Algebra (Period 1)

Using Equations That Factor 6-9


WORD PROBLEMS WITH FACTORING

DRAW A PICTURE IF NECESSARY TO HELP YOU UNDERSTAND THE PROBLEM!
You are supposed to know basic Geometry Formulas!!!


1) Translate the words into an equation

2) If necessary, move all terms to the left side leaving only zero on the right side of the equation

3) Factor the left side

4) Set each factor equal to zero and solve.


5) If the problem calls for real life things like area or time, eliminate the NEGATIVE answer because certain real life things can never be negative!

The product of one more than a number and one less than the number is 8

Write a let statement
x = the number
so
(x +1)(x -1) = 8

you must multiple the two terms
x² -1 = 8
now using the zero products property have all terms on the left
x² - 9 = 0
WOW-- its the difference of two squares...
(x+3)(x-3) = 0
set each to zero
x+ 3 = 0 and x- 3 = 0
or
x = -3 and x = 3
{-3, 3}

The square of a number minus twice the number is 48. Find the number...
Let n = the number

n² - 2n = 48
n² - 2n -48 = 0 Now factor
(n -8)(n+ 6) = 0
n = 8 and n = -6
{-6, 8}


The product of two consecutive integers is 156, Find the integers...
Let x represent the 1st integer then
x + 1 is the 2nd integer

x(x +1) = 156
x² + x = 156

x² + x- 156 = 0
(x + 13)(x -12) = 0
x = -13 and x = 12

But wait you have found only one of the integers..
if x = -13 x + 1 = -13 + 1 = -12

and if x = 12 then x + 1 = 13 so you have two pairs of answers
{-13,-12,} and {12, 13}

The length of a rectangle is 5 cm greater than the width. The area is 84 cm²
Find the length and the width...
Okay, we know A = lw

Re reading the information we decide to
let w = the width
and then w +5 = the length
(w + 5)w = 84
or w (w + 5) = 84
w² + 5w = 84
w² + 5w - 84 = 0
(w + 12)(w -7) =84
so
w = -12 or w = 7
BUT a width can't be negative so we don't need to use -12
if the width is 7,
then w + 5 or 7 + 5= 12 must be the length
SOLUTION: width is 7 cm and the length is 12 cm