Algebra I : Semester II : Polynomials

Sections:

Introduction  |   Section 1  |   Section 2  |   Section 3  |  Section 4  |  Section 5  |  Section 6

Section Three

Part 1  |  Part 2  |   Part 3  |  Part 4  |  Part 5

Algebra 1: Section 3: Polynomials Multiplying Using FOIL   Click here for a presentation on Using FOIL When multiplying two binomials, you can distribute and keep track by using a rule called FOIL. This technique makes it simpler to multiply and some students learn to do the addition of the like terms in their head when using this method. That allows them to multiply more quickly. Note that you may not use this with trinomials and must distribute as shown on the previous page.   FOIL Multiply the FIRST terms in each polynomial. Multiply the OUTER terms in the polynomials. Multiply the INNER terms in the polynomials. Multiply the LAST terms in the polynomials. Combine like terms. Example 1: Using Foil Use FOIL to multiply each of the following. (x + 8) (x + 2) Note: Some say that this looks like a happy face when you do it correctly. Put arrows for the first and last at the top and arrows for the outer and inner at the bottom.       F(first)    x(x) = x2 O(outer) x(2) = 2x I(inner)   8(x) = 8x L(last)    8(2) = 16 Add the outer and inner together: (x + 8)(x + 2) = x2 + 10x + 16 (x + 8) (x – 2) Draw the arrows for FOIL: F   x(x) = x2 O   x(-2) = -2x I    8(x) = 8x L   8(-2) = -16 (x + 8)(x – 2) = x2 + 6x – 16 (2x + 3)(5x – 7) Draw the arrows: F   2x(5x) = 10x2 O  2x(-7) = -14x I    3(5x) = 15x L   (3)(-7) = -21 (2x + 3)(5x – 7) = 10x2 + x – 21   Practice Click to get a new problem. Multiply the polynomials and then click to check your solution. Try all three levels, as you will have some of each on the homework and quizzes. Easy Binomial Level Medium Binomial Level Trinomials and Two Variables   Practice Find the area of each figure below. Rectangle: A = LW A = LW A = (5n + 8)(3n + 1) A = 15n2 + 29n + 8 Triangle: A = ½ bh or A = 0.5 bh A = ½ bh A = ½ (2n + 1)(4n – 6) Use the associative property to multiply the binomials first A = ½ (8n2 – 8n – 6) A = 4n2 – 4n - 3 Trapezoid: A = ½ (b1 + b2) h or A = 0.5(b1 + b2) h A = ½ (b1 + b2) h A = ½ (5n – 3 + n + 1)(3n – 2) A = ½ (6n – 2)(3n – 2) A = ½ (18n2 – 18n + 4) A = 9n2 – 9n + 2 Parallelogram: A = bh A = bh A = (2n + 2)(n – 3) A = 2n2 – 4n – 6 Circle: A = π r2 A = πr2 A = 3.14 (n + 1)2 A = 3.14 (n + 1)(n + 1) A = 3.14 (n2 + 2n + 1) A = 3.14n2 + 6.28n + 3.14 Find the volume of the box. Rectangular Prism: V = LWH V = LWH V = (n + 1)(n + 3)(3n + 8) V = (n2 + 4n + 3)(3n + 8) Use the distributive property, as you cannot use FOIL with trinomials. V = (n2)(3n) + (n2)(8) + (4n)(3n) + (4n)(8) + 3(3n) + 3(8) V = 3n3 + 8n2 + 12n2 + 32n + 9n + 24 V = 3n3 + 20n2 + 41n + 24 Now go on to the next part

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