Making a Polynomial Exactly Divisible Video Explanation Question What must be added to the polynomial \[ f(x) = x^4 + 2x^3 – 2x^2 + x – 1 \] so that the resulting polynomial is exactly divisible by \[ g(x) = x^2 + 2x – 3 \; ? \] Solution Step 1: Apply the Division Algorithm […]
Finding the Value of k Using Division Algorithm Video Explanation Question For what value of \(k\) is the polynomial \[ f(x) = 3x^4 – 9x^3 + x^2 + 15x + k \] completely divisible by \[ g(x) = 3x^2 – 5 \; ? \] Solution Step 1: Apply the Division Algorithm By the division algorithm,
Finding All Zeroes of a Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = 2x^4 – 9x^3 + 5x^2 + 3x – 1, \] if two of its zeroes are \(2+\sqrt{3}\) and \(2-\sqrt{3}\). Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the given zeroes are conjugates,
Finding All Zeroes of a Cubic Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = x^3 + 3x^2 – 2x – 6, \] if two of its zeroes are \( -\sqrt{2} \) and \( \sqrt{2} \). Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the given
Finding All Zeroes of a Cubic Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = 2x^3 + x^2 – 6x – 3, \] if two of its zeroes are \( -\sqrt{3} \) and \( \sqrt{3} \). Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the given
Finding All Zeroes of a Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = 2x^4 + 7x^3 – 19x^2 – 14x + 30, \] if two of its zeroes are \( \sqrt{2} \) and \( -\sqrt{2} \). Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the
Finding All Zeroes of a Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = x^4 + x^3 – 34x^2 – 4x + 120, \] if two of its zeroes are \(2\) and \(-2\). Solution Step 1: Form the Quadratic Factor from Given Zeroes Since \(2\) and \(-2\) are zeroes, \[
Finding All Zeroes of a Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = 2x^4 – 2x^3 – 7x^2 + 3x + 6, \] if two of its zeroes are \[ -\frac{\sqrt{3}}{2} \text{ and } \frac{\sqrt{3}}{2}. \] Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the
Finding All Zeroes of a Polynomial Video Explanation Question Obtain all the zeroes of the polynomial \[ f(x) = x^4 – 3x^3 – x^2 + 9x – 6, \] if two of its zeroes are \( -\sqrt{3} \) and \( \sqrt{3} \). Solution Step 1: Form the Quadratic Factor from Given Zeroes Since the zeroes
Finding All Zeroes of a Cubic Polynomial Video Explanation Question Obtain all the zeroes of the polynomial \[ f(x) = x^3 + 13x^2 + 32x + 20, \] if one of its zeroes is \(-2\). Solution Step 1: Use the Given Zero Since \(-2\) is a zero of the polynomial, \((x + 2)\) is a