Understanding zeroes and factors of polynomials

Write a quadratic function in factored form with one of the solutions being

 $-4+\sqrt{5}$  

•  $h\left(x\right)=\left(x+4-\sqrt{5}\right)$  

•  $f\left(x\right)=\left(x+4-\sqrt{5}\right)\left(x+4+\sqrt{5}\right)$  

•  $p\left(x\right)=\left(x+4\right)\left(x-\sqrt{5}\right)$  

•  $k\left(x\right)=\left(x-4\sqrt{5}\right)\left(x+4\sqrt{5}\right)$  

Choose the function in factored form that would match the graph shown.

HINT: Use the zeros, multiplicities, y-intercept, and end behavior!

• $f\left(x\right)=-\frac{1}{15}\left(x+3\right)\left(x-2\right)\left(x-5\right)$

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

• $f\left(x\right)=\frac{1}{30}\left(x+3\right)\left(x-2\right)^2\left(x-5\right)$

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

Which polynomial expression matches the graph?

• 2x³ - 4x² - 2
• -2x³ - 4x² - 2
• 2x² - 4x - 2
• -2x² - 4x - 2

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Write a polynomial of least degree with roots -2 and 4.

Mathematical Equivalence

ON

Select the simplest polynomial function that has zeros at -1, 0, and √3.

• f(x) = x⁴ + x³ - 3x² - 3x
• f(x) = x³ + x² - 3x - 3
• f(x) = x⁴ + x³ + 3x² + 3
• f(x) = x³ + x² + 3x + 3

Using the following roots, write in factored form.

-6, √6, 3

• (x+6)(x+√6)(x-3)

• (x-6)(x-√6)(x+3)

• (x+6)(x-√6)(x+3)

• (x+6)(x-√6)(x-3)

For the following problem write a polynomial in factored form with the following roots:

 $1\ +\sqrt{2}and\ 9$  

•  $4x^3\ +\ 11x^2\ +\ 7x\ +1$  

•  $x^3\ -\ 11x^2\ +\ 17x\ +9$  

•  $-11x^3\ -\ x^2\ +\ 9x\ +17$  

• Peanut Butter

Which polynomial function represents this graph?

• f(x) = (x + 6)(x² – 14x + 40)

• f(x) = (x – 6)(x² + 14x + 40)

• f(x) = (x + 6)(x² + 14x + 40)