Final answer:
The quadratic equation x²−3x−28=0 can be factored into (x + 4)(x − 7) = 0 by finding two numbers that multiply to −28 and add to −3, which are 4 and −7. Factoring is used to solve quadratic equations and apply the zero product property to find the solutions for x.
Step-by-step explanation:
To write the equation x²−3x−28=0 in factored form, we are looking for two numbers that multiply to −28 and add up to −3. The numbers that fit this criteria are 4 and −7, since (4)(−7) = −28 and 4 + (−7) = −3. Therefore, the factored form of the equation is (x + 4)(x − 7) = 0.
Factoring is a fundamental skill in algebra that is often used to solve quadratic equations, which are equations of the form ax²+bx+c = 0. When a quadratic equation is factored, it is rewritten as a product of two binomials set equal to zero. From there, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. This allows us to solve for the unknown variable x.
To summarize the factoring process for the given equation: we determined the two numbers that fit the criteria for factoring, then wrote the binomials that contained the roots of the equation based on those numbers, resulting in the factored equation (x + 4)(x − 7) = 0.