Question

Factor 6" alt=" {x}^{2} + x - 6" align="absmiddle" class="latex-formula">

Answer 1

This is in standard form Ax² + Bx + C. To factor this, you must find two numbers whose sum is B and whose product is C. In this case, B is positive (1) and C is negative (-6), so we know the two numbers will be a positive and a negative (a positive times a negative is always negative). Let's go through the possible pairs.

-6 × 1 = -6; -6 + 1 = -5
6 × -1 = -6; 6 + (-1) = -5
2 × -3 = -6; 2 + (-3) = -1
-2 × 3 = -6; -2 + 3 = 1

The numbers which add to equal 1 and which multiply to equal -6 are -2, 3.

The factored polynomial is (x - 2)(x + 3).