Factorizing Algebraic Expressions Worksheet Page 9
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
185. Factorize further:
4x(x + 5) + (x + 5) = (x + 5)(4x + 1)
Exercises:
1. Factorize the following quadratics using the ‘ACE’ method:
2
2
(a) 2x
+ 11x + 12
(f) 2x
5x
3
2
2
(b) 3x
+ 16x + 5
(g) 3x
10x
8
2
2
(c) 6x
+ 17x + 12
(h) 3x
11x
20
2
2
(d) 2x
+ 9x + 10
(i) 5x
+ 17x + 6
2
2
(e) 12x
+ 11x + 2
(j) 10x
+ 19x + 6
Section 5
The quadratic formula
When there is no obvious whole-number solution to the quadratic factorization, the quadratic
formula must be used. It can be shown by the method of completing the square that the
2
solutions to ax
+ bx + c = 0 are given by
√
2
4ac
b ±
b
x =
2a
If we let the roots be k and l, say, then
√
2
b +
4ac
b
k =
2a
√
2
4ac
b
b
l =
2a
Then
2
+ bx + c = a(x
ax
k)(x
l)
2
When factorizing using this method be sure to multiply throughout by the coefficient of x
.
2
Example 1 : Factorize x
+ 5x + 3. We try the ‘ACE’ method. The obvious factors
2
of 3x
are 3x and 1x, which won’t add to 5x. We abandon this method, and go to
Page 9
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education