Solution by Factorisation
Learn to solve quadratic equations by factoring them into linear factors and finding the roots.
Ch. 4 Quadratic Equations 4.3 Solution of Quadratic Equations by Factorisation Medium
Instructions
- Read the given quadratic equation in standard form ax² + bx + c = 0.
- Find two numbers whose sum equals b and product equals ac (for factorisation).
- Rewrite the middle term using these numbers and factor by grouping.
- Write the equation in factored form (px + q)(rx + s) = 0.
- Apply the zero product property to find both roots.
Problem
Generating problem...
Progress 0/5 steps completed
Step 1 — Identify coefficients a, b, c
From the equation ax² + bx + c = 0, identify the values of a, b, and
c.
a =
Enter the coefficient of x squared
b =
Enter the coefficient of x
c = Enter the constant term
Look at the equation ax² + bx + c = 0. Identify the numbers in front
of x², x, and the constant term.
Step 2 — Find two numbers for splitting middle term
Find two numbers whose sum = b and product
= ac.
Number 1:
Enter the first number whose sum and product match the
requirements
Number 2:
Enter the second number whose sum and product match the
requirements
Find two numbers that add up to b and multiply to give a×c. Try
different factor pairs of a×c.
Step 3 — Split middle term and group
Rewrite bx as mx + nx and factor by grouping. Enter the grouped
expression.
Enter the expression after splitting the middle term and grouping
Replace the middle term with the two numbers you found, then group
terms in pairs and factor out common factors.
Step 4 — Write in factored form
Express as a product of two linear factors: (px + q)(rx + s) = 0
(
Enter the coefficient p in the first factor
x +
Enter the constant q in the first factor
)(
Enter the coefficient r in the second factor
x +
Enter the constant s in the second factor
) = 0
After grouping, factor out the common binomial to get two linear
factors in the form (px + q)(rx + s).
Step 5 — Find the roots
Apply zero product property: if (px + q)(rx + s) = 0, then px + q =
0 or rx + s = 0.
x =
Enter the first solution of the equation
or x =
Enter the second solution of the equation
Set each factor equal to zero: px + q = 0 and rx + s = 0. Solve for
x in each case.
Concept Mastery
Coefficient ID
Factor Finding
Grouping
Root Solving
Visualization (GeoGebra)
The parabola and roots will appear as you progress through the steps.
Why This Matters
Factorization is fundamental for solving quadratic equations and appears in:
- Engineering calculations for projectile motion and optimization
- Economics for profit and cost analysis
- Physics for modeling parabolic trajectories
- Computer graphics for curve fitting and animation
Learning Connection
This activity builds algebraic manipulation skills essential for
advanced mathematics and real-world problem solving.
Challenge Level
Select problem difficulty level
Choose your challenge level before generating a new problem.