Factoring Polynomials: math test, Grade 9

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Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

Sommaire

Factor out the GCF: \(20x^3y - 15x^2y^2 + 35xy\).

Factor: a) \(x^2 + 13x + 36\) b) \(x^2 - 4x - 60\) c) \(3x^2 + 14x + 8\) d) \(2x^2 - 11x + 12\).

Factor: a) \(2x^3 - 6x^2 + 5x - 15\) b) \(81x^2 - 16\) c) \(36x^2 + 60x + 25\).

Solve: a) \((2x - 1)(x + 8) = 0\) b) \(x^2 - 3x - 40 = 0\) c) \(5x^2 - 45x = 0\) d) \(9x^2 - 64 = 0\).

A patio is 4 feet longer than it is wide, and its area is 96 square feet. Find its dimensions.

A student solves \(x^2 - 6x + 9 = 0\) and writes \((x - 3)(x + 3) = 0\), so \(x = 3\) or \(x = -3\). Find the mistake, factor correctly and solve.

Test yourself: quick challenge for Grade 9