Factorize the equation- x3 - 3x2 - 9x - 5 - Maths Q-A

Step 1: Split the middle termsLet f(x)=x^3 3x^2 9x 5f(x)=x^3+x^2 4x^2 4x 5x 50ex0exf(x)=x^2(x+1) 4x(x+1) 5(x+1)0ex0exf(x)=(x+1)(x^2 4x 5)Step 2: Factorize the q ...

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Mathematics

Solving a Quadratic Equation by Factorization Method

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Question

Factorize the equation: $x^{3} - 3 x^{2} - 9 x - 5$ .

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Solution

Step 1: Split the middle terms
Let $f (x) = x^{3} - 3 x^{2} - 9 x - 5$
$f (x) = x^{3} + x^{2} - 4 x^{2} - 4 x - 5 x - 5 f (x) = x^{2} (x + 1) - 4 x (x + 1) - 5 (x + 1) f (x) = (x + 1) (x^{2} - 4 x - 5)$
Step 2: Factorize the quadratic equation
$f (x) = (x + 1) (x^{2} - 5 x + x - 5) f (x) = (x + 1) [x (x - 5) + 1 (x - 5)] f (x) = (x + 1) (x - 5) (x + 1)$
Hence, the factorized form of the polynomial $x^{3} - 3 x^{2} - 9 x - 5$ is $(x + 1) (x + 1)$ $(x - 5)$ .

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Factorize the equation: x3-3x2-9x-5.

Step 1: Split the middle termsLet f(x)=x3-3x2-9x-5f(x)=x3+x2-4x2-4x-5x-5f(x)=x2(x+1)-4x(x+1)-5(x+1)f(x)=(x+1)(x2-4x-5)Step 2: Factorize the quadratic equationf(x)=(x+1)(x2-5x+x-5)f(x)=(x+1)x(x-5)+1(x-5)f(x)=(x+1)(x-5)(x+1)Hence, the factorized form of the polynomial x3-3x2-9x-5 is (x+1)(x+1)x-5.

Factorize the equation: $x^{3} - 3 x^{2} - 9 x - 5$ .