Resolve each of the following quadratic trinomials into factors:
11x2 – 54x + 63
Here, coefficient of x2 = 11, coefficient of x = - 54 and constant term = 63
We shall now split up the coefficient of x i.e., -54 into two parts whose sum is - 54 and product is 11 * 63 = 693
Clearly,
-33x - 21x = - 54x and,
(-33) * (-21) = 693
So, we write middle term - 54x as - 33x - 21x
Thus, we have
11x2 – 54x + 63 = 11x2 - 33x - 21x – 6
= 11x (x – 3) - 21 (x – 3)
= (11x – 21) (x – 3)