Question

Pls solve the following questions in the image:

Also solve this:

9. If the polynomials 2x³ + ax² + 3x - 5 and x³ + x² - 4x + a leave the same remainder when divided by x-2, find the value of a.

10. The polynomials ax³ + 3x² - 3 and 2x³3 -5x + a when divided by (x-4) leave the remainders R₁ and R₂ respectively. Find the values of a in each of the following cases, if

(i) R₁ = R₂

(ii) R₁ + R₂ = 0

(iii) 2R₁ - R₂ = 0.

11. If the polynomials ax³ + 3x² - 13 and 2x³-5x + a, when divided by (x - 2) leave the same remainder, find the value of a.
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Answer 1

Answer:

Step-by-step explanation:

Let the given polynomials be f(x) and g(x).

When f(x) and g(x) are divided by (x-2) they leave the same remainder.

I.e (x-2) is a factor of f(x) and g(x). It means 2 is the zero of f(x) and g(x)

So that,

f(2) = g(2)

2x³+ax²+3x-5 = x³+x²-4x+a

2(2)³+a(2)²+3(2)-5 = 2³+2²-4(2)+a

2(8)+a(4)+6-5 = 8+4-8+a

16+4a+1 = 4+a

17+4a = 4+a

4a-a = 4-17

3a = -13

a = -13/3.