Question

What number should be added to 3x3 - 4x2 - 5x so that (x - 2) is a factor?​

Answer 1

Answer:

2 Should be added.

Step-by-step explanation:

• Let a be added to added to the given polynomial.

Therefore,

$f(x) = {3x}^{3} - {4x}^{2} - 5x + a$

Since ( x - 2) is a factor,

Therefore,

$f(2) = 3( {2}^{3} ) - 4( {2}^{2} ) - 5(2) + a = 0$

$3(8) - 4(4) - 5(2) + a = 0$

$3 \times 8 - 4 \times 4 - 5 \times 2 = - a$

$24 - 16 - 10 = - a$

$- 2 = - a$

$a = 2$

Therefore, a = 2 should be added.

Hope it helps.

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