CBSE Class 9 Answered
Using
factor theorem, show that x2 + 5x + 6 is a factor of x4
+ 5x3 + 9x2 + 15x + 18.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
We have,
x2 + 5x + 6
= x2 + 3x + 2x + 6
= x (x + 3) +2 (x + 3)
= (x + 2) (x + 3)
Let p(x) = x4 + 5x3 + 9x2 + 15x + 18
Put x = -2
p(-2) = (-2)4 + 5(-2)3 + 9(-2)2 + 15 (-2) + 18
= 16 - 40 + 36 - 30 + 18
=
70 - 70 = 0 
(x + 2) is a
factor
Put x = -3
p(-3) = (-3)4 + 5(-3)3 + 9(-3)2 + 15 (-3) + 18
= 81 - 135 + 81 - 45 + 18
=
180 - 180 = 0 (x + 3) is a
factor
Hence x2 + 5x + 6
Is a factor of p(x).
Answered by | 04 Jun, 2014, 03:23: PM
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