The Quadratic Formula
Watch these videos and complete the interactive exercises.
Quadratics by factoring (intro) - Questions
Answers
1.
To factor , we need to find numbers and such that and .
and satisfy both conditions, so our equation can be re-written:
According to the zero-product property, we know that
which means
In conclusion,
Both and are perfect squares, since and .
Additionally, is twice the product of the roots of and , since .
So we can use the square of a sum pattern to factor:
So our equation can be re-written:
The only possible solution is when , which is
3.
To factor as , we need to find numbers and such that
and satisfy both conditions, so our equation can be re-written:
According to the zero-product property, we know that
which means
In conclusion,
Both and are perfect squares, since .
Additionally, is twice the product of the roots of .
So we can use the square of a sum pattern to factor:
So our equation can be re-written: