*t**2 - 165*t + 5*t**4.
5*t*(t - 33)*(t + 1)**2
Let b(q) be the first derivative of 8*q**3/3 + 1302*q**2 - 1304*q - 624. Find r such that b(r) = 0.
-326, 1/2
Let u(d) be the first derivative of -d**5/150 + 38*d**4/15 - 5776*d**3/15 - d**2 + 5*d - 42. Let t(q) be the second derivative of u(q). What is c in t(c) = 0?
76
Let u(q) = 3*q**2 + 3*q - 6. Let c(b) be the second derivative of -b**4/12 + b**3/3 - b**2/2 + 50*b. Let z(x) = -4*c(x) - 2*u(x). Let z(o) = 0. What is o?
-8, 1
Let d = -322 + 337. Solve -12 - d*m - 11 + 0*m**2 - 3*m**2 + 9 - 4 = 0 for m.
-3, -2
Let y(s) = -6*s**2 + 1020*s + 242. Let n(o) = 4*o**2 - 647*o - 161. Let z(u) = 8*n(u) + 5*y(u). Let z(v) = 0. What is v?
-1, 39
Let w(f) be the first derivative of f**5/150 + f**4/18 + 8*f**3/45 + 4*f**2/15 - 47*f + 58. Let y(k) be the first derivative of w(k). Factor y(j).
2*(j + 1)*(j + 2)**2/15
Suppose -6*c + 275 = 611. Let a be (-1)/(c/1352)*13. Factor -507/7*z - a - 39/7*z**2 - 1/7*z**3.
-(z + 13)**3/7
Suppose -13242/17*b**3 + 280/17*b**4 + 219236/17*b**2 - 351256/17*b - 2/17*b**5 - 584016/17 = 0. Calculate b.
-1, 3, 46
Let d(n) be the second derivative of -3*n**5/40 - 7*n**4 - 55*n**3/4 - 2160*n + 2. Find r such that d(r) = 0.
-55, -1, 0
Let s be (132/(-40) - -3) + 9077/9390. Factor s*p**3 - 10/3*p - 4/3*p**2 + 4.
2*(p - 3)*(p - 1)*(p + 2)/3
Factor 4441*i**4 - 8882*i**4 - 25*i + 10 + 5*i**3 + 4*i**2 + 4436*i**4 + 8*i**2 + 3*i**2.
-5*(i - 1)**3*(i + 2)
Suppose -2*r = -2*w + 20, -8*r + 12*r = w - 25. Let o be (0 + 2 + 0)/(35/25). Determine j so that 2/7*j**w + 2*j**3 - 16/7*j - o*j**4 + 8/7 + 2/7*j**2 = 0.
-1, 1, 2
Suppose g = -991316 + 991318. Factor 2/5*s**2 + 12/5 - g*s.
2*(s - 3)*(s - 2)/5
Let d(o) be the third derivative of -5*o**2 - 1/84*o**7 + 1/80*o**6 + 17/120*o**5 + 0*o + 1/672*o**8 + 10 + o**3 - 7/12*o**4. Solve d(w) = 0 for w.
-2, 1, 2, 3
Suppose -o - 120*o + 363 = 0. Let f(v) be the third derivative of 1/300*v**5 + 14*v**2 + 0 + 0*v + 1/5*v**o - 7/120*v**4. Let f(h) = 0. Calculate h.
1, 6
Let p(u) = -14*u**2 + 3601*u - 3602. Let q(h) = 10*h**2 - 3604*h + 3604. Let d(l) = 2*p(l) + 3*q(l). Find m, given that d(m) = 0.
1, 1804
Let v = -561115/2 + 280560. Solve -1 + 1/2*z**3 + v*z - 2*z**2 = 0 for z.
1, 2
Factor -601526/9 + 26132/9*n**3 + 2/9*n**5 - 398/9*n**4 - 1176118/9*n - 548060/9*n**2.
2*(n - 67)**3*(n + 1)**2/9
Let q(z) be the third derivative of 2*z**2 + 0 - 17/7*z**4 - 8/147*z**7 + 211/105*z**5 - 22/35*z**6 + 0*z + 32/21*z**3. Find y such that q(y) = 0.
-8, 2/5, 1/2
Let t(d) be the second derivative of -7*d**4/4 - 27*d**3/2 - 30*d**2 + 210*d - 6. Factor t(r).
-3*(r + 1)*(7*r + 20)
Let s(k) = -7*k**4 + 11*k**3 - 150*k**2 - 366*k + 6. Let j(c) = 2*c**4 - c**3 + c - 1. Let o(y) = -6*j(y) - s(y). Factor o(l).
-5*l*(l - 6)*(l + 3)*(l + 4)
Let b(g) = 3*g**3 - 32*g**2 + 107*g - 556. Let a be b(9). Solve -10/9*p - 22/9*p**a + 0 - 4/9*p**3 = 0.
-5, -1/2, 0
Let l(f) be the first derivative of 0*f**2 + 3/2*f**4 - 1/4*f**6 + 8*f + 7/10*f**5 - 16/3*f**3 - 184. Suppose l(r) = 0. Calculate r.
-2, -2/3, 1, 2
Factor -405887 - 16*f - 66*f + f**2 + 404432.
(f - 97)*(f + 15)
Let i(m) be the second derivative of 1176*m**2 + 1/4*m**4 + 0 + 28*m**3 + 27*m. Solve i(c) = 0 for c.
-28
Let r be 8 - 1*(-14)/(-8)*(38 - 2133/63). Factor r*f**3 - 9/2*f**2 - 3*f + 18.
3*(f - 6)*(f - 2)*(f + 2)/4
Suppose 159 - 219 = -5*c. Suppose 22*x**3 - 36*x - c*x**2 + 15*x**3 - 9*x**4 - 10*x**3 + 30*x**3 + 0*x**3 = 0. What is x?
-2/3, 0, 1, 6
Let s(c) be the first derivative of c**4/4 - 68*c**3/3 - 71*c**2/2 + 138*c + 5158. Let s(g) = 0. What is g?
-2, 1, 69
Let r = -535735/18 - -59527/2. Factor -4/9*m**2 + r + 2/9*m**3 - 2/9*m.
2*(m - 2)*(m - 1)*(m + 1)/9
Let o(j) be the second derivative of 0 + 1/48*j**4 + 17/6*j**3 + 289/2*j**2 - 9*j. Let o(d) = 0. What is d?
-34
Let g(r) be the first derivative of -r**6/3 - 12*r**5/5 - 5*r**4 + 11*r**2 + 12*r + 5860. Let g(p) = 0. What is p?
-3, -2, -1, 1
Suppose x - 3*x + 4 = 0. Let n(r) = -7*r - 33. Let b be n(-6). Determine y, given that 14*y**2 + 4*y**2 + 30*y - 8 - 19*y**2 + b*y**x = 0.
-4, 1/4
Suppose 4 = -10*b + 6*b. Let g(f) = 5*f**2 + 88*f + 405. Let s(o) = 2*o**2 + 43*o + 58. Let c be s(-20). Let q(y) = y. Let x(n) = b*g(n) + c*q(n). Factor x(h).
-5*(h + 9)**2
Let k(y) be the first derivative of 2*y**3/21 + 314*y**2/7 - 1264*y/7 + 5118. Let k(g) = 0. Calculate g.
-316, 2
Suppose -4*a + 10 = 5*o - 5*a, -4*o = 3*a - 8. Suppose -210*r**3 + 3*r**o + 108*r**3 + 99*r**3 + 0*r**2 = 0. What is r?
0, 1
Let w be 1/(-4) + 299/92. Suppose 19*m**w + 15*m**2 + 50 - 85*m + 8*m**4 + 6*m**3 - 25*m**4 + 12*m**4 = 0. Calculate m.
-2, 1, 5
Let o(w) be the first derivative of -5*w**9/3024 + w**7/84 - w**5/24 - 62*w**3/3 - w**2/2 + 104. Let c(q) be the third derivative of o(q). Factor c(n).
-5*n*(n - 1)**2*(n + 1)**2
Let r = -40 - 1. Let y = -29 - r. Solve 119 - 2*t**3 - 3*t**4 + 14*t**3 + y*t - 122 - 18*t**2 + 0*t**3 = 0.
1
Let a(t) = 25*t**3 - 5*t**2 - 25*t + 25. Let w(y) = -y**3 - y**2 + y. Suppose 0 = -3*o + 5*q - 22, q - 5*q + 19 = -o. Let c(r) = o*a(r) + 20*w(r). Factor c(p).
5*(p - 5)*(p - 1)*(p + 1)
Let t(u) be the first derivative of -u**6/9 + 2*u**5/3 + 17*u**4/6 - 34*u**3/9 - 32*u**2/3 + 56*u/3 + 4738. Solve t(r) = 0 for r.
-2, 1, 7
Let c(g) be the third derivative of -1/90*g**6 + 11*g + 0 - 2/45*g**5 + 1/12*g**4 + 2*g**2 + 0*g**3 - 1/504*g**8 + 4/315*g**7. Let c(f) = 0. Calculate f.
-1, 0, 1, 3
Determine x so that -757*x**2 + 57*x**3 + 711*x**2 - 52*x - 40*x**5 + 22*x**4 + 16*x**5 + 24 + 19*x**5 = 0.
-2, -1, 2/5, 1, 6
Let n(l) be the third derivative of 0*l**5 + 1/672*l**8 + 0*l**4 + 0*l + 0*l**3 + 0 + 1/140*l**7 + 1/120*l**6 + 48*l**2. Let n(b) = 0. Calculate b.
-2, -1, 0
Let n(s) = 3*s**3 + 8*s**2 + 3*s. Let h(u) = 5*u - 2*u**3 - 2*u**3 + 15*u**2 + 9*u**3. Let l be (-19)/(-3) - 12/54*6. Let y(b) = l*n(b) - 2*h(b). Factor y(v).
5*v*(v + 1)**2
What is b in -350/9 - 1/9*b**2 - 19/3*b = 0?
-50, -7
Let l(t) be the third derivative of 3*t**5/50 - 239*t**4/60 + 158*t**3/45 - 955*t**2. Factor l(x).
2*(3*x - 79)*(9*x - 2)/15
Suppose 112/11*l**2 + 2/11*l**4 - 210/11 - 68/11*l - 28/11*l**3 = 0. Calculate l.
-1, 3, 5, 7
Find x such that -3698*x**2 - 364532*x**3 + 6960*x - 5*x**4 + 366292*x**3 - 3858*x**2 + 576*x**2 = 0.
0, 2, 348
Let y(x) = -2*x**3 - 32*x**2 - 55*x + 20. Let h be y(-14). Let z(i) = -i**2 + 29*i - 136. Let v be z(h). Determine t, given that 40/7*t - 44/7 + 4/7*t**v = 0.
-11, 1
Let m = 394115/181902 - -1/30317. Factor 8/3*i**2 + 0 - 1/2*i - m*i**3.
-i*(i - 1)*(13*i - 3)/6
Suppose z = 3*s + 13, 26*z = 22*z + 5*s + 66. Determine m so that -373*m + 0*m**2 + m**2 + 355*m - z = 0.
-1, 19
Let g = 28 + -26. Factor 120*t + 36*t**2 + 108 + g*t**3 + 6*t**3 - 4*t**3 - 12*t.
4*(t + 3)**3
Let k(p) be the first derivative of -p**4/14 + 160*p**3/21 - 453*p**2/7 + 1332*p/7 - 147. Factor k(s).
-2*(s - 74)*(s - 3)**2/7
Let t(k) = 42*k + 170. Suppose -12*h + 4*h - 32 = 0. Let p be t(h). Factor -6/7 - 4/7*b + 2/7*b**p.
2*(b - 3)*(b + 1)/7
Let u = 6485 - 6483. Let j = -2 - -5. Factor j*n - 21/2*n**u + 0.
-3*n*(7*n - 2)/2
Let i(q) be the first derivative of -7*q**5/200 - q**4/3 - 17*q**3/20 + 9*q**2/10 - q + 74. Let u(k) be the first derivative of i(k). Factor u(p).
-(p + 3)**2*(7*p - 2)/10
Let p(o) = 16*o**2 + 4*o - 8. Let g be p(2). Factor 4*q**2 + g*q + 68*q + 76*q - 200*q.
4*q*(q + 2)
Let l be (8261/7510)/(198/135). Determine q so that -l*q**3 + 3/4*q**2 + 1/4*q**4 - 1/4*q + 0 = 0.
0, 1
Suppose -7*g + 74*g = -9*g. Let a be (-11 + g)/22 + 6/8. Factor -a*s**2 - 3/4 - s.
-(s + 1)*(s + 3)/4
Suppose -42*r**2 - 15/2*r**4 - 24*r - 27*r**3 - 3/4*r**5 + 0 = 0. What is r?
-4, -2, 0
Let g(l) be the second derivative of -l**7/84 + l**6/10 + 17*l**5/40 - 13*l**4/4 + 14*l**3/3 + 3495*l. Solve g(h) = 0.
-4, 0, 1, 2, 7
Let t(z) = z**3 + 14*z**2 - 43*z + 28. Let c = -250 - -220. Let y(w) = w**2 - 1. Let l(n) = c*y(n) - 5*t(n). Suppose l(x) = 0. Calculate x.
-22, 1
Let f(q) be the first derivative of -q**4/9 - 256*q**3/27 - 1130*q**2/9 - 600*q - 4614. Find p, given that f(p) = 0.
-54, -5
Let w be (-7 - -3 - -67)*(-7 - -6)/(-3). Let q(m) be the first derivative of w - 1/7*m**2 + 10/21*m**3 - 2/7*m - 3/14*m**4. Solve q(v) = 0.
-1/3, 1
Let j(m) be the first derivative of m**6/3 - 26*m**5/5 - 49*m**4/2 + 