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3.05 Zeros and factors

Adaptive
Worksheet

Interactive practice questions

The expression $\left(x-3+\sqrt{10}\right)$(x3+10) is a factor of the polynomial $f\left(x\right)=x^3-10x^2+23x+4$f(x)=x310x2+23x+4. Which two of the following expressions are also factors of $f\left(x\right)$f(x)?

$\left(x+3\right)$(x+3)

A

$\left(x-3-\sqrt{10}\right)$(x310)

B

$\left(x+3+\sqrt{10}\right)$(x+3+10)

C

$\left(x-4\right)$(x4)

D
Medium
< 1min

Determine the remaining zero of a polynomial with rational coefficients and with:

Medium
< 1min

Determine the remaining zero of a polynomial with rational coefficients and with:

Medium
< 1min

Given $\left(x+8\right)$(x+8) is a factor of the function $f\left(x\right)=x^3+2x^2-75x-216$f(x)=x3+2x275x216.

Medium
1min
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Outcomes

A2.EI.6

The student will represent, solve, and interpret the solution to a polynomial equation.

A2.EI.6a

Determine a factored form of a polynomial equation, of degree three or higher, given its zeros or the x-intercepts of the graph of its related function.

A2.EI.6b

Determine the number and type of solutions (real or imaginary) of a polynomial equation of degree three or higher.

A2.F.2

The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically.

A2.F.2a

Determine and identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, including graphs with discontinuities.

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