1. Ch. 4.4 Factor Quadratic Equation I can find common binomial factors of quadratic expression with lead coefficient of 1
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On a suspension bridge, the roadway is hung from cables hanging between support towers. The cable of one bridge is in the shape of the parabola
y = 0.1x2  7x + 150, where y is the height in feet of the cable above the roadway at the distance x feet from a support tower.
a. What is the closest the cable comes to the roadway?
b. How far from the support tower does this occur?
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Today’s Agenda
Factor ax2 + bx + c when a is ±1
Find common Factors
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Lesson
Assignment

2. Factoring Trinomials x + bx + c Positive b and c2
Factoring Trinomials x + bx + c Positive b and c
Ex x x + 24
( )( )
Trinomials can factor into
2 binomials.
When the lead coefficient is 1,
the first terms are the square
root of the variable.
x x
1. The signs are determined by
term c. If c is positive the signs
are the same.
2. Then look at the sign of the b
term, if it is (-) they are
both (-). If it is (+) then both
signs are (+).

3. Factoring Trinomials x + bx + c Positive b and c2
Factoring Trinomials x + bx + c Positive b and c
Ex x x + 24
( )( )
3. Determine the factors of c. 24
x x
4. Because the signs are the
same we add the factors
together to find the middle
value. These are the factors
of the trinomial

4. Practice A. x2 + 5x + 6 B. -x2 - 13x - 30 C. x2 + 20x + 75
D. x2 + 7x + 5

5. Factoring Trinomials x - bx + c negative b and positive c2
Factoring Trinomials x - bx + c negative b and positive c
Ex x x + 22
( )( )
1. Look at sign for c.
(positive means same sign)
x x
2. Look at the sign for b (-).
Then they are both (-).
3. Factor c
4. What factors are the
sum of b?

6. Practice A. x2 - 5x + 4 B. x2 - 15x + 36 C. x2 - 18x + 45
D. -x2 + 7x - 12

7. Factoring Trinomials x2 - bx - c with negative c
Ex x2 - 8x – 20
( )( )
1. Look at sign for c.
(negative means opposite signs)
x x
2. Find the factors of c. 20
3. Since signs are opposite
you must subtract factors
to find the middle term. Keep
the signs with the terms.

8. Practice A. -x2 + 5x + 14 B. x2 - 5x - 36 C. x2 + 18x - 40
D. x2 + 18x - 40