Question

Mathematics
Class - 9th
Unit - 2 Polynomials
Exercise - 2.4
Q.1 Determine which of the following polynomials has (x+1) a factor :
x⁴ + 3x³ + 3x² + x + 1

Answer 1

Answer:

Apply remainder theorem

x+1=0

x=−1

Put the value of x=−1 in all equations.

(i) x

3

+x

2

+x+1=(−1)

3

+(−1)

2

+(−1)+1=−1+1−1+1=0

Then x+1 is the factor of equation

Answer 2

Answer:

$let \: p(x) = {x}^{4} + 3 {x}^{3} + 3 {x}^{2} + x + 1$

$the \: zero \: of \: x + 1 \: is - 1$

$p( - 1) = {( - 1)}^{4} + 3 {( - 1)}^{3} + 3 {( - 1)}^{2} + ( - 1) + 1$

$p( - 1) = 1 - 3 + 3 - 1 + 1$

$cut \: - 3 + 3 - 1 + 1$

$p( - 1) = 1$

p(-1) = 1≠0

$by \: factor \: theorem \: x + 1 \: is \: not \: a \: factor \: of \: {x}^{4} + 3 {x}^{3} + 3 {x}^{2} + x + 1$

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