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4.06 Roots and zeros

Interactive practice questions

Consider the function $f\left(x\right)=x^4-7x^3+12x^2+4x-16$f(x)=x47x3+12x2+4x16.

a

Is $5$5 a zero of the function?

Yes

A

No

B
b

Is $4$4 a zero of the function?

Yes

A

No

B
c

Is $-1$1 a zero of the function?

Yes

A

No

B
Easy
1min

Consider the function $f\left(x\right)=\left(x+1\right)^2\left(x-6\right)\left(x+2\right)^5$f(x)=(x+1)2(x6)(x+2)5.

Easy
1min

Consider the function $f\left(x\right)=-3\left(x-6\right)^4\left(x+2\right)^5x^3$f(x)=3(x6)4(x+2)5x3.

Easy
1min

Consider the function $f\left(x\right)=x^3-3x^2-5x+15$f(x)=x33x25x+15.

Easy
3min
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Outcomes

A2.7.C

Determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two

A2.7.D

Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods

A2.7.E

Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping

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