Factoring Polynomials: math test solutions, Grade 9 – download the PDF

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Test solutions with the detailed point scale. Add up your points and spot what to review.

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

Sommaire

GCF of 20, 15, 35 is 5 (1 pt); smallest exponents give \(xy\), so the GCF is \(5xy\) (1 pt).

\(20x^3y - 15x^2y^2 + 35xy = 5xy(4x^2 - 3xy + 7)\) (1 pt).

a) \((x + 4)(x + 9)\) (1 pt).

b) \((x - 10)(x + 6)\) (1 pt).

c) \(ac = 24\): 12 and 2. \(3x(x + 4) + 2(x + 4) = (x + 4)(3x + 2)\) (1 pt).

d) \(ac = 24\): \(-8\) and \(-3\). \(2x(x - 4) - 3(x - 4) = (x - 4)(2x - 3)\) (1 pt).

a) \(2x^2(x - 3) + 5(x - 3) = (x - 3)(2x^2 + 5)\) (1 pt).

b) \((9x - 4)(9x + 4)\) (1 pt).

c) \(2 \cdot 6x \cdot 5 = 60x\), so \((6x + 5)^2\) (1 pt).

a) \(x = \dfrac{1}{2}\) or \(x = -8\) (1 pt).

b) \((x - 8)(x + 5) = 0\), so \(x = 8\) or \(x = -5\) (1 pt).

c) \(5x(x - 9) = 0\), so \(x = 0\) or \(x = 9\) (1 pt).

d) \((3x - 8)(3x + 8) = 0\), so \(x = \pm\dfrac{8}{3}\) (1 pt).

Let \(w\) be the width: \(w(w + 4) = 96\) (1 pt), so \(w^2 + 4w - 96 = 0\) and \((w + 12)(w - 8) = 0\) (1 pt).

The width must be positive: \(w = 8\) ft, length 12 ft. Check: \(8 \cdot 12 = 96\) (1 pt).

\((x - 3)(x + 3) = x^2 - 9\), which is not the given trinomial (1 pt).

The trinomial is a perfect square: \(x^2 - 6x + 9 = (x - 3)^2\) (1 pt).

So \(x = 3\) is the only solution; check: \(9 - 18 + 9 = 0\) (1 pt).

Test yourself: quick challenge for Grade 9