Mon, 5/2 SWBAT…add and subtract polynomials Agenda 1. WU (10 min) 2. Adding & subtracting polynomials (30 min) Warm-Up: 1. What do you need to combine.

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Simplify each polynomial Adding and Subtracting Polynomials.

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Mon, 5/2 SWBAT…add and subtract polynomials Agenda 1. WU (10 min) 2. Adding & subtracting polynomials (30 min) Warm-Up: 1. What do you need to combine like terms? 2. x + x = 3. x 2 + x 2 = 7. (x)(x) = 4. 3x 3 + 5x 3 = 8. (2x)(-x) = 5. -4x – 3x = 9. (10b)(-6b 2 ) = 6. x – x = 10. (-x)(x 3 ) = HW#6: Adding & Subtracting Polynomials

Reminder! Like terms have:  The same variable AND  The same exponent x + x = 2x or x 2 – x 2 = 0x 2 = 0 (when adding or subtracting do not touch the exponents) (x)(x) = x 2 or (x 2 )(x 2 ) = x 4 (when multiplying add the exponents)

Polynomials A polynomial is a monomial or the sum or difference of monomials Some polynomials have special names:  A monomial has one term  A binomial is the sum or difference of two monomials  A trinomial is the sum or difference of three monomials

ExpressionIs it a polynomial? Why? Monomial, binomial, or trinomial? 4y – 5xz x 3 + 4x + x + 3 Fill out the chart above!

ExpressionIs it a polynomial? Why? Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial x 3 + 4x + x + 3

ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3

ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3

ExpressionIs it a polynomial?Monomial, binomial, or trinomial? 4y – 5xzYes; 4y – 5xz is the difference of two monomials. Binomial -6.5Yes; -6.5 is a constantMonomial 6x 3 + 4x + x + 3 Yes; 6x 3 + 4x + x + 3 = 6x 3 + 5x + 3, the sum of three monomials Trinomial

Adding and subtracting polynomials Find each sum or difference and arrange in standard form: 1. (3x 2 + 5) + (5x 2 + 7) 2. (2x 2 – 4x + 3) + (x 2 – 3x + 1)

Adding and subtracting polynomials Find each sum or difference and arrange in standard form: 1. (3x 2 + 5) + (5x 2 + 7) = 8x (2x 2 – 4x + 3) + (x 2 – 3x + 1) = 3x 2 – 7x + 4

Adding and subtracting polynomials Find each sum or difference and arrange in standard form: 3.(6c 2 + 5c – 3) – (4c 2 + 4c) 4.(5n 2 – 7) – (2n 2 + n – 3)

Adding and subtracting polynomials Find each sum or difference and arrange in standard form: 3. (6c 2 + 5c – 3) – (4c 2 + 4c + 0) = 2c 2 + c – 3 4.(5n 2 + 0n – 7) – (2n 2 + n – 3) = 3n 2 – n – 4

Adding and subtracting polynomials Find each sum or difference and arrange in standard form: 1. (3x 2 + 5) + (5x 2 + 7) = 8x (2x 2 – 4x + 3) + (x 2 – 3x + 1) = 3x 2 – 7x (6c 2 + 5c – 3) – (4c 2 + 4c) = 2c 2 + c – 3 4. (5n 2 – 7) – (2n 2 + n – 3) = 3n 2 – n – 4

Work on HW#6: Adding & subtracting polynomials

Tues, 5/3 SWBAT…multiply a monomial by a polynomial and solve eqns with polynomials Agenda 1. WU (10 min) 2. White boards activity (30 min) Warm-Up: 1.) Find the difference & arrange in standard form: (4y 4 + 2y 3 – 5y + 7) – (7y 3 + 4y ) 2.) Find the product & arrange in standard form: 9b²(2b³ + 3b² + b) 3.) Solve for c: 3(2c – 3) – 1 = -4(2c + 1) + 8 HW#7: Multiplying a Monomial by a Polynomial

1/7

2/7 Simplify: -x(x 3 – x 2 ) -x 4 + x 3

3/7 Simplify: 3ab(5a 2 – a – 2) + 2a(b + 1) 15a 3 b – 3a 2 b – 4ab + 2a

4/7 Solve for x: 2(4x – 7) = 5(-2x – 9) – 5 x = -2

5/7 Simplify: t²(t² + 3) t 4 + 3t²

6/7 9c(c – 11) + 10(5c – 3) = 3c(c + 5) + c(6c – 3) – 30 c = 0

7/7 2k(-3k + 4) + 6(k ) = k(4k + 8) – 2k(2k + 5) k = -6

HW#6 and HW#7 will be due and collected tomorrow Quiz tomorrow on this material!!! 2 Qon adding & subtracting 3 Q on solving equations

Wed, 5/4 SWBAT…multiply a monomial by a polynomial and solve eqns with polynomials Agenda 1. WU (15 min) 2. Work on HW 6/7 (10 min) 3. Quiz (15 min) Warm-Up: 1.) Find the difference & arrange in standard form: (y 3 – 10y – 3) – (7y 3 + 9y 2 – 10) 2.) Find the product & arrange in standard form: -7y²(2y³ + 3xy² – 9xyz) 3.) Solve for x: 5x(x² – 6) + 10x = 5(x 3 – 3) + 35

HW#6 and HW#7 will be collected in 10 minutes Quiz in 10 minutes: 2 Qon adding & subtracting 3 Q on solving equations

Extra Credit: Complete on the back of the quiz If f(x) = 4x + 1 and g(x) = x² – 2, what is the value of f(g(x))?