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Find the remainder when f(x)=x^4-3x^2+4 ...

Find the remainder when `f(x)=x^4-3x^2+4` is divided by `g(x)=x-2` is.

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To find the remainder when \( f(x) = x^4 - 3x^2 + 4 \) is divided by \( g(x) = x - 2 \), we can use the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial \( f(x) \) by \( g(x) = x - c \) is equal to \( f(c) \). ### Step-by-Step Solution: 1. **Identify the value of \( c \)**: - Since \( g(x) = x - 2 \), we set \( g(x) = 0 \) to find \( c \): \[ x - 2 = 0 \implies x = 2 ...
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RD SHARMA-FACTORIZATION OF POLYNOMIAL-All Questions
  1. f(x)=4x^3-12 x^2+14 x-3,\ g(x)=2x-1

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  2. f(x)=x^3-6x^2+2x-4,\ g(x)=1-2x

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  3. Find the remainder when f(x)=x^4-3x^2+4 is divided by g(x)=x-2 is.

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  4. f(x)=9x^3-3x^2+x-5, g(x)=x-2/3

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  5. f(x)=3x^4+2x^3-(x^2)/3-x/9+2/(27), g(x)= x+2/3

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  6. If the polynomials a x^3+3x^2-13 and 2x^3-5x+a , when divided by (x-2)...

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  7. The polynomials a x^3+3x^2-3 and 2x^3-5x+a when divided by (x-4) leave...

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  8. If the polynomials a x^3+3x^2-13 and 2x^3-5x+a , when divided by (x-2)...

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  9. Find the remainder when x^3+3x^2+3x+1 is divided by (i) x+1 (ii) x...

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  10. Find the remainder when x^3+3x^2+3x+1 is divided by (i) x+1 (ii) x-...

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  11. Show that (x-3) is a factor of the polynomial x^3-3x^2+4x-12

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  12. Show that (x-1) is a factor of x^(10)-1 and also of x^(11)-1.

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  13. Show that x+1 and 2x-3 are factors of 2x^3-9x^2+x+12

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  14. Without actual division prove that 2x^4- 6x^3 +3x^2+3x-2 is exactly di...

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  15. Find the value of a , if x-a is a factor of x^3-a^2x+x+2

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  16. Find the value of k , if x+3 is a factor of 3x^2+k x+6.

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  17. Determine the value of a for which the polynomial 2x^4-a x^3+4x^2+2x+1...

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  18. Find the value of a and b so that the polynomial x^3-a x^2-13 x+b has ...

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  19. Find the values of a and b so that the polynomial x^3+10 x^2+a x+b is ...

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  20. For what values of a is 2x^3+a x^2+11 x+a+3 exactly divisible by (2x-1...

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