Question

Show two different ways to evaluate the polynomial f(x)=-3x^(4)-2x^(3)+7x^(2)-9 when x=-4.

Answer 1

To evaluate the polynomial f(x)=-3x^(4)-2x^(3)+7x^(2)-9 when x=-4, you can substitute x=-4 into the polynomial and simplify the expression. Two different ways to do this are provided: Method 1 involves direct substitution and simplification, while Method 2 involves calculating the powers of -4 individually and multiplying them with each term of the polynomial.

Step-by-step explanation:

To evaluate the polynomial f(x)=-3x^(4)-2x^(3)+7x^(2)-9 when x=-4, we can substitute x=-4 into the polynomial and simplify the expression.

Method 1:

1. Substitute x=-4 into the polynomial: f(-4)=-3(-4)^(4)-2(-4)^(3)+7(-4)^(2)-9.
2. Simplify the expression: f(-4)=-3(256)-2(-64)+7(16)-9.
3. Calculate the result: f(-4)=-768+128+112-9 = -537.

Method 2:

1. Calculate the powers of -4 individually: (-4)^(4) = 256, (-4)^(3) = -64, (-4)^(2) = 16.
2. Multiply each term of the polynomial by the corresponding power of -4: -3(256)-2(-64)+7(16)-9.
3. Simplify the expression: -768+128+112-9 = -537.

Therefore, when x=-4, f(x)=-3x^(4)-2x^(3)+7x^(2)-9 = -537.