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

What is the cube root of 729?

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

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If x:y = 2:3 and z:y = 4:3, what is x:z?

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

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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

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What is the area of an equilateral triangle with side length 10 cm?

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What is the value of x if 3x + 7 = 16?

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If the sum of three consecutive integers is 72, what are the integers?

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