5*r**3 + 183*r**2. Factor v(n).
2*(n + 105)**2/3
Factor 18/7*k - 32/7 - 1/7*k**2.
-(k - 16)*(k - 2)/7
Let v(i) = i**5 - 5*i**4 - 28*i**3 + 22*i**2 + 40*i - 4. Let j(m) = 2*m**5 - m**3 - m**2 + 2. Let u(g) = 2*j(g) + v(g). Factor u(w).
5*w*(w - 2)**2*(w + 1)*(w + 2)
Determine w, given that 20*w**3 - 8*w**4 - 24*w**4 - 178*w**2 - w**5 - 239*w + 119*w**3 + 311*w = 0.
-36, 0, 1, 2
Let o(r) be the first derivative of -r**5/60 - r**4/8 - 12*r**2 - 20. Let i(w) be the second derivative of o(w). Let i(s) = 0. What is s?
-3, 0
Let w = 3264 + -2132. Factor 4*x - 1130*x**3 + w*x**3 + 6*x**2 + 0*x**2.
2*x*(x + 1)*(x + 2)
Factor 18/5*n**2 - 6*n - 2/5*n**3 - 10.
-2*(n - 5)**2*(n + 1)/5
Solve 75*a**2 - 315*a**3 - 5*a + 245*a**4 - 4075 + 4075 = 0 for a.
0, 1/7, 1
Suppose -5*m + u + 3 = 0, -72 + 81 = -5*m - 3*u. Factor 0 + 0*t**2 + m*t + 1/4*t**3.
t**3/4
Let c = -619 - -619. Let k(m) be the second derivative of c*m**3 + 1/15*m**6 - m + 1/3*m**4 + 0*m**2 - 3/10*m**5 + 0. Suppose k(x) = 0. What is x?
0, 1, 2
Let z be 3/7 - (-242)/154. Factor 8*q**3 - 7*q**2 - 11*q**z - 24 - 45*q - 5*q**3.
3*(q - 8)*(q + 1)**2
Let h = 127 - 133. Let z be (-8)/4*(h - -5). Factor 2/3*x**z - 8/3 + 0*x.
2*(x - 2)*(x + 2)/3
Let k(a) = a**3 - 9*a + 3. Let z be k(-3). Determine g, given that -16*g**4 + z*g**2 - 12*g**3 + 4 - 3 + 17*g**2 - 5 + 12*g = 0.
-1, 1/4, 1
Suppose -4061*a + 324*a**2 - 4*a**3 - 2252 + 2830 - 2335*a - 7302 = 0. Calculate a.
-1, 41
Suppose -4*k + 184 = 16. Factor -k*b**5 + 86*b**5 - 42*b**5.
2*b**5
Factor -46*r**3 + 28*r**3 - 195*r - 60*r**3 - 3*r**4 - 627*r**2 - 1257*r.
-3*r*(r + 4)*(r + 11)**2
Suppose 4*i = -46 + 146. Suppose -2*k = 10, 2*t - k - i = 2*k. Factor -p**t + 2*p**2 - 3*p**2 + 2*p**3 + p**3 - p**2.
-p**2*(p - 1)**2*(p + 2)
Let o(d) = -d**2 + 13*d + 15. Let r be o(14). Let j be r + (-3)/6 + 0. Factor -1/2*k**3 + 0 - j*k**2 + 1/2*k + 1/2*k**4.
k*(k - 1)**2*(k + 1)/2
Let f = 4117/10295 + 1/10295. Determine i so that -8/5*i**2 - 6/5*i + 0 + 4/5*i**3 + f*i**5 + 8/5*i**4 = 0.
-3, -1, 0, 1
Let c = 1427/15 + -95. Factor 2/3*v - 8/15 - c*v**2.
-2*(v - 4)*(v - 1)/15
Let h(q) be the third derivative of q**9/60480 - q**8/6720 + q**6/180 - 13*q**5/60 - 11*q**2. Let m(r) be the third derivative of h(r). Let m(c) = 0. What is c?
-1, 2
Suppose 2*h = 63 - 53. Let a be 282/54 - (-4)/(-18) - h. Factor -2/11*y**3 + 0*y + a + 4/11*y**2.
-2*y**2*(y - 2)/11
Suppose 6*f - f = 5. Let d(x) = -x - 1. Let v(n) = -12*n**2 - 6*n - 21. Let c(j) = f*v(j) - 18*d(j). Determine u so that c(u) = 0.
1/2
Solve 32*g**3 + 26*g**3 - 3*g**5 - 6*g**4 - 17*g**5 - 2*g**2 - 46*g**3 = 0 for g.
-1, 0, 1/5, 1/2
Suppose 19*x - 59 = 36. Let z(y) be the third derivative of 1/30*y**4 + 3*y**2 + 0*y**3 + 1/300*y**6 + 1/50*y**x + 0 + 0*y. Let z(d) = 0. Calculate d.
-2, -1, 0
Let t(g) be the third derivative of g**9/30240 - g**8/10080 - 2*g**5/5 + 7*g**2. Let u(o) be the third derivative of t(o). Solve u(x) = 0 for x.
0, 1
Let s(v) = 6*v**2 - 5*v - 18. Let b(x) = 10*x**2 - 18*x**2 + 6*x**2 + 2*x + 6. Let t(q) = -14*b(q) - 4*s(q). Suppose t(k) = 0. What is k?
-1, 3
Let n(w) be the third derivative of 0 - 8/21*w**3 - 1/35*w**5 + 32*w**2 - 1/420*w**6 + 5/28*w**4 + 0*w. Solve n(i) = 0 for i.
-8, 1
Let z be ((-4)/(-6))/((-12)/(-18)). Let y(w) = -w + 1. Let j be y(-1). Find f such that 5 - j*f**3 - z - 6*f - 1 - 5 - 6*f**2 = 0.
-1
Let a = -10 + 30. Find j such that -4 + a*j**2 + 7 - 23*j**2 = 0.
-1, 1
Let k(o) be the third derivative of o**5/36 - 2*o**2 + 219*o. Factor k(n).
5*n**2/3
Let s(r) be the first derivative of -7/9*r**2 - 20/9*r - 1 - 2/27*r**3. Factor s(a).
-2*(a + 2)*(a + 5)/9
Let a(g) be the first derivative of g**5/300 - g**4/10 + 6*g**3/5 - 33*g**2/2 + 9. Let z(u) be the second derivative of a(u). Solve z(w) = 0.
6
Let c be (-1)/(5/(-2) - -2). Suppose 130*w - 158*w = -84. Suppose 10/7*s**c - 18/7 + 2/7*s**w + 6/7*s = 0. What is s?
-3, 1
Let z(v) = 1. Let c(j) = j**2 - j - 6. Let f(r) = -c(r) - 6*z(r). Let o be f(0). Factor 0 + 1/5*w**3 + 1/5*w**4 + o*w**2 + 0*w.
w**3*(w + 1)/5
Suppose 2*n**3 - 4 + 7*n - 6*n**2 - 3*n - 2*n**2 + 6*n = 0. Calculate n.
1, 2
Let x(o) = 20*o**3 - 416*o**2 + 624*o - 32. Let i(r) = 3*r**3 - 64*r**2 + 96*r - 5. Let n(h) = -32*i(h) + 5*x(h). Solve n(j) = 0 for j.
0, 2, 6
Let g(j) be the third derivative of 1/1344*j**8 + 0*j**4 + 1/480*j**6 + 0 - 27*j**2 + 0*j**5 + 1/420*j**7 + 0*j**3 + 0*j. Find k such that g(k) = 0.
-1, 0
Factor 1/4*c**3 + 17/4*c + 0 + 9/2*c**2.
c*(c + 1)*(c + 17)/4
Suppose 2 = 2*r - w, -4*w + 22 = r + 3. Let h be (1*r)/(5/(10/3)). Suppose 0 - 1/4*n**3 + 1/2*n**h - 1/4*n = 0. What is n?
0, 1
Let z(b) be the second derivative of 0*b**2 + 1/189*b**7 + 0*b**3 + 1/135*b**6 + 8*b + 0*b**5 + 0 + 0*b**4. Factor z(r).
2*r**4*(r + 1)/9
Let m = -183/35 + 38/7. Suppose 1/5 + 3/5*s**2 - 3/5*s - m*s**3 = 0. Calculate s.
1
Suppose 13 = q + 4*a + 2, q + a - 5 = 0. Factor 12/5*t + 18/5*t**q + 3/5*t**4 + 0 + 27/5*t**2.
3*t*(t + 1)**2*(t + 4)/5
Let i(l) be the first derivative of -55/3*l**3 - 30*l + 5/2*l**4 + 14 + 85/2*l**2. Suppose i(m) = 0. What is m?
1/2, 2, 3
Factor 1229*y**2 - 1226*y**2 + 12*y - 4 - 11.
3*(y - 1)*(y + 5)
Let q = 547323 - 3837481/7. Let j = q + 890. Suppose -j*p - 6/7*p**2 - 4/7 = 0. Calculate p.
-1, -2/3
Let d(j) be the third derivative of j**8/224 - 3*j**7/28 + 15*j**6/16 - 25*j**5/8 + 20*j**2 + j. Determine v, given that d(v) = 0.
0, 5
Let k(z) be the first derivative of -8*z**2 + 2/3*z**3 - 46 + 24*z. Solve k(n) = 0 for n.
2, 6
Let x(l) be the second derivative of l**4/3 - 4*l**3 + 18*l**2 - 7*l. Let d(u) = 2*u**2 - 12*u + 18. Let o(q) = -5*d(q) + 2*x(q). Factor o(k).
-2*(k - 3)**2
Let g = 17/29 - 605/1131. Let j(d) be the first derivative of -g*d**3 + 0*d**2 - 1 + 2/13*d. Factor j(a).
-2*(a - 1)*(a + 1)/13
Suppose -22*u = -16*u. Suppose a - 3*c - 9 = 0, -2*a + 5*c = -u*c - 15. Find m such that -3/5*m**4 + a + 9/5*m**3 - 9/5*m**2 + 3/5*m = 0.
0, 1
Let 0 - 12*h**2 - 10*h - 9/2*h**3 - 1/2*h**4 = 0. What is h?
-5, -2, 0
Let h(m) be the first derivative of m**3/5 + 12*m**2/5 + 48*m/5 + 67. Solve h(b) = 0 for b.
-4
Suppose 5*j = 8*j - 6. Factor -4*l + 8*l**j + 35 - 25*l**2 + 12*l**2 - 26*l.
-5*(l - 1)*(l + 7)
Let z(k) = -9*k**3 + 5*k**2 + 5*k - 9. Let q(g) = -19*g**3 + 10*g**2 + 10*g - 19. Let t = -22 + 31. Let c(b) = t*z(b) - 4*q(b). Let c(f) = 0. What is f?
-1, 1
Let d(t) = -19*t**3 + 23*t**2 - 48*t. Let o(b) = 9*b**3 - 12*b**2 + 24*b. Let j(u) = 6*d(u) + 13*o(u). Let j(q) = 0. Calculate q.
0, 2, 4
Let u(p) = -p + 5. Let o be u(-10). Suppose -4*m - 4*v = -7*v - 12, 2*v = -5*m + o. Let -93 + 93 - a**2 - a**4 + 2*a**m = 0. What is a?
0, 1
Let a(f) be the third derivative of 1/105*f**6 + 18*f**2 + 0 - 1/30*f**5 + 1/42*f**4 + 0*f + 4/735*f**7 + 0*f**3. Find l, given that a(l) = 0.
-2, 0, 1/2
Let v(d) be the second derivative of -d**6/15 + 7*d**5/10 + 3*d**4/2 - 7*d**3/3 - 8*d**2 + 60*d. Find z, given that v(z) = 0.
-1, 1, 8
Factor -63/2*i - 54 - 23/8*i**3 + 39/2*i**2 + 1/8*i**4.
(i - 12)*(i - 6)**2*(i + 1)/8
Let b(s) be the second derivative of 5/3*s**4 + 0 + 0*s**2 + 0*s**3 - 15*s - s**5 - 1/2*s**6. Determine y, given that b(y) = 0.
-2, 0, 2/3
Let w be -7 - (520/(-90) - 4) - 6/(-27). Determine g, given that 6*g**2 + 60/7*g + 9/7*g**w + 24/7 = 0.
-2, -2/3
Let b(k) be the third derivative of -5*k**5/3 + 235*k**4/3 - 4418*k**3/3 - 7*k**2 + 11*k. Determine s so that b(s) = 0.
47/5
Suppose 72/5 + 46/5*x**3 - 4/5*x**4 - 96/5*x - 118/5*x**2 = 0. What is x?
-1, 1/2, 6
Suppose 2/5*h**3 - 24/5 + 6/5*h**2 - 8/5*h = 0. What is h?
-3, -2, 2
Suppose 4*b - 26 = -4*u + 14, u - 14 = -3*b. Suppose 0 = 5*m - 3*m - u. Factor 5*k**3 - 7*k**m + 0*k**4 - 61*k + 65*k + 16*k**2.
-k*(k - 2)*(k + 1)*(7*k + 2)
Let h be ((-42)/(-18) - -2)*(-3)/(-5). Let a = h - 29/15. Find r such that 6 + a*r**2 + 4*r = 0.
-3
Let r(c) be the second derivative of -c**6/30 - 22*c**5/5 - 923*c**4/6 + 660*c**3 - 2025*c**2/2 - 42*c + 2. Factor r(d).
-(d - 1)**2*(d + 45)**2
Let k(v) be the second derivative of 5*v**4/12 + 10*v**3/3 - 25*v**2/2 - 36*v. Solve k(o) = 0.
-5, 1
Determine z, given that -6 + 2/3*z**2 - 16/3*z = 0.
-1, 9
Determine w so that w**5 + 8/5*w**4 - 2/5*w**2 + 0*w + 0 + 1/5*w**3 = 0.
-1, 0, 2/5
Let c(o) be the third derivative of 0*o - 5/84*o**6 + 3/35*o**5 - 5/2352*o**8 + 0 + 0*o**3 +