Enter a function in factored and standard form for the given k and set of x-intercepts. x-intercepts: −7 and 9; k = −5

We want to find a factorized function for the given leading coefficient and x-intercepts.

We know that for a polynomial of degree n with the leading coefficient k and the x-intercepts {x₁, x₂, ..., xₙ}

Can be written as:

p(x) = k*(x - x₁)*(x - x₂)*...*(x - xₙ)

Here we have:

k = -5

x-intercepts: {-7, 9}

The the factorized polynomial is just:

p(x) = -5*(x - (-7))*(x - 9)

p(x) = -5*(x + 7)*(x - 9)

If you want to learn more, you can read:

link

See below in bold.

Step-by-step explanation:

Factored form:

f(x) = -5(x + 7)(x - 9)

Standard form:

f(x) = -5(x^2 + 7x - 9x - 63)

f(x) =  -5(x^2 - 2x - 63)

f(x) = -5x^2 + 10x + 315.

-6 is the correct option from the above given options