Topic Details (Notes format)

How to Solve Quadratic Equations by Factoring

Subject: Mathematics

Book: Maths Mastery

Factoring is a more intuitive method for solving ax² + bx + c = 0 when the polynomial can be expressed as a product of two binomials. For instance, x² + 5x + 6 factors to (x + 2)(x + 3) = 0, giving solutions x = –2 or x = –3. The approach requires identifying two numbers that multiply to ac and add to b. While factoring is not always possible with neat integers, it’s efficient when applicable. This method is widely used in geometry, business break-even analyses, and logic puzzles. Practicing with different coefficients develops a keen sense for pattern recognition and polynomials.

Practice Questions

The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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If a number is divisible by 9, it is also divisible by which of the following?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If 2a + b = 10 and a - b = 4, what is the value of a?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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What is the sum of the interior angles of a hexagon?

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The probability of rolling a sum of 7 with two dice is:

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