How to solve Polynomial long division

Question

equation X^3+14x^2+49x

What are the steps to solving this equation using long division?

Answer 1

x=0, -7

factor

x^3+14x^2+49x

=x(x+7)^2

set each factor = 0

long division really isn't necessary

but if you see one factor, divide into the 3D polynomial to get a quadratic

see another factor, divide again to get a linear factor

set each factor = 0, solve for x

Answer 2

Hi Megan.

You can start off by dividing the equation by x because it's a common element in all of the terms.

This gives you a straightforward quadratic equation x²+14x+49 which you can solve by factoring or the quadratic formula.

Answer 3

Hi Megan,

This is an example of an expression as opposed to an equation. Equations always have an equal/less than/greater than symbol between two expressions or numbers. (This is important in science when a teacher asks for an equation!!! Don't just give an expression.)

Anyway we can simplify this expression: x³+14x²+49x

I would first divide every thing by x leaving:

x(x²+14x+49)

You can then factor the expression in the parenthesis

x( x + 7)(x +7)

We found this by figuring out what two numbers when added together equal 14 and when multiplied are 49

We can check our work using FOIL we get

First: x × x = x²

Outer 7×7 = 49

Inner: 7 × x = 7x

Last: 7 × x = 7x

IF the expression was set to zero, the values for x would be zero (0) because 0 times anything is zero and

-7 as that makes our expression (-7+7) = 0

Answer 4

an equation requires an equality denoted by an equal sign, = . If you want to perform division, then you must have a divisor.