Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

Question

I used: (x^2 + 2x + 1)(x - 4) where x - 4 is the factor (right??)

But for part 2, so... can you just do something like: (x^2 + 2x + 1 + 3)(x - 4) to get a different factor? I put in a + 3. Does that change the factor?
Did I do this correctly? Thanks

Answer 1

This is called the factor theorem.

If the division by some binomial leaves a remainder of zero, then that binomial is a factor

the same is true for numbers.
e.g. 12÷3 = 4 with Remainder of 0
so 3 is a factor of 12

12÷5 = 2 with remainder of 2, so 5 is NOT a factor of 12

I have no idea what you are doing in that second part, you will have to divide
(x^2 + 2x + 1) by (x - 4)

Do you know how to do long algebraic division?
Do you know how to do synthetic division?

Answer 2

can u give the proof of factor theorem