factorise x^3-3x^2-9x-5
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Answered by
27
hello.....
x3 - 3x2 - 9x - 5
Ans) p(x) = x3 - 3x2 - 9x - 5
Factors of 5 = 1,5,-1,-5
p(1) = 13 - 3 x (1)2 - 9 x (1) - 5
= 1 -3 - 9 - 5
= 1 - 17 = - 16 ≠ 0
p(-1) = (-1)3 x 3 x (-1)2 - 9 x (-1) -5
= -1 - 3 + 9 - 5 = -9 + 9 = 0
p(-1) =0
∴ (x+1) is a factor of p(x)
p(x) ÷ (x+1)
x3 - 3x2 - 9x - 5 ÷ x + 1
= x2 - 4x - 5
x2 - 4x - 5
x2 - 5x + 1x - 5
= x ( x - 5) + 1 ( x - 5)
= ( x - 5) ( x + 1)
I hope it help u.
x3 - 3x2 - 9x - 5
Ans) p(x) = x3 - 3x2 - 9x - 5
Factors of 5 = 1,5,-1,-5
p(1) = 13 - 3 x (1)2 - 9 x (1) - 5
= 1 -3 - 9 - 5
= 1 - 17 = - 16 ≠ 0
p(-1) = (-1)3 x 3 x (-1)2 - 9 x (-1) -5
= -1 - 3 + 9 - 5 = -9 + 9 = 0
p(-1) =0
∴ (x+1) is a factor of p(x)
p(x) ÷ (x+1)
x3 - 3x2 - 9x - 5 ÷ x + 1
= x2 - 4x - 5
x2 - 4x - 5
x2 - 5x + 1x - 5
= x ( x - 5) + 1 ( x - 5)
= ( x - 5) ( x + 1)
I hope it help u.
Aasthakatheriya1:
ur welcome
Answered by
1
Step-by-step explanation:
Given Equation is x^3 - 3x^2 - 9x - 5
= > x^3 - 4x^2 + x^2 - 5x - 4x - 5
= > x^3 - 4x^2 - 5x + x^2 - 4x - 5
= > x(x - 4x - 5) + 1(x^2 - 4x - 5)
= > (x + 1)(x^2 - 4x - 5)
= > (x + 1)(x^2 + x - 5x - 5)
= > (x + 1)(x(x + 1) - 5(x + 1))
= > (x + 1)(x + 1)(x - 5)
= > (x + 1)^2(x - 5).
Hope this helps!
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