a=1
Identify the b and c values in the trinomial:
x2+5x+6
b=5, c=6
Check if First & Last Terms are Perfect Squares
9x2 - 30x + 25
Yes
Make sure your leading coefficient (a value) is 1. If not, divide the entire equation by the leading coefficient.
Which equations have an A value of 1, or can be MADE 1?
1.)2x2+7x+3
2.)x2-10x+25
3.)2x2+8x-10
4.)6x2+11x-10
2.) a=1
3.) a=1 after dividing everything by 2
Factor x2+6x+9
(x+3)2
Factor the Perfect Square Trinomial
-x2-12x-36
-(x+6)2
To factor, find two numbers that add to 5 and multiply to 6. What are the two factors?
a. 1 and 6
b. 2 and 3
b. 2 and 3
Find the Square Roots of First & Last Term
9x2 - 30x + 25
3x and 5
Second step, isolate the variable term
Isolate x2+6x-7=0
x2+6x=7
you add 7 to both sides
Is 36x2+110x+81 a perfect square trinomial?
No
A school is planning on building a field on its campus. The area of it is 25x2+80x+64. Find the side length of the area of the field.
(5x+8)
After finding the magic numbers, write the trinomial as two binomials next to the variable x. Which is the correct factored form?
a. x2+2x+3x+6
b. (x+2)+(x-3)
c. (x+2)(x+3)
c. (x+2)(x+3)
Verify the Middle Term
2 x (3x) x (5) = 30x
Find the value to complete the square, through the equation (b/2)2
Ex.) 8x is the b term, so 8/2=4, 42=16
Find the value to complete the square with a b value of 6.
The value to complete the square for a b-value of 6 is 9!
Factor x2 - 4x + 8
PRIME
Factor: 1/2x2 + 1/2x - 10
1/2(x + 5)(x - 4)
Factor again to check. What method could you use to check it?
FOIL
Is the binomial in 9x2 - 30x + 25,
+ or -
(-) Negative, inside the parentheses
The next step is part a.) adding the squared value to both sides of the equation x2+6x=7
Part b.) Rewriting the equation as a squared binomial by factoring. Reminder on how to factor, find 2 values that add up to the b value, but also multiply into the c value. Then, separate the equations into two parentheses and simplify.
equation:
Part a.) x2+6x+9=16
part b.) (x+3)2=16
Factor x2 + 6x = 16
by completing the square
(x+3)2=25
Solve for x:
2x2+8x-10=0
Hint: How can we make "a," or the leading coefficient, equal to 1?
x=-5 x=1
Is (x+2)(x+3) correct?
Yes
Box/Circle your Answer
Factored form is (3x-5)2
Laslty, solve the equations using square roots.
A.) Solve (x+3)2=16 using square roots
x-3=4
X+3=4
Answer: x=1, x=7
A city is planning on building a park. The area of the park is 150 square feet. The city wants the length to be 5 feet greater than the width. Write the equation for the area in factored form. Extra credit: Find the length and width! (2 solutions)
w2 + 5w - 150 = 0
Length = 15, width = 10
4x2+5x-6=0
x=-2, x=3/4