How to Solve Quadratic Equation by Factorization on GMAT

Short Answer

Split the middle term so its parts multiply to the product of the first and last coefficients.

Example: x² – 7x + 12 = 0, 1×12 = 12, so split –7x as –3x and –4x since –3×–4 = 12.

Then x²–3x–4x+12 = (x–3)(x–4)=0 → x=3 or 4.

Overview

Quadratic equations are elegant once you notice their pattern and easy to solve when you approach them with the right method. The GMAT tests your ability to recognize structure and break down problems efficiently. One of the most reliable ways to handle quadratic equations is the factorization method, where the middle term is split into two parts whose product equals the product of the first and last coefficients. This simple but powerful technique eliminates the need for memorizing formulas in your GMAT preparation course and helps you solve quickly under exam pressure on GMAT mocks as well as the real exam.

 

 Solving Quadratic Equations on the GMAT

The general form of a quadratic equation is:

ax² + bx + c = 0

An equation of the form ax² + bx + c = 0 can be expressed as ax² + b1x + b2x + c = 0, where b1 × b2 = a × c. This approach ensures clarity and speed, both critical in test conditions.

A Simple Example

Solve: x² + 5x + 6 = 0

1.Find two numbers that add to 5 and multiply to 6

1. • These are 2 and 3.
2. Split the middle term: x² + 2x + 3x + 6 = 0.
3. Group terms: x(x + 2) + 3(x + 2) = 0.
4. Factor the common part: (x + 2)(x + 3) = 0.

Solutions: x = −2 or x = −3.

A Slightly Difficult Example

Solve: 2x² + x – 10 = 0

1. Find two numbers that add to 1 and multiply to −20

1. • These are 5 and −4.

2. Split the middle term: 2x² + 5x − 4x − 10 = 0.
3. Group terms: (2x² + 5x) + (−4x − 10) = 0.
4. Factor each group: x(2x + 5) − 2(2x + 5) = 0.
5. Factor the common part: (2x + 5)(x − 2) = 0.

Solutions: x = −5/2 or x = 2.

A GMAT-like Word Problem

A two-digit number, when multiplied by a number 7 less than it, gives 120 as the product. What is the number?

Solve: x(x – 7) = 120

Expanding, we get:

x² – 7x – 120 = 0

Here, a × c = –120 and b is –7.

We split –7x into –15x + 8x.

So, x² – 15x + 8x – 120 = 0

Factoring:

x(x – 15) + 8(x – 15) = 0

(x – 15)(x + 8) = 0

Thus, x = 15 or x = –8.

Since the question specifies a two-digit number, x = 15 is the correct answer.

Key Learning

The factorization method is not only systematic but also efficient. By focusing on structure rather than memorization, you can solve quadratic equations quickly and accurately during the exam. For more practice, explore our free GMAT simulation, where these concepts are explained with depth and reinforced with application-focused examples.

 

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Parting Thought

Factorization teaches a quiet habit: when a problem looks crowded, look for structure, split it into meaningful parts, and let a simple truth emerge. In GMAT preparation, this becomes daily practice: break topics into small drills, group insights, and let clarity guide speed and accuracy. In the very meaningful MBA application process, gather experiences, values, and goals, then group them into one coherent message that reveals purpose without noise. In life, complex days also factor: identify what multiplies progress and what cancels it, keep the useful pieces, and solve for action. Seek patterns and organize. Simplicity reveals the answer!