Question

Prove that 2x4 – 6x3 + 3x2+ 3x – 2 is exactly divisible by x2 – 3x+ 2
i. By actual division
ii. Without actual division

Answer 1

Answer:

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Step-by-step explanation:

First we factorize divisor x² - 3x+2

= x² -2x - x +2 = x(x-2) -1 ( x - 2)

= ( x-2) (x-1)

Now, dividend p(x) = 2x^4 - 6x^3 + 3x² + 3x -2

If p(x) is dividible by ( x-2) & (x-1) each, then p(x) is also divisible by its product.

& by remainder theorem , if p(2) = 0 & p(1) =0

Then, p(x) is divisible by the divisor.

P( 2) = 2* 2^4 - 6* 2^3 + 3* 2² + 3*2 -2

= 32 - 48 + 12 + 6 - 2 = 50 - 50

= 0 ….. (1)

Answer 2

Answer:

Without actual division, prove that 2x4 – 5x3 + 2x2 – x+ 2 is divisible by x2-3x+2.

Thinking Process

(i) Firstly, determine the factors of quadratic polynomial by splitting middle term.

(ii) The two different values of zeroes put in bioquadratic polynomial.