Algebra(2(Honors( Summer(Packet( ( ( Work(on(this(packet(during(the(summer.( ( ( There(will(be(an(in=class(quiz(on(the(material(the(
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1 Algebra((Honors( Summer(Packet( ( ( Work(on(this(packet(during(the(summer.( ( ( There(will(be(an(in=class(quiz(on(the(material(the( first(week(of(school.( ( ( Please(visit(the(CHS(website(to(view(answers(to( these(problems(along(with(additional(practice( problems,(if(needed.( ( ( If(ou(have(an(questions,(please(e=mail(me:( donnellc@cranfordschools.org( ( ( Have(a(great(summer!( Ms.(Donnell(
2 Factoring Tpe I: Factoring out the GCF (Greatest Common Factor) Eample: 7p + p 7p(p + ). w + w , z + a 9 z 5 + w 9 0 z
3 Tpe II Factoring + b + c where the leading coefficient of is one. Rule : Check to see if there is a GCF a) If there is a GCF factor it out! This must be done FIRST. Rule : Eamine the trinomial. Find two numbers that multipl to the last number (c) and add to the middle number (b). Eample : ( + )( + ) ()() is which = the last number, while + = 0 which is the middle number. Eample : + 5 The terms have a in common. This is the GCF! Factor it out! ( + 8) Ask what multiplies to -8, adds to? ( + 7)( ) 7 and - satisf this condition Factor:
4
5 Tpe : Factoring a difference of squares If two square terms are being subtracted, and the are not like terms, ou can factor them as a product of the sum and difference of their square roots. Rule: a b = (a + b)(a b) Eample: ( + )( ) Eample: 9 ( + 7)( 7) (GCF!) 8. 7 (GCF!) ( ) ( + )( ) (GCF!) (GCF!)
6 Tpe : Factoring a + b + c The leading coefficient of is a value not equal to Step : Find two numbers that multipl to a Step : Find two numbers that multipl to c Step : Check the outside product and inside product using FOIL to see if the values add up to the b value. If it does not, switch the order of the c values, or tr new c values, or tr new a values. Eample: Break up the into and ( + )( + ) Ask what multiplies to? (, ) (, ) (, ) Guess and check to see which set of values work The outside product is 8 The inside product is 8 + = 9 which is the b value middle term. Eample: Break up into and ( + )( + ) Break up the c value of into or Check the outside product. Check the inside Product. Does this add up to 5? Yes, + = 5. Your turn:. +. a a. 9a + 8a
7 (GCF!) (GCF!) a - a (GCF first!)
8 Eponents n m nm Rule : a a a Same base variable being multiplied, add the eponents Eample: ( )( ). ( )( ) = ( ) = Rule : (a n ) m n m = a One base with a power raised to another power, multipl the powers! Eample: (a ) 5 = a 0 Eample: ( z 5 ) = 9 8 z 0. (a b ) 5 =. ( ) =. (ab c ) =. (-a bc ) =
9 a ab Rule : b When ou have the same variable being divided, ou subtract the eponents Eample: a b c. a b c 5 z 5. 5 z. 5 z 9 n a a Rule : = b b n When a fraction is being raised to a power, ou distribute that power to the numerator and denominator of the fraction. Eample: 5 5 = 5 n. =. a b =. ab = a b Note: Make sure ou distributed the eponent to the whole numbers!
10 Rule 5: a 0 = Anthing raised to the zero power =. 0 0 =. 0 =. ( ) 0 =. ( ) 0 = Rule : Negative Eponents a -n = n a and n n a a If a term has a negative eponent in the numerator, ou move it to the denominator and make the eponent positive. If a term has a negative eponent in the denominator, ou move it to the numerator and make the eponent positive. Eample: - = Eample: a b a a b b b a b a. -. () -. a -. 9 abc z z
11 Simplif with onl positive eponents in our final answer:. 7 5 z z z z. ab b a n m n m c b a c b a
12 Radicals Rule: Find the largest perfect square that goes into the number in the radical. 8 =
13 Multipling Radicals Multipl and Simplif Your Final Answer ) * = ) * = ) * = ) * = 5) * = ) * = 7) * = 8) * = 9) * = 0) * = ) * = ) * =
14 Dividing with Radicals Radicals CANNOT be left in the denominator (bottom) of a fraction! Sometimes we will see situations where there is a radical in the denominator and we will have to get rid of it. To get rid of it, multipl the numerator (top) and denominator (bottom) b the radical that we are tring to get rid of ) ) ) ) 5) ) 7) 8)
15 Multipl and simplif where necessar:
16 Divide and simplif:
17 Slope Find the slope of the line passing through the following points:. (, ) (7, ). (0, 5) (, 9) m = 7. (-, ) (, ). (-5, -8) (-, -) 5. (, 0) (, 0). (, 0) (0, ) 7. What is the slope of a horizontal line? 8. What is the slope of a vertical line? 9. Find the slope of l and l L = L = Are these lines parallel?
18 0. Are the lines parallel, perpendicular, or neither? Slope of P = Slope of P =.
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Unit, Lesson Factoring Recall that a factor is one of two or more numbers or expressions that when multiplied produce a given product You can factor certain expressions by writing them as the product of
MHF4U - Practice Mastery #8
MHF4U - Practice Master #8 Multiple Choice Identif the choice that best completes the statement or answers the question.. If, then a. b. c. d. 2.. The graph illustrates the motion of a person walking toward