Warm up: Match: Constant Linear Quadratic Cubic x3 – 2x 7

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Presentation transcript:

Warm up: Match: Constant Linear Quadratic Cubic x3 – 2x 7

-4x2 + 2x – 1 lead co: -4 quadratic trinomial HW answers: -4x2 + 2x – 1 lead co: -4 quadratic trinomial 5y2 – 3y + 8 5 quadratic trinomial 14w4 + 9w2 14 binomial -4t4 + 3t3 – 9t2 – 15 -4 polynomial 4y 4 linear monomial -8a2 + 39a + 74 -8 quadratic trinomial -a4 + 3a3 + 3a2 + a 5y2 + 7 3x2 – 6x 7x4 – x3 – 7x2 + 5x – 9 8y3 + 2y2 + 9y – 11 -4a2 + 4a – 1 -y3 + 8 2a3 – 7a2 + a + 7

Objective The student will be able to: multiply two polynomials using the FOIL method, Box method and the distributive property.

There are three techniques you can use for multiplying polynomials. Distributive Property FOIL Box Method

1) Multiply. (2x + 3)(5x + 8) Using the distributive property, multiply 2x(5x + 8) + 3(5x + 8). 10x2 + 16x + 15x + 24 Combine like terms. 10x2 + 31x + 24 A shortcut of the distributive property is called the FOIL method.

FOIL Method The FOIL method is ONLY used when you multiply 2 binomials. It is an acronym and tells you which terms to multiply.

FOIL F O I L First terms Outer terms Inner terms Last terms

FOIL Method (x – 3)(x + 1)

FOIL Method FIRST (x – 3)(x + 1) x2

FOIL Method OUTER (x – 3)(x + 1) x2 + x

FOIL Method INNER (x – 3)(x + 1) x2 + x - 3x

FOIL Method LAST (x – 3)(x + 1) - 3 x2 + x - 3x

FOIL Method Combine like terms (x – 3)(x + 1) - 3 x2 + x - 3x x2 – 2x - 3

FOIL Method (2x +2)(3x – 4)

FOIL Method FIRST (2x +2)(3x – 4) 6x2

FOIL Method OUTER (2x +2)(3x – 4) 6x2 - 8x

FOIL Method INNER (2x +2)(3x – 4) - 8x 6x2 + 6x

FOIL Method LAST (2x +2)(3x – 4) 6x2 - 8x + 6x - 8

FOIL Method Combine like terms (2x +2)(3x – 4) 6x2 - 8x + 6x - 8 6x2 - 2x - 8

Sneedlegrit: Multiply (y + 4)(y – 3) Which is correct? E. y2 + y – 12 F. y2 – y + 12 G. y2 + 7y + 12 H. y2 – 7y + 12

Sneedlegrit: Multiply (2a – 3b)(2a + 4b) Which is correct? 4a2 + 14ab – 12b2 4a2 – 14ab – 12b2 4a2 + 8ab – 6ba – 12b2 4a2 + 2ab – 12b2 4a2 – 2ab – 12b2

Group and combine like terms. 5) Multiply (2x - 5)(x2 - 5x + 4) You cannot use FOIL because they are not BOTH binomials. You must use the distributive property. 2x(x2 - 5x + 4) - 5(x2 - 5x + 4) 2x3 - 10x2 + 8x - 5x2 + 25x - 20 Group and combine like terms. 2x3 - 10x2 - 5x2 + 8x + 25x - 20 2x3 - 15x2 + 33x - 20

Multiply (2p + 1)(p2 – 3p + 4)

This will be modeled in the next problem along with FOIL. The third method is the Box Method. This method works for every problem! Multiply (3x – 5)(5x + 2) Draw a box. Write a polynomial on the top and side of a box. It does not matter which goes where. This will be modeled in the next problem along with FOIL. 3x -5 5x +2

4) Multiply (7p - 2)(3p - 4) 7p -2 3p -4 21p2 -28p -6p 21p2 -6p +8 First terms: Outer terms: Inner terms: Last terms: Combine like terms. 21p2 – 34p + 8 7p -2 3p -4 -28p -6p 21p2 -6p +8 -28p +8

5) Multiply (2x - 5)(x2 - 5x + 4) You cannot use FOIL because they are not BOTH binomials. You must use the distributive property or box method. x2 -5x +4 2x -5 2x3 -10x2 +8x Almost done! Go to the next slide! -5x2 +25x -20

5) Multiply (2x - 5)(x2 - 5x + 4) Combine like terms! +4 2x -5 2x3 -10x2 +8x -5x2 +25x -20 2x3 – 15x2 + 33x - 20

Ex) (x – 3)3

Sneedlegrit: Multiply (4p + 1)(p2 – 2p + 3) Summary: Distributive Property FOIL Box Method Sneedlegrit: Multiply (4p + 1)(p2 – 2p + 3) Homework: pg.30(53 – 59,61,62,70,89)