Question:
Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x), or not:
$f(x)=x^{3}-6 x^{2}+11 x-6, g(x)=x^{2}-3 x+2$
Solution:
Here, $f(x)=x^{3}-6 x^{2}+11 x-6$
$g(x)=x^{2}-3 x+2$
First we need to find the factors of $x^{2}-3 x+2$
$\Rightarrow x^{2}-2 x-x+2$
⟹ x(x - 2) -1(x - 2)
⟹ (x - 1) and (x - 2) are the factors
To prove that g(x) is the factor of f(x),
The results of f(1) and f(2) should be zero
Let, x – 1 = 0
x = 1
substitute the value of x in f(x)
$f(1)=1^{3}-6(1)^{2}+11(1)-6$
= 1 – 6 + 11 – 6
= 12 – 12
= 0
Let, x – 2 = 0
x = 2
substitute the value of x in f(x)
$f(2)=2^{3}-6(2)^{2}+11(2)-6$
= 8 – (6 * 4) + 22 – 6
= 8 – 24 + 22 - 6
= 30 – 30
= 0
Since, the results are 0 g(x) is the factor of f(x)
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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