Video Transcript
Factor 𝑥 squared minus eight
𝑥 minus 20.
To factor this quadratic
expression, we wish to write it as the product of two binomials. We will do this by first
rewriting the middle term as the sum of two terms with coefficients whose sum is
the coefficient of 𝑥 and whose product is the constant term. We first consider the factor
pairs of 20. As the product of the two
numbers must be negative 20, the two numbers must have different signs. If we choose the second factor
pair of two and 10 and choose the two to be positive and the 10 to be negative,
then the sum of these two numbers is two plus negative 10, which is equal to
negative eight as required.
We then rewrite the trinomial
with the middle term expressed as the sum of two terms with coefficients of two
and negative 10, that is, 𝑥 squared plus two 𝑥 minus 10 𝑥 minus 20. Separating this four-term
expression into two binomials and factoring gives us 𝑥 multiplied by 𝑥 plus
two minus 10 multiplied by 𝑥 plus two. Finally, we factor the entire
expression by the shared binomial factor of 𝑥 plus two to give 𝑥 plus two
multiplied by 𝑥 minus 10. This is the fully factored form
of 𝑥 squared minus eight 𝑥 minus 20.
