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 area of an equilateral triangle with side length 10 cm?

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What is the sum of all odd numbers from 1 to 99?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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What is the sum of all even numbers between 1 and 100?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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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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What is the cube root of 729?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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

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The probability of getting an even number when rolling a die is:

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