Question

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Answer 1

Correct Question:

What should be subtracted from 3x³ - 8x² + 4x - 3, so that the resulting expression has (x + 2) as a factor?

Solution:

Let k be the required number.

f(x) = 3x³ - 8x² + 4x - 3 - k    

Applying Factor theorem,

(x + 2) = 0

⇒ x = -2

Since (x + 2) is a factor,

f(-2) = 0

Now, Substituting x as -2.

f(-2) = 3(-2)³ - 8(-2)² + 4(-2) - 3 - k

⇒ 0 = 3(-8) - 8(4) - 8 - 3 - k

⇒ 0 = -24 - 32 - 8 - 3 - k

⇒ 0 = -67 - k

∴ k = -67

Alternate method:

On dividing 3x³ - 8x² + 4x - 3 by (x + 2),

                           

  x + 2  ) 3x³ - 8x² + 4x - 3 ( 3x² - 14x + 32

          [-]  3x³ + 6x²

                      - 14x² + 4x

                [-]   - 14x² - 28x

                                  32x - 3

                          [-]     32x + 64

                                       -67

∴ -67 should be subtracted.

We get the same answer in both the methods.

Answer 2

Answer:

=>0=-67-a

Step-by-step explanation:

The simplification is in the attachment..

Hope it's help you didi