End Behaviour of Polynomials - Grade 12 Advanced Functions (Math Hacks)

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In this video, we are covering the end behaviour of polynomials. The end behaviour of a polynomial refers to the behaviour of the polynomial as the value of “x” approaches negative or positive infinity. If we can graph our function easily, you can visually inspect to see what the polynomial end behaviours; however, for more complex polynomials, we need to use the degree and leading coefficient of the polynomial.

1. The degree of the polynomial refers to the largest exponent on an "x" term. If this degree is even, the end behaviours will be the same (either both positive infinity or both negative infinity). If the degree is odd, the end behaviours will be opposite (one will be positive infinity and one will be negative infinity).

2. The leading coefficient refers to the coefficient in front of the "x" with the largest exponent. If the leading coefficient is positive, the end behaviour at positive infinity (x value) will be go to positive infinity (y value). If the leading coefficient is negative, the end behaviour at negative infinity (x value) will go to negative infinity (y value).

Make sure to expand your polynomial first, into standard form, before you determine the degree and leading coefficient of your polynomial.