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

If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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What is the value of log₃(27)?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If 2x = 16, what is the value of x?

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

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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