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

If x² - 9x + 18 = 0, what are the roots of the equation?

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What is the remainder when 5^100 is divided by 3?

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

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

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What is the sum of all even numbers between 1 and 50?

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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 base of a triangle is 10 cm and its height is 6 cm. What is its area?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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If 3x = 81, what is the value of x?

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