Question

Check whether the following are factors of x3 - 5x² – 2x+24 or not. (ii) (x + 3) (iii) (x + 2) (iv) (X + 8 X () (x + 4) 15.​

Answer 1

Step-by-step explanation:

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Class 9

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>>Determine which of the foll...

Question

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Determine which of the following polynomials has (x+1) a factor:

(i) x

3

+x

2

+x+1

(ii) x

4

+x

3

+x

2

+x+1

(iii) x

4

+3x

3

+3x

2

+x+1

(iv) x

3

−x

2

−(2+

2

)x+

2

Medium

Solution

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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

(ii) x

4

+x

3

+x

2

+x+1=(−1)

4

+(−1)

3

+(−1)

2

+(−1)+1=1−1+1−1+1=1

This is not zero.Then x+1 is not the factor of equation

(iii) x

4

+3x

3

+3x

2

+x+1=(−1)

4

+3(−1)

3

+3(−1)

2

+(−1)+1=1

This is not zero.Then x+1 is not the factor of equation

(iv)x

3

−x

2

−(2+

2

)x+

2

=(−1)

3

−(−1)

2

−(2+

2

)(−1)+

2

=−1−1+2−

2

+

2

=0

This is zero. Then x+1 is the factor of equation

Answer 2

Answer:

(x + 2) is a factor of $x^3 -5x^2 -2x + 24$ .

Step-by-step explanation:

Take x + 3

$x = -3$

$x^3 -5x^2 -2x + 24$

$= (-3)^3 - 5(-3)^2 – 2(-3) + 24$

$=- 27 -5(9)+6 + 24$

$= -27 -45 + 30$

$= -42$

So (x + 3) is not factor

Take x + 2

x = -2

$x^3 -5x^2 -2x + 24$

$= (-2)^3 - 5(-2)^2 – 2(-2) + 24$

$=- 8 -5(4)+4 + 24$

$= -8 -20 + 28$

= 0

So (x + 2) is a factor