Give an example of a polynomial with degree 3 such that when factored, it contains the two factors (x+5) and (2x-1), i.e., the polynomial looks like (x+5) (2x -1) ( ? ).
How many such polynomials you think there are?
what is wrong with any factor containing an x? x-4; x-1; x; and so on. Maybe I am missing something.
Now I get it. Put any factor with an x in it as the last term, then multiply the three factors.
okay thanks I'll try it
To find an example of a polynomial with degree 3 that contains the factors (x+5) and (2x-1), we can use the concept of factorization.
To reconstruct the polynomial, we can multiply the factors together.
(x+5) * (2x-1) = 2x^2 + 9x - 5
So, an example of a polynomial with degree 3 that satisfies the given conditions is 2x^2 + 9x - 5.
Now, let's consider how many such polynomials there are.
In general, if you have two linear factors (ax + b) and (cx + d), you can multiply them together to get a quadratic polynomial: (ax + b) * (cx + d).
Taking this into account, the number of polynomials with degree 3 that contain the factors (x+5) and (2x-1) can be found by multiplying these factors together with a quadratic factor.
So, the number of such polynomials is infinite. You can obtain different polynomials by applying different coefficients to the quadratic term (2x^2).
Therefore, there are infinitely many polynomials with degree 3 that contain the factors (x+5) and (2x-1).