
1, 2
Let s(v) be the first derivative of -v**3/12 + 35*v**2/4 + 36*v - 6179. Determine d, given that s(d) = 0.
-2, 72
Let z be (-1)/((-1)/5) + -58 + 61. Let f be z/(-21)*1161/(-516). Solve -23/7*d - f - d**2 = 0 for d.
-3, -2/7
Let b(o) = 23*o**2 + 2*o + 2. Let l(h) = 22*h**2 + 257*h - 252. Let d(z) = 5*b(z) - 5*l(z). Determine i, given that d(i) = 0.
1, 254
Let r(y) be the second derivative of y**4/84 + 2974*y**3/21 + 4422338*y**2/7 - 6764*y. Determine z so that r(z) = 0.
-2974
Let x(b) be the first derivative of -b**7/70 + 7*b**6/20 - 3*b**5 + 9*b**4 - 25*b**2 + 61. Let y(t) be the second derivative of x(t). Factor y(q).
-3*q*(q - 6)**2*(q - 2)
Find c, given that 80/9 - 2/9*c - 1/9*c**2 = 0.
-10, 8
Let m be (-4)/(-48) + (-27)/324. Let d(w) = 44*w - 132. Let t be d(3). Factor 12/5*f**3 + t - 4/5*f**2 - 12/5*f**4 + m*f + 4/5*f**5.
4*f**2*(f - 1)**3/5
Let y(w) be the third derivative of 0*w - 20*w**2 + 1/10*w**5 - 1/120*w**6 + 0*w**3 + 0 - 1/3*w**4. Suppose y(r) = 0. Calculate r.
0, 2, 4
Solve 9/5*k**3 + 9042/5*k**2 - 3012/5 + 6021/5*k = 0 for k.
-1004, -1, 1/3
Let w be (-252)/(-756)*((-3)/5)/((-8)/60). Factor 246*y + w*y**2 + 10086.
3*(y + 82)**2/2
Factor -16/5*u + 0 - 3*u**2 + 1/5*u**3.
u*(u - 16)*(u + 1)/5
Let f(s) be the first derivative of -3 - 1/360*s**5 - s**3 + 0*s - 11*s**2 - 1/12*s**4. Let t(c) be the second derivative of f(c). Find i such that t(i) = 0.
-6
Solve -168 - 2/5*b**2 + 86/5*b = 0.
15, 28
Suppose 0 = -t + 12*t + 77*t. Factor 5/2*x**2 + t + 5/4*x**5 - 5/2*x**4 + 0*x**3 - 5/4*x.
5*x*(x - 1)**3*(x + 1)/4
Let c(d) be the first derivative of d**7/21 + 4*d**6/15 + 2*d**5/5 - 38*d - 48. Let j(h) be the first derivative of c(h). Factor j(q).
2*q**3*(q + 2)**2
Let o(p) be the first derivative of -2*p**3/21 + 257*p**2/7 - 512*p/7 - 2626. Let o(r) = 0. What is r?
1, 256
Let f(d) be the first derivative of 4*d**5/5 + 588*d**4 - 4*d**3/3 - 1176*d**2 - 4879. Factor f(l).
4*l*(l - 1)*(l + 1)*(l + 588)
Let b = 9683/2 + -4839. Let o(t) be the third derivative of 0 + 1/20*t**5 + 22*t**2 - 3/4*t**4 + b*t**3 + 0*t. Factor o(l).
3*(l - 5)*(l - 1)
Let m = 44 + 742. Let l = 8651/11 - m. Solve -6/11 + l*y + 1/11*y**2 = 0.
-6, 1
Let c(l) be the first derivative of -26*l**2 + 6*l**3 + 40*l + 1/4*l**4 - 1/5*l**5 + 138. Factor c(k).
-(k - 2)**3*(k + 5)
Let z = -1301 - -1304. Let y(c) be the third derivative of -1/60*c**6 - 1/30*c**5 - 7*c**2 + 1/6*c**4 + 0*c + 0 + 0*c**z. Factor y(s).
-2*s*(s - 1)*(s + 2)
Factor 240*i**2 - 718*i**2 + 239*i**2 + 234*i**2 - 45 - 40*i + 10.
-5*(i + 1)*(i + 7)
Let g(k) = -k - 4. Suppose -3*t - 2*t = 35. Let s be g(t). Factor -f**s + 4*f**2 + 6*f**3 + 0*f**3 - f**3.
4*f**2*(f + 1)
Suppose -14*g - 38 = -150. Let d(o) = -5*o**2 + 92*o + 596. Let j(y) = -2*y**2 + 31*y + 199. Let c(i) = g*j(i) - 3*d(i). Factor c(h).
-(h + 14)**2
Factor 44/9*k + 2/9*k**2 + 14/3.
2*(k + 1)*(k + 21)/9
Let t(x) = -28*x**2 - 792*x + 1707. Let v(z) = 10*z**2 + 264*z - 572. Let b(q) = -4*t(q) - 11*v(q). Factor b(y).
2*(y - 2)*(y + 134)
Let u(k) be the third derivative of -k**5/30 - 361*k**4/12 - 718*k**3/3 - 1955*k**2. Factor u(w).
-2*(w + 2)*(w + 359)
Let y(r) = 2*r + 23. Let m be y(-10). Suppose 5*i = 2*a + 166, 99 = m*i - 4*a + 3*a. Find q such that -32*q + i*q + 2 - 2*q**2 = 0.
-1, 1
Let o(c) be the first derivative of c**5/12 - 5*c**4/2 + 55*c**3/6 + c**2/2 - 14*c - 148. Let d(n) be the second derivative of o(n). Let d(u) = 0. What is u?
1, 11
Let b(j) = 2*j**3 - 4*j**2 - 392*j + 1517. Let q be b(4). Find n, given that -5/2*n**2 + q*n - 5/2 = 0.
1/5, 5
Suppose 14*k - 4650 = 8552. Suppose -2*t + k = -691. What is f in -817 + t + 4*f**2 + 60*f + f**2 = 0?
-12, 0
Let v(a) be the first derivative of 5*a**3/3 - 5*a**2/2 - 3633. Let v(g) = 0. Calculate g.
0, 1
Let m(t) be the third derivative of t**5/40 + 141*t**4/16 - 365*t**3/2 + 2696*t**2. Factor m(z).
3*(z - 5)*(z + 146)/2
Suppose -5*v - 828 = -31*v - 20*v. Let u(y) be the second derivative of 0*y**2 + 0 - 3/80*y**5 + v*y - 1/8*y**4 - 1/8*y**3. Factor u(c).
-3*c*(c + 1)**2/4
Let c = 49 + -47. Let r(s) = s**2 - 4*s + 7. Let q be r(c). Factor -7*t**q - 4*t**4 - 6*t**2 + 11*t**3 - 7*t**3 + 7*t**4.
3*t**2*(t - 2)*(t + 1)
Solve -61 - 27 + 340*j - 260*j + 2*j**3 - 14*j**2 - 4*j**3 = 0 for j.
-11, 2
Let c be 50/8 - 1/4. Let t be (c/8)/(5 + 19/(-4)). Let 27*v**t - 6*v**4 - 15 - 4 - 63*v**2 + 3*v**4 + 1 + 57*v = 0. Calculate v.
1, 6
Determine z, given that -1744*z - 4890 + 73*z**5 + 27*z**5 + 10448*z**2 + 10720*z**4 + 4890 - 19524*z**3 = 0.
-109, 0, 2/5, 1
Let q(k) be the third derivative of -1/60*k**6 - 1/5*k**5 + 0*k + 1/210*k**7 + 0 - 5/6*k**3 - 7/12*k**4 - 67*k**2. Suppose q(b) = 0. Calculate b.
-1, 5
Factor 2/7*i**2 + 1552/7*i + 1550/7.
2*(i + 1)*(i + 775)/7
Factor -1/4*i**3 + 378 - 223*i + 35/2*i**2.
-(i - 54)*(i - 14)*(i - 2)/4
Let x(v) be the first derivative of -52*v**5/15 + 41*v**4/3 - 20*v**3 + 38*v**2/3 - 8*v/3 - 1039. Let x(r) = 0. What is r?
2/13, 1
Suppose -3*h + 0*h = -15*h. Let u(v) be the second derivative of -13*v + h + 2/15*v**3 + 1/15*v**4 + 0*v**2. Factor u(b).
4*b*(b + 1)/5
Let n be 2/6*((-23 - -27) + 2). Let g(s) be the second derivative of 4/21*s**3 + 1/42*s**4 + 10*s + 0 + 4/7*s**n. Factor g(a).
2*(a + 2)**2/7
Factor 44*z**2 - 24*z**4 - 540*z**3 - 63*z**4 - 33*z**4 - 440*z**2 + 5*z**5 - 164*z**2.
5*z**2*(z - 28)*(z + 2)**2
Suppose 0 = -5*l - m + 248, -4*l - 3*m + 206 = -6*m. Let g = -38 + l. Factor -6*j**5 + 4*j**5 + 8*j**2 - 2*j + 10 + 8*j**4 - g*j**3 - 10.
-2*j*(j - 1)**4
Let w(o) = o**2 - o + 2. Let p be w(2). Suppose 5*b = 9*b - 24. Factor -9*g**2 - p*g**4 + g**2 - 18*g**3 + b*g**3 + 0*g**4.
-4*g**2*(g + 1)*(g + 2)
Suppose 34*u - 2*u = 64. Find d such that 8*d**u + 19 - 4*d**3 + 2*d**2 + 2*d**3 - 5 + 66*d - 40*d = 0.
-1, 7
Let w(j) be the third derivative of j**8/10080 - j**7/720 + j**6/240 + j**5/30 - 3*j**3 - 68*j**2. Let l(f) be the third derivative of w(f). Factor l(r).
(r - 3)*(2*r - 1)
Let b(j) be the second derivative of 0*j**2 - 3/140*j**5 + 6*j - 3 + 2/7*j**4 + 9/14*j**3. Determine k so that b(k) = 0.
-1, 0, 9
Suppose -1281 = -5*j - 1261. Solve 503*q**3 + q**4 - q**j - 256*q**3 - q**4 - 251*q**3 + 5*q**2 = 0.
-5, 0, 1
Suppose 2*s - 4*d - d - 26 = 0, 3*d + 18 = 2*s. Suppose 0 = 6*r - 7*r + 3*x - 1, s*r - 8 = -2*x. Let 2/7*t**r + 2/7*t - 12/7 = 0. Calculate t.
-3, 2
Let t(j) = -j**4 - 14*j**3 + 13*j**2 - 2*j. Let q = -186 - -184. Let g(h) = -h**4 - h. Let c(i) = q*g(i) + t(i). Factor c(z).
z**2*(z - 13)*(z - 1)
Let l(t) be the first derivative of 4*t**3/3 + 120*t**2 + 464*t + 1165. Factor l(n).
4*(n + 2)*(n + 58)
Let h(q) = 4*q**2 - 33*q + 111. Let o(c) = 18*c**2 - 131*c + 439. Let k(m) = 26*h(m) - 6*o(m). Suppose k(w) = 0. What is w?
-21, 3
Factor 22707 + 3/4*w**2 - 261*w.
3*(w - 174)**2/4
Determine m, given that 4*m - 302*m**2 + 27*m**2 + 110*m + 93*m**2 - 3*m**3 + 71*m**2 = 0.
-38, 0, 1
Factor -3/2 - 1/10*m**2 - 8/5*m.
-(m + 1)*(m + 15)/10
Let t(d) be the first derivative of d**7/84 + d**6/30 - 59*d**5/60 - d**4 + 54*d**3 - d + 308. Let k(s) be the third derivative of t(s). Factor k(p).
2*(p - 3)*(p + 4)*(5*p + 1)
Let s(y) be the first derivative of y**3 - 807*y**2/2 + 217083*y/4 + 9170. Factor s(n).
3*(2*n - 269)**2/4
Let c(k) be the second derivative of -k**6/280 + k**4/56 - 69*k**2/2 - 3*k + 27. Let b(p) be the first derivative of c(p). Determine z, given that b(z) = 0.
-1, 0, 1
Let s(l) = 137*l**4 + 214*l**3 + 240*l**2 + 45*l - 19. Let c(m) = 185*m**4 + 285*m**3 + 320*m**2 + 60*m - 25. Let j(f) = -11*c(f) + 15*s(f). Factor j(v).
5*(v + 1)**2*(v + 2)*(4*v - 1)
Let m(z) be the second derivative of -z**5/230 + 10*z**4/69 + 427*z**3/69 + 1666*z**2/23 + 1265*z. Let m(i) = 0. Calculate i.
-7, 34
Let q = -52 - -54. Suppose 0 = 10*u + q*u - 156. Factor 19*c**5 - 16*c**5 - 120*c**3 + 29*c**4 - 94*c**4 - u*c**5 - 45*c**2.
-5*c**2*(c + 3)**2*(2*c + 1)
Let z = 24/11 - 15/22. Let w(i) = -i**2 + 97*i - 943. Let p be w(86). Let -3/2*y**2 - p*y - z = 0. What is y?
-1
Let d(b) = -b**2 - 2*b - 1. Let x(w) = w**3 + 8*w**2 + 12*w + 5. Let h be (-2)/(-12)*-2*(22 + -7). Let f(k) = h*d(k) - x(k). Determine p so that f(p) = 0.
-2, -1, 0
Let d(i) be the first derivative of -8/27*i**3 + 8/45*i**5 + 1/3*i**4 - 5/9*i**2 - 1/27*i**6 + 0*i - 15. Find z, given that d(z) = 0.
-1, 0, 1, 5
