \: \: \: \: \: \: \: \: \: = - 3 - 5 + 11 - 3 \\ \: \: \: \: \: \: \: \: \: = - 11 + 11 \\ \: \: \: \: \: \: \: \: \: = 0 \\ \\ \\ hence \: verified$

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HOPE it helps to you!!!