n(r).
r**2*(r + 1)**3
Suppose -17*x + 0 = -0 - 0. Determine n so that -8/9*n**3 + x - 2/9*n**4 + 2/9*n**2 + 0*n + 8/9*n**5 = 0.
-1, 0, 1/4, 1
Let f(a) be the second derivative of a**4/3 + 10*a**3/3 + 12*a**2 + 61*a. Factor f(k).
4*(k + 2)*(k + 3)
Let a = -212 + 214. Let v(h) be the third derivative of 13/180*h**5 + 1/630*h**7 + 0*h + 1/60*h**6 + h**a + 0 + 1/6*h**4 + 2/9*h**3. Let v(q) = 0. Calculate q.
-2, -1
Let r = -15857/5 + 3173. Let 2/5*a**4 + 6/5*a**2 - 8/5*a + r*a**3 - 8/5 = 0. Calculate a.
-2, -1, 1
Suppose 5*u - 3*f = 3*u + 3, -4*u + 41 = f. Let s be u - (8 + -4) - 2. Factor -2*m - m**2 + 6*m**2 + 2*m**s - 5*m**4 + 0*m**2 + 0*m**2.
-m*(m - 1)*(m + 1)*(5*m - 2)
Let f(h) be the first derivative of h**5/20 - 61*h**4/16 + 899*h**3/12 + 961*h**2/8 - 647. What is p in f(p) = 0?
-1, 0, 31
Let f be (32/(-80))/((-1)/10). Suppose -6*q**3 + 0*q + 9*q**3 + f*q**5 - 4*q - 16*q**2 + 13*q**4 = 0. Calculate q.
-2, -1/4, 0, 1
Suppose 3*c + k = -k + 14, -c - 5*k + 9 = 0. Suppose -2*i = -c - 0. Suppose -4*p + i - 1/2*p**3 + 5/2*p**2 = 0. What is p?
1, 2
Let o = -57 - -57. Suppose o*h = 2*h + 2*h. Let 2/7*k**2 - 4/7*k + h = 0. What is k?
0, 2
Let x(v) be the first derivative of 2*v**3/21 + 5*v**2/7 - 4*v - 127. Factor x(l).
2*(l - 2)*(l + 7)/7
Suppose 0 = -3*y + 18 + 33. Suppose -8*v**2 - 2 + y*v + 0*v**2 - 4*v**2 - 6*v - v**3 + 4*v**4 = 0. Calculate v.
-2, 1/4, 1
Let u(d) be the second derivative of 1/27*d**3 + 2/9*d**2 - 1/54*d**4 + 7*d + 0. Factor u(v).
-2*(v - 2)*(v + 1)/9
Let h = 19427/7 - 2775. Suppose 0 + h*w**2 + 2/7*w = 0. What is w?
-1, 0
Let c(w) be the second derivative of -w**5/10 - 3*w**4/4 - 2*w**3 - 5*w**2/2 + 2*w - 37. Factor c(g).
-(g + 1)**2*(2*g + 5)
Let x(a) = -4*a - 71 + 67 + 2*a**4 + a**4 - a**3 + 6*a**2. Let r(h) = 4*h**4 - h**3 + 7*h**2 - 5*h - 5. Let t(w) = -4*r(w) + 5*x(w). Let t(p) = 0. Calculate p.
-2, 0, 1
Let n = 21 - 18. Suppose r = 4*v - 17, 0 = -n*v - 5*r - 17 + 1. Factor 4*k + v*k**2 + k**2 + 24 + 12 + 20*k.
4*(k + 3)**2
Let p(k) be the first derivative of 5*k**3/3 - 15*k**2/2 - 227. Factor p(a).
5*a*(a - 3)
Suppose 2*l - 6*a = -8*a + 6, -4*a = -3*l - 12. Suppose 2*r + 2 - 8 = l. What is i in -4*i**2 + 4*i - 8/7 + 8/7*i**r = 0?
1/2, 1, 2
Let s(h) be the second derivative of 5*h**4/12 + 4*h**3/3 - 2*h**2 - 2*h + 23. Factor s(j).
(j + 2)*(5*j - 2)
Let y(p) be the first derivative of 49*p**4/9 - 476*p**3/27 - 160*p**2/9 - 16*p/3 - 252. Find b such that y(b) = 0.
-2/7, 3
Let i(w) be the third derivative of -w**6/220 - w**5/15 - 7*w**4/132 - 17*w**2 - 4*w. Factor i(f).
-2*f*(f + 7)*(3*f + 1)/11
Let z(a) be the second derivative of -a**7/1050 - a**6/200 - a**5/150 - 3*a**2 + 11*a. Let s(q) be the first derivative of z(q). Factor s(v).
-v**2*(v + 1)*(v + 2)/5
Let g(t) be the third derivative of 5*t**5/12 - 335*t**4/24 + 65*t**3/3 + 180*t**2. Factor g(c).
5*(c - 13)*(5*c - 2)
Let m be ((-9)/(-8))/(21/126). Let y = m - 21/4. Find x such that 1/6 + x + y*x**2 = 0.
-1/3
Let q(s) be the first derivative of -10/3*s**3 + 0*s - 5/4*s**4 + 0*s**2 + 11. Factor q(f).
-5*f**2*(f + 2)
Let s be (4/(-6))/(4/39948*-10). Let b = s - 655. Find a such that -2/5*a**2 - 36/5*a**4 - 2/5 + b*a**3 - 14/5*a = 0.
-1/3, -1/6, 1
Let n(p) be the second derivative of p**7/189 + 7*p**6/135 - 3*p**5/10 + 29*p**4/54 - 10*p**3/27 - p + 10. Factor n(q).
2*q*(q - 1)**3*(q + 10)/9
Let p be 6/15 - (-5781)/1485. Let a = -37/9 + p. Solve 2/11*s**2 - a*s + 0 = 0.
0, 1
Let d(g) be the third derivative of g**7/1470 - g**6/105 - g**5/30 + g**3/6 + 7*g**2. Let u(l) be the first derivative of d(l). Solve u(o) = 0.
-1, 0, 7
Let 2943*p - 5*p**3 + 948*p**2 + p**3 - 49324*p + 1972156 - 28511*p = 0. Calculate p.
79
Let k(o) = 179*o**2 + 461*o - 21. Let g(w) = 88*w**2 + 230*w - 10. Let j(c) = 18*g(c) - 8*k(c). Factor j(m).
4*(m + 3)*(38*m - 1)
Let d(t) = -70*t - 420. Let z be d(-6). Suppose -j**4 + 0*j + 0*j**2 + z - 1/5*j**5 - 6/5*j**3 = 0. Calculate j.
-3, -2, 0
Let g be 34/10 - 27/(-45). Let f(m) be the first derivative of -g + 0*m - 1/3*m**2 + 2/9*m**3. Let f(q) = 0. What is q?
0, 1
Let j(q) = 98*q**4 - 214*q**3 + 168*q**2 - 56*q - 6. Let b(k) = -k**4 + k + 1. Let g(f) = 10*b(f) + j(f). Let g(i) = 0. Calculate i.
2/11, 1/4, 1
Suppose -2*g + 4*d = 0, -2*g = -2*d + d. Let k(v) be the first derivative of -3 + 0*v - 1/3*v**3 + g*v**2. Suppose k(n) = 0. What is n?
0
Let f(h) = -5*h + 3. Let j be f(4). Let n = -14 - j. What is x in -3*x**n + 2*x**2 + x**2 + 0*x**3 = 0?
0, 1
Let a(r) be the second derivative of -r**9/3024 - r**8/672 + r**7/504 + r**6/72 + 5*r**4/12 + 5*r. Let u(l) be the third derivative of a(l). Factor u(d).
-5*d*(d - 1)*(d + 1)*(d + 2)
Let y be 171/114*10/3. Let q(r) be the third derivative of 0 + 1/15*r**y - 1/12*r**4 + 0*r - 1/60*r**6 + 0*r**3 + 6*r**2. Factor q(n).
-2*n*(n - 1)**2
Let y = 822 - 820. Let b(g) be the third derivative of 0*g - 1/8*g**4 + 0*g**3 - 1/20*g**5 + y*g**2 + 0. Factor b(w).
-3*w*(w + 1)
Suppose 48/19 - 20/19*p - 2/19*p**2 = 0. What is p?
-12, 2
Let y = 35167/9 - 3907. Find m, given that -2/9*m + 0*m**2 - 2/9*m**5 + 0 + y*m**3 + 0*m**4 = 0.
-1, 0, 1
Let x(s) be the third derivative of -s**10/90720 - s**9/45360 + s**8/10080 + s**4 - 17*s**2. Let m(j) be the second derivative of x(j). Factor m(b).
-b**3*(b - 1)*(b + 2)/3
Let d be 6/(-4)*6/9. Let h(f) = -f**5 + f**4 + f**2 - f + 1. Let g(j) = 5*j**5 - j**4 + 3*j**3 - 3*j**2 + 4*j - 4. Let t(a) = d*g(a) - 4*h(a). Factor t(c).
-c**2*(c + 1)**3
Let d be (-12)/10*(-15)/6. What is i in 12*i**d - 5*i**5 - 19*i**4 + 24*i**4 - 2*i**3 = 0?
-1, 0, 2
Let c(q) be the third derivative of -q**5/12 - 124*q**2. Factor c(r).
-5*r**2
Let o(f) be the second derivative of f + 1/60*f**6 - 1/3*f**4 - 4/3*f**3 - 1/2*f**2 + 1/30*f**5 + 0. Let j(m) be the first derivative of o(m). Factor j(b).
2*(b - 2)*(b + 1)*(b + 2)
Let q = -13/17 - -103/68. Let w(m) be the first derivative of -3/8*m**4 + 3 + 3/20*m**5 - q*m**3 - 3*m + 3*m**2. Suppose w(c) = 0. Calculate c.
-2, 1, 2
Let q(s) = 15*s**4 + 210*s**3 - 15*s**2 - 160*s + 50. Let i(r) = 2*r**4 + 26*r**3 - 2*r**2 - 20*r + 6. Let f(p) = -25*i(p) + 3*q(p). What is b in f(b) = 0?
-4, -1, 0, 1
Let o be (-6)/(-7)*(-196)/(-42). Suppose 24*n - 18*n**3 + 5*n**2 - 3*n**5 - 11*n**4 - 4*n**2 + 11*n**2 - 4*n**o = 0. Calculate n.
-2, 0, 1
Let q(x) be the first derivative of x**4/26 - 16*x**3/39 - 20*x**2/13 + 124. Factor q(m).
2*m*(m - 10)*(m + 2)/13
Solve 0*t - 2/7*t**4 + 4/7*t**3 + 0*t**2 - 2/7*t**5 + 0 = 0 for t.
-2, 0, 1
Let b(g) = g**2 - g - 1. Let p(t) = -t**3 + 5*t**2 - 7*t + 10. Let w be p(4). Let k(s) = -s**4 + 2*s**3 - s - 1. Let a(y) = w*b(y) + 2*k(y). Factor a(i).
-2*i**2*(i - 1)**2
Let b be (-18 + 16)*(-1)/14*10. Factor -b*n**3 + 0 + 12/7*n**2 - 2/7*n.
-2*n*(n - 1)*(5*n - 1)/7
Let o(f) be the second derivative of f**6/90 - f**5/30 - f**4/3 + 5*f**3/3 - 7*f. Let a(y) be the second derivative of o(y). Factor a(b).
4*(b - 2)*(b + 1)
Let x(k) be the first derivative of k**5/10 + 5*k**4/8 + 7*k**3/6 + 3*k**2/4 - 178. Find w such that x(w) = 0.
-3, -1, 0
Let c = 72/595 - -14/85. Find s such that 4/7*s**3 + 0 + 0*s**4 - 2/7*s - c*s**5 + 0*s**2 = 0.
-1, 0, 1
Let c(r) = -r**3 + 6*r**2 + 3*r - 15. Let p be c(6). Determine s, given that 4 - 5*s + s + 2*s**p - 7*s**4 - 3*s**2 + 8*s**4 = 0.
-2, 1
Let o = -12964 + 12964. Factor 0 - 5/6*z**2 + o*z.
-5*z**2/6
Let q(f) = -f**3 + 3*f**2 + 3*f + 2. Let k be q(4). Let g = k + 4. Factor 3 + 3 - 4*b**2 - 9*b + b**g - 3*b**4 + 3*b**3 + 6*b**3.
-3*(b - 2)*(b - 1)**2*(b + 1)
Let l(r) be the first derivative of r**6/40 + 3*r**5/40 - 3*r**4/16 - 19*r - 36. Let z(h) be the first derivative of l(h). Factor z(c).
3*c**2*(c - 1)*(c + 3)/4
Factor 45*h**4 - 5794*h + 5794*h - 215*h**3 - 50*h**2.
5*h**2*(h - 5)*(9*h + 2)
Let r(q) be the second derivative of 1/60*q**5 + 0 + 9*q - 2/3*q**3 + 7/2*q**2 + 0*q**4. Let k(c) be the first derivative of r(c). Factor k(f).
(f - 2)*(f + 2)
Let c be 16*(2 - (-2 + 3)). Factor 13*g**3 - 2*g**4 - 27*g**3 + c*g**3.
-2*g**3*(g - 1)
Factor 1521/5 + 10491/10*z + 7/10*z**3 - 272/5*z**2.
(z - 39)**2*(7*z + 2)/10
Let g(s) = 83*s + 3. Let k be g(1). Suppose -k*j + 3*j**2 - 82*j + 9 + 156*j = 0. What is j?
1, 3
Let g(r) be the first derivative of -r**4/12 - 46*r**3/3 - 1058*r**2 - 97336*r/3 + 110. Solve g(d) = 0 for d.
-46