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4.02 Zeros and factors

Adaptive
Worksheet

Interactive practice questions

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.

a

Write $f\left(x\right)$f(x) as a product of linear factors.

b

State all of the roots of $f\left(x\right)$f(x) in the form $x=a$x=a on the same line separated by commas.

Medium
1 min

Given $\left(x-6\right)$(x6) is a factor of the function $f\left(x\right)=x^3-3x^2-28x+60$f(x)=x33x228x+60.

Medium
1 min

If $6i$6i is a root of $g\left(x\right)$g(x), what must also be a root of $g\left(x\right)$g(x)?

Medium
< 1 min

Given $\left(x-6i\right)$(x6i) is a factor of the function $f\left(x\right)=x^3+2x^2+36x+72$f(x)=x3+2x2+36x+72.

Medium
1 min
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Outcomes

HSN.CN.C.9 (+)

Know the fundamental theorem of algebra; show that it is true for quadratic polynomials.

HSA.SSE.A.2(A2)

Use the structure of an expression to identify ways to rewrite it.

HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

HSF.BF.A.1(A2)

Write a function that describes a relationship between two quantities.

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