factorise x3+2x²_13x+10
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8th
Maths
Factorisation
Factorisation
The factors of x3 - 2x2 - 1...
MATHS
The factors of x
3
−2x
2
−13x−10 are
EASY
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ANSWER
Let p(x)=x
3
−2x
2
−13x−10
By trail, we find that p(−1)=(−1)
3
−2(−1)
2
−13(−1)−10=−1−2+13−10=0. So (x+1) is factor of p(x).
Now, x
3
−2x
2
−13x−10=x
3
+(x
2
−3x
2
)−(3x+10x)−10
=(x
3
+x
2
)−(3x
2
+3x)−(10x+10)
=x
2
(x+1)−3x(x+1)−10(x+1)
=(x+1)(x
2
−3x−10)
=(x+1)[x
2
−5x+2x−10]
=(x+1)[x(x−5)+2(x−5)]
=(x+1)(x−5)(x+2)
=(x−5)(x+1)(x+2)
Option D is correct.
Step-by-step explanation:
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