x^3+3x^2-54x=0
To factor, check if there is anything that is in all of the terms. In this case, there is an x in each term. If you divide by x, you then have x(x^2+3x-54)=0. You can put an x out in front of the rest of the equation. Next, you factor what is inside the parentheses. To do this, you need to know the factors of -54. These include (6,-9), (-6,9), (3,-18), (-3,18), (2,-27), (-2,27). When added together, the factors need to equal positive 3. The only factors that equal positive 3 when added together are -6 and 9. If we forget the outside x, the equation looks like (x+9)(x-6). This gives a final factoring of x(x+9)(x-6)=0. Checking gives x(x^2-6x+9x-54)= x^3+3x^2-54x=0.
To solve, you use the factored equation. Because you are multiplying for 0, one term of the equation must equal 0. This means the first x=0. From x+9=0, you subtract 9 meaning x=-9. From x-6=0, you add 6 meaning x=6.
Factoring is one method of solving quadratic equations. When an equation has been factored, you are able to plug in 0 to solve for x because the factoring involves multiplying.
To factor, check if there is anything that is in all of the terms. In this case, there is an x in each term. If you divide by x, you then have x(x^2+3x-54)=0. You can put an x out in front of the rest of the equation. Next, you factor what is inside the parentheses. To do this, you need to know the factors of -54. These include (6,-9), (-6,9), (3,-18), (-3,18), (2,-27), (-2,27). When added together, the factors need to equal positive 3. The only factors that equal positive 3 when added together are -6 and 9. If we forget the outside x, the equation looks like (x+9)(x-6). This gives a final factoring of x(x+9)(x-6)=0. Checking gives x(x^2-6x+9x-54)= x^3+3x^2-54x=0.
To solve, you use the factored equation. Because you are multiplying for 0, one term of the equation must equal 0. This means the first x=0. From x+9=0, you subtract 9 meaning x=-9. From x-6=0, you add 6 meaning x=6.
Factoring is one method of solving quadratic equations. When an equation has been factored, you are able to plug in 0 to solve for x because the factoring involves multiplying.