(l + 5)
Let k = 1071 - 1069. Let u(q) be the first derivative of 4/5*q + 7/5*q**k + 9 - 7/10*q**4 - 4/15*q**3. Find t such that u(t) = 0.
-1, -2/7, 1
Let n(j) = -j**3 + 5*j**2 - 2*j + 6. Let q be n(4). Factor m**3 - 6*m**5 + q*m**4 + 2*m**5 - 5*m**3 - 6*m**4.
-4*m**3*(m - 1)**2
Factor -38 - 5*g - 897085*g**3 + 897084*g**3 - 12*g + 20*g**2.
-(g - 19)*(g - 2)*(g + 1)
Factor 38986*c**3 + 2*c - 5*c**4 - 38866*c**3 - 2*c - 115*c**2.
-5*c**2*(c - 23)*(c - 1)
Let r(l) = -201*l**3 + 2*l - 1. Let t be r(1). Let s = t + 815/4. Let 39/4*j - 9/2 + s*j**2 = 0. What is j?
-3, 2/5
Let a(f) be the first derivative of -4 + 1/42*f**4 + 4/63*f**3 - 4/21*f - 1/21*f**2. Suppose a(u) = 0. Calculate u.
-2, -1, 1
Solve -434*i**3 + 176*i + 18 + 336*i**4 + 2*i**2 + 4*i**2 - 70*i - 32*i**5 = 0 for i.
-1/4, 1, 9
Let l(m) be the second derivative of -2*m**7/21 + m**6/9 + 7*m**5/24 + 5*m**4/24 - m**3 + 9*m. Let t(r) be the second derivative of l(r). Factor t(j).
-5*(j - 1)*(4*j + 1)**2
Suppose -y + x + 6 = 0, 5*x - 24 + 27 = -4*y. Let -2/17*n - 6/17*n**y + 20/17*n**2 - 12/17 = 0. Calculate n.
-2/3, 1, 3
Factor -6*r - 4/5*r**2 + 2/5*r**3 + 0.
2*r*(r - 5)*(r + 3)/5
Let g = -6 + 22. Let j(q) = -6*q + 98. Let b be j(g). Factor -1/3*r**3 + 2/3*r**b + 0 - 1/3*r.
-r*(r - 1)**2/3
Let j be -1 + (3 - 5) + -57. Let y be ((-12)/10)/(18/j). Factor y*k**4 - k**2 + 12*k - 13*k - 8*k**3 + 6*k**2.
k*(k - 1)*(2*k - 1)**2
Let a(r) = r**5 + r**4 + r**2 - r + 1. Let n(s) = -4*s**5 - s**4 - 5*s**2 + 4*s - 3. Let q(y) = -3*a(y) - n(y). Factor q(u).
u*(u - 1)**3*(u + 1)
Determine l so that 4 + 15*l**4 - 5*l**2 + 16 + 9*l**3 - 4*l**3 - 5*l**5 + 13*l**2 - 43*l**2 = 0.
-1, 1, 2
Let -3/5*m**5 + 0*m + 0 + 0*m**2 + 18/5*m**3 + 3/5*m**4 = 0. Calculate m.
-2, 0, 3
Let z be (-5)/(-20)*2 + 6/15. Let h(a) be the first derivative of -1/5*a**3 - 4 + z*a**2 - 6/5*a. Factor h(c).
-3*(c - 2)*(c - 1)/5
Let b = -4/13239 + 530542/4413. Let l = -120 + b. Factor l + 4/9*h + 2/9*h**2.
2*(h + 1)**2/9
Suppose -12 = -g - 4*c, 4*c = -5*g - 52 + 128. Let z be 27 - 0*3/12. Factor z*k**4 + g - 76*k**3 - 4*k**5 + 100*k**2 - 21*k + k**4 + 0 - 43*k.
-4*(k - 2)**2*(k - 1)**3
Let s = -688/7 + 3461/35. Find z, given that 0*z + 3/5*z**5 + 1/5*z**2 - s*z**3 - 1/5*z**4 + 0 = 0.
-1, 0, 1/3, 1
Let k(y) = 4*y**2 - 36*y + 24. Let l(q) = q - 1. Let n be -3 + ((-216)/(-16))/(1/2). Let j(d) = n*l(d) + k(d). Factor j(s).
4*s*(s - 3)
Let a = 24 + -3. Let g = -17 + a. Factor 3*l**2 + g*l**3 - 4*l**3 + 3*l**3.
3*l**2*(l + 1)
Factor 3/5*f**2 - 21/5 + 18/5*f.
3*(f - 1)*(f + 7)/5
Let a(f) be the first derivative of -2*f**6/9 - 8*f**5/5 + 128*f**3/9 - 12. Factor a(p).
-4*p**2*(p - 2)*(p + 4)**2/3
Let t(k) be the third derivative of -13/3*k**5 + 23/12*k**6 + 0*k + k**2 + 0*k**3 + 5/3*k**4 + 0 - 11/42*k**7. Suppose t(p) = 0. What is p?
0, 2/11, 2
Let o(k) = 9*k**2 + 99*k - 10 - 71*k - 2*k**2 - 3 - 25*k**3. Let c(d) = -300*d**3 + 85*d**2 + 335*d - 155. Let b(s) = 3*c(s) - 35*o(s). Let b(m) = 0. What is m?
-1, 2/5, 1
Let w be 2*(10/(-8))/(14/84). Let k = 15 + w. Suppose k + 3/4*n**2 + 1/4*n + 3/4*n**3 + 1/4*n**4 = 0. Calculate n.
-1, 0
Let w(d) be the second derivative of 2*d**7/63 + d**6/15 - d**5/6 - 5*d**4/18 + d**3/3 + 2*d**2/3 - 6*d + 3. Suppose w(q) = 0. Calculate q.
-2, -1, -1/2, 1
Find q, given that -q + 1/8*q**2 + 2 = 0.
4
Suppose 279/7*z**2 + 804357/7 - 25947/7*z - 1/7*z**3 = 0. What is z?
93
Let s(w) be the second derivative of -w**7/42 + 5*w**6/18 - 9*w**5/20 - w**4/4 + 7*w**3/9 + 666*w. Solve s(c) = 0.
-2/3, 0, 1, 7
Let o(b) be the second derivative of -b**4/84 + b**3/21 - 482*b. Factor o(c).
-c*(c - 2)/7
Let l(u) be the second derivative of u**7/7 + 44*u**6/15 + 86*u**5/5 + 25*u**4 - 69*u**3 - 162*u**2 + 226*u. Suppose l(c) = 0. What is c?
-9, -3, -2/3, 1
Let f = -1/58 - -989/174. Let w = 458/341 + -10/1023. Determine d, given that -d**5 + 23/3*d**2 - w - 11*d**3 + 0*d + f*d**4 = 0.
-1/3, 1, 2
Let r(p) be the third derivative of p**6/390 + 83*p**5/390 - 32*p**4/39 + 43*p**3/39 + 939*p**2. Suppose r(u) = 0. What is u?
-43, 1/2, 1
Let b(r) be the second derivative of 14/3*r**3 + r - 5/3*r**4 - 4*r**2 + 0. What is w in b(w) = 0?
2/5, 1
Let u(f) = 11*f**4 - 66*f**3 + 427*f**2 - 676*f - 1188. Let r(t) = 4*t**4 - 22*t**3 + 142*t**2 - 225*t - 396. Let l(k) = 8*r(k) - 3*u(k). Factor l(d).
-(d - 11)*(d - 6)**2*(d + 1)
Let v(o) be the second derivative of 5*o**7/126 + 4*o**6/45 - o**5/15 - 5*o**4/18 - o**3/18 + o**2/3 + 14*o. Factor v(a).
(a - 1)*(a + 1)**3*(5*a - 2)/3
Let o(d) = d**3 - d**2 + d + 3. Let t be o(0). Let q be 7*(-20)/70*(255/(-90))/17. Factor 1/3*u**t + 0 - q*u**4 + 0*u + 0*u**2.
-u**3*(u - 1)/3
Let n be 1 - -1 - 39/13. Let s be (-2)/((-1)/(n + 3)). Determine d so that 9*d - s*d**2 - 1 + 13 - d = 0.
-1, 3
Let n = 457/27800 - 1/695. Let d = n - -1573/1800. Let -d*g + 8/9*g**4 + 2/9*g**5 - 8/9*g**2 + 2/3*g**3 + 0 = 0. What is g?
-2, -1, 0, 1
Let b(u) be the second derivative of 2*u**6 + 17*u**5/5 + 2*u**4/3 - 134*u. Factor b(r).
4*r**2*(r + 1)*(15*r + 2)
Let a(i) be the third derivative of -i**9/5040 + i**8/2240 + i**7/840 - i**6/240 + i**4/3 + 4*i**2. Let u(w) be the second derivative of a(w). Solve u(c) = 0.
-1, 0, 1
Let o(n) be the second derivative of n**4/3 + 8*n**3/3 + 6*n**2 - 9*n - 2. Factor o(d).
4*(d + 1)*(d + 3)
Let o(n) be the first derivative of n**8/3360 - n**7/420 - 46*n**3/3 + 54. Let b(r) be the third derivative of o(r). Solve b(x) = 0 for x.
0, 4
Let c(s) be the third derivative of s**7/840 + s**6/40 + 23*s**5/120 + 5*s**4/8 + 25*s**3/24 - 82*s**2. Factor c(i).
(i + 1)**2*(i + 5)**2/4
Suppose -28 = -3*c - 1. Let s be 3/c + (-8)/(-48). Factor t**2 - s*t**5 + 3/2*t - t**3 - 3/2*t**4 + 1/2.
-(t - 1)*(t + 1)**4/2
Factor -2/15*j**2 - 1352/15 - 104/15*j.
-2*(j + 26)**2/15
Let z(k) = -2*k**2 - 9*k - 10. Let v(h) = -10*h**2 - 46*h - 50. Suppose -1 = -3*m - 19. Let u(s) = m*v(s) + 28*z(s). Factor u(w).
4*(w + 1)*(w + 5)
Let x(u) be the first derivative of u**4/30 + 2*u**3/15 + 240. Solve x(o) = 0 for o.
-3, 0
Factor -4/3*s**3 - 76/15*s - 26/15 + 2/15*s**4 - 24/5*s**2.
2*(s - 13)*(s + 1)**3/15
Suppose 53*h = 51*h + 102. Let z = h + -48. Factor 3/2*w**4 + z + 21/2*w + 15/2*w**3 + 27/2*w**2.
3*(w + 1)**3*(w + 2)/2
Let k(x) = 3*x + 11. Let v be k(-3). Let d be (-10)/(-2 + 7) - (-10)/v. Solve 0*i**d + 2/3*i**4 + 0 + 0*i - 2/3*i**2 = 0.
-1, 0, 1
Suppose -o - 2*d = -9 - 6, 0 = 2*o - 2*d. Let b(g) be the first derivative of 2/15*g**o + 0*g**2 - 11 + 1/12*g**4 + 0*g + 0*g**3. Solve b(p) = 0.
-1/2, 0
Let i(j) = -11*j**2 + 132*j + 30. Let p(l) = 9*l**2 - 132*l - 25. Let o(b) = 5*i(b) + 6*p(b). Factor o(y).
-y*(y + 132)
Suppose 10 = -6*q + 11*q. Factor -24*b**q + 19*b**2 + 0*b - 5*b.
-5*b*(b + 1)
Let t be 8/36*6*3. Let o(j) be the first derivative of -1 + 0*j**3 + 0*j + 1/14*j**t - 1/7*j**2. Factor o(v).
2*v*(v - 1)*(v + 1)/7
Let i be (-8)/(-75)*3*(19 + (-639)/36). Factor -i - 6/5*a**2 + 6/5*a + 2/5*a**3.
2*(a - 1)**3/5
Let m = 50 + -45. Determine p, given that 0 - 5*p + 1 - m - 6 + 5*p**2 = 0.
-1, 2
Let w(s) be the third derivative of s**8/20160 - s**7/2520 + s**6/1080 - 7*s**4/12 - 20*s**2. Let h(y) be the second derivative of w(y). Factor h(a).
a*(a - 2)*(a - 1)/3
Find c, given that 35*c**2 + 3*c**4 + 42*c**2 + 36 - 8587*c + 8495*c - 22*c**3 - 2*c**4 = 0.
1, 2, 18
Let x(b) be the second derivative of 4*b**7/105 + 13*b**6/75 + 11*b**5/50 + b**4/15 + 194*b. Solve x(k) = 0.
-2, -1, -1/4, 0
Solve -11*c**3 + c**2 - 8 + 5*c**2 - 5*c**3 + 28*c**3 - 10*c**3 = 0.
-2, 1
Let f be 41 - (5 - (0 - -3)). Factor 27*m**3 - 5*m**4 + 10 + 27*m**3 - 5*m**2 - f*m**3 - 15*m.
-5*(m - 2)*(m - 1)**2*(m + 1)
Let s(i) be the third derivative of 0 + 0*i**3 + 0*i + 1/60*i**6 + 1/5*i**5 + 3/4*i**4 - 25*i**2. Factor s(o).
2*o*(o + 3)**2
Suppose 3*h - 19 = -5*a, a + 2*h + 13 = 7*h. Find c, given that -3*c + 2 + 12*c**a - 11*c**2 + 0 = 0.
1, 2
Let f = 3311 + -36417/11. Factor 10/11*u + 2/11*u**3 - 8/11*u**2 - f.
2*(u - 2)*(u - 1)**2/11
Let b(t) = -t**4 - t**3 - t + 1. Let y(c) = 5*c - 12 - 20*c**2 - c**3 + 47*c**3 + 11*c - 6*c**3. Let d(f) = 12*b(f) + y(f). Solve d(x) = 0 for x.
0, 1/3, 1
Let j(o) be the third derivative of o**6/240 + 4*o**5/5 + 64*o**4 + 8192*o**3/3 - 45*o**2. Factor j(k).
(k + 32)**3/2
Factor 0*b**3 + 8/3*b**2 - 8/3*b**4 - 4/3*b + 4/3*b**5 + 0.