Here are the steps to solve Exercise 3B: 2) Factorize completely: (x - 3)(x + 3) 3) Factorize completely: (x - 1)(x - 5) 4) Factorize completely: 4a(c - b) 5) Factorize completely: 5a(c - b) 6) Cannot be factorized further: 6bdg 7) Factorize completely: 7a(c - b) 8) Cannot be factorized further: 8

1. Sketching Polynomials

2. Sketching Polynomials
When drawing y = P(x)

3. Sketching Polynomials
When drawing y = P(x)
• y intercept is the constant

4. e.g. y   x  1 x  1  x  2 
3 2
 y




x
       






5. Sketching Polynomials
When drawing y = P(x)
• y intercept is the constant
• x intercepts are the roots, solve P(x)=0

6. e.g. y   x  1 x  1  x  2 
3 2
 y




x
       






7. Sketching Polynomials
When drawing y = P(x)
• y intercept is the constant
• x intercepts are the roots, solve P(x)=0
• as x   , P(x) acts like the leading term

8. e.g. y   x  1 x  1  x  2 
3 2
 y




x
       






9. e.g. y   x  1 x  1  x  2 
3 2
 y
graph starts here 



x
       






10. e.g. y   x  1 x  1  x  2 
3 2
 y
graph starts here  graph finishes here



x
       






11. Sketching Polynomials
When drawing y = P(x)
• y intercept is the constant
• x intercepts are the roots, solve P(x)=0
• as x   , P(x) acts like the leading term
• even powered roots look like or

12. e.g. y   x  1 x  1  x  2 
3 2
 y
graph starts here  graph finishes here



x
       






13. e.g. y   x  1 x  1  x  2 
3 2
 y
graph starts here  graph finishes here



x
       






14. Sketching Polynomials
When drawing y = P(x)
• y intercept is the constant
• x intercepts are the roots, solve P(x)=0
• as x   , P(x) acts like the leading term
• even powered roots look like or
• odd powered roots look like or

15. e.g. y   x  1 x  1  x  2 
3 2
 y
graph starts here  graph finishes here



x
       






16. e.g. y   x  1 x  1  x  2 
3 2
 y
graph starts here  graph finishes here



x
       






17. e.g. y   x  1 x  1  x  2 
3 2
 y




x
       






18. Sketching Polynomials
When drawing y = P(x)
• y intercept is the constant
• x intercepts are the roots, solve P(x)=0
• as x   , P(x) acts like the leading term
• even powered roots look like or
• odd powered roots look like or
• if the curve can be written as  x  a  , then it is a basic curve.
n

19. (ii )  x  1  x  3  0
2

20. (ii )  x  1  x  3  0
2
y
–3 1 x

21. (ii )  x  1  x  3  0
2
y
–3 1 x

22. Q: for what values of x is the
(ii )  x  1  x  3  0
2
curve below the x axis?
y
–3 1 x

23. Q: for what values of x is the
(ii )  x  1  x  3  0
2
curve below the x axis?
y
–3 1 x

24. Q: for what values of x is the
(ii )  x  1  x  3  0
2
curve below the x axis?
x  3 or x  1 y
–3 1 x

25. Exercise 3B; 2, 3, 4ac, 5ac, 6bdg, 7ac, 8