7*t**3/54 - 49*t**2/9 - 36*t. Find u, given that r(u) = 0.
2, 7
Let f(a) = -a**3 - 18*a**2 - 32*a + 4. Let i be f(-16). Determine k, given that -3*k**4 - 10*k**3 - 2*k**i - 5*k**3 = 0.
-3, 0
Let w(b) = -b**5 - b**4. Suppose 22 - 20 = 2*k. Let n(g) = -5*g**4 - 5*g**3. Let r(v) = k*w(v) + n(v). Suppose r(d) = 0. Calculate d.
-5, -1, 0
Let z(d) be the first derivative of -d**5/15 + d**4/6 + 5*d**3/3 - 6*d**2 - 371. Find j, given that z(j) = 0.
-4, 0, 3
Let f(s) = 22*s**2 + 1876*s - 232311. Let l(y) = -10*y**2 - 940*y + 116156. Let g(k) = 6*f(k) + 13*l(k). Factor g(b).
2*(b - 241)**2
Find j such that 1/2*j - 1/2*j**3 + 9/2*j**2 - 9/2 = 0.
-1, 1, 9
Let n(m) be the second derivative of 5/57*m**3 + 0 - 6/19*m**2 + 26*m - 1/114*m**4. What is g in n(g) = 0?
2, 3
Let v(i) be the first derivative of -2*i + 0*i**3 - i - i**3 - 35 - 3*i**2 + 52. Factor v(p).
-3*(p + 1)**2
Let c be (-2)/4*(-3 + -1). Suppose -4 = c*l - 10. Factor -2*b**2 + 6*b**3 + 0*b**3 + 8*b**4 + 4*b**l - 4*b**3.
2*b**2*(b + 1)*(4*b - 1)
Suppose -j = -0*j. Suppose -5*i - 6 + 81 = j. What is b in -5*b**4 + 3*b**4 - 3*b**4 + 21*b + i*b**3 + 8*b**4 + 6 + 27*b**2 = 0?
-2, -1
Let c(k) be the first derivative of -9*k**4/8 + 13*k**3/2 - 39*k**2/4 + 9*k/2 - 137. Factor c(l).
-3*(l - 3)*(l - 1)*(3*l - 1)/2
Let g(y) be the third derivative of 5/24*y**4 - 2/21*y**7 + 0*y + 5/336*y**8 + 1/4*y**6 - 12*y**2 + 0*y**3 - 1/3*y**5 + 0. Let g(d) = 0. Calculate d.
0, 1
Let y(c) be the first derivative of -2*c**5/55 + 5*c**4/22 + 4*c**3/11 + 24. Factor y(p).
-2*p**2*(p - 6)*(p + 1)/11
Solve -3*n - 3/5*n**2 - 18/5 = 0 for n.
-3, -2
Suppose 2*j - 8 = -4*u, -3 = -u - 1. Find p, given that 1/7 + j*p - 3/7*p**2 - 2/7*p**3 = 0.
-1, 1/2
Factor -1/2*r - 1/4*r**2 + 1/4*r**4 + 1/2*r**3 + 0.
r*(r - 1)*(r + 1)*(r + 2)/4
Let b(c) be the first derivative of -10*c + 10/3*c**3 + 5/2*c**2 + 29 - 5/4*c**4. Factor b(k).
-5*(k - 2)*(k - 1)*(k + 1)
Suppose 6*s - 15 = -27. Let w = s - -6. Suppose 2/15*o**w + 0 + 4/15*o**3 + 2/15*o**2 + 0*o = 0. What is o?
-1, 0
Let k(g) be the first derivative of g**4/28 - 19*g - 17. Let l(m) be the first derivative of k(m). Factor l(b).
3*b**2/7
Let w(t) = -t**2 + 5*t - 1. Let o be w(4). Let h be (-39)/(-2) + (-3)/(-2). Factor -21 + h - o*k**2.
-3*k**2
Let t(k) be the first derivative of -5*k**6/18 + 2*k**5/5 + 9*k**4/4 + 363. What is w in t(w) = 0?
-9/5, 0, 3
Factor 2/15*s**3 - 68/15 - 38/15*s + 32/15*s**2.
2*(s - 2)*(s + 1)*(s + 17)/15
Suppose 2 = -4*m + 10. Factor 0*t - 2 - 4*t + 3*t + t**m.
(t - 2)*(t + 1)
Let m(x) = -x**2 + 2*x + 1. Let y(v) = -v**2 - 4*v + 14. Let f(l) = 2*m(l) - y(l). Factor f(w).
-(w - 6)*(w - 2)
Let p = 21 - 24. Let h be 1/(28/(-8) - p) - -4. Determine c so that 1/4*c + 3/4*c**h - 1/2 = 0.
-1, 2/3
Let n(y) be the third derivative of y**7/525 - y**5/50 + y**4/30 + 3*y**2 - 17*y. Solve n(q) = 0.
-2, 0, 1
Let p = -716/3 + 239. Factor 2/3 - 2/3*u**2 - p*u**3 + 1/3*u.
-(u - 1)*(u + 1)*(u + 2)/3
Let c be (-2)/3 + 754/6. Suppose -c - 14*f - 24*f + 5*f - 17*f - 5*f**2 = 0. What is f?
-5
Let i(r) be the second derivative of -r**6/105 + 4*r**5/35 + 3*r**4/14 - r + 186. Factor i(d).
-2*d**2*(d - 9)*(d + 1)/7
Let p(i) = i**2 - 17*i - 13. Let l(s) = -s**2 + 25*s + 19. Let r be ((-14)/3)/((-20)/(-30)). Let a(m) = r*p(m) - 5*l(m). Solve a(t) = 0 for t.
-2, -1
Let f(a) be the first derivative of 0*a + 5/3*a**3 + 10*a**2 + 10. Find t, given that f(t) = 0.
-4, 0
Suppose -18 = -8*c + 2*c. Suppose -2*x = 4*d, 0 = 2*x + 2*d + c*d. Factor 0*j + 1/5*j**2 + x.
j**2/5
Factor 1/4*n**3 + 7/6*n**2 + 1/2 - 23/12*n.
(n - 1)*(n + 6)*(3*n - 1)/12
Factor 3/2*r**3 - 8*r**2 + 1/6*r**4 + 26/3*r + 0.
r*(r - 2)**2*(r + 13)/6
Let u(l) be the second derivative of -l**7/252 - l**6/45 - l**5/20 - l**4/3 - 19*l. Let v(i) be the third derivative of u(i). Factor v(k).
-2*(k + 1)*(5*k + 3)
Let a be 4/(-6)*6/4. Let c(p) = 3*p**4 + 8*p**3 - 19*p**2 + 4*p + 4. Let g(n) = -n**3 + n. Let h(j) = a*c(j) - g(j). Determine b so that h(b) = 0.
-4, -1/3, 1
Let t(z) be the second derivative of z**8/33600 - z**7/2520 + z**6/450 - z**5/150 - z**4/2 - z. Let u(l) be the third derivative of t(l). What is y in u(y) = 0?
1, 2
Let x(l) be the first derivative of -l**4/6 + 56*l**3/9 - 52*l**2/3 + 13. Let x(i) = 0. Calculate i.
0, 2, 26
Solve -1/3*o**3 + 5 - 23/3*o + 3*o**2 = 0.
1, 3, 5
Let g(m) be the first derivative of m**4/26 - 4*m**3/13 + 23. Determine k so that g(k) = 0.
0, 6
Let c = 75 + -63. Solve 35*k - c - 4*k**2 - 12*k - 7*k = 0.
1, 3
Let l(r) be the second derivative of -r**6/12 + 15*r**5/8 - 35*r**4/2 + 260*r**3/3 - 240*r**2 + 2*r + 69. Let l(y) = 0. What is y?
3, 4
Let f(v) be the third derivative of 0*v + 1/480*v**6 + 0*v**5 + 0*v**3 + 0 + 0*v**4 - 34*v**2. Suppose f(x) = 0. Calculate x.
0
Let r = 362/973 - 12/139. Factor -r*h**2 + 1/7 + 1/7*h**4 + 0*h**3 + 0*h.
(h - 1)**2*(h + 1)**2/7
Let k = 1929/805 - -3/805. Find o such that -4/5*o**2 - k + 16/5*o = 0.
1, 3
Suppose -z - 3*z - 8 = -4*k, 4*k - 9 = 3*z. Let n(q) be the second derivative of 0*q**2 - 7/20*q**4 - 3/20*q**5 - 1/5*q**k + q + 0. Factor n(r).
-3*r*(r + 1)*(5*r + 2)/5
Let y(h) be the second derivative of 0*h**2 + 1/6*h**4 - 6*h - 1/10*h**5 - 1/15*h**6 + 0 + 1/3*h**3. Factor y(p).
-2*p*(p - 1)*(p + 1)**2
Let i(k) = 2*k**3 + 2*k**2 - 2*k + 3. Let a be i(2). Factor a*p**2 + 11*p**2 + 135 + 71*p + 11*p**2 + 64*p + 5*p**3.
5*(p + 3)**3
Let k(f) = f**2 + 18*f - 16. Let m be k(-19). Factor -4 + 17*s**3 + 4*s**2 - 13*s**m + 4.
4*s**2*(s + 1)
Let k(u) be the first derivative of -10*u**6/3 + 88*u**5/5 + 22*u**4 - 128*u**3/3 - 34*u**2 + 40*u - 78. Solve k(n) = 0.
-1, 2/5, 1, 5
What is z in -4/3*z**5 - 1/3*z**4 + 5/3*z**2 - 4/3 + 20/3*z**3 - 16/3*z = 0?
-2, -1, -1/4, 1, 2
Let t(r) = 3*r**5 - 18*r**4 - 9*r**3 + 4*r**2 - 4*r + 4. Let b(o) = -6*o**5 + 39*o**4 + 18*o**3 - 9*o**2 + 9*o - 9. Let g(f) = -4*b(f) - 9*t(f). Factor g(c).
-3*c**3*(c - 3)*(c + 1)
Suppose -16*u - 15*u = 0. Let z(a) be the second derivative of -27/14*a**2 + 5*a + 15/14*a**3 + u - 1/4*a**4 + 3/140*a**5. Factor z(f).
3*(f - 3)**2*(f - 1)/7
Let y(n) be the first derivative of -2*n**5/5 + 11*n**4/2 - 6*n**3 - 11*n**2 + 20*n - 409. Factor y(f).
-2*(f - 10)*(f - 1)**2*(f + 1)
Let f(t) be the first derivative of t**4/6 + 8*t**3/9 + 5*t**2/3 + 4*t/3 + 84. Find o, given that f(o) = 0.
-2, -1
Let l(s) be the second derivative of -s**7/112 - 17*s**6/80 - 39*s**5/20 - 35*s**4/4 - 21*s**3 - 27*s**2 + 4*s + 42. What is w in l(w) = 0?
-6, -2, -1
Let v(q) be the third derivative of -q**5/240 - q**4/6 + 7*q**2 + 4*q. Factor v(c).
-c*(c + 16)/4
Let f(o) be the second derivative of o**6/115 + 7*o**5/115 - 5*o**4/138 + 2*o + 4. Factor f(x).
2*x**2*(x + 5)*(3*x - 1)/23
Factor 8/5*k**2 + 14/5*k + 6/5.
2*(k + 1)*(4*k + 3)/5
Suppose y - 52 + 50 = 0. Determine t, given that -2/7*t**y - 4/7*t - 2/7 = 0.
-1
Let x(d) be the first derivative of d**4 - 28*d**3/3 + 12*d**2 + 179. Factor x(f).
4*f*(f - 6)*(f - 1)
Let u(k) be the second derivative of 0 + 11/2*k**2 + 9*k + 0*k**3 - 1/90*k**5 - 1/36*k**4. Let c(b) be the first derivative of u(b). Factor c(y).
-2*y*(y + 1)/3
Let l(u) be the first derivative of u**7/1260 + u**6/240 + u**5/180 + 13*u**2/2 - 8. Let m(p) be the second derivative of l(p). Factor m(f).
f**2*(f + 1)*(f + 2)/6
Let l(y) be the first derivative of 16*y**3/3 + 106*y**2 + 52*y - 62. What is w in l(w) = 0?
-13, -1/4
Suppose -2*o = -3*f + 18, 2*f - 5*o + 9*o = -20. Find x such that 0*x + 2/3*x**3 + 0 + 2/9*x**5 - 2/3*x**4 - 2/9*x**f = 0.
0, 1
Suppose -3*a + 10*k = 15*k - 31, -5*k + 23 = -a. Let p be ((-3)/10)/((-2)/5). Suppose p*u**a + 3/2*u + 0 = 0. Calculate u.
-2, 0
Let j(y) be the third derivative of -1/90*y**5 + 0*y**3 + 0*y**4 - 14*y**2 + 1/360*y**6 + 0 + 0*y + 1/630*y**7. What is i in j(i) = 0?
-2, 0, 1
Let j(x) be the second derivative of x**5/10 + x**4/3 - 3*x**3 - 18*x**2 - 103*x + 3. Factor j(o).
2*(o - 3)*(o + 2)*(o + 3)
Let x be 5/(10/8) - 0. Suppose 9 = x*k - 7. Factor -1 + 2 + 3*t - k*t**2 + 7 + t.
-4*(t - 2)*(t + 1)
Let h(d) = -21*d**2 - 27*d + 138. Let p(u) = -10*u**2 - 14*u + 68. Let m(f) = 6*h(f) - 13*p(f). Factor m(i).
4*(i - 2)*(i + 7)
Let n(z) = 2*z**3 + 3*z**2 + 5*z - 3. Let w(y) = y**2 + y**2 + y**3 + 0*y**3 + 3*y - 2. Let d(v) = -4*n(v) + 7*w(v). Let d(f) = 0. Calculate f.
-1, 1, 2
Suppose 0