Evaluating Polynomials (Direct and Synthetic Substitution)

Evaluating Polynomials (Direct and Synthetic Substitution)

By Cynthia Williams

​To EVALUATE a polynomial means to find the value of the function for a given value of x.

​

f(x) means the same thing as "y". However f(3), means what is the value of y when x = 3.​ The number in parenthesis identifies the value of x.

Multiple Choice

Use Direct Substitution to evaluate:

$$f\left(x\right)=x^4-3x^3-12x^2+15x-34$$  at x=5

• -9

• 8

• -1

• 6

Multiple Choice

Use direct substition to evaluate:

$$f\left(x\right)=x^3+7x^2+5x-6$$  at x=-2

• -1

• 0

• 5

• 4

Multiple Choice

Use Direct Substitution to evaluate:

$$f\left(x\right)=4x^3+3x^2-8x+13$$  at x=-2

• 5
  

• 10

• 0

• 9

Multiple Choice

Use direct substition to evaluate:

$$f\left(x\right)=4x^3+3x^2-8x+13$$  for f(-2)

• 5
  

• 10

• 0

• 9

Multiple Choice

Use Direct Substitution to evaluate:

$$f\left(x\right)=x^4-3x^3-12x^2+15x-34$$  at x=5

• -9

• 8

• -1

• 6

Multiple Choice

Use direct substition to evaluate:

$$f\left(x\right)=3x^3+16x^2+7x+10$$  at x=-5

• -4

• 0

• 8

• -10

Multiple Choice

Use Synthetict Substitution to evaluate:

$$f\left(x\right)=4x^3+3x^2-8x+13$$  at x=-2

• 5
  

• 10

• 0

• 9

Multiple Choice

Use direct substition to evaluate:

$$f\left(x\right)=x^3+3x^2+x+5$$  for f(-3)

• -3

• 10

• 2

• -7

Multiple Choice

Use Synthetict Substitution to evaluate:

$$f\left(x\right)=x^4-x^3-14x^2+12x-12\$$  at x=4

• 1

• 3

• 4

• -5

Multiple Choice

Use direct substition to evaluate:

$$f\left(x\right)=x^4-x^3-2x^2-17x+25$$  at x=3

• 6

• 10

• -2

• 9

Multiple Choice

Use Synthetict Substitution to evaluate:

$$f\left(x\right)=3x^3+16x^2+7x+10$$  at x=-5

• -4

• 0

• 8

• -10

Fill in the Blanks

Use synthetic substitution to evaluate:

$f\left(x\right)=\ -5x^5-x^4+x^3-6x^2-1$  for f(-1)

Multiple Choice

Use Direct or Synthetict Substitution to evaluate:

$$f\left(x\right)=x^3+3x^2+x+5$$  at x=-3

• -3

• 10

• 2

• -7

Multiple Choice

Use synthetic substitution to evaluate: $$f\left(x\right)=x^4+5x^3-9x^2-18x-5\ at\ x=-6$$  

• -10

• -7

• -5

• 11

Multiple Choice

Use Direct or Synthetict Substitution to evaluate:

$$f\left(x\right)=x^3+7x^2+5x-6$$  at x=-2

• -1

• 0

• 5

• 4

Fill in the Blanks

Use synthetic substitution to evaluate:

$f\left(x\right)=x^3+7x^2-12x-1$  for f(-5)

Multiple Choice

Use Direct or Synthetict Substitution to evaluate:

$$f\left(x\right)=x^3-6x^2+9x+5\$$  at x=2

• 7

• -6

• 6

• -4

Multiple Choice

Use synthetic substitution to evaluate: $$f\left(x\right)=-4x^4+9x^3+8x^2+9x-13\ at\ x=3$$  

• -11

• 10

• 11

• 5

Multiple Choice

Use Direct or Synthetict Substitution to evaluate:

f(x) = -4x³ + 3x - 5 when x=2

• 33

• -33

• 31

• -31

Fill in the Blanks

Use synthetic substitution to evaluate:

$f\left(x\right)=-3x^3+15x^2-12x-23$  for f(3)

Fill in the Blanks

Use synthetic substitution or direct substition to evaluate:

$f\left(x\right)=x^3+9x^2+13x-37$   for f(-6)

Multiple Choice

Use synthetic substitution or direct substition to evaluate:

$$f\left(x\right)=x^4-3x^3-12x^2+15x-34$$  at x=5

• -9

• 8

• -1

• 6

Multiple Choice

Use synthetic substitution or direct substition to evaluate: $$f\left(x\right)=x^4-x^3-14x^2+12x-12\$$ for f(4)

• 1

• 3

• 4

• -5

Multiple Choice

Use synthetic substitution or direct substition to evaluate: $$f\left(x\right)=x^3-6x^2+9x+5\$$  at x=2

• 7

• -6

• 6

• -4

Multiple Choice

Use synthetic substitution or direct substition to evaluate: $$f\left(x\right)=4x^3+21x^2+5x+10\$$  for f(-5)

• 10

• 2

• -5

• -1

Fill in the Blanks

The profits of Clyde’s Corporation can be modeled by the polynomial

P( y) = y⁴ - 4y³ + 2y² + 10y - 200,

where y is the number of years after the business was started.

Find Clyde's profit for year 10. Find f(10).