Factorize the following by factor theorem
x3 +9x2 +23x +15
Answers
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)
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