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2 or 5

Q: If the factors of a polynomial are x - 2 and x - 5 what values of x make that polynomial 0?

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The graph of a polynomial in X crosses the X-axis at x-intercepts known as the roots of the polynomial, the values of x that solve the equation.(polynomial in X) = 0 or otherwise y=0

zero polynomial which is 0 and only 0 = 0.

Assuming the polynomial is written in terms of "x": It means, what value must "x" have, for the polynomial to evaluate to zero? For example: f(x) = x2 - 5x + 6 has zeros for x = 2, and x = 3. That means that if you replace each "x" in the polynomial with 2, for example, the polynomial evaluates to zero.

The polynomial P(x)=(x-3)(x-0)(x+3)(x-1) is of the fourth degree.

Suppose p(x) is a polynomial in x. Then p(a) = 0 if and only if (x-a) is a factor of p(x).

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The values that make each of the factors zero. In other words, you need to solve:x - 2 = 0 and: x - 5 = 0

4 and 5 -4 and -8

-2 and -6

2 and 7.

-6 Check: -6+4-6+8 = 0

If either factor is zero, so is the polynomial. The first factor is zero when x = 3 and the second factor when x = 4. Thus the required values of x are 3 and 4.

If (x + 3)(x +7) = 0 then either: x + 3 = 0 or x + 7 = 7 Hence x = -3 or -7.

If a polynomial has factors x-6 and x-3 it will equal 0 if either factor equals 0 since the other factor then would be multiplied by 0. ie. 0 * (x-6)=0 and 0 * (x-3)=0. so x=3 or 6

The graph of a polynomial in X crosses the X-axis at x-intercepts known as the roots of the polynomial, the values of x that solve the equation.(polynomial in X) = 0 or otherwise y=0

Not quite. The polynomial's linear factors are related - not equal to - the places where the graph meets the x-axis. For example, the polynomial x2 - 5x + 6, in factored form, is (x - 2) (x - 3). In this case, +2 and +3 are "zeroes" of the polynomial, i.e., the graph crosses the x-axis. That is, in an x-y graph, y = 0.

The "roots" of a polynomial are the solutions of the equation polynomial = 0. That is, any value which you can replace for "x", to make the polynomial equal to zero.

With difficulty. Plot a graph of the polynomial and see where it crosses the x axis. If it does, then y=0 at that point, and (x-a) is a factor. Sometimes you might spot where the polynomial is zero just by trying various values.