What is the remainder of X ^ 3 – 3x ^ 2 -4x + 4, if (x - 2) is a factor of polynomial.
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Factorize : x2–3x. [2014] Find the value of k, if x – 2 is a factor of p(x) = 2x2 + 3x – k. [2015] 5. Find the value of k, if 2x – 1 is a factor of the ...
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9th
Maths
Polynomials
Remainder Theorem
On dividing x3 - 3x2 + x + ...
MATHS
On dividing x
3
−3x
2
+x+2 by a polynomial g(x) the quotient and remainder were x−2 and −2x+4 respectively. Find g(x).
December 20, 2019avatar
Purmangi Dheple
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ANSWER
Dividend = Divisor × Quotient + Remainder
x
3
−3x
2
+x+2=g(x)×(x−2)+(−2x+4)
x
3
−3x
2
+x+2−(−2x+4)=g(x)×(x−2)
x
3
−3x
2
+3x−2=g(x)×(x−2)
x−2
x
3
−3x
2
+3x−2
=g(x)
x−2 )x
3
−3x
2
+3x−2( x
2
−x+1
x
3
−2x
2
------------------------------------------------------
−x
2
+3x−2
−x
2
+2x
------------------------------------------------------
x−2
x−2
-------------------------------------------------------
0
g(x)=x
2
−x+1
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