Question

I need some interesting facts about polynomials please I need I 10 minutes please help me​

Answer 1

Answer:

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Answer 2

Answer:

Nine facts about Polynomials:-

1. If the degree n of a polynomial is even, then the arms of the graph are either both up or both down.

2. If the degree n is odd, then one arm of the graph is up and one is down.

3. If the leading coefficient an is positive, the right arm of the graph is up.

4. If the leading coefficient an is negative, the right arm of the graph is down.

5. If P(x) is a polynomial of degree n in one variable, with complex coeffi-

cients, then it factors into linear terms:

P(x) = C(x − r1)(x − r2)· · ·(x − rn)

where r1, . . . , rn are the roots of P(x) – these are often complex numbers.

6. If P(x) is a polynomial in one variable, and P(a) = 0, then P(x) is divisible

by x − a: that is, there exists Q(x) such that

P(x) = (x − a)Q(x)

7. A polynomial of degree n in one variable has at most n different roots.

8. If P(x) is a polynomial of degree n in one variable with real coefficients,

then P(x) factors as a product of linear and quadratic terms with real

coefficients.

9. If P(x) and D(x) are polynomials in one variable, then we can write

P(x) = Q(x)D(x) + R(x)

where the degree of R(x) is less than the degree of D(x). Here, R(x)

stands for the remainder of P(x) when divided by D(x).