Q: Is the degree of the polynomial 3x4 plus 4x3 - 3x4 plus 5x plus 1 is 3 true or false?

Write your answer...

true.

true!

True Yes. Although the term 'quad' stands for four, a quadratic equation is a polynomial of second degree.

False. The height of the degree does not really matter in this case. There just have to be other monomials in the problem to be considered a polynomial. "Poly" means many.

its false

true :) apex! * * * * * APEX gets it wrong - again! A quadratic polynomial has degree 2. Not greater than, nor less than but exactly equal to 2.

True

True

False (apex)

False.

False. It has to be either "- 24x" or "+ 36". These would factor as (3x - 4)2 and (3x - 6)2 respectively.

If the coefficients of a polynomial of degree three are real it MUST have a real zero. In the following, asymptotic values are assumed as being attained for brevity: If the coeeff of x3 is positive, the value of the polynomial goes from minus infinity to plus infinity as x goes from minus infinity to plus infinity. The reverse is true if the coefficient of x3 is negative. Since all polynomials are continuous functions, the polynomial must cross the x axis at some point. That's your root.

false

False.

false

True

true

false

true

Is |-8|+|3|=|-8+3| true or false?

Yes, it is true.

True.

True.

Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)