Neco 2022 Further Mathematics Question 3

Practice essay / theory question 3 from the 2022 Neco Further Mathematics examination. This question covers Polynomials, Algebraic Expressions, Factor Theorem, Remainder Theorem, Vieta's formulas .

Neco 2022 Further Mathematics Essay / Theory

Topics: Polynomials Algebraic Expressions Factor Theorem Remainder Theorem Vieta's formulas

Question 3 NECO • 2022 • FURTHER_MATHEMATICS • essay

A polynomial \(P(x) = 2x^{4} - 3x^{3} + kx^{2} + 5x - 12\) is such that \((x-2)\) is a factor of \(P(x)\) and the remainder when \(P(x)\) is divided by \((x+1)\) is \(4\).

Question Parts

( a )

Determine the value of the constant \(k\).

( b )

Using the value of \(k\) found in part (a), factor \(P(x)\) completely over the real numbers.

( c )

Find the sum of all real roots of the equation \(P(x)=0\).

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About This Question

This is Neco 2022 Further Mathematics Question 3. It is one of the essay questions from the 2022 Neco Further Mathematics examination.

The question covers Polynomials, Algebraic Expressions, Factor Theorem, Remainder Theorem, Vieta's formulas .

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