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5. What is a cubic polynomial function in standard form with zeros 1, –2, and 2? (1 point)

= x3 + x2 – 3x + 4
= x3 + x2 – 4x – 2
= x3 + x2 + 4x + 4
= x3 – x2 – 4x + 4

2 Answers

1 vote
Hello,

Answer D
(x-1)(x+2)(x-2)=(x-1)(x²-4)=x^3-x²-4x+4

User Anton Grigoryev
by
8.5k points
4 votes

Answer:

Option D is correct

The cubic polynomial function in standard form is :


x^3-x^2-4x+4

Explanation:

Given the zeroes of the polynomial function 1 , -2 and 2.

i.e, x = 1 , -2 and 2 where x is the zero of the polynomial function.

we can write this as

x - 1 = 0,

x + 2 = 0 or

x - 2 = 0

(x - 1)(x + 2)(x - 2) =0

Using identities
(a+b)(a-b) =a^2-b^2

then;


(x-1)(x^2-4)=0

Multiply the first term of the first expression with second expression;


x (x^2-4) =x^3-4x

also,

Multiply the second term of the first expression with second expression;


1(x^2-4) = x^2 -4

Now, subtract
x^3-4x and
x^2 -4

we get;


x^3-4x-x^2+4

then, we have;


x^3-x^2-4x+4=0

Cubic function is any function of the form
y = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a≠0

therefore, the given function is cubic function;

so, the cubic function f(x) =
x^3-x^2-4x+4


User Maxwelll
by
8.3k points

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