Topic Details (Notes format)

How to Factor Quadratic Expressions with Leading Coefficients > 1

Subject: Mathematics

Book: Maths Mastery

When a quadratic ax²+bx+c has a>1, factoring is trickier. For example, factor 6x²+13x+6. Look for two numbers that multiply to a×c=36 and add to b=13. These are 9 and 4. Rewrite 13x as 9x+4x, group, and factor in pairs: 6x²+9x+4x+6 = 3x(2x+3)+2(2x+3) → (3x+2)(2x+3). This approach helps solve harder quadratics or rational expressions. Proficiency ensures you won’t rely solely on the quadratic formula, letting you elegantly reduce or solve polynomial equations, essential for advanced algebra or geometry tasks involving factorization.

Practice Questions

The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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What is the sum of the first 50 positive integers?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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If x^2 + 4x + 4 = 0, what is the value of x?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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