2 - 4047*i + t*i**3 - 2*i**4.
-2*i**2*(i - 3)*(i - 1)
Let l(i) be the first derivative of -4*i**3/3 + 64*i**2 + 1081. Factor l(h).
-4*h*(h - 32)
Let x(p) = -2*p**5 + 10*p**4 - 24*p**3 - 8*p**2 + 8*p - 8. Let z(q) = -q**3 - 2*q**2 + q - 1. Let j(n) = x(n) - 8*z(n). Determine l, given that j(l) = 0.
0, 1, 2
Let r be ((-51543)/486)/(-83) + (-5)/6. Let f(y) be the first derivative of -2/27*y**3 - 15 + 1/3*y**2 - r*y. Factor f(h).
-2*(h - 2)*(h - 1)/9
Let c(q) be the second derivative of 1/8*q**4 + 0 + 1/20*q**5 + 7/2*q**2 + 10*q + 0*q**3. Let i(d) be the first derivative of c(d). Factor i(s).
3*s*(s + 1)
Let t(r) be the second derivative of -r**4/84 + 9*r**3/14 + 2*r**2 + 89*r - 6. Suppose t(x) = 0. What is x?
-1, 28
Let 3/4*u**3 + 12 - 21/4*u**2 - 15/2*u = 0. What is u?
-2, 1, 8
Let n(x) = -144*x**2 + 18*x + 27. Let c(s) = 29*s**2 + s - 1. Let z(o) = 15*c(o) + 3*n(o). Solve z(i) = 0.
-22, -1
Let p(m) be the second derivative of m**4/48 - 187*m**3/6 - 4344*m. Let p(z) = 0. Calculate z.
0, 748
Suppose -18*w + 15*w - 21 = -3*n, 4*n - 8 = -w. Suppose 3*h + 313 = 2*p, -4*p - 2*h + 617 = h. Factor -6*c**3 - p*c**2 + 155*c**2 - 3 + n*c**4 + 6*c.
3*(c - 1)**3*(c + 1)
Suppose 8*m + 24 = 5*t + 11*m, t + 3*m - 12 = 0. Suppose -28*v - 191 = -527. Factor 13/3*f**2 + 16*f + 1/3*f**t + v.
(f + 1)*(f + 6)**2/3
Let d = 5654/2513 - 500/359. Factor 0 - 2/7*r**3 + d*r + 4/7*r**2.
-2*r*(r - 3)*(r + 1)/7
Let n = -588 + 590. Determine x, given that 16*x**3 - 57*x**n + 4*x**2 + 32*x**4 + 36*x - 25*x**2 = 0.
-2, 0, 3/4
Let k(q) be the third derivative of 0*q + 1/360*q**6 + 0 + 63*q**2 - 1/9*q**4 - 1/90*q**5 + 0*q**3. Suppose k(n) = 0. Calculate n.
-2, 0, 4
Let h(r) = -22749*r + 136494. Let w be h(6). Factor w - 2/13*m**3 - 86/13*m**2 + 0*m.
-2*m**2*(m + 43)/13
Determine y so that -17578125*y - 1/3*y**4 - 375*y**3 - 140625*y**2 + 0 = 0.
-375, 0
Let h(a) be the third derivative of 7/3*a**4 + 0 + 0*a**3 - 1/30*a**6 + 0*a + 1/3*a**5 - 31*a**2. Let h(x) = 0. Calculate x.
-2, 0, 7
Let y(z) = 3*z**4 + 8*z**3 - 10*z - 7. Let u = 396 + -351. Let f(x) = -65*x**4 - 175*x**3 + 220*x + 155. Let p(v) = u*y(v) + 2*f(v). Let p(t) = 0. Calculate t.
-1, 1
Let j(g) = -g**3 + 9*g**2 + 2*g. Let b(h) = -3*h**3 + 18*h**2 + 5*h. Suppose 6*v = 11*v + 10. Let r(u) = v*b(u) + 5*j(u). Let r(o) = 0. Calculate o.
-9, 0
Let b = -10198813/11 + 927165. Suppose 8/11*d**3 + 0 - 10/11*d**2 + 0*d + b*d**4 = 0. What is d?
-5, 0, 1
Let b(l) be the first derivative of 4*l**5/35 + 99*l**4/7 + 388*l**3/7 + 578*l**2/7 + 384*l/7 + 1152. Factor b(d).
4*(d + 1)**3*(d + 96)/7
Let z(m) be the first derivative of 3*m**5/40 + m**4/2 - m**3/4 - 3*m**2 - 73*m + 64. Let l(b) be the first derivative of z(b). Find f such that l(f) = 0.
-4, -1, 1
Let z be 33718/(-345) + 8/6. Let t = z - -491/5. What is h in 84/5*h**2 + t*h**3 + 21/5*h - 54/5 = 0?
-9, -1, 2/3
Let p = -9 + 11. Suppose -27*c + 17162 = -5059. Factor c*i**2 - 823*i**p - 3 + 12*i**3 - 9*i.
3*(i - 1)*(2*i + 1)**2
Let f = 302 + -152. Factor 60*b**2 - 5*b**3 + 40*b + 63*b - 135*b + 247*b + f.
-5*(b - 15)*(b + 1)*(b + 2)
Suppose -32*z + 400 = -37*z. Let k be z/(-12)*24/20. Factor -k - 1/2*b**2 - 4*b.
-(b + 4)**2/2
Let n be 8/60 - 2*(-4)/18. Let f = n - -4/45. Find y, given that -5/6*y**2 + 0 + f*y**3 - 1/3*y + 1/2*y**4 = 0.
-2, -1/3, 0, 1
Let o(p) = -p**2 + 18*p - 57. Let s be o(13). Suppose -4*g - 16 = 4*l, 5*g - 7*g = s. Factor -12/7*j + 10/7*j**2 + l - 2/7*j**3.
-2*j*(j - 3)*(j - 2)/7
Let m be (-14)/30 - (-32 + (-1008)/(-32)). Let f(j) be the third derivative of -1/60*j**6 - m*j**7 + 0*j**5 + 0 - 16*j**2 + 0*j**4 + 0*j**3 + 0*j. Factor f(s).
-s**3*(7*s + 2)
Let y(b) = 15*b**3 - b**2 + 5*b. Let i(p) = -59*p**3 - 470*p**2 - 971*p - 476. Let o(q) = i(q) + 4*y(q). Determine r so that o(r) = 0.
-1, 476
Let u(h) be the second derivative of -1/20*h**5 - 8/15*h**3 - 65*h + 0*h**2 + 2 + 11/30*h**4 - 1/150*h**6. Factor u(c).
-c*(c - 2)*(c - 1)*(c + 8)/5
Let m be (-56)/(-98) + (-16)/28. Let o = 443 - 439. Factor 0*k - 2/19*k**o + 0 + m*k**2 + 2/19*k**3.
-2*k**3*(k - 1)/19
Let s(t) = -173*t**3 - 5*t**2 - 10*t. Let u be s(-4). Solve 12*n**2 - 80*n**3 - 92*n**2 + u*n**4 - 11027*n**4 + 5*n**5 = 0 for n.
-4, -1, 0, 4
Let t(v) be the first derivative of 3*v**5/10 + 15*v**4/2 - 29*v**3/2 - 117*v**2 + 378*v + 1718. Find y such that t(y) = 0.
-21, -3, 2
Let l(s) be the third derivative of s**6/840 - 431*s**5/420 - 31*s**4/3 - 290*s**3/7 - 5*s**2 - 2*s - 28. Factor l(p).
(p - 435)*(p + 2)**2/7
Let j(m) be the second derivative of 5*m**4/12 - 10*m**3/3 - 25*m**2/2 + 75*m - 6. Factor j(s).
5*(s - 5)*(s + 1)
Suppose -804*f + 304 = -785*f. Let i be (-2)/f*-54*104/195. Factor 3/5*u**3 + 27/5*u + i*u**2 + 0.
3*u*(u + 3)**2/5
Find y, given that -38295/4*y**3 - 39675/2*y**2 + 171*y**4 + 0 - 3/4*y**5 + 0*y = 0.
-2, 0, 115
Let b(o) be the third derivative of -o**6/60 + 106*o**5/15 - 211*o**4/12 - 1719*o**2 + o. Solve b(l) = 0 for l.
0, 1, 211
Let h = 80781 + -80781. Let s**3 - 1/2*s**2 + 0*s + h - 1/2*s**4 = 0. What is s?
0, 1
Suppose 10*j = -2828 + 2828. Suppose 0 = -l + 4 - 1. Solve -5/2*w**2 + 5/2*w**4 + w**l + j - w = 0.
-1, -2/5, 0, 1
Suppose 0 = -307*y - 207*y. Factor y*p + 2/7*p**4 - 12/7*p**3 + 0*p**2 + 2/7*p**5 + 0.
2*p**3*(p - 2)*(p + 3)/7
Let q(c) = -61*c**3 - 2*c**2 + 2*c - 1. Let h be q(1). Let t = 66 + h. Determine m, given that m**t + 2*m**3 + 3*m**5 - m**5 + 3*m**4 = 0.
-1, 0
Suppose 76*u + 39389 = -19*u + 39769. Factor 0 + 9/5*k + 1/5*k**5 + 12/5*k**2 - 2/5*k**3 - 4/5*k**u.
k*(k - 3)**2*(k + 1)**2/5
Let b = -43 - -46. Suppose q + 5*h + b = 0, -q = -3*q + 2*h + 6. Factor -16807/2 + 245*f**3 - 35/2*f**4 + 12005/2*f + 1/2*f**5 - 1715*f**q.
(f - 7)**5/2
Suppose -3*j = -j + 2*j. Let u(w) = -w**3 - w + 79. Let b be u(j). Factor -25*s + b*s + 94 - 78 - 7*s**2.
-(s - 8)*(7*s + 2)
Suppose -306 = 23*k - 29*k. Factor -597*a + 72*a**2 + 0*a**3 - 2*a**3 - k*a.
-2*a*(a - 18)**2
Let n(v) be the second derivative of -v**4/16 + 9*v**3 + 192*v - 5. Solve n(j) = 0.
0, 72
Let a(r) = -4*r**3 - 18*r**2 + 112*r - 78. Let y(i) = -4*i**3 - 17*i**2 + 110*i - 79. Let o = 901 - 895. Let p(u) = o*y(u) - 5*a(u). Factor p(d).
-4*(d - 3)*(d - 1)*(d + 7)
Let g(x) be the second derivative of x**4/16 + 1199*x**3/8 - 450*x**2 + 3663*x. Factor g(m).
3*(m - 1)*(m + 1200)/4
Let l be ((-37128)/(-1430))/119 - 4/(-22). Factor l*x**5 + 64/5*x**3 - 28/5*x**4 + 0 + 256/5*x**2 + 0*x.
2*x**2*(x - 8)**2*(x + 2)/5
Let t(g) be the first derivative of -2*g**3/15 + 23*g**2/5 - 204*g/5 - 769. Factor t(z).
-2*(z - 17)*(z - 6)/5
Suppose -154*f - 1275 = -157*f. Let c = f - 1255/3. Suppose 12*j**2 + 4/3*j**4 + c*j**3 + 28/3*j + 8/3 = 0. Calculate j.
-2, -1
Solve 24*w**3 - 13915*w + 2595*w**2 + 28559*w + 8748 + 13175*w + 33840*w + 8649*w = 0.
-54, -1/8
Let a(p) be the first derivative of 44*p**2 + 37 - 4/3*p**3 - 484*p. What is s in a(s) = 0?
11
Let u(q) be the second derivative of q**5/20 + 4*q**4 + 126*q**3 + 1944*q**2 + 2178*q. Solve u(a) = 0.
-18, -12
Suppose 2*j + 0*j - 6 = -2*b, 2*j + 4*b = 6. Let f be ((-2)/(-1))/((-2)/(-3)). Factor 6 - m**f + 4*m + j*m**2 - 8 + 2.
-m*(m - 4)*(m + 1)
Let v = 3197 + -3197. Let c(r) be the third derivative of 0*r**3 + 0 + 14*r**2 - 5/8*r**4 + v*r + 1/6*r**5 + 1/24*r**6. Factor c(x).
5*x*(x - 1)*(x + 3)
Let d(n) be the third derivative of 0 + 16/51*n**3 + 7/255*n**5 + 0*n + 246*n**2 + 31/204*n**4 - 1/1020*n**6. Factor d(f).
-2*(f - 16)*(f + 1)**2/17
Let x(b) be the first derivative of -95 - 1/5*b**3 - 12/5*b**2 + 27/5*b. Factor x(w).
-3*(w - 1)*(w + 9)/5
Let i(t) = -9*t + 179. Let q be i(20). Let m(s) = -s**2 + s. Let z(j) = -8*j**2 - 58*j - 144. Let x(h) = q*z(h) + 10*m(h). Suppose x(l) = 0. What is l?
-2, 36
Factor 2850/7 + 3/7*q**2 - 1431/7*q.
3*(q - 475)*(q - 2)/7
Suppose -4*x = 4*a - 84, 5*a + x = 93 + 8. Suppose 4*o + 12 = -2*b, o = -4*o - a. Determine g so that -3/2*g - 3 + 3/2*g**3 + 3*g**b = 0.
-2, -1, 1
Solve -120/13 + 16/13*d**4 - 136/13*d**2 - 254/13*d + 2/13*d**5 + 12/13*d**3 = 0.
-5, -4, -1, 3
Let r(b) be the first derivative of b**4/14 + 4*b**3/3 + 16*b**2/7 - 192*b/7 - 6895. Factor r(s).
2*(s - 2)*(s + 4)*(s + 12)/7
Let s(h) = -2*h**2 + 4. Let l(t) = t**2. Let v = 90 + -85. Suppose -r - 3*d + 2*d - 2 = 0, -v*r = -4*d - 26. Let x(w) = r*s(w) + 2*l(w). Factor x(q).
-2*(q - 2)*(q +