
-3*r*(r - 2)*(r + 3)
Let v(g) be the first derivative of 6*g + 60*g**3 - 52 + 69/2*g**2 - 27*g**4. What is h in v(h) = 0?
-1/6, 2
Let c(y) be the third derivative of -2*y**7/525 + 71*y**6/150 - 977*y**5/75 - 2171*y**4/30 - 748*y**3/5 - 2*y**2 + 6*y - 1189. Suppose c(h) = 0. Calculate h.
-1, 22, 51
Let a = 2742 - -18290. Let -a*h**3 - 3*h**5 + 7*h + 20978*h**3 + 60*h**2 - 31*h + 21*h**4 = 0. What is h?
0, 1, 2
Suppose -18*p + 159 = 69. Suppose -4*t + 8*t = c + 10, p*c = -10. Suppose 1/6*u**t + 121/6 - 11/3*u = 0. What is u?
11
Factor -1415 + 95 + 4*r**2 - 2*r - 47*r + 125*r.
4*(r - 11)*(r + 30)
Let b(t) be the first derivative of -t**4/2 - 40*t**3/3 + 43*t**2 - 44*t + 183. Suppose b(n) = 0. Calculate n.
-22, 1
Let c(i) = 7*i**2 + 470*i + 55696. Let q(o) = 17*o**2 + 939*o + 111392. Let x(p) = -10*c(p) + 4*q(p). Find v, given that x(v) = 0.
-236
Let z(c) be the first derivative of c**4/4 - 148*c**3/3 - 303*c**2/2 + 450*c + 170. Factor z(q).
(q - 150)*(q - 1)*(q + 3)
Let v(x) = -x**2 - 19*x + 22. Let u be v(-20). Suppose -k**3 + 3*k**5 + 3*k**4 + u*k**4 - 7*k**4 + 4*k**4 = 0. What is k?
-1, 0, 1/3
Let p(u) = -u**2 + 16*u - 53. Suppose 0 = 6*v - 9*v + 21. Let c be p(v). Factor 8/5*r**3 + 18/5 + c*r**2 + 84/5*r.
2*(r + 3)**2*(4*r + 1)/5
Let g(m) be the first derivative of -3 + 42*m - 1/6*m**4 + 4*m**2 + 4/3*m**3 - 1/10*m**5. Let a(r) be the first derivative of g(r). Solve a(k) = 0 for k.
-2, -1, 2
Let r(v) be the second derivative of v**7/147 - 2*v**6/21 - 5*v**5/7 - 40*v**4/21 - 55*v**3/21 - 2*v**2 - 473*v. Factor r(q).
2*(q - 14)*(q + 1)**4/7
Let l(p) be the first derivative of 0*p**4 + 0*p**2 - 172 - 2/3*p + 4/9*p**3 - 2/15*p**5. Determine a so that l(a) = 0.
-1, 1
Let l(x) = 5*x**5 + 16*x**4 + 78*x**3 + 11*x**2 + 11*x. Let k(r) = r**5 + 3*r**4 + 14*r**3 + 2*r**2 + 2*r. Let y(p) = -22*k(p) + 4*l(p). Factor y(d).
-2*d**3*(d - 1)*(d + 2)
Let f(q) be the first derivative of q**6/3 + 52*q**5/5 + 83*q**4 + 352*q**3/3 - 815*q**2 - 1700*q - 4097. Suppose f(d) = 0. Calculate d.
-17, -5, -1, 2
Let s(j) be the first derivative of -j**6/10 + 3*j**5/10 + j**4/4 - j**3 + 22*j + 17. Let x(b) be the first derivative of s(b). Factor x(d).
-3*d*(d - 2)*(d - 1)*(d + 1)
Let j(r) be the second derivative of r**4/8 + 797*r**3/2 + 1905627*r**2/4 + 3347*r. Suppose j(z) = 0. What is z?
-797
Let g(h) be the second derivative of h**7/42 + 3*h**6/10 + h**5/4 - 29*h**4/12 - 7*h**3 - 8*h**2 + h + 55. Find q such that g(q) = 0.
-8, -1, 2
Find n, given that -235*n**2 + 543*n**4 - 308*n**4 + n + 70*n**3 - 40*n**5 - 26*n - 5*n = 0.
-1, -1/8, 0, 1, 6
Let l = 1/2887 - 66411/28870. Let b = l - -12/5. Solve -1/5 + 3/10*k - b*k**2 = 0.
1, 2
Let o(l) be the second derivative of l**6/6 + 59*l**5/4 + 115*l**4 + 270*l**3 + 2158*l. Factor o(k).
5*k*(k + 2)*(k + 3)*(k + 54)
Let n(v) be the first derivative of v**5/20 + 23*v**4/16 + 31*v**3/6 + 5*v**2 - 608. Find t, given that n(t) = 0.
-20, -2, -1, 0
Let o = -5515 + 5518. Let c(z) be the first derivative of 1/4*z**4 - 2*z**2 + z**o + 0*z - 17. Factor c(t).
t*(t - 1)*(t + 4)
Let j(y) = 32*y**4 + 1191*y**3 + 4911*y**2 + 5400*y + 1785. Let v(w) = -3*w**3 - w**2 + 1. Let a(c) = j(c) - 3*v(c). Find n, given that a(n) = 0.
-33, -3, -3/4
Let t(z) be the second derivative of 9*z**5/4 - 1628*z**4 + 434*z**3 + 8791*z - 1. Factor t(f).
3*f*(f - 434)*(15*f - 2)
Suppose 0 - 2*z**2 + 3/4*z**5 + 0*z - 7/2*z**4 + 5*z**3 = 0. What is z?
0, 2/3, 2
Find j such that 0 - 1/5*j**3 - 68*j + 37/5*j**2 = 0.
0, 17, 20
Factor 75*t + 19*t**2 - 39*t**2 + 525*t - 4*t**3 - 56*t**2.
-4*t*(t - 6)*(t + 25)
Let b(t) = -3*t**2 + 47*t + 63. Let z(x) = -x**2 + 24*x + 31. Let c = -72 - -28. Let f be (-8)/c + (-128)/(-22). Let r(h) = f*b(h) - 13*z(h). Factor r(i).
-5*(i + 1)*(i + 5)
Let l(q) = q**2 - 2*q - 3. Let b = -25 - -27. Let w(f) = 11 + 4*f - 10 - 4*f + f**b. Let g(t) = l(t) + 3*w(t). Factor g(x).
2*x*(2*x - 1)
Let j(m) be the first derivative of -m**7/3360 + m**6/1440 - m**3/3 + 5*m**2 - 66. Let b(g) be the third derivative of j(g). Factor b(t).
-t**2*(t - 1)/4
Determine s so that 264627/2 + 3/2*s**2 - 891*s = 0.
297
Find s such that 3/2*s**2 + 231/2 + 117*s = 0.
-77, -1
Let b be 48/(-30)*3*10. Let j be (b/(-32))/(2/4). Determine d, given that 6*d**4 + 3*d**3 - 4*d**4 - 5*d**j = 0.
0, 1
Let j(y) be the third derivative of y**5/15 + 823*y**4 + 4063974*y**3 + 46*y**2 - 51. Let j(r) = 0. Calculate r.
-2469
Let c(i) = -i**5 - 2*i**4 - i**3 - i**2 - i - 1. Let a(l) = -24*l**4 - 6*l**3 + 15*l**2 - 3*l - 3. Let t(m) = a(m) - 3*c(m). Factor t(x).
3*x**2*(x - 6)*(x - 1)*(x + 1)
Let m(c) be the third derivative of c**7/6 + c**6/24 - c**5/2 + 3*c**2 + 383. Factor m(p).
5*p**2*(p + 1)*(7*p - 6)
Let h be 0 + ((-1)/(-17) - (-3828)/1972). Solve -2/17*x**h - 12/17 - 10/17*x = 0 for x.
-3, -2
Suppose 2*c + 6*k - 24 = 2*k, -5*c - 2*k = -28. Let d(u) = 685*u**2 - 2380*u - 505. Let p(z) = 49*z**2 - 170*z - 36. Let h(y) = c*d(y) - 55*p(y). Factor h(r).
5*(r - 4)*(9*r + 2)
Let q = 72 + -68. Let v(p) = -p**4 + p**2 + p. Let a(s) = -6*s**4 + 10*s**3 - 2*s**2 - 14*s. Let d(y) = q*v(y) - a(y). Find b, given that d(b) = 0.
-1, 0, 3
Let v(w) be the second derivative of 35*w**4/4 - 100*w**3/3 - 10*w**2 + 430*w + 7. Factor v(u).
5*(u - 2)*(21*u + 2)
Let s(l) = 102*l**3 + 4239*l**2 + 4175*l - 8450. Let z(b) = -19*b**3 - 848*b**2 - 835*b + 1690. Let r(t) = 2*s(t) + 11*z(t). Factor r(f).
-5*(f - 1)*(f + 2)*(f + 169)
Let j(s) be the first derivative of -s**3 - 927*s**2/2 - 5549. What is w in j(w) = 0?
-309, 0
Let o = -19067272 + 23262073289/1220. Let n = o - -3/244. Suppose -7/10*j**2 + n - 4*j = 0. Calculate j.
-6, 2/7
Let o(l) = -l**5 - l**3 + l**2 - l + 1. Let q(d) = -20*d**5 + 20*d**4 + 690*d**3 + 5138*d**2 + 14332*d + 13518. Let k(x) = 36*o(x) - 2*q(x). Factor k(w).
4*(w - 27)*(w + 2)*(w + 5)**3
Let k(b) be the first derivative of -65*b**2 + 133 + 14/3*b**3 + 36*b. Factor k(p).
2*(p - 9)*(7*p - 2)
Let l(x) = 15*x**3 + 134*x**2 + 512*x + 504. Let z(c) = -141*c**3 - 1204*c**2 - 4606*c - 4536. Let p(d) = 19*l(d) + 2*z(d). Let p(m) = 0. Calculate m.
-42, -2
Suppose -12*n = n - 26. Suppose 8 = -2*b + 4*h, -b + n = -5*h + 12. Suppose 2*r**2 + b + 4/3*r = 0. Calculate r.
-2/3, 0
Let h(n) = -n**3 + 29*n**2 + 96*n + 16. Let j be h(32). Suppose 5*c = 5*l, 5*c = -l - 2*l + j. Determine q, given that 8/3 - 8/3*q**c + 4/3*q**3 - 4/3*q = 0.
-1, 1, 2
Suppose 71*g + 15 = 3*x + 76*g, x - 9 = -3*g. Let p(n) be the second derivative of 0 + 0*n**3 + 0*n**4 + 1/10*n**5 + 11*n + x*n**2. Find f such that p(f) = 0.
0
Solve 11094 - 21927/2*n**2 - 23217/4*n**3 + 5805*n - 261/2*n**4 - 3/4*n**5 = 0.
-86, -2, -1, 1
Factor -502*j**4 + 5*j**5 + 20*j**2 + 311*j**4 + 176*j**4.
5*j**2*(j - 2)**2*(j + 1)
Let t(i) = 6*i**4 + 66*i**3 + 257*i**2 + 125*i - 77. Let y(s) = -3*s**4 - 34*s**3 - 129*s**2 - 62*s + 38. Let z(h) = 2*t(h) + 5*y(h). Factor z(n).
-(n + 1)*(n + 6)**2*(3*n - 1)
Suppose a - 3*l = 23, 5*a - 57 = 2*l - 7. Let m(o) = 12*o**2 - 64*o - 332. Let t(n) = -2*n**2 - n + 1. Let p(q) = a*t(q) + m(q). Let p(b) = 0. Calculate b.
-9
Let t be 1*((-1770)/10 + 9). Let d be ((-1)/5)/(84/t). Let 2/5*n**3 - 2/5*n**4 - 2/5*n + d*n**2 + 0 = 0. What is n?
-1, 0, 1
Let k(x) be the first derivative of 114*x**2 + 116*x + 2/3*x**6 - 58*x**4 - 108/5*x**5 - 13 - 8/3*x**3. Let k(v) = 0. Calculate v.
-1, 1, 29
Let s = -2241 + 2243. Suppose -2*i + 2*q = 0, -5*q = 7*i - 11*i - 3. Find p such that 30/7*p**s + 3/7 - 15/7*p - 30/7*p**i + 15/7*p**4 - 3/7*p**5 = 0.
1
Let t = 19 + -11. Suppose 0 = 2*u + 3*h - 4, 0 = -4*u - 2*h + t. Determine a, given that -a**u + 5*a**3 - 5*a + 101 - 91 - 9*a**2 = 0.
-1, 1, 2
Let d(b) = b**2 - 5*b - 12. Let z be d(5). Let s = -10 - z. Factor 2*w**s + 61 + 5*w - 3*w - 73.
2*(w - 2)*(w + 3)
Let i(j) = -4*j**3 - 268*j**2 + 6959*j + 20. Let t be i(20). Factor t*f - 2*f**5 + 0 + 27/2*f**2 - 45/2*f**3 + 12*f**4.
-f**2*(f - 3)*(2*f - 3)**2/2
Let t(v) be the first derivative of -v**3 - 1431*v**2 + 5736*v + 4767. Find j such that t(j) = 0.
-956, 2
Let k(p) be the second derivative of p**5/20 + 493*p**4/4 + 182533*p**3/2 + 546121*p**2/2 - 1375*p. What is s in k(s) = 0?
-739, -1
Let y(h) = -h**2 - h + 3. Let f be y(-6). Let x be 0/(-9*3/f). Factor x + 4/17*l + 2/17*l**2.
2*l*(l + 2)/17
Let s(u) be the second derivative of u + 12