If (x + 1) is a factor of the polynomial (2x2 + kx) then k = ?

Foundation

Mathematics Foundation

Factor theorem

Question

If (x + 1) is a factor of the polynomial (2x² + kx) then k = ?

–3

–2

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If (x + 1) is a factor of the polynomial, then the polynomial equals zero when x = -1 (Factor Theorem).

Substitute x = -1 into the polynomial and set it equal to zero:

$2 {(- 1)}^{2} + k (- 1) = 0$

Simplify the equation:

$2 (1) - k = 0$

$2 - k = 0$

Therefore, k = 2.

Final Answer: 2