 + 6389*j**2 + 1 + 5*j - 6390*j**2.
-(j - 9)*(j + 1)
Let a(h) be the first derivative of h**5/20 - 5*h**4/8 + 2*h**3 - 19*h**2 - 15. Let c(k) be the second derivative of a(k). Solve c(t) = 0.
1, 4
Let k(p) be the first derivative of p**6/2 + 9*p**5/5 - 4*p**3 + 325. Factor k(u).
3*u**2*(u - 1)*(u + 2)**2
Factor 3/2*f**5 + 39/2*f**4 + 36 + 123*f + 171/2*f**3 + 309/2*f**2.
3*(f + 1)**3*(f + 4)*(f + 6)/2
Let h(c) be the second derivative of -c**6/30 - 17*c**5/20 - 20*c**4/3 - 32*c**3/3 - 278*c. Suppose h(u) = 0. What is u?
-8, -1, 0
Let n be -6*(4*(-4)/(-32))/(-1). Determine j so that -9*j**3 + 4*j**2 - 1 + 11*j**n - 2*j - 3 = 0.
-2, -1, 1
Let b = 305/299 - 11/13. Let k = 110/161 + b. Factor -8/7*s - 2/7 - k*s**2.
-2*(s + 1)*(3*s + 1)/7
Suppose q + 3*x = -3, 1 = -4*q - 136*x + 135*x. Factor 2/3*c + q + 2/9*c**2.
2*c*(c + 3)/9
Suppose -4*u - 188 = 3*k, 4*k + 69 = 4*u - 135. Let l = k + 60. Determine t so that -6*t**3 - 6 + 21/2*t**2 - 9/2*t**l + 6*t = 0.
-2, -1, 2/3, 1
Suppose 4*z**2 + 56/3*z - 2/3*z**4 + 16 - 2*z**3 = 0. What is z?
-2, 3
Determine j, given that 5*j**2 + 42*j + 25 + 0*j + 3*j - 12*j - 3*j = 0.
-5, -1
Let k(l) = 4*l**4 - 7*l**3 - 3*l + 3. Let c(n) = 3*n**4 - 6*n**3 + n**2 - 2*n + 2. Let s(q) = 3*c(q) - 2*k(q). Suppose s(v) = 0. What is v?
0, 1, 3
Let n(f) be the second derivative of -f**7/210 - f**6/150 + 3*f**5/50 - f**4/30 - f**3/6 + 3*f**2/10 + 802*f. Suppose n(j) = 0. What is j?
-3, -1, 1
Let b be (2 - 1)/((-2)/(-252)*2). Factor 61 + 0*y - b + y**2 - y.
(y - 2)*(y + 1)
Solve 2*l + 8/9 - 5/9*l**2 = 0 for l.
-2/5, 4
Let g = -165 - -833/5. Let a = 31/10 - g. Find s, given that a*s + 0*s**2 + 1 - 1/2*s**3 = 0.
-1, 2
Let v(j) = j**3 + j**2 - 2*j - 1. Let b(s) = 16*s**3 - 64*s**2 + 232*s - 252. Let h(k) = b(k) - 12*v(k). Suppose h(w) = 0. Calculate w.
2, 15
Let k(q) be the third derivative of -q**10/1512 + 5*q**9/1008 + q**8/336 + q**4/24 + 7*q**3/3 - 52*q**2. Let z(m) be the second derivative of k(m). Factor z(b).
-5*b**3*(b - 4)*(4*b + 1)
Let j(f) be the first derivative of 3*f**4/28 - 6*f**3/7 + 27*f**2/14 - 12*f/7 - 14. What is w in j(w) = 0?
1, 4
Let y be (9*(-5)/(-270))/(5/(-3))*-8. Solve -1/5*q**3 + y - 3/5*q**2 + 0*q = 0 for q.
-2, 1
Suppose -3*q + 11 = -g + 2, 0 = 4*q + 2*g - 12. Let f(i) be the first derivative of 3*i**q - 3/4*i**4 + 0*i - 3*i**2 + 1. Find y, given that f(y) = 0.
0, 1, 2
Let z(d) be the third derivative of -d**6/30 + d**5/20 - d**4/12 + 12*d**2. Let w(h) = h**4 + h**3 + h. Let u(v) = 3*w(v) + 3*z(v). Factor u(k).
3*k*(k - 1)**3
Suppose 73 = 8*d + 25. Let o be (10/d)/(-5)*(-6)/8. Factor -o*g**2 + 3/4 - 1/2*g.
-(g - 1)*(g + 3)/4
Let n(i) be the second derivative of -11*i - 1/90*i**4 + 8/45*i**3 - 16/15*i**2 + 0. Solve n(t) = 0.
4
Suppose -16 = u + 2*w, -4*u - 2*w + 145 = 161. Factor j + u - 1/2*j**2.
-j*(j - 2)/2
Let q(b) be the first derivative of 1/9*b**3 + 0*b**2 - 7/36*b**6 + 9 - 1/8*b**4 - 2/5*b**5 + 0*b. Suppose q(n) = 0. What is n?
-1, 0, 2/7
Let q(i) = 37*i**4 + 5 - 36*i**4 + i**2 - 4. Let c(h) = -3*h**4 - 40*h**3 - 131*h**2 - 160*h - 63. Let a(y) = c(y) - q(y). Factor a(x).
-4*(x + 1)**2*(x + 4)**2
Find k such that 24/11*k**2 + 6/11*k**5 + 60/11*k**3 + 34/11*k**4 - 16/11*k + 0 = 0.
-2, 0, 1/3
Let u = 860 + -857. Let f(y) be the first derivative of -6 + 4/9*y**u + 2/45*y**5 + 2/9*y**4 + 4/9*y**2 + 2/9*y. Factor f(g).
2*(g + 1)**4/9
Let x(s) = s**2 - s. Let q(t) = 7*t**2 - 59*t + 20. Let o(z) = -q(z) - 5*x(z). Let o(l) = 0. What is l?
1/3, 5
Suppose -3*o + 96 = -3*j, 2*o - 4*j - 23 = 37. Determine x, given that -o*x**4 + 28*x**4 + 3*x**5 - 9*x**3 + x + 11*x + 12*x**2 = 0.
-1, 0, 2
Suppose -4*u + r - 296 = -0*r, 3*u = 3*r - 231. Let w = 75 + u. Factor -3*l**4 + 0*l**w + 3/2*l**3 + 0 + 3/2*l**5 + 0*l.
3*l**3*(l - 1)**2/2
Let m(v) be the second derivative of v**4/4 - 11*v**3/2 - 18*v**2 + 69*v. Factor m(x).
3*(x - 12)*(x + 1)
Let q(l) = 2*l**2 - 7*l + 3. Let i(t) = 2*t**2 - 7*t + 3. Let p(z) = -4*i(z) + 3*q(z). Let g be p(3). Let -o**2 + g + 0*o - 1/2*o**3 = 0. What is o?
-2, 0
Suppose 990 = -24*t + 27*t. Let h = t + -327. Factor 6/5*q - 3/5*q**h + 0 - 3/5*q**2.
-3*q*(q - 1)*(q + 2)/5
Let m(q) = -9*q**2 - 1167*q - 34596. Let i(d) = -3*d**2 - 390*d - 11532. Let g(r) = -17*i(r) + 6*m(r). Let g(n) = 0. What is n?
-62
Let h = -89437 + 2950913/33. Let b = -44/3 - h. Suppose 2/11*k**3 + b*k - 6/11*k**4 + 16/11*k**2 + 0 = 0. Calculate k.
-1, -2/3, 0, 2
Let b(n) = -32*n**2 + 4*n - 38. Let r be b(-5). Let v be r/(-221) - 4/(-34). Determine s, given that -2/3*s + 1/3 - 1/3*s**v + 2/3*s**3 + 0*s**2 = 0.
-1, 1
Let c(v) be the second derivative of 3*v**5/25 + 11*v**4/20 + v**3/2 - 3*v**2/5 + 228*v. Solve c(n) = 0.
-2, -1, 1/4
Suppose 4*a = -54 + 42. Let p be 87/12 + a - 4. Solve -1/2*s**2 + 1/2 - 1/4*s + p*s**3 = 0 for s.
-1, 1, 2
Suppose 0 = k + 4*k + 25. Let g(s) = 6*s**2 - 24*s + 24. Let h(w) = 4*w**2 - 16*w + 16. Let a(j) = k*g(j) + 8*h(j). Suppose a(y) = 0. Calculate y.
2
Factor 10373*c**2 - 1086 - 359 - 170*c - 10378*c**2.
-5*(c + 17)**2
Factor 1/2*b**2 - 15/2*b + 7.
(b - 14)*(b - 1)/2
Let y(p) = 1 + 2*p**3 + 2*p - 44*p**2 - p + 38*p**2. Let f be y(3). Suppose -3/4 + 0*r**2 + 3/4*r**f - 3/2*r + 3/2*r**3 = 0. Calculate r.
-1, 1
Let l(o) = -4*o**2 - 146*o + 150. Let c(r) = 2*r**2 + 72*r - 74. Let m(j) = -5*c(j) - 3*l(j). Factor m(y).
2*(y - 1)*(y + 40)
Let z(s) be the second derivative of -1/24*s**4 + 0 + 0*s**2 + 11*s + 1/6*s**3. Factor z(b).
-b*(b - 2)/2
Let s(t) be the first derivative of 50*t**3/21 - 40*t**2/7 + 32*t/7 - 24. Suppose s(m) = 0. Calculate m.
4/5
Let x(n) be the third derivative of 0 + 1/240*n**5 + 0*n + 0*n**3 + 14*n**2 + 1/96*n**4. Determine w, given that x(w) = 0.
-1, 0
Let n be 4/(-38) + (-111)/((-18981)/1386). Factor -28/3*d - 4/3*d**2 - n.
-4*(d + 1)*(d + 6)/3
Let x be ((2/24)/(6/16))/((-8)/(-18)). Find i, given that -1/4*i**3 + 1/2*i**2 + 1/4*i - x = 0.
-1, 1, 2
Let p(y) be the second derivative of 3*y**5/20 - 3*y**4 + 10*y**3 - 366*y. Factor p(t).
3*t*(t - 10)*(t - 2)
Let 6*y**5 - 69*y**3 - 35*y**2 + 115*y**4 + 4*y**3 - 21*y**5 = 0. What is y?
-1/3, 0, 1, 7
Let i be 6*12/(-54)*30/(-8). Let m(l) be the third derivative of 1/20*l**i + 0*l - 1/4*l**4 + 0 - 6*l**2 + 1/2*l**3. Solve m(g) = 0 for g.
1
Factor -4*z**2 - 22*z**3 + 11*z**3 - 3*z**3 + 8*z**4.
2*z**2*(z - 2)*(4*z + 1)
Factor h**2 + 2 + 10*h + 5*h**2 + 2*h**2 - 10 - 11*h**2.
-(h - 2)*(3*h - 4)
Let f = -28 + 30. Factor 20*w**4 - 8*w**2 - 25*w**3 - 15*w**f + 8*w + 3*w**2 + 17*w**3.
4*w*(w - 1)*(w + 1)*(5*w - 2)
Let y(t) = t**3. Let a(r) = 21*r**3 + 47*r**2 - 67*r + 4. Let k(c) = -a(c) + 5*y(c). Let k(p) = 0. What is p?
-4, 1/16, 1
Let v(o) = 3*o**2 + 3*o + 2. Let s = 3 + -5. Let d be v(s). Suppose d*z + 4*z**3 + 8*z - 5*z**2 - 5*z**2 - 6*z**2 = 0. What is z?
0, 2
Let s(t) be the first derivative of t**7/420 - t**6/45 + t**5/15 + 35*t**3/3 - 38. Let c(w) be the third derivative of s(w). Find z such that c(z) = 0.
0, 2
Let n = 4 + 0. Suppose -u = -4 + 1. Let -j**2 - 38*j**u + 5*j**2 + 2*j**5 - n*j**4 + 36*j**3 = 0. Calculate j.
-1, 0, 1, 2
Let x = 157 - 109. Find g, given that x - 5*g**3 + 15*g**2 - 48 = 0.
0, 3
Let j be (-12)/(-2) + (8/(-18))/((-278)/(-2919)). Let j - 2/3*n - 2/3*n**2 = 0. Calculate n.
-2, 1
Let n(t) = t**3 - 6*t**2 - 4*t - 10. Let u be n(7). Let f(r) = -r + 14. Let i be f(u). Factor 9*c**3 + i*c**3 + 10*c**2 - 18*c**2.
4*c**2*(3*c - 2)
Let c(x) be the second derivative of -x**6/72 + x**5/12 + 7*x**3/6 - 3*x. Let p(w) be the second derivative of c(w). Factor p(v).
-5*v*(v - 2)
Let m(h) be the third derivative of h**7/168 + h**6/12 + 3*h**5/8 + 5*h**4/6 - 2*h**3 + 10*h**2. Let y(s) be the first derivative of m(s). Factor y(i).
5*(i + 1)**2*(i + 4)
Let w(v) = -11*v**3 + 28*v**2 - v - 40. Let j(y) = -23*y**3 + 54*y**2 - 3*y - 80. Let z(m) = 6*j(m) - 13*w(m). Determine u, given that z(u) = 0.
-1, 1, 8
Let p(a) be the third derivative of -a**6/1080 + a**5/360 + a**4/12 + a**3 + 10*a**2. Let l(o) be the first derivative of p(o). Factor l(c).
-(c - 3)*(c + 2)/3
Let b(p) = -p**2 + 51*p - 72 - 62 - 7. Let l(w) = -2*w**2 + 154*w - 422. Let u(f) = 10*b(f) - 3*l(f). Suppose u(r) = 0. Calculate r.
6
Let a(m) be the second derivative of -2/3*m**2 + 0 - 1/54*m**4 - 5/27*m**3 + 3*m. Find f, given that a(f) = 0.
-3, -2
Determine f, g