Question

Solve w^2+13w+42=0 by factoring.

Answer 1

Answer: {-7, -6}

Explanation: When an equation has a squared term in it,

it's called a polynomial equation.

The rule for solving a polynomial equation

is to first set it equal to 0, then factor.

Since this equation is already set equal to 0, we can factor the left side.

The left side is a trinomial that can be

factored as the product of two binomials.

The first term in each binomial will be a factor of the w².

Since w² factors a w · w, we use a w as our first term.

For the last terms, we use factors of 42 that add

to 13 and these factors are +7 and +6.

So we have (w + 7)(w + 6) = 0.

So either w + 7 = 0 or w + 6 = 0.

Solving for w in each equation, we find that our solution set is {-7, -6}.