Mastering Zero Product Property

If the product of two factors is zero, then at least one of the factors must be zero.

Set each factor to zero: 2x - 3 = 0 or x + 5 = 0. Solutions are $$x = \frac{3}{2}$$ or $$x = -5$$ .

The factored form is $$(x + 2)(x + 3)$$ .

Set each factor to zero: x + 4 = 0 or x - 7 = 0. Solutions are $$x = -4$$ or $$x = 7$$ .

The solution is $$x = -2$$ .

It means the graph of the quadratic does not intersect the x-axis, indicating the discriminant is less than zero.

The discriminant is the part of the quadratic formula under the square root: $$b^2 - 4ac$$ .

If the discriminant is positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

The factored form is $$(x - 3)(x + 3)$$ .

The factored form is $$(x + 2)(x + 5)$$ .