Question

Q02: Factorize the following by Factor theorem:

a) x² +9x² +23x+15 b) x² +6x² + 11x +6​

Answer 1

Answer:

a) x³ + 9x² + 23x +15

Factors of the constant term 15 = ± 1 , ± 3 , ± 5 , ± 15

Let us pick any factor of constant randomly that when put at place of x gives 0

\implies⟹ Let x = -1

x³ + 9x² + 23 x + 15

= (-1)³ + 9(-1)² + 23 (-1) + 15

= -1 + 9 -23 + 15

= 24 - 24

= 0

\implies⟹ Let x = -3

(-3)³ + 9 (-3)² + 23 (-3) + 15

= -27 + 81 - 69 + 15

= 96 - 96

= 0

\implies⟹ Let x = -5

(-5)³ + 9(-5)² + 23 (-5) + 15

= -125 + 225 - 115 + 15

= 240 - 240

x = -1 , -3 and -5

Therefore

x³ + 9x² + 23x +15 = (x+1)(x+3)(x+5)

_____________________________

b) x³ - 6x² +11x -6

Factors of constant 6 = ±1 , ±2 , ± 3 and ± 6

\implies⟹ Let x = 1

(1)³ - 6(1)² + 11(1) - 6

= 1 -6 +11 -6

= 12-12

= 0

\implies⟹ Let x = 2

(2)³ - 6(2)² + 11(2) - 6

= 8 - 24 + 22 - 6

= 30 - 30

= 0

\implies⟹ Let x = 3

(3)³ - 6(3)² + 11(3) -6

= 27 - 54 + 33 - 6

= 60 -60

= 0

Hence , x = 1 , 2 and 3

Therefore ,

x³ - 6x² + 11x - 6 = (x-1)(x-2)(x-3)

Step-by-step explanation:

hope it is helpful for you and please mark me brainiest please follow and give lots of thanks also