*4/2 - 6*o**3/5 + 38*o - 4. Determine c, given that v(c) = 0.
-3, 0, 1, 6
Let g(f) be the first derivative of 5*f**6/6 - f**5 - 5*f**4/4 + 5*f**3/3 - 140. Find u, given that g(u) = 0.
-1, 0, 1
Let t be (23 - 23)*2/(-10). Let b be (-34)/10 + (25/5 - 1). Solve t - 1/5*a**3 + 7/5*a**2 - 2/5*a + b*a**5 - 7/5*a**4 = 0.
-1, 0, 1/3, 1, 2
Factor 1/3*w**5 - 14/3*w**2 - 2/3*w**4 + 0 - 5/3*w - 4*w**3.
w*(w - 5)*(w + 1)**3/3
Let b(l) = -13*l**3 + l**2 + 10*l + 12. Let d(y) = 7*y**3 - y**2 - 5*y - 5. Let a(j) = -4*b(j) - 10*d(j). Factor a(c).
-2*(c - 1)*(3*c + 1)**2
Let i be -5 + (58/(-667) - (-627)/69). Determine h so that -1/2*h**3 + 0 + 0*h - 1/4*h**2 - 1/4*h**i = 0.
-1, 0
Let b(y) be the first derivative of -y**6/15 - y**5/20 + y**4/6 + y**3/6 + 37*y + 34. Let g(x) be the first derivative of b(x). Factor g(f).
-f*(f - 1)*(f + 1)*(2*f + 1)
Let j be (3/(-4))/(23/(-184)). Factor j*o**2 - 7*o**2 + 4*o**3 + 13*o**2.
4*o**2*(o + 3)
Suppose 165 = 57*t - 63. Let y(d) be the second derivative of 8/3*d**3 + 2*d - 4/3*d**t + 1/5*d**5 + 0 + 0*d**2. Factor y(g).
4*g*(g - 2)**2
Let s = -11 + 13. Suppose 2*o + 3*a + 8 = 0, -5*o + 0*a + 18 = -s*a. Suppose -8*r**3 - 2*r**2 - 4*r**3 + r**o - 2*r**2 + 3*r**4 + 12*r**5 = 0. Calculate r.
-1, -1/4, 0, 1
What is h in -13*h**3 - 185*h**2 - 6*h**3 + 0*h**3 + 29*h**3 + 2080*h - 6400 - 5*h**3 = 0?
5, 16
Let g = 3231 + -6451/2. Find a such that 33/4*a**2 + g*a**3 + 5*a + 1 + 5/4*a**4 = 0.
-2, -1, -2/5
Let a be -13 + 11 - 140/(-63). Factor -a*s - 2/3*s**2 - 4/9*s**3 + 0.
-2*s*(s + 1)*(2*s + 1)/9
Factor 19773 - 167*l + 11432 + 5*l**2 - 623*l.
5*(l - 79)**2
Suppose -4*d + 6 = -3*n, 2*d + 2*d - 10 = n. Factor 5*q**2 + 0*q**3 - n*q**3 - 5*q**2.
-2*q**3
Let y be 3/(-6)*19/(-38). Let f(z) = z**2 - 3*z + 3. Let d be f(2). Determine j, given that -y*j**2 + j - d = 0.
2
Let z(n) = n**2 + 2. Let d(h) = h**2 - 159*h - 58. Let y(t) = -d(t) - 6*z(t). Factor y(r).
-(r - 23)*(7*r + 2)
Let r(f) be the first derivative of 61 + 2/5*f**5 + 1/4*f**4 + 0*f + f**2 - 5/3*f**3. Factor r(y).
y*(y - 1)*(y + 2)*(2*y - 1)
Let k(s) be the third derivative of -1/4*s**3 + 0 + 0*s + 0*s**6 - 1/140*s**7 - 12*s**2 + 1/20*s**5 + 0*s**4. Factor k(r).
-3*(r - 1)**2*(r + 1)**2/2
Let a(m) = -m**4 + 49*m**3 + 99*m**2 - 203*m - 415. Let i(p) = p**4 - 49*p**3 - 98*p**2 + 204*p + 416. Let y(w) = 8*a(w) + 7*i(w). Factor y(b).
-(b - 51)*(b - 2)*(b + 2)**2
Let v(a) be the second derivative of a**7/84 + a**6/15 - a**5/40 - a**4/6 - 78*a - 1. Determine n, given that v(n) = 0.
-4, -1, 0, 1
Let r(a) = a**3 + 4*a**2 + 2*a - 2. Let x be r(-2). Let v be (x/4 - -1)*(-8)/(-6). Find p such that -2/3*p**v + 0*p + 0 = 0.
0
Let y(m) be the second derivative of -m**5/390 + 7*m**4/78 - 49*m**3/39 + 5*m**2/2 + 21*m. Let i(g) be the first derivative of y(g). Factor i(j).
-2*(j - 7)**2/13
Let l(d) be the first derivative of -9*d**5/5 - 3*d**4/4 + 17*d**3 - 57*d**2/2 + 18*d + 186. Determine v so that l(v) = 0.
-3, 2/3, 1
Let o(r) = -14*r + 87. Let q be o(6). Factor 1/3*t**q + 0*t + t**2 - 4/3.
(t - 1)*(t + 2)**2/3
Let v(p) = p**3 - 8*p**2 - 37*p - 16. Let r(k) = k**3 - 7*k**2 - 38*k - 16. Let m(g) = 6*r(g) - 7*v(g). Factor m(c).
-(c - 16)*(c + 1)**2
Find r, given that 2*r**3 - 2/3*r**4 + 110/3*r**2 + 60 + 94*r = 0.
-3, -1, 10
Let k = -54 - -56. What is x in 75*x + 24*x**2 + x**k + 10*x**2 + 5*x**3 + 45 = 0?
-3, -1
Suppose 0 = 5*s + 11*s. Let n(k) be the first derivative of s*k**3 - 5 + 0*k + 0*k**2 + 1/2*k**4. Factor n(h).
2*h**3
Let u be (-125)/(-4)*76/570 - 4. Let -1/6*r**3 + u*r**2 + 0*r + 0 = 0. What is r?
0, 1
Let g(j) = 2*j**3 + 2*j. Let i(a) = 37*a**3 - 1148*a**2 - 680*a - 96. Let f(w) = -6*g(w) - i(w). Factor f(y).
-(y - 24)*(7*y + 2)**2
Let v be (2 - 1)*(1 + -48). Let r = v + 68. Factor r*z - 5*z**2 - 3*z**2 + 2*z**3 - 15*z.
2*z*(z - 3)*(z - 1)
Let i be (10/(300/(-18)))/(2/(-10)). Let z(d) be the first derivative of 1/5*d**2 + 4/15*d**i + 1/10*d**4 + 0*d - 4. Find h such that z(h) = 0.
-1, 0
Let m(h) be the third derivative of -h**8/1008 - 4*h**7/105 - h**6/8 - 11*h**5/90 - 12*h**2 - 4*h. Suppose m(o) = 0. What is o?
-22, -1, 0
Let l(w) be the third derivative of 0*w**4 - 1/735*w**7 + 0 - 1/21*w**3 + 1/105*w**5 - 6*w**2 + 0*w**6 + 0*w. Let l(t) = 0. What is t?
-1, 1
Let u = 1/15451 + 16903387/108157. Let t = u - 156. Suppose -4/7*s**2 + 2/7 + t*s**4 + 0*s + 0*s**3 = 0. Calculate s.
-1, 1
Let i(v) = 8*v**4 - 20*v**3 - 40*v**2 + 52*v - 8. Let z(h) = 7*h**4 - 21*h**3 - 39*h**2 + 53*h - 6. Let d(r) = 3*i(r) - 4*z(r). Let d(n) = 0. What is n?
-2, 0, 1, 7
Let s(d) = -d**3 + 11*d**2 + 12*d + 3. Let t be s(12). Let h = -718 - -722. What is y in 14/13*y**h + 2*y**2 + 0 - 30/13*y**t - 2/13*y**5 - 8/13*y = 0?
0, 1, 4
Let t(w) = -9*w**3 - 287*w**2 - 28225*w - 912675. Let j(v) = 40*v**3 + 1146*v**2 + 112899*v + 3650701. Let z(o) = -2*j(o) - 9*t(o). Solve z(h) = 0.
-97
Let v(g) be the first derivative of -g**4/2 - 5*g**3/3 + 2*g**2 + 5*g - 44. Let i be v(-3). Find d, given that 0 + 4/5*d - d**3 + 3/5*d**4 - 4/5*d**i = 0.
-1, 0, 2/3, 2
Find w such that -30*w**2 + 9/2*w**3 - 16 - 46*w = 0.
-2/3, 8
Factor -2 + 144*m**2 - m + 0 + 145*m**2 - 288*m**2.
(m - 2)*(m + 1)
Let i(z) = 7*z**5 - z**4 + 31*z**3 - 61*z**2 + 50*z - 13. Let w(h) = -3*h**5 - 15*h**3 + 30*h**2 - 24*h + 6. Let u(g) = 6*i(g) + 13*w(g). Factor u(q).
3*q*(q - 2)*(q - 1)**2*(q + 2)
Let c(z) be the first derivative of -z**4/3 + 16*z**3/9 + 50*z**2/3 - 112*z/3 + 47. Factor c(k).
-4*(k - 7)*(k - 1)*(k + 4)/3
Let a(w) be the first derivative of w**7/735 - 11*w**5/210 - 3*w**4/14 - 8*w**3/21 - 10*w**2 + 12. Let p(o) be the second derivative of a(o). Factor p(i).
2*(i - 4)*(i + 1)**2*(i + 2)/7
Let 15/2*p**2 + 385/2 + 580*p = 0. Calculate p.
-77, -1/3
Let g(h) be the second derivative of h**6/60 + h**5/60 - h**4/12 - h**3/6 - 7*h**2 - 15*h. Let y(r) be the first derivative of g(r). What is t in y(t) = 0?
-1, -1/2, 1
Let s(z) = -4*z**3 - 54*z**2 + 732*z + 794. Let r(l) = -l**3 + 4*l**2 + 2*l - 1. Let u(n) = 12*r(n) - 2*s(n). Solve u(o) = 0.
-1, 20
Let i(t) be the third derivative of -t**8/1680 + t**7/50 - 11*t**6/40 + 23*t**5/12 - 25*t**4/4 - 3*t**2 - 18*t. Solve i(q) = 0 for q.
0, 5, 6
Let x = -32917/65923 - -1452/461. Let t = -19/11 + x. Let 18/13 - t*k + 2/13*k**2 = 0. What is k?
3
Let s = 24 - 22. Factor 0*i**2 + 8*i + 0*i**2 - 3*i**s + 5*i**2 + 6.
2*(i + 1)*(i + 3)
Let r = 13327/45 + -2660/9. Suppose b + 16 = 4*t, 5*b + 5 = -t + 3*b. Let 0 + 9/5*z + 12/5*z**2 + r*z**t = 0. Calculate z.
-3, -1, 0
Let b(t) = t - 3 + 3 - 1 + t**2. Let o(g) be the third derivative of g**5/30 - g**3/2 - 3*g**2. Let d(w) = -12*b(w) + 4*o(w). Solve d(p) = 0 for p.
-3, 0
Factor -3/5*k**2 - 3/5*k**3 + 0 + 3/5*k**4 + 3/5*k.
3*k*(k - 1)**2*(k + 1)/5
Let g = -5611 + 50501/9. Factor 10/9*z - 2/3 - 2/9*z**2 - g*z**3.
-2*(z - 1)**2*(z + 3)/9
Let z(l) be the second derivative of 0 - 10*l + 1/20*l**5 - 1/45*l**6 + 1/6*l**3 + 0*l**2 + 1/12*l**4. Let m(v) be the second derivative of z(v). Factor m(j).
-2*(j - 1)*(4*j + 1)
Let v(q) = -4 - 9*q + 6 + 3*q**3 - 2*q**3 - 8*q**2. Let s be v(9). Factor -6*n - 7 + 6*n**s - 2 + 0 - 7*n**2.
-(n + 3)**2
Let j be (4/8)/(2/(-32)). Let r = j + 10. Determine q so that 6*q + r + 2 + 2*q**2 + 0*q**2 = 0.
-2, -1
Determine x so that -10*x - 169*x**2 - 21*x**3 - 4*x**3 + 134*x**2 = 0.
-1, -2/5, 0
Let p(l) be the second derivative of -l**6/1080 + 7*l**5/360 - l**4/12 + 5*l**3/6 - 30*l. Let o(i) be the second derivative of p(i). Let o(z) = 0. What is z?
1, 6
Suppose 3*a - 976 + 1010 = 4*v, a + 14 = 2*v. Factor 0 - 8/11*b**v + 0*b + 0*b**3 + 2/11*b**2.
-2*b**2*(2*b - 1)*(2*b + 1)/11
Let n = 87 + -65. Suppose 8 = 15*v - n. Determine s so that 10/3*s - v*s**2 - 4/3 = 0.
2/3, 1
Let x be 2/((-12)/(-3))*-164. Let y = 165/2 + x. Suppose y*w**4 - 2 - 3/2*w**2 - w**3 + 4*w = 0. What is w?
-2, 1, 2
Let f(t) be the third derivative of 0*t**4 + 0 + 0*t**3 - 1/200*t**6 + 0*t - 1/100*t**5 - 6*t**2. Let f(i) = 0. What is i?
-1, 0
Let j(u) be the first derivative of -1/2*u**4 - 2*u**3 + 8 + u**2 + 6*u. Factor j(r).
-2*(r - 1)*(r + 1)*(r + 3)
Let w(o) = 34*o**2 + 15*o + 11. Let d(j) = -3*j**2 - j - 1. Let l(z) = -44*d(z) - 4*w(z). Suppose l(p) = 0. What is p?
-4, 0
Let m = -2302/105 + 112/5. Factor m + 4/7*n + 2/21*n**2.
2*(n + 1)*(n + 5)/21
Let i(h) = h**3 - 13*