posted by .

I'm sorry I'm posting so many questions, I promise this is the last one tonight :)

The leading coefficient of a cubic polynomial P is 2, and the coefficient of the linear term is -5. If P(0)=7 and P(2)=21, find P(3).

I DO NOT understand how to even start this one. I thought as you write out the equation, you also have to add the constant at the end that makes the equation comply with the P(0)=... terms above, but that doesn't work. ANY help is greatly appreciated! :D

  • Precalculus -

    Let the cubic polynomial be
    P(x)=Ax³ + Bx² + Cx + D

    "The leading coefficient of a cubic polynomial P is 2", so A=2.

    "and the coefficient of the linear term is -5.", so C=-5

    P(0)=7, i.e. when x=0, P(0)=7, so D=7.

    The only unknown is B.
    P(x)= 2x³ + Bx² -5x + 7

    "P(2)=21". If we substitute x=2, we obtain P(2)=4B+13 = 21

    The polynomial is now completely determined:
    P(x)= 2x³ + 2x² -5x + 7
    P(3)= 2*3³+2*²-5*(3)+7

  • Precalculus -

    how do you convert 18 miles to meters?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math (polynomial functions)

    Hi there, Can someone please help me understand the relationship between the FINITE DIFFERENCE and leading coefficient in a polynomial?

    The cubic polynomial f(x) is such that the coefficient of x^3 is -1. and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x)has a remainder of 8 when divided by (x-3), find the value of k. okay, this is what i did: -x^3 …
  3. Math

    1. Identify the degree, leading term and leading coefficient of each polynomial function. A. f(x)= x(x+1)(3x+1)(x-2) B. f(x)= -16+3x^4 - 9x^2 - x^6 + 4x^8 2. Describe the end behavior of a ninth-degree polynomial function with a negative …
  4. math algebra 2

    polynomial complete the table for -7x^4+8x^3-3x^2+5x-9 not sure if this is correct sorry I did not post my answer to check to see if they were correct. term -7x^4 8x^3 3x^2 5x -9 coefficient -4 8 3 5 8 degree of term 4 3 2 1 0 degree …
  5. Math

    Determine whether the following statement makes sense or does not make sense, and explain your reasoning: When I'm trying to determine end behavior, it's the coefficient of the leading term of a polynomial function that I should inspect. …
  6. Pre Calculus

    1. Find all rational zeros of the polynomial. Then determine any irrational zeros, and factor the polynomial completely. 3x^4-11x^3+5x^2+3x 2. Find the polynomial with leading coefficient 1 that has a degree of 4, a zero of multiplicity …
  7. Maths

    Check my answer please? Not sure if I did this right. Let y = f(x) be a cubic polynomial with leading coefficient a = 2 and f(-2) = f(1) = f(2) = 0. find the factored form of f. I got: f(x) = 2(x + 2)(x - 1)(x - 2)
  8. algebra

    A cubic polynomial function f(x) has leading coefficient -2 and intercepts the y-axis at 2. If f(1)=1, and f(-2)=-2, find f(-1) and write the complete function.
  9. Algebra

    Sketch the graph of a polynomial of degree 2 with a leading coefficient of -3 whose zeros are -5 and 1.
  10. pre-calculus math

    A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over . 3, −3 − 2i;    degree …

More Similar Questions