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Question

For what value of 'a' the polynomial 2x-1 divides the polynomial 4x^3 + ax + 1? Justify.

 

plz. show steps if possible

Answer 1

Question: For what value of 'a' does the polynomial 2x-1 divide the polynomial 4x^3 + ax + 1? Justify.

If (2x - 1) divides the polynomial 4x^3 + ax + 1, then that polynomial is factorisable, and can be factored into the form shown below, the product of a linear term and a quadratic term.

(px - 1)(qx^2 + rx - 1) = pqx^3 + prx ^2 - px - qx^2 - rx + 1 = pqx^3 +(pr - q)x^2 - (p+r)x - 1

(px - 1)(qx^2 + rx - 1) = pqx^3 +(pr - q)x^2 - (p+r)x - 1

where p = 2, pq = 4, hence q = 2, giving

(2x - 1)(2x^2 + rx - 1) = 4x^3 + (2r - 2)x^2 - (2+r)x - 1

in order to exclude the x^2-term, we need r = 1, this gives the final expression as,

(2x - 1)(2x^2 + x - 1) = 4x^3 - (3)x + 1

Answer: a = -3

 

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thnx man......

plz. also give the answer of other unanswered questions......