ࡱ> _ AbjbjzXzX ?2@\2@\5   \\\    L '&LLLLLj%l%l%l%l%l%l%$')%Q\0%  LL%[#[#[#v 8L\Lj%[#j%[#[##D#L9;K#V%%0'&#m*S m*#m*\#[#%%!#:'&m*> : Name Class Date  Solving Polynomial Equations 5-3 Reteaching What are the real or imaginary solutions of the polynomial equation 2x3 + 16 = 0? 2x3 + 16 = 0 2(x3 + 8) = 0 2(x + 2)(x2 " 2x + 4) = 0 x + 2 = 0 or x2 " 2x + 4 = 0 x = "2 or  EMBED Equation.DSMT4  x = "2 or  EMBED Equation.DSMT4  x = "2 or  EMBED Equation.DSMT4  The solutions are "2 and  EMBED Equation.DSMT4 . Exercises Find the real or imaginary solutions of each polynomial equation. 1. x3 " 8 = 0 2. 4x3 + 4 = 0 3. x4 " x2 " 72 = 0 4. x4 + 9x2 = "20 5. x4 " 27x = 0 6. 8x3 = "1 7. 7x4 = "28x2 " 21 8. x3 = 64 9. 8x3 + 27 = 0 10. x4 " 7x2 = "12 11. 2x4 + 16x2 = 40 12. 2x4 " 16x = 0 13. 9x4 " 25 = 0 14. 2x4 " x2 = 3 15. x4 + 5x2 = "4 16. x4 " 7x2 " 8 = 0 17. 2x3 + 16 = 0 18. x4 " 5x2 " 24 = 0 Prentice Hall Algebra 2 " Teaching Resources Copyright by Pearson Education, Inc., or its affiliates. All Rights Reserved. 29 Name Class Date  Solving Polynomial Equations 5-3 Reteaching (continued)  You have a brother and a sister. Your brother is 3 years older than you. Your sister is 2 years older than your brother. The product of all three ages is 3744. How old are you and your siblings? Step 1 Define the variables. Let your age = x. Your brothers age = x + 3. Your sisters age = x + 3 + 2 = x + 5. Step 2 Write an equation. Because the product of all three ages equals 3744, x(x + 3)(x + 5) = 3744. Step 3 Rewrite the equation in (x2 + 3x)(x + 5) = 3744 P(x) = 0 form. x3 + 3x2 + 5x2 + 15x = 3744 x3 + 8x2   (,.024lntvxz˼weTFjh+,UmHnHu h+,h|DCJ:OJQJ^JaJ:#h+,h|DCJ:OJQJ\^JaJ:h+,h|DCJaJ h+,h|DCJOJQJ^JaJh@7h|DCJOJQJaJ%jh@7h lCJOJQJUaJ h@7h|Dh@7h|DCJOJQJaJhL ghDGOJQJ^J!hL ghDGB*OJQJ^Jph,jhL ghDGOJQJU^JmHnHu *,.04nvxn]~d-DM ]~^gd+,J&`#$+D-D/&M gdT &`+D~/& -DM dm-DM ^gdDG-DM ^gdf -DM gdDG z " $ & . 0 : < > B J L R T X Z \ ^ ` h j n p v z | ź~vvg\h6CJ]aJh7yh|DCJOJ^JaJhgCJaJ"jhz^GCJUaJmHnHuh_wCJaJh^MCJaJh7yh|DCJH*aJh7yh|D6CJ]aJh7yh|DCJaJh@7h|DCJOJQJaJ h@7h|D h+,h|DCJ OJQJ^JaJ &h+,h|D5CJ OJQJ\^JaJ #8 R r 2 ~ 8 {ddQj-DM ^jgd C-DM ^gdO ! ^`gd) d-DM ^gdz^G d-DM ^ 0-DM ^d-DM ^ ]qdd-DM ]^qgd+, ŹulaYaQjhYUh<0OJ^JhYhYOJ^Jh<06OJ^Jh<0h<06OJ^Jh7yhz^GCJH*aJhz^GCJaJh7yhz^GCJaJhz^G6CJ]aJh7yhz^G6CJ]aJh|DCJOJ^JaJh7yh|DCJOJ^JaJh6CJ]aJh7yh|D6CJ]aJh7yh|DCJaJhCJaJ & ( * , . 0 2 6 8 : < F H v x z | ~ Ђug\\QjU!N h+,UVh7yhOCJaJh7yhO6CJ]aJjh+,h+,EHUjU!N h+,UVjhOUhOCJaJh7yh|DCJaJhO6CJ]aJh7yh|D6CJ]aJh+,h|DCJaJhvhOjhYUjhIhIEHU%j*N hICJOJUV^JaJhY . 0 2 4 8 J L p r Ĺ㘍tiYK=hFyh|D6CJ]aJhFyh|D5CJ\aJhFyh|D5OJQJ\^Jhd[5CJ\aJhW5CJ\aJh@7h|D5CJ\aJh]%Gh|DCJaJ&h]%Gh|D5CJOJQJ\^JaJj hh]%GEHUjU!N h]%GUVhjhUh7yh|DCJaJhCJaJ h7yh|DjhOUjP hOh+,EHU8 L V  ^ nYYY xdM-DM ^x dM-DM ^  dM-DM ^gd9  dM&-DM ^gd9  d&-DM ^gd9 >@dc-DM ]@^`jdc-DM ^j            " * , 2 6 8 : < > @ D F H J L N P V Z \ ^ ` b d j n p v z | ~ ͿͿͿͿ豘ͿhFyh'6CJ]aJhFyh'CJaJhFyh|D6CJ]aJhFyh|D5CJ\aJhFyh|D5OJQJ\^JhFyhTCJaJhFyh|DCJaJhFyh|DCJH*aJ<          " $ * , . 0 2 : @ B D F H J L 꾲꾲̾꾲̾꾲꾲꾲꾲hFyh|DCJH*aJhFyh|D6CJ]aJhFyh|D5CJ\aJhFyh|D5OJQJ\^JhFyh|DCJaJhFyh'CJaJFL R V X ^ d f h j l n p x z ɻɻɻɻɻhFyh'CJaJhFyh|DCJH*aJhFyh|D5CJ\aJhFyh|D5OJQJ\^JhFyh'6CJ]aJhFyh|D6CJ]aJhFyh|DCJaJ=   "&(*,.68>npr68<̾꾲ꢔo`oL&hUK h|D5CJOJQJ\^JaJh@7h|DCJOJQJaJ h@7h|DCJOJQJ^JaJ h@7h|Dh@7h|DOJQJ^Jh@7h|D5OJQJ\h@7h|D5OJQJ\^JhFyh|DCJH*aJhFyh|D6CJ]aJhFyh|D5CJ\aJhFyh|D5OJQJ\^JhFyh|DCJaJhFyh=CJaJ >8>@L\jlnpund -DM dm-DM ^gdDG-DM ^gdDG -DM gdDG:-DM ^$<-DM a$gdZk$-DM a$gdmF$-DM a$gdz^G xdM-DM ^x <@BJLNPZ\^`hlnprtq`NChSh|DCJ:aJ:#hSh|DCJ:OJQJ\^JaJ: h!Mh|DCJOJQJ^JaJh@7h|DCJOJQJaJ%j h@7h lCJOJQJUaJ h@7h|Dh@7h|DCJOJQJaJ,jhL gh.OJQJU^JmHnHuhL ghDGOJQJ^J!hL ghDGB*OJQJ^Jph,jhL ghDGOJQJU^JmHnHuhUK h|DCJaJptd0-DM ]^ &`#$+D/`'dd[ -DM ~d-DM ]~^gd!MJc&`#$+D--D/&M gd. &`+D~/& Ľ~jVI8I hkBqh|DCJOJQJ^JaJhkBqh|DCJQJaJ&hkBqh{#5CJOJQJ\^JaJ&hkBqh|D5CJOJQJ\^JaJh@7h|DCJaJjh!MUmHnHuh!MCJaJh@7h|DCJOJQJaJh@7h|DCJOJQJaJ h@7h|D hYh|Dh!Mh|DOJQJ^J&hYh|D5CJ OJQJ\^JaJ &h!Mh|D5CJ OJQJ\^JaJ  #$'()+,067IJoq~˲˲˲ː|k^˲˲˲hkBqh)CJQJaJ hkBqh|DCJOJQJ^JaJ&hkBqh)5CJOJQJ\^JaJ&hkBqh|D5CJOJQJ\^JaJhkBqhH6CJ]aJhkBqh|D6CJ]aJhkBqhHCJaJhkBqh|DCJaJhkBqh|D6CJQJ]aJhkBqh|DCJQJaJhkBqhHCJQJaJ$ 0$:&:mYHd-DM ^d-DM ^gd!M d-DM ^gd!M d-DM ^gd'pb .-DM ^`gd)vd-DM ^vgdfvd-DM ^v d-DM ^gdfµyiy[[PhkBqh?CJaJhkBqh|D6CJ]aJhkBqh?6CJQJ]aJhkBqh?CJQJaJhkBqh|DCJH*QJaJhkBqh|D6CJQJ]aJ hkBqh|DCJOJQJ^JaJhkBqh|DCJQJaJ&hkBqh'pb5CJOJQJ\^JaJ&hkBqh|D5CJOJQJ\^JaJhkBqhHCJaJhkBqh|DCJaJ::: :::::&:(:4:6::ױ̣{nhkBqh|DCJQJaJ&hkBqh'pb5CJOJQJ\^JaJ&hkBqh|D5CJOJQJ\^JaJjh^CUmHnHuUhkBqh?6CJ]aJhkBqh?CJaJhkBqh|DCJaJhkBqh|DCJH*aJhkBqh|D6CJ]aJhkBqh|DCJOJ^JaJ' + 15x " 3744 = 0 Step 4 Using a graphing calculator, graph the equation. Use the Zero feature to solve for x. Step 5 Once you have the value of x (your age), you can solve for the other ages. Since x = 13, your brother s age is x + 3 = 16. Your sister s age is x + 5 = 18. Exercises 19. A slice of wood 3 in. thick is cut of a cube of wood. The remaining solid has a volume of 320 in.2. What are the dimensions of the original block of wood? 20. The water level in a rectangular fish tank is 4 in. from the top. The depth of the water is the same as the width of the tank, which is half of its length. The volume of the water in the tank is 4394 in.3. What is the volume of the fish tank? Prentice Hall Algebra 2 " Teaching Resources Copyright by Pearson Education, Inc., or its affiliates. All Rights Reserved. 30 Factor out the GCF. In this case, it is 2. Factor the remaining cubic expression. Use the Zero-Product Property. Solve each equation for x. Use the Quadratic Formula when necessary. 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