Sample questions
A few samples from this topic — try one, then show the answer.
Connect Factors to Solutions
How does x 2 + 3 x − 40 = 0 x^{2} \; + \; 3x\, \; - \; 40 \; = \; 0 x 2 + 3 x − 40 = 0 factor?
( x + 5 ) ( x − 8 ) = 0 (x + 5)(x - 8) \; = \; 0 ( x + 5 ) ( x − 8 ) = 0 ( x + 40 ) ( x − 1 ) = 0 (x + 40)(x - 1) \; = \; 0 ( x + 40 ) ( x − 1 ) = 0 ( x − 5 ) ( x − 8 ) = 0 (x - 5)(x - 8) \; = \; 0 ( x − 5 ) ( x − 8 ) = 0 ( x + 8 ) ( x − 5 ) = 0 (x + 8)(x - 5) \; = \; 0 ( x + 8 ) ( x − 5 ) = 0
Show answer Answer: ( x + 8 ) ( x − 5 ) = 0 (x + 8)(x - 5) \; = \; 0 ( x + 8 ) ( x − 5 ) = 0
Connect Factors to Solutions
The solutions of x 2 + 7 x − 18 = 0 x^{2} \; + \; 7x\, \; - \; 18 \; = \; 0 x 2 + 7 x − 18 = 0 are:
x = − 2 x \; = \; -2 x = − 2 , x = 9 x \; = \; 9 x = 9 x = − 18 x \; = \; -18 x = − 18 , x = 1 x \; = \; 1 x = 1 x = − 9 x \; = \; -9 x = − 9 , x = 2 x \; = \; 2 x = 2 x = 2 x \; = \; 2 x = 2 , x = 9 x \; = \; 9 x = 9
Show answer Answer: x = − 9 x \; = \; -9 x = − 9 , x = 2 x \; = \; 2 x = 2
Connect Factors to Solutions
What are the roots of x 2 − x = 0 x^{2} \; - \; x\, \; = \; 0 x 2 − x = 0 ? enter both roots separated by a comma, e.g., − 3 , 0 or − 1 2 , 3 \quad {\scriptsize\color{gray}{\textrm{enter both roots separated by a comma, e.g.,}\;-3,\;0\;\textrm{or}\;-\frac{1}{2},\;3}} enter both roots separated by a comma, e.g., − 3 , 0 or − 2 1 , 3 Show answer
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A worked example
How does x 2 + 3 x − 40 = 0 x^{2} \; + \; 3x\, \; - \; 40 \; = \; 0 x 2 + 3 x − 40 = 0 factor?
We need to factor x 2 + 3 x − 40 x^{2} \; + \; 3x\, \; - \; 40 x 2 + 3 x − 40 . Find two numbers that multiply to -40 and add to 3 . ( 8 ) × ( − 5 ) = − 40 ✓ ( 8 ) + ( − 5 ) = 3 ✓ \\ (8) \times (-5) \; = \; -40 \;\checkmark \\ (8) \; + \; (-5) \; = \; 3 \;\checkmark ( 8 ) × ( − 5 ) = − 40 ✓ ( 8 ) + ( − 5 ) = 3 ✓ The correct factoring is ( x + 8 ) ( x − 5 ) = 0 ✓ (x + 8)(x - 5) \; = \; 0 \;\checkmark ( x + 8 ) ( x − 5 ) = 0 ✓ Why not the other options? ( x + 5 ) ( x − 8 ) = 0 → \\ (x + 5)(x - 8) \; = \; 0 \to ( x + 5 ) ( x − 8 ) = 0 → expanding this does not give x 2 + 3 x − 40 x^{2} \; + \; 3x\, \; - \; 40 x 2 + 3 x − 40 ✘ ( x + 40 ) ( x − 1 ) = 0 → \\ (x + 40)(x - 1) \; = \; 0 \to ( x + 40 ) ( x − 1 ) = 0 → expanding this does not give x 2 + 3 x − 40 x^{2} \; + \; 3x\, \; - \; 40 x 2 + 3 x − 40 ✘ ( x − 5 ) ( x − 8 ) = 0 → \\ (x - 5)(x - 8) \; = \; 0 \to ( x − 5 ) ( x − 8 ) = 0 → expanding this does not give x 2 + 3 x − 40 x^{2} \; + \; 3x\, \; - \; 40 x 2 + 3 x − 40 ✘
Skills covered
Recognize Quadratic Equations
Write Quadratic Equations in Standard Form
Connect Factors to Solutions
Factor and Solve Simple Quadratics
Solve with Special Factoring Patterns
Solve Non-Monic Quadratics by Factoring
Find Both Roots and Catch Missing Solutions
Connect Factors, Roots & Coefficients
Decide When Factoring Works
Model and Solve Quadratic Problems
Quadratic Equations in other grades
For parents & teachers
Your child learns to recognise quadratic equations and write them in standard form ax² + bx + c = 0, then solves them by factoring — simple trinomials, difference of squares and perfect squares, and trinomials with a leading coefficient greater than 1 — using the Zero Product Property to find both roots.
Standard form and the identification of a, b and c; the Zero Product Property applied to already-factored equations; solving by factoring across monic, special-pattern and non-monic cases; lost and repeated roots; recovering a missing coefficient from the roots; and quadratic word problems.