Video Transcript
Identify the solutions to the
equation 𝑥 minus three multiplied by 𝑥 plus eight is equal to zero.
In this question, we have the
product of two binomial expressions, 𝑥 minus three and 𝑥 plus eight. And we’re told that this product is
equal to zero. In fact, what we have is the
factored form of a quadratic equation. We’re asked to identify the
solutions to this equation, which means we need to determine the values of 𝑥 that
satisfy the equation.
To do this, we recall that the only
way the product of two values can be zero is if at least one of the values is itself
equal to zero. So either the value of 𝑥 minus
three or the value of 𝑥 plus eight must be equal to zero. This gives two simple linear
equations that we need to solve. The first equation can be solved by
adding three to each side to give 𝑥 equals three. The second equation can be solved
by subtracting eight from each side, leading to 𝑥 equals negative eight.
These are the two solutions to the
given equation. When 𝑥 equals three, the first
expression in the product equals zero. And when 𝑥 equals negative eight,
the second expression in the product equals zero. In both cases, this makes the
overall product zero as required.
The solutions to the given
equation, which is a quadratic equation in its factored form, are 𝑥 equals three or
equals negative eight.
