Evaluating a Polynomial for a Given Value

Learning Outcomes

• Evaluate a polynomial for integer values

Previously we evaluated expressions by “plugging in” numbers for variables. Since polynomials are expressions, we’ll follow the same procedures to evaluate polynomialsâ€”substitute the given value for the variable into the polynomial, and then simplify.

example

Evaluate $3{x}^{2}-9x+7$ when

1. $x=3$
2. $x=-1$

Solution

 1. $x=3$ $3{x}^{2}-9x+7$ Substitute $3$ for $x$ $3{\left(3\right)}^{2}-9\left(3\right)+7$ Simplify the expression with the exponent. $3\cdot 9 - 9\left(3\right)+7$ Multiply. $27 - 27+7$ Simplify. $7$
 2. $x=-1$ $3{x}^{2}-9x+7$ Substitute $âˆ’1$ for $x$ $3{\left(-1\right)}^{2}-9\left(-1\right)+7$ Simplify the expression with the exponent. $3\cdot 1 - 9\left(-1\right)+7$ Multiply. $3+9+7$ Simplify. $19$

try it

The following video provides another example of how to evaluate a quadratic polynomial for a negative number.

example

The polynomial $-16{t}^{2}+300$ gives the height of an object $t$ seconds after it is dropped from a $300$ foot tall bridge. Find the height after $t=3$ seconds.