Loading....
Coupon Accepted Successfully!

 

General Trinomials

 

The expression
x2 + (a + b)x + ab tells us that we need two numbers whose product is the last term and whose sum is the coefficient of the middle term. Consider the trinomial x2 + 5x + 6.  Now, two factors of 6 are 1 and 6, but 1 + 6 ≠ 5. However, 2 and 3 are also factors of 6, and 2 + 3 = 5. Hence, x2 + 5x + 6 = (x + 2)(x + 3).
 
Example

Which of the following could be a solution of the equation x2 – 7x – 18 = 0 ?

  1. –1
  2. 0
  3. 2
  4. 7
  5. 9
Solution

Now, both 2 and –9 are factors of 18, and 2 + (–9) = –7.

Hence, x2 – 7x – 18 = (x + 2)(x – 9) = 0.

 

Setting each factor equal to zero yields x + 2 = 0 and x – 9 = 0.

 

Solving these equations yields x = –2 and 9.

 

The answer is (E).
 





Test Your Skills Now!
Take a Quiz now
Reviewer Name