Algebra 1 Factoring Polynomials Quiz: 10 Questions with Explanations

A \(6\)B \(6x\)C \(12x\)D \(3x^{2}\)

The GCF of 18 and 24 is 6, and the lowest power of x is x¹.

A \((x + 1)(x + 6)\)B \((x + 2)(x + 3)\)C \((x – 2)(x – 3)\)D \((x + 5)(x + 1)\)

The numbers 2 and 3 multiply to 6 and add to 5.

A \((x + 5)(x – 3)\)B \((x – 5)(x – 3)\)C \((x + 15)(x – 1)\)D \((x – 5)(x + 3)\)

Product -15 and sum -2 give -5 and 3. Check the middle term: 3x – 5x = -2x.

A \((x + 2)(x + 5)\)B \((x + 1)(x + 10)\)C \((x + 7)(x + 10)\)D \((x – 2)(x – 5)\)

The side lengths are x + 2 and x + 5, because 5x + 2x = 7x and 5 × 2 = 10.

A \((x – 10)^{2}\)B \((x + 10)^{2}\)C \((x – 50)(x + 2)\)D \((x – 10)(x + 10)\)

A difference of squares factors as a sum times a difference.

A \((x – 8)(x + 8)\)B \((x – 8)^{2}\)C \((x – 16)(x – 4)\)D \((x + 8)^{2}\)

64 = 8² and 2(8) = 16, so it is a perfect square trinomial with a negative middle term.

A \(3(x^{2} + 2x)\)B \(x(3x + 6)\)C \(3x(x + 2)\)D \(3x(x + 6)\)

Factor out the greatest common factor 3x. The other choices leave a common factor in the parentheses.

A \(x^{2} + 12\)B \(x^{2} + 7x + 7\)C \(x^{2} + 7x + 12\)D \(2x + 14\)

(x + 4)(x + 3) = x² + 3x + 4x + 12.

A \(x = 3\) and \(x = -8\)B \(x = -3\) and \(x = 8\)C \(x = 3\) and \(x = 8\)D \(x = -3\) and \(x = -8\)

Set each factor equal to 0: x – 3 = 0 gives 3 and x + 8 = 0 gives -8.

A They are equivalent expressionsB They are never equalC They are equal only at x = 6D The first is a perfect square

Factoring does not change the value. The two expressions are equal for every x, as the difference of squares shows.