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Algebra I Part 2
Unit 3 Day 3 - Factoring, Solving Quadratic Equations with a = 1 (8-3)
Objective:
Factor trinomials of the form x2 + bx + c. Solve equations of the form x2 + bx + c = 0.
Factor x2 + bx + c:
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

You learned how to multiply two binomials by using the FOIL method.
Each of the binomials was a ___________ of the product.
The pattern for multiplying two binomials can be used to factor certain types of trinomials.
(x + 3)(x + 4) =
Use the FOIL method.
Simplify
Notice that the coefficient of the middle term, _____, is the sum of ___ and ___, and the last term,
_____, is the product of ___ and ___.
Observe the following pattern in this multiplication.
(x + 3)(x + 4) = x2 + (3 + 4)x + (3 • 4)
(x + m)(x + p) = x2 + (m + p)x + (mp)
Let 3 = m and 4 = p.
= x2 +
bx
+ c
b = m + p and c = mp
Notice that the coefficient of the middle term is the ________ of m and p, and the last term is the
____________ of m and p. This pattern can be used to factor trinomials of the form x 2 + bx + c.
When c is positive, its factors have the _________ signs. Both of the factors are positive or negative
based upon the sign of b. If b is positive, the factors are positive. If b is negative, the factors are
negative.
x2 + bx + c = (x + m)(x + p)
x2 – bx + c = (x – m)(x – p)
Example 1: Factor x2 + 11x + 24.
b = _____
Factors of c
c = _____
Sums
Check Your Progress: Choose the best answer for the following.
Factor
A.
B.
C.
D.
x2 + 3x + 2.
(x + 3)(x + 1)
(x + 2)(x + 1)
(x – 2)(x – 1)
(x + 1)(x + 1)
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Algebra I Part 2
Unit 3 Day 3 - Factoring, Solving Quadratic Equations with a = 1 (8-3)
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Example 2: Factor x2 – 12x + 27.
b = _____
Factors of c
c = _____
Sums
Check Your Progress: Choose the best answer for the following.
Factor
A.
B.
C.
D.
x2 – 10x + 16.
(x + 4)(x + 4)
(x + 2)(x + 8)
(x – 2)(x – 8)
(x – 4)(x – 4)
When c is negative, its factors have _____________ signs. To determine which factor is positive and
which is negative, look at the sign of b. The factor with the greater absolute value has the same sign as b.
x2 + bx – c = (x + m)(x – p) with m > p
x2 – bx – c = (x + m)(x – p) with p > m
Example 3: Factor each polynomial.
a.
x2 + 3x – 18
b. x2 – x – 20
b = _____ and c = _____
Factors of c
Sums
b = _____ and c = _____
Factors of c
Sums
Check Your Progress: Choose the best answer for the following.
A. Factor x2 + 4x – 5.
A. (x + 5)(x – 1)
B. (x – 5)(x + 1)
C. (x – 5)(x – 1)
D. (x + 5)(x + 1)

B. Factor x2 – 5x – 24.
A. (x + 8)(x – 3)
B. (x – 8)(x – 3)
C. (x + 8)(x + 3)
D. (x – 8)(x + 3)
Let’s go back and look at the graphs of the previous examples and compare the x-intercepts (or
__________) to the factors. What do you notice?
Algebra I Part 2
Unit 3 Day 3 - Factoring, Solving Quadratic Equations with a = 1 (8-3)
Solve Equations by Factoring:
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
A quadratic equation can be written in the standard form ax 2 + bx + c = 0, where a ≠ 0.
Some equations of the form x2 + bx + c = 0 can be solved by factoring and then using the Zero Product
Property.
Example 4: Solve x2 + 2x = 15. Check your solutions.
Check Your Progress: Choose the best answer for the following.
Solve x2 – 20 = x. Check your solution.
A. {-5, 4}
B. {5, 4}
C. {5, -4}
D. {-5, -4}
Example 5: Marion wants to build a new art studio that has three times the area of her old studio by
increasing the length and width of the old studio by the same amount. What should be the
dimensions of the new studio?
Check Your Progress: Choose the best answer for the following.
Adina has a 4 x 6 photograph. She wants to enlarge the photograph by increasing the length and width by
the same amount. What dimensions of the enlarged photograph will produce an area twice the area of the
original photograph?
A. 6 x -8
B. 6 x 8
C. 8 x 12
D. 12 x 18
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