Question

factorise the following by factor theorum x3+9x2+23x+15

Answer 1

Answer:

hey mate here is your answer

Step-by-step explanation:

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

Step-by-step explanation:

Given : Equation  x³ = 9² + 23 x + 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 p/q  = ± 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 = -5

= (-5)³+9 (-5)²+ 23( -5) + 15

= -125 +125-115+5

= 0

= put x = -3

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

= -27 + 18  -69 + 15

= 0

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

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

thank you