This is a free lesson from our course in Algebra II
In this lesson you'll learn concepts of quadratic functions and the approach of identifying a perfect square trinomial. A quadratic function f is a function of the form f(x) = ax^{2}
+ bx + c; where a, b and c
are real numbers and a not equal to zero. E.g. f(x) = x^{2}
+ 3x + 2. A perfect square trinomial is about looking for compatible factors that would fit in the last term when multiplied and in the second term if added/subtracted (considering the signs of each polynomial). For example, 64x^{2} + 32x + 4 is a perfect square trinomial, which is the square of binomial (8x + 2)^{2}.Simply saying in an example of a quadratic equation in which first and last term are both perfect squares and middle term is two times the square root of the first and last term, it simplifies the quadratic to a binomial product or just one binomial raised to the second power.
(More text below video...)
(Continued from above)
So to identify perfect square trinomial:
check whether the first term is a perfect square.
if it is, note its perfect square root.
check whether the last term is a perfect square.
if it is, note its square root.
remember that aē  2ab + bē = (a  b)ē
check to see if the middle term is equal to twice the product of the perfect square root of the first term and the perfect square root of the last term.
if yes, apply the values from steps 2 and 4 to the formula.
In order to convert an expression of the form x^{2} + yx; into a perfect square trinomial, we need to rewrite the second term as 2{y/2x} and also add the square of y/2. It may appear to be hard to understand, but will be much easier once you learn it with the help of some examples instructor explains using audio, video presentation in own hand writing.
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