10.5.3b.notes.pdf

5.2 Extra Practice:
1. GCF: a) 14, b) 81, c) 24, d) 15, e) 24
2. LCM: a) 156, b) 36, c) 30, d) 60, e) 880
3. GCF of terms: a) 5x2, b) 8xy, c) x, d) 9y2, e) 2πx
4. Factored polynomials: a) 5(x + 7), b) not possible, c) 2(7x – 4y), d) 6x(x + 4), e) 3x(1 + 3y + 2z)
5. Missing factors: a) 3a, b) x – y, c) 5 – 2b, d) 3x, e) 3x2 – xy + 6y2
6. Factored polynomials: a) 8(x2 + 4y3), b) 5a(2 + a – 5a2), c) 2b(12ac – 3a + 4c), d) 3xy(–4xy + y2 – 5x2), e) 9πx2 – 6xy + 12πxy2
7. Factored expressions: a) (y + 1)(x + 4), b) (a + b)(3x – y), c) (y + 3)(4y + 1), d) not possible, e) (x – 5)(3y + 4)
8. Factored by grouping: a) (x + 3y)(5 + m), b) (y + 4)(x + 5), c) (b – c)(3a + 2b), d) (5y – 3)(2x – 1), e) (2x + z)(x + 3y)
9. Area of shaded regions: a) 3x(5x + 2y), b) 2x(2πx – 3y)
5.3 Warm-Up:
1. Expanded expressions: a) (3x – 5)(x + 4) = 3x2 + 7x – 20, b) (x + 4y)(2x – 5y) = 2x2 – 17xy + 20y2
2. GCF factored: a) 3x(x + 3), b) y(8x – 6y)
3. Factored by grouping: a) (x + 2)(x – 5), b) (2x + 5y)(x + 2y)
4. Pairs of integers: a) 12: (1, 12), (2, 6), (3, 4), b) 7: (1, 7), c) –7: (1, –7), (–1, 7)
5. a) Pairs of integers that multiply to –6: (1, –6), (2, –3), (–1, 6), (–2, 3), b) Pair that adds to 1: (2, –3) + 2 – 3 = –1 (not 1), c) Pair that adds to –5: (–2, 3) + –2 + 3 = 1 (not –5), (–1, 6) + –1 + 6 = 5 (not –5), (1, –6) + 1 – 6 = –5
5.3a Factoring Trinomials of the form ax2 + bx + c:
Trinomial represented by algebra tiles: x2 + 5x + 6
Factors: (x + 3) and (x + 2)
Trinomial as product: (x + 3)(x + 2) = x2 + 5x + 6
Binomial factors for given trinomials:
x2 + 5x + 6 = (x + 3)(x + 2), x2 + 3x + 2 = (x + 2)(x + 1)
Pattern: factors of c term add to b term
Factor x2 + 11x + 24: factors of 24 that add to 11: 8 and 3, (x + 8)(x + 3)
5.3b Factoring Trinomials of the form ax2 + bx + c:
Trinomial represented by algebra tiles: 2x2 + 7x + 6
Factors: (2x + 3) and (x + 2)
Trinomial as product: (2x + 3)(x + 2) = 2x2 + 7x + 6
Binomial factors for given trinomial: 2x2 + 7x + 6 = (2x + 3)(x + 2)