x^3-x^2-42x Factor?

Answer 1

Common Factor the x

x³ - x³ - 42x = 0

x(x² - x - 42) = 0

The middle term inside the parenthesis is - x

The first tern x² = 1

Find the sum of the middle term

Multiply the first term 1 times the last term 42 equals 42 and factor

factors of 42

1 x 42
2 x 21
3 x 14
6 x 7. . .←. .use these factors

- 7 and + 6 satisft the sum of the middle term

insert - 7x and + 6x into the equation

x(x² - x - 42) = 0

x(x² - 7x + 6x - 42 ) = 0

Group factor inside the parenthesis

x(x² - 7x) + (6x - 42) = 0

x[x(x - 7) + 6(x - 7) = 0

x(x + 6)(x - 7) = 0

- - - - - - -

Roots

x = 0

- - - - - - - -

Roots

x + 6 = 0

x + 6 - 6 = 0 - 6

x = - 6

- - - - - - - -

Roots

x - 7 = 0

x - 7 + 7 = 0 + 7

x = 7

- - - - - - - -s-

Answer 2

x^3-x^2-42x

Here is the principle

Take out as much as you can that is common to all elements - in this case 'x'

This leaves x(x^2-x-42)

To factor the part in brackets we need to be able to work out two brackets (x+a)(x+b) that when expanded come to x^2-x-42

If we expand (x+a)(x+b) we get (x^2+ (a+b)x + ab) so in effect we are looking for two numbers that when multiplied together make -42 (so one will be minus) and that when added together total -1 (or you could regard the difference in absolute values as being 1)

The answer is obvious (6 & -7) but in other cases you would write down the factors and see which pair met your requirments. Later on you will be taught an equation to solve a general equation of the form ax^2 + bx + c (called a quadratic equation)

So the answer is x(x+6)(x-7)

Answer 3

x (x^2 - x - 42)
x (x - 7) (x + 6)

Answer 4

x^3-x^2-42x
=x(x^2-x-42)
=x(x+6)(x-7)

Answer 5

x(x-7)(x+6)

Answer 6

x(x^2-x-42)

x(x-7)(x+6)

Answer 7

Wow why don't yu help me??

Answer 8

This is x(x-7)(x+6). Please put extra effort in your studies. Don't take these short cuts. Thanks.