Test: Quadratic trinomials and factorisation

This test focuses on transforming and factorising quadratic trinomials. Tasks cover expansion, completing the square, vertex form and selecting an appropriate algebraic method for a given expression.

Question qty: 10
Duration in minutes: 20
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Sample questions

Find k so that x² + kx + c equals (x + a)².
Factorise x² + sx + p.
What does a positive discriminant of a quadratic trinomial mean?
When factoring using roots x₁ and x₂, why is the form (x − x₁)(x − x₂) used?
Expand (x − (a))(x − (b)).
For y = (x − (m))² + (n), give the vertex.
Write x² + a2x + a_sq as a perfect square.
Factorise x² − sx + p.

Quadratic trinomials and factorisation

A quadratic trinomial ax² + bx + c can be factored using the roots of its corresponding equation: ax² + bx + c = a(x − x₁)(x − x₂). A repeated root gives a(x − x₀)².

Vieta formulas

The roots satisfy x₁ + x₂ = −b/a and x₁x₂ = c/a. These relationships help select factors and check roots. Take out a common factor first; if the discriminant is negative, the trinomial has no factorisation into real linear factors.

Test: Quadratic trinomials and factorisation

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Question Nr. 10 out of 10

Sample questions

Quadratic trinomials and factorisation

Vieta formulas

Test: Quadratic trinomials and factorisation

Question Nr. 1 out of 10

Question Nr. 2 out of 10

Question Nr. 3 out of 10

Question Nr. 4 out of 10

Question Nr. 5 out of 10

Question Nr. 6 out of 10

Question Nr. 7 out of 10

Question Nr. 8 out of 10

Question Nr. 9 out of 10

Question Nr. 10 out of 10

Sample questions

Quadratic trinomials and factorisation

Vieta formulas

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