What must be subtracted from 16x 3 - 8x 2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor ?

The number to be subtracted = Remainder obtained on dividing 16x 3 - 8x 2 + 4x + 7 by 2x + 1. 2x + 1 = 0 ⇒ x = . Remainder = Value of 16x 3 - 8x 2 + 4x + 7 at x = . Hence, no. to be added = 1.

Mathematics

What must be subtracted from 16x³ - 8x² + 4x + 7 so that the resulting expression has 2x + 1 as a factor ?

Factorisation

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Answer

The number to be subtracted = Remainder obtained on dividing 16x³ - 8x² + 4x + 7 by 2x + 1.

2x + 1 = 0 ⇒ x = $-\dfrac{1}{2}$ .

Remainder = Value of 16x³ - 8x² + 4x + 7 at x = $-\dfrac{1}{2}$ .

$= 16\Big(-\dfrac{1}{2}\Big)^3 - 8\Big(-\dfrac{1}{2}\Big)^2 + 4\Big(-\dfrac{1}{2}\Big) + 7 \\[1em] = -\dfrac{16}{8} - \dfrac{8}{4} - 2 + 7 \\[1em] = -2 - 2 - 2 + 7 \\[1em] = -6 + 7 = 1.$

Hence, number to be subtracted = 1.

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Mathematics

What must be subtracted from 16x³ - 8x² + 4x + 7 so that the resulting expression has 2x + 1 as a factor ?

Factorisation

Answer

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Mathematics

What must be subtracted from 16x3 - 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor ?

Factorisation

Answer

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