True or false any nonzero integer divided by 0 equal 0

The correct option is,

⇒ The graph crosses the x-axis at x = -2 and x = 1 and touches the x-axis at x = 0.

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given function is,

f(x) = x⁴ + x³ - 2x²

Now, We can simplify as;

f(x) = x⁴ + x³ - 2x²

    = x²(x² + x - 2)

    = x²(x² + 2x - x - 2)

    = x²[x(x + 2) - 1(x + 2)]

    = x²(x + 2)(x - 1)

So the factored form of the polynomial function is,

f(x) = x²(x + 2)(x - 1)

For x - intercepts,

F(x) = x²(x + 2)(x - 1) = 0

x = -2, 1

This function has even multiplicity = 2 at x = 0.

Therefore, graph of the function will touch the x-axis at x = 0

And at other roots x = -2, 1 has odd multiplicity = 1, so the graph will cross the x-axis.

Thus, Option (3) will be the correct option.

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Answer: C. The graph crosses the x-axis at x=-2 and x=1 & touches the x-axis at x=0

Step-by-step explanation:

You can tell this by factoring the equation to get the zeros. To start, pull out the greatest common factor.

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

Since each term has at least x^2, we can factor it out.

f(x) = x^2(x^2 + x - 2)

Now we can factor the inside by looking for factors of the constant, which is 2, that add up to the coefficient of x. 2 and -1 both add up to 1 and multiply to -2. So, we place these two numbers in parenthesis with an x.

f(x) = x^2(x + 2)(x - 1)

Now we can also separate the x^2 into 2 x's.

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

To find the zeros, we need to set them all equal to 0

x = 0

x = 0

x + 2 = 0

x = -2

x - 1 = 0

x = 1

Since there are two 0's, we know the graph just touches there. Since there are 1 of the other two numbers, we know that it crosses there.