Factorizing Algebraic Expressions Worksheet Page 12
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Example 3 : Solve (x + 3)
= x + 5.
2
+ 6x + 9 = x + 5
x
2
+ 5x + 4 = 0
x
(x + 4)(x + 1) = 0
This is true when either x = 4 or x = 1. In other words, just one of the factors
needs to be zero for the original equation that we started with to be true.
It is a good idea to know what to expect from the equation by first examining the discriminant
2
∆ = b
4ac. This is the expression under the square-root sign in the quadratic formula.
2
Given the equation y = ax
+ bx + c, and using our knowledge of square roots, we find the
following:
a > 0
a < 0
6
6
O
∆ > 0 There will be 2 distinct so-
-
-
lutions, so the curve crosses
W
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the x-axis twice.
∆ = 0 There will only be one solu-
6
6
6
6
tion, so the curve will only
-
-
touch the x-axis.
This is
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?
called a double root.
6
6
∆ < 0 The curve does not touch
6
6
the x-axis. We will deal with
-
-
this case in detail later.
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Exercises:
1. Factorize and then simplify the following algebraic expressions:
2
+3x
x
(a)
x+3
2
6x
8
(b)
2x
2
x
+3x+2
(c)
3x+6
2
x
7x 18
(d)
2
x
6x 27
2
x
16
(e)
2x+8
2
3x
9x
(f)
18x
Page 12
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