Factorization of x3−3x2−9x−5 will be ____.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

We are given a quadratic equation x3−3x2−9x−5.
Let f(x) = x3−3x2−9x−5
According to the Factor Theorem, k is a zero of f(x) if and only if (x−k) is a factor of f(x).
Substituting x = 1 in f(x), we have
⇒ f(1) = 13−3(1)2−9(1)−5 = −16 ≠ 0
So, x−1 is not a factor of f(x) .
Substituting x = −1 in f(x), we have
⇒f(−1) = (−1)3−3(−1)2−9(−1)−5
Applying the exponent, we get
⇒f(−1) = −1−3+9−5
Adding and subtracting the terms, we get
⇒f(−1) = 9−9 = 0
So, is a factor of f(x).
Now, by using synthetic division, we have So, Divisor = x2−4x−5 and Remainder = 0.
Now by using the formula Dividend = Quotient × Divisor + Remainder, we can write x3−3x2−9x−5 = (x+1)⋅(x2−4x−5)+0
⇒x3−3x2−9x−5 = (x+1)⋅(x2−4x−5)
By factoring, we get
⇒x3−3x2−9x−5 = (x+1)⋅(x2+x−5x−5)
Now taking common factors, we get
⇒x3−3x2−9x−5 = (x+1)⋅(x(x+1)−5(x+1))
Factoring out common terms, we get
⇒x3−3x2−9x−5 = (x+1)(x+1)(x−5)
⇒x3−3x2−9x−5 = (x+1)2(x−5)
Thus the factors are (x+1)2, (x−5)
x3−3x2−9x−5 = (x+1)2(x−5)

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th