I need help on the questions!? The question looks so confusing and complicated..
1) How can i find the value of k when (x+3) is a factor of (2x+5)^9 + (3x+k)^3
2) How can i find the value of k of (3x^k - 7x^2 +15) / (x-2) and has a remainder of 11.
1) How can i find the value of k when (x+3) is a factor of (2x+5)^9 + (3x+k)^3
2) How can i find the value of k of (3x^k - 7x^2 +15) / (x-2) and has a remainder of 11.
-
1)
f(x) = (2x+5)⁹ + (3x+k)³
(x+3) is a factor of f(x) if f(−3) = 0
(2(−3)+5)⁹ + (3(−3)+k)³ = 0
(−1)⁹ + (−9+k)³ = 0
−1 + (−9+k)³ = 0
(−9+k)³ = 1
−9 + k = 1
k = 10
2)
f(x) = 3x^k − 7x² +15
Since f(x) has remainder of 11 when divided by (x−2), then f(2) = 11
3(2^k) − 7(2)² +15 = 11
3(2^k) − 28 + 15 = 11
3(2^k) − 13 = 11
3(2^k) = 24
2^k = 8
2^k = 2^3
k = 3
f(x) = (2x+5)⁹ + (3x+k)³
(x+3) is a factor of f(x) if f(−3) = 0
(2(−3)+5)⁹ + (3(−3)+k)³ = 0
(−1)⁹ + (−9+k)³ = 0
−1 + (−9+k)³ = 0
(−9+k)³ = 1
−9 + k = 1
k = 10
2)
f(x) = 3x^k − 7x² +15
Since f(x) has remainder of 11 when divided by (x−2), then f(2) = 11
3(2^k) − 7(2)² +15 = 11
3(2^k) − 28 + 15 = 11
3(2^k) − 13 = 11
3(2^k) = 24
2^k = 8
2^k = 2^3
k = 3