Math Help - Algebra 2 question factoring polynomial

hi can anyone help me solve these 2 problems
1)Direction: solve each polynomial equation by factoring
4x cubed + 7x squared - 5x = 6

2)Direction:Identify the roots of each equation.state the mutiplicity of each root
x to the fourth power + 2x cubed -11x squared - 12x +36=0

and can you please explain to me how you would factor it if its factorable because im having a hard time factoring when x isnt to like the second power.hope this made sense..thanks

Originally Posted by miemie11

ynomial equation by factoring
4x cubed + 7x squared - 5x = 6

There is no "nice" way to factor this thing (that I can see), so I'd use the rational root theorem to get a factor to start with then factor the rest in the "usual" way.

Possible rational roots are .

I'll cut to the chase. x - 1 is a factor. So do your division (synthetic or long) and you get that


You can do the rest.

-Dan

Originally Posted by miemie11

2)Direction:Identify the roots of each equation.state the mutiplicity of each root
x to the fourth power + 2x cubed -11x squared - 12x +36=0

Again this is a job for the rational root theorem.

Possible rational roots are , so 18 possibles in all.

Starting off, I get that x - 2 is a factor. So


Now let's apply the rational root theorem to the second factor. Possible rational roots of this are: (Only 12 possibles this time!)

Again I get that x - 2 is a factor. So

which I'm sure you can finish up on your own.

-Dan

Originally Posted by miemie11

hi can anyone help me solve these 2 problems
1)Direction: solve each polynomial equation by factoring
4x cubed + 7x squared - 5x = 6

2)Direction:Identify the roots of each equation.state the mutiplicity of each root
x to the fourth power + 2x cubed -11x squared - 12x +36=0

and can you please explain to me how you would factor it if its factorable because im having a hard time factoring when x isnt to like the second power.hope this made sense..thanks

1) By trial and error you should be able to establish that x = 1 and x = -2 are roots of the equation . Therefore (x - 1) and (x + 2) are factors of .

Divide these factors in to get the remaining linear factor and hence solve for the remaining root.

Alternatively . Therefore and it should be obvious what the value of a and b must be .......

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2) Show that x = 2 and x = -3 are roots. In fact, they are repeated roots ......