The first 3 are examples of the difference of 2 squares so you use the identity a^2 - b^2 = (a + b)(a - b) x^2 - 49 = 0 so (x + 7)(x - 7) = 0 so either x + 7 = 0 or x - 7 = 0 giving x = -7 and 7. Number 7 reduces to 3x^2 =12, x^2 = 4 so x = +/- 2 Number 8 take out GCf (d) to give d(d - 2) = 0 so d = 0 , 2 9 and 10 are more difficult to factor you use the 'ac' method Google it to get more details 2x^2 - 5x + 2 multiply first coefficient by the constant at the end that is 2 * 2 = 4 Now we want 2 numbers which when multiplied give + 4 and when added give - 5:- -1 and -4 seem promising so we write the equation as:-
2x^2 - 4x - x + 2 = 0
now factor by grouping 2x(x - 2) - 1(x - 2) = 0
(x - 2) is common so
(2x - 1)(x - 2) = 0 and 2x - 1 = 0 or x - 2 = 0 and now you can find x.
The number 690 is called the numerator or dividend, and the number 8 is called the denominator or divisor. The quotient of 690 and 8, the ratio of 690 and 8.
