Create a polynomial function in factored form that crosses through the x-axis at -2 and touches the x-axis and turns around at 4.​

Given:

A polynomial crosses through the x-axis at -2 and touches the x-axis and turns around at 4.​

To find:

The polynomial function in factored form.

Solution:

If the graph of a polynomial intersect the x-axis at , then is a factor of the polynomial.

If the graph of a polynomial touches the x-axis at , then is a factor of the polynomial with multiplicity 2. In other words is the factor of the polynomial.

It is given that the polynomial crosses through the x-axis at -2. So, is a factor of required polynomial.

It is given that the polynomial touches the x-axis and turns around at 4. So, is a factor of required polynomial.

Now, the required polynomial is:

Therefore, the required polynomial is .

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1