9th Math factorisation 2 (SMT)

9th Math factorisation 2

(Splitting the Middle Term)

Multiple Choice

Find to numbers to get 'b' and 'ac':

2x² - 11x + 12

(explanation is on next slide)

• -8 and -3

• -8 and 3

• -12 and 1

• 11 and 1

• 4 and 3

​How to look for 2 numbers?

​Always multiply a and c.

​2 * 12 = 24

​

​Then find 2 numbers that their product is 24. (start using 2, then 3 ...)

​2x12, then 3x8, then 4x6, nothing with 5, 6 already used, ....

​

​Use the negative sign accordingly. 24 is positive, both have to be either positive or negative.

​ No combination using 2 and 12.

​

​ +3 and +8 = +11 (does not match b = -11)

​ -3 and -8 = -11 (it matches!)

​

​no need to combine 4 and 6.

Multiple Select

Find the next step using the two numbers:

2x² - 11x + 12

(explanation is on next slide)

• 2x² - 3x - 8x + 12

• 2x² - 8x - 3x + 12

• 2x² + 8x - 3x + 12

​After splitting the middle term...

​

​Then we apply the common factor every two terms...

Multiple Choice

Apply the common factor every 2 terms:

2x² - 3x - 8x + 12

(explanation is on next slide)

• x (2x - 3) -4 (2x - 3)

• x (2x - 3) 4 (2x - 3)

• x (2x - 3) + 4 (2x - 3)

Multiple Choice

Apply the common factor:

x (2x - 3) -4 (2x - 3)

(explanation is on next slide)

• (2x - 3) (x - 4)

• (2x - 3) (x + 4)

• (2x + 3) (x - 4)

​Summary

​To factorise expressions where a ≠ 1. (SMT)

​

​a. Look for 2 numbers to get a*c.

​b. If 'b' is positive, means that both are either positive or negative.

​c. Apply common factor every 2 terms.

​d. Apply common factor at the end.