1. Perfect Squares and Factoring

2. Perfect square trinomials are the squares of binomials… WATCH…
Square of a Difference
These are
binomials
Square of a Sum
Remember the short cut?
Square the first term.
Square the last term.
Middle term is twice the product
of the first and last terms

3. Middle term is twice the product of the first and last terms
Square of a Difference
Remember the
short cut?
Square the first term.
Square the last term.
Middle term is twice the product
of the first and last terms

4. When factoring a perfect square trinomial, we can reverse this process by revising our 3 statements.
OLD STATEMENTS:
Square the first term…
Square the last term…
Middle term is twice the product of the first and last terms.
NEW QUESTIONS:
Is the first term a perfect square?
Is the last term a perfect square?
Is the middle term twice the product of the square roots of the first and last term?

5. Like this.... Is the middle term twice the product of the
first and last
factors?
Is the first term a
perfect square?
Is the last term a
perfect square?
Yes
Yes
IF you answer YES
to each question,
it is a perfect
square trinomial.
You can write your
answer as either the
sum or difference
of two squares.
Yes

6. First term a perfect square? Last term a perfect square?
YES... of 3x
YES... of 2
Middle term twice the product?
2(3x)(2) = 12x ... YES
You answered YES to everything, now write your answer.

7. First term a perfect square? Last term a perfect square?
YES... of 4x
YES... of 3
Middle term twice the product?
2(4x)(3) = 24x... YES
You answered YES to everything, now write your answer.

8. What about these? First term a perfect square? Can you do this one
without the questions?
YES... of 3x
Last term a perfect square?
Now would be a
good time to
remind you that
perfect squares
are ALWAYS
Positive….
WHY?
YES... of 4
Middle term twice the product?
2(3x)(4) = 24x ... YES
You answered YES to everything, now write your answer.

9. Prime Remember your questions: Is the first term a perfect square?
Is the last term a perfect square?
Is the middle term twice the product of the first and last factors?
If you answer NO to ANY of these questions, you must try another way of factoring.
YES... of 4x
YES... of 1
2(4x)(1) = 8x .... NO
Press if
You get NO
Prime
YES... of 5x NO
Press if
You get NO
Press if
DONE

10. Scratch paper..... Press After #6
What factors of 16x2 will ADD to give +32x
1x(16x) NO
2x(8x) NO
4x(4x) NO
None of these will ADD to give me 32x
What factors of 150x2 will SUBTRACT to give -5x
1x(150x) NO
2x(75x) NO
3x(50x) NO
5x(30x) NO
6x(25x) NO
10x(15x) YES
+10x – 15x
= -5x
Press
After #7

11. So what have we learned?
If the answer to all 3 questions is YES, then we can use the short cut to factor.
If even ONE answer is NO, then we must use an alternate method to try to factor.
If it can’t be factored, the answer is PRIME.