f(x) = x4+2x-13x2-12x+21 is divisible by x2-4x+3 .find r(x).
Answers
2x-3
Step-by-step explanation:
Given : Dividend = x^{4} +2x^{3} -13x^{2} -12x+21x
4
+2x
3
−13x
2
−12x+21
Divisor = x^{2} - 4x+3x
2
−4x+3
Solution :
Since we know that :
Dividend = divisor * quotient +remainderDividend=divisor∗quotient+remainder
x^{4} +2x^{3} -13x^{2} -12x+21 = (x^{2} - 4x+3)*x^{2} + (6x^{3}-16x^{2}-12x+21)x
4
+2x
3
−13x
2
−12x+21=(x
2
−4x+3)∗x
2
+(6x
3
−16x
2
−12x+21)
x^{4} +2x^{3} -13x^{2} -12x+21 = (x^{2} - 4x+3)*(x^{2}+6x) + (8x^{2}-30x+21)x
4
+2x
3
−13x
2
−12x+21=(x
2
−4x+3)∗(x
2
+6x)+(8x
2
−30x+21)
x^{4} +2x^{3} -13x^{2} -12x+21 = (x^{2} - 4x+3)*(x^{2}+6x+8) + (2x-3)x
4
+2x
3
−13x
2
−12x+21=(x
2
−4x+3)∗(x
2
+6x+8)+(2x−3)
Since the remainder is 2x-3
So, 2x-3 must be subtracted from x^{4} +2x^{3} -13x^{2} -12x+21x
4
+2x
3
−13x
2
−12x+21 so that the resulting polynomial is exactly divisible by x^{2} - 4x+3x
2
−4x+3
Answer:
2x-3 is the value of r(X)
hope this will help you plz mark as Brainliest answers
