Question

The factors of x²-2x - 3 will be:​

Answer 1

Answer:

The roots are -1,3

Step-by-step explanation:

x²-2x - 3 = 0

$- b + - \sqrt{ {b}^{2} - 4ac \div 2a$

b = -2, a = 1, c = -3

{2 +- √[(-2)^2-4(1)(-3)]}/2(1)

{2 +- √[4-4(-3)]}/2

{2 +- √[4+12]}/2

{2 +- √16}/2

{2 +- 4}/2

Roots are

{2+4}/2 , {2-4}/2

6/2 , -2/2

3 , -1

Answer 2

since remaining is zero (2x-3) is a factor of

$2 {x}^{2} - 9x + x + 12$

by division algorithm use have

Step-by-step explanation:

$2 {x}^{2} - 9x + x + 12 = (2x - 3)( {x }^{2} - 3x - 4) \\ = (2x - 3)( {x}^{2} - 4x + x - 4) \\ = (2x - 3)(x(x - 4) + 1(x - 4) \\ = (2x - 3)(x - 4)(x + 1)$

hence remaining factors (x-4) (x+1)