Adding and Subtracting Polynomials

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Presentation transcript:

Adding and Subtracting Polynomials ALGEBRA 1 LESSON 9-1 Simplify each expression. Then name each polynomial by its degree and number of terms. 1. –4 + 3x – 2x2 2. 2b2 – 4b3 + 6 3. (2x4 + 3x – 4) + (–3x + 4 + x4) 4. (–3r + 4r2 – 3) – (4r2 + 6r – 2) –2x2 + 3x – 4; quadratic trinomial –4b3 + 2b2 + 6; cubic trinomial 3x4; fourth degree monomial –9r – 1; linear binomial 9-1

Multiplying and Factoring ALGEBRA 1 LESSON 9-2 1. Simplify –2x2(–3x2 + 2x + 8). 2. Find the GCF of 16b4 – 4b3 + 8b2. 3. Factor 3x3 + 9x2. 4. Factor 10y3 + 5y2 – 15y. 6x4 – 4x3 – 16x2 4b2 3x2(x + 3) 5y(2y + 3)(y – 1) 9-2

Multiplying Binomials ALGEBRA 1 LESSON 9-3 Simplify each product using any method. 1. (x + 3)(x – 6) 2. (2b – 4)(3b – 5) 3. (3x – 4)(3x2 + x + 2) 4. Find the area of the shaded region. x2 – 3x – 18 6b2 – 22b + 20 9x3 – 9x2 + 2x – 8 2x2 + 3x – 1 9-3

Multiplying Special Cases ALGEBRA 1 LESSON 9-4 Find each square. 1. (y + 9)2 2. (2h – 7)2 3. 412 4. 292 5. Find (p3 – 7)(p3 + 7). 6. Find 32 • 28. y2 + 18y + 81 4h2 – 28h + 49 1681 841 p6 – 49 896 9-4

Factoring Trinomials of the Type x2 + bx + c ALGEBRA 1 LESSON 9-5 Factor each expression. 1. c2 + 6c + 9 2. x2 – 11x + 18 3. g2 – 2g – 24 4. y2 + y – 110 5. m2 – 2mn + n2 (c + 3)(c + 3) (x – 2)(x – 9) (g – 6)(g + 4) (y + 11)(y – 10) (m – n)(m – n) 9-5

Factoring Trinomials of the Type ax2 + bx + c ALGEBRA 1 LESSON 9-6 Factor each expression. 1. 3x2 – 14x + 11 2. 6t2 + 13t – 63 3. 9y2 – 48y – 36 (x – 1)(3x – 11) (2t + 9)(3t – 7) 3(3y + 2)(y – 6) 9-6

Factoring Special Cases ALGEBRA 1 LESSON 9-7 Factor each expression. 1. y2 – 18y + 81 2. 9a2 – 24a + 16 3. p2 – 169 4. 36x2 – 225 5. 5m2 – 45 6. 2c2 + 20c + 50 (y – 9)2 (3a – 4)2 (p + 13)(p – 13) (6x + 15)(6x – 15) 5(m + 3)(m – 3) 2(c + 5)2 9-7

Factor each expression. 1. 10p3 – 25p2 + 4p – 10 Factoring by Grouping ALGEBRA 1 LESSON 9-8 Factor each expression. 1. 10p3 – 25p2 + 4p – 10 2. 36x4 – 48x3 + 9x2 – 12x 3. 16a3 – 24a2 + 12a – 18 (5p2 + 2)(2p – 5) 3x(4x2 + 1)(3x – 4) 2(4a2 + 3)(2a – 3) 9-8