5.2factoringquads
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Factoring Quadratics 5.2 p. 256
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Transcript of 5.2factoringquads
Factoring QuadraticsFactoring Quadratics
5.2p. 256
5.2p. 256
Factoring QuadraticsFactoring Quadratics
Factoring breaks apart something into smaller pieces.
Factoring breaks apart something into smaller pieces.
Factoring Quadratics a=1Factoring Quadratics a=1
1. List all the pairs of factors of the constant term.
1. List all the pairs of factors of the constant term.
x2 - 12x - 28x2 - 12x - 28
Factoring Quadratics a=1Factoring Quadratics a=1
1. List all the pairs of factors of the constant term.
1. List all the pairs of factors of the constant term.
x2 - 12x - 28x2 - 12x - 28
-1, 28
1, -28
-2, 14
2, -14
-4, 7
4, -7
Factoring Quadratics a=1Factoring Quadratics a=1
1. List all the pairs of factors of the constant term.
2. Pick the pair whose sum is the coefficient of the x term.
1. List all the pairs of factors of the constant term.
2. Pick the pair whose sum is the coefficient of the x term.
x2 - 12x - 28x2 - 12x - 28
-1, 28
1, -28
-2, 14
2, -14
-4, 7
4, -7
Factoring Quadratics a=1Factoring Quadratics a=1
1. List all the pairs of factors of the constant term.
2. Pick the pair whose sum is the coefficient of the x term.
1. List all the pairs of factors of the constant term.
2. Pick the pair whose sum is the coefficient of the x term.
x2 - 12x - 28x2 - 12x - 28
-1, 28 27
1, -28 -27
-2, 14 12
2, -14 -12
-4, 7 3
4, -7 -3
Factoring Quadratics a=1Factoring Quadratics a=1
1. List all the pairs of factors of the constant term.
2. Pick the pair whose sum is the coefficient of the x term.
1. List all the pairs of factors of the constant term.
2. Pick the pair whose sum is the coefficient of the x term.
3. Write as factors (x + 2)(x - 14).
3. Write as factors (x + 2)(x - 14).
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
1. List all the factors of AC.
3x2 - 17x + 103x2 - 17x + 10
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
3(10) = 30
1. List all the factors of AC.
3(10) = 30
3x2 - 17x + 103x2 - 17x + 10
1, 30
-1, -30
2, 15
-2, -15
3, 10
-3, -10
5, 6
-5, -6
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.
3x2 - 17x + 103x2 - 17x + 10
1, 30
-1, -30
2, 15
-2, -15
3, 10
-3, -10
5, 6
-5, -6
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.
3x2 - 17x + 103x2 - 17x + 10
1, 30 31
-1, -30 -31
2, 15 17
-2, -15 -17
3, 10 13
-3, -10 -13
5, 6 11
-5, -6 -11
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
3x2 - 17x + 103x2 - 17x + 10
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
3x2 - 17x + 103x2 - 17x + 10
Ax2
1st number times
x
2nd number times
x
C
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
3x2 - 17x + 103x2 - 17x + 10
3x2
1st number times
x
2nd number times
x
C
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
3x2 - 17x + 103x2 - 17x + 10
3x2
1st number times
x
2nd number times
x
10
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
3x2 - 17x + 103x2 - 17x + 10
3x2 -2x
2nd number times
x
10
Factoring Quadratics a1Factoring Quadratics a1
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
1. List all the factors of AC.
3(10) = 302. Find the pair that
adds to get B.3. Organize into
box
3x2 - 17x + 103x2 - 17x + 10
3x2 -2x
-15x 10
Factoring Quadratics a1Factoring Quadratics a1
4. Factor each row and column.
4. Factor each row and column.
3x2 - 17x + 103x2 - 17x + 10
3x2 -2x
-15x 10
Factoring Quadratics a1Factoring Quadratics a1
4. Factor each row and column.
4. Factor each row and column.
3x2 - 17x + 103x2 - 17x + 10
3x2 -2x
-15x 10
3x
Factoring Quadratics a1Factoring Quadratics a1
4. Factor each row and column.
4. Factor each row and column.
3x2 - 17x + 103x2 - 17x + 10
3x2 -2x
-15x 10
3x 2
Factoring Quadratics a1Factoring Quadratics a1
4. Factor each row and column.
4. Factor each row and column.
3x2 - 17x + 103x2 - 17x + 10
3x2 -2x
-15x 10
3x 2
x
Factoring Quadratics a1Factoring Quadratics a1
4. Factor each row and column.
4. Factor each row and column.
3x2 - 17x + 103x2 - 17x + 10
3x2 -2x
-15x 10
3x -2
x
-5
Factoring Quadratics a1Factoring Quadratics a1
4. Factor each row and column.
4. Factor each row and column.
3x2 - 17x + 103x2 - 17x + 10
3x2 -2x
-15x 10
3x -2
x
-5Sign of box closest goes with the factor.
Factoring Quadratics a1Factoring Quadratics a1
4. Factor each row and column.
5. These new expressions are the factors of the quadratic.
4. Factor each row and column.
5. These new expressions are the factors of the quadratic.
3x2 - 17x + 103x2 - 17x + 10
3x2 -2x
-15x 10
3x -2
x
-5
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