Question

factorise by factor theorem. x³+9x²+23x+15

Answer 1

Answer:

The factor form is $x^3+9x^2+23x+15=(x+1)(x+3)(x+5)$            

Step-by-step explanation:

Given : Equation $x^3+9x^2+23x+15$

To find : Factories by factor theorem?

Solution :

Applying rational root theorem state that factor of constant by factor of coefficient of cubic term gives you the possible roots of the equation.

Coefficient of cubic term = 1

Factor = 1

Constant term = 15

Factor of constant term = 1,3,5,15.

Possible roots are $\frac{p}{q}= \pm\frac{1,3,5,15}{1}$

Possible roots are 1,-1,3,-3,5,-5,15,-15.

Substitute all the roots when equation equate to zero then it is the root of the equation.

Put x=-1,

$=(-1)^3+9(-1)^2+23(-1)+15$

$=-1+9-23+15$

$=0$

Put x=-3,

$=(-3)^3+9(-3)^2+23(-3)+15$

$=-27+81-69+15$

$=0$

Put x=-5,

$=(-5)^3+9(-5)^2+23(-5)+15$

$=-125+225-115+15$

$=0$

Therefore, The roots of equation is x=-1,-3,-5.

The factor form is $x^3+9x^2+23x+15=(x+1)(x+3)(x+5)$

Answer 2

Answer:

Answer:

The factor form is x^3+9x^2+23x+15=(x+1)(x+3)(x+5)x

3

+9x

2

+23x+15=(x+1)(x+3)(x+5)

Step-by-step explanation:

Given : Equation x^3+9x^2+23x+15x

3

+9x

2

+23x+15

To find : Factories by factor theorem?

Solution :

Applying rational root theorem state that factor of constant by factor of coefficient of cubic term gives you the possible roots of the equation.

Coefficient of cubic term = 1

Factor = 1

Constant term = 15

Factor of constant term = 1,3,5,15.

Possible roots are \frac{p}{q}= \pm\frac{1,3,5,15}{1}

q

p

=±

1

1,3,5,15

Possible roots are 1,-1,3,-3,5,-5,15,-15.

Substitute all the roots when equation equate to zero then it is the root of the equation.

Put x=-1,

=(-1)^3+9(-1)^2+23(-1)+15=(−1)

3

+9(−1)

2

+23(−1)+15

=-1+9-23+15=−1+9−23+15

=0=0

Put x=-3,

=(-3)^3+9(-3)^2+23(-3)+15=(−3)

3

+9(−3)

2

+23(−3)+15

=-27+81-69+15=−27+81−69+15

=0=0

Put x=-5,

=(-5)^3+9(-5)^2+23(-5)+15=(−5)

3

+9(−5)

2

+23(−5)+15

=-125+225-115+15=−125+225−115+15

=0=0

Therefore, The roots of equation is x=-1,-3,-5.

The factor form is x^3+9x^2+23x+15=(x+1)(x+3)(x+5)x

3

+9x

2

+23x+15=(x+1)(x+3)(x+5)

Plz mark me as brainliest.