SOLUTION: 1. Factorise: X^6 - 7X^3 - 8
2. Find the factor for X^2 + 5√2x + 12
3. If x^11 + 101 is divided by x+1, then what is the reminder?
4. Find value of polynomial x^2 -
Algebra ->
Polynomials-and-rational-expressions
-> SOLUTION: 1. Factorise: X^6 - 7X^3 - 8
2. Find the factor for X^2 + 5√2x + 12
3. If x^11 + 101 is divided by x+1, then what is the reminder?
4. Find value of polynomial x^2 -
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Question 1095133: 1. Factorise: X^6 - 7X^3 - 8
2. Find the factor for X^2 + 5√2x + 12
3. If x^11 + 101 is divided by x+1, then what is the reminder?
4. Find value of polynomial x^2 - 9 for x=97
5. if X^3 + 3X^2 + 3x + 1 is divided by x+1 then what is the reminder?
1. Factorise: X^6 - 7X^3 - 8
= = .
2. Find the factor for X^2 + 5√2x + 12
3. If x^11 + 101 is divided by x+1, then what is the reminder?
The remainder is (-1)^11 + 101 = -1 + 101 = 100 (The remainder theorem).
4. Find value of polynomial x^2 - 9 for x=97
It is 97^2 - 9 = (97+3)*(97-3) = 100*94 = 9400 (mental solution without a calculator).
5. if X^3 + 3X^2 + 3x + 1 is divided by x+1 then what is the remainder ?
The remainder is (-1)^3 + 3*(-1)^2 + 3*(-1) + 1 = -1 + 3 - 3 + 1 = 0.
By the way, X^3 + 3X^2 + 3x + 1 = (X + 1)^3.
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