t d be 6 + 1 + (s/35 - 6). Factor d*k**2 + 0 - 1/7*k**3 + 2/7*k.
-k*(k - 2)*(k + 1)/7
Let i(a) = 1017*a - 38642. Let g be i(38). Factor 0 + 0*p + 6/7*p**g + 4/7*p**2 + 10/7*p**3.
2*p**2*(p + 1)*(3*p + 2)/7
Let r(h) be the third derivative of h**6/30 - 32*h**5/15 + 45*h**4/2 - 3732*h**2 + 2. Let r(m) = 0. What is m?
0, 5, 27
Suppose 0 = 4*j - 115 + 107. Suppose -5*m = -j*q - 10, -m + 5*q = -11 - 14. Determine f so that -4/3*f**5 + m*f**3 - 8/3*f**2 + 0 + 8/3*f**4 + 4/3*f = 0.
-1, 0, 1
Let h(z) = 4*z**3 + 100*z**2 + 2*z + 50. Let v be h(-25). Let n(b) be the second derivative of -1/60*b**4 - 1/5*b**3 + 0 + 36*b + v*b**2. Factor n(t).
-t*(t + 6)/5
Suppose -2*z = -5*p + 496 + 984, 0 = 3*p - 4*z - 874. Let j = p + -298. Factor j - 6/5*d**3 + 6/5*d - 2/5*d**2 + 2/5*d**4.
2*d*(d - 3)*(d - 1)*(d + 1)/5
Let r(y) be the first derivative of 5*y**4/4 + 100*y**3/3 + 605*y**2/2 + 1050*y - 1607. Determine m, given that r(m) = 0.
-10, -7, -3
Let r(t) be the second derivative of -13*t + 1/50*t**6 - 1/20*t**4 + 0*t**2 + 1/5*t**3 - 3/50*t**5 - 1. Factor r(k).
3*k*(k - 2)*(k - 1)*(k + 1)/5
Let c(n) be the third derivative of -n**6/80 - n**5/20 + 211*n**4/16 - 52*n**3 - 56*n**2 - 23. Solve c(i) = 0.
-16, 1, 13
Let r(o) = -7*o**2 + 30*o - 4. Let z be r(4). Let -2*y**3 + 20*y**4 - 6*y**z + 18*y**2 - 11*y**4 + 17*y**3 = 0. Calculate y.
-3, -2, 0
Let c(d) be the second derivative of -25*d**4/36 + 340*d**3/3 - 6936*d**2 + d + 244. Factor c(u).
-(5*u - 204)**2/3
Let s(o) = 2*o**4 - 77*o**3 - 90*o**2 + 74*o + 70. Let x(q) = q**4 - 76*q**3 - 84*q**2 + 74*q + 71. Let r(h) = 2*s(h) - 3*x(h). Let r(z) = 0. What is z?
-73, -1, 1
Let y(m) be the second derivative of 3*m**5/20 - 7*m**4/2 + 49*m**3/2 - 9*m + 7. Factor y(d).
3*d*(d - 7)**2
Let y(u) = u - 10. Let v(m) = -6*m + 49. Let r(o) = 6*v(o) + 33*y(o). Let l be r(-13). Factor 1741*c**2 - 4*c**l - 34 - 94 - 1717*c**2.
-4*(c - 4)**2*(c + 2)
Let -29/4*j**3 + 0 + 2*j**5 - 19/2*j**4 + 19/2*j**2 + 21/4*j = 0. What is j?
-1, -1/2, 0, 1, 21/4
Let o be (29/(-5) - -1)*(-30)/4. Suppose 784*f**2 - o*f + 4*f**4 - 786*f**2 + 16 - 10*f**3 + 28*f**3 = 0. What is f?
-4, -2, 1/2, 1
Suppose 12*k - 42*k - 22*k = -4*k. Suppose -9/5*r**4 - 3/5*r**2 + k*r - 3/5*r**5 - 9/5*r**3 + 0 = 0. What is r?
-1, 0
Let f(p) be the second derivative of -p**4/4 - 732*p**3 - 803736*p**2 + 267*p. Suppose f(h) = 0. What is h?
-732
Let l(k) be the second derivative of 0*k**2 - 2*k**3 - 1/3*k**4 + 0 - 15*k. Factor l(z).
-4*z*(z + 3)
Let z(b) be the second derivative of b**6/30 + 2*b**5/15 - b**4/2 - 29*b**2 + 50*b. Let w(u) be the first derivative of z(u). Let w(q) = 0. Calculate q.
-3, 0, 1
Let v(i) = 3*i**2 - 1. Let z(x) = -35*x**2 + 4*x - 7. Let m(j) = 2*j**2 - 1. Let d(b) = 6*m(b) + z(b). Let s(r) = -5*d(r) - 40*v(r). Factor s(f).
-5*(f - 3)*(f + 7)
Let p = 43/8948 - -23467/4474. Solve 3/4*t**5 + 15/4*t**3 - 9/2*t + 21/4*t**2 - p*t**4 + 0 = 0 for t.
-1, 0, 1, 6
Suppose -a = j + 8, 3 = -5*j + 2*a + 19. Let f = -14 + 114/7. Let -40/7*d**2 - f*d - 6/7*d**4 + j - 4*d**3 = 0. What is d?
-2, -2/3, 0
Let w(i) be the second derivative of 0 + 0*i**2 + i**5 + 1/45*i**6 + 50/3*i**4 + 1000/9*i**3 - 170*i. Suppose w(q) = 0. Calculate q.
-10, 0
Let f(o) be the second derivative of -7*o**4/2 + 26*o**3/9 + 5*o**2/3 + 225*o - 3. Factor f(x).
-2*(7*x + 1)*(9*x - 5)/3
Let o = 17076 + -52813/3. Let b = -528 - o. Factor 0*r - 2/3*r**3 - b*r**4 + 0 - 1/3*r**2.
-r**2*(r + 1)**2/3
Let i(s) be the second derivative of s**6/10 + 9*s**5/4 - s**4 - 30*s**3 + 7676*s. Solve i(f) = 0 for f.
-15, -2, 0, 2
Suppose -18*t + 7*t = -1320. Solve 40*x - t*x + 37*x**2 - 39*x**2 - 800 = 0 for x.
-20
Suppose 17*i + 59*i - 5*i = -17*i. Suppose -w**3 + 0*w - 5/4*w**2 + i + 1/4*w**4 = 0. Calculate w.
-1, 0, 5
Let o(y) = -y**2 + 47*y + 4006. Let h be o(-44). What is q in 2/7*q**4 + 202/7*q**h - 34/7*q**3 + 300/7 - 470/7*q = 0?
1, 5, 6
Let u(o) be the first derivative of 265 + 0*o + 1/3*o**2 + 10/27*o**3. Determine j so that u(j) = 0.
-3/5, 0
Suppose 1477*b - 3002*b + 1499*b = 0. Factor 6*t + 1/2*t**2 + b.
t*(t + 12)/2
Factor -13749287 + 6523*g**4 + 646000*g - 6633*g**4 + 79700*g**2 - 690713 + 5*g**5 - 3595*g**3.
5*(g - 20)**3*(g + 19)**2
Let r(m) be the third derivative of m**7/50 + 1209*m**6/200 + 411*m**5/20 + 511*m**4/40 - 171*m**3/5 + 18*m**2. Determine a so that r(a) = 0.
-171, -1, 2/7
Suppose -3*m**5 - 14954*m**2 + 100*m + 264*m**3 - 12 + 14706*m**2 - 124*m**4 + 23*m**5 = 0. What is m?
1/5, 1, 3
Factor 2/7*m**3 + 60/7 - 46/7*m - 16/7*m**2.
2*(m - 10)*(m - 1)*(m + 3)/7
Suppose 0 = -7*a - 56, -8*p + 0*a + a - 4 = -12. Solve -10/3*j - 10 + p*j**3 + 15/2*j**2 - 5/6*j**4 = 0.
-3, -1, 2
Suppose 1263*m - 1261*m - 3*t = 40, -3*m - 54 = 5*t. What is p in 1/2*p**m - 2*p - 5/2 = 0?
-1, 5
Let o be (-2)/(-32) - 62156/8200*15/(-24). Factor -o + 33/5*a**2 + 126/5*a.
3*(a + 4)*(11*a - 2)/5
Factor 0*n - 2*n**3 + 0 + 6/5*n**2 + 2/5*n**5 + 2/5*n**4.
2*n**2*(n - 1)**2*(n + 3)/5
Solve 45/2*x**3 + 0*x**2 + 0 - 3/4*x**4 + 0*x = 0.
0, 30
Let g(b) = -14*b**3 - 13*b**2 - 13*b - 43. Let o be g(-5). Let i = o + -1444. Factor 0 - 2/5*c**5 - 8/5*c + 12/5*c**4 - 26/5*c**i + 24/5*c**2.
-2*c*(c - 2)**2*(c - 1)**2/5
Suppose v - 5*o = 31, 1 = -v - 4*o + o. Suppose 0 = -q + 4*k - 8, v = -6*q + 8*q + k. Factor q*f**4 + 2/5*f**2 + 9/5*f**5 + 0 + 13/5*f**3 + 0*f.
f**2*(f + 1)**2*(9*f + 2)/5
Factor 1/2*l**3 + 19/2*l - 9/2 - 11/2*l**2.
(l - 9)*(l - 1)**2/2
Suppose -38*d + 39*d + 4 = 0. Let p(l) = 11*l**4 - 2*l**3 - 4*l**2 + 9*l + 7. Let w(k) = 6*k**4 - 2*k**2 + 4*k + 4. Let u(b) = d*p(b) + 7*w(b). Factor u(f).
-2*f*(f - 4)*(f - 1)*(f + 1)
Let 599136/11 + 203504/11*n + 2/11*n**3 + 1270/11*n**2 = 0. Calculate n.
-316, -3
Let p(m) be the second derivative of -m**5/15 - 2*m**4/3 - 61*m**2/2 + 27*m. Let x(s) be the first derivative of p(s). Factor x(j).
-4*j*(j + 4)
Let r(f) be the second derivative of 0*f**2 + 0*f**3 + 0 - f**4 - 1/630*f**7 + 1/30*f**5 + 0*f**6 + f. Let u(m) be the third derivative of r(m). Factor u(a).
-4*(a - 1)*(a + 1)
Let j(n) = n**2 + 3*n + 1. Let a(r) = 4*r**2 - 81*r + 65. Let t(z) = a(z) - 2*j(z). Let h be t(43). Solve h + 4/5*p**2 + 8*p = 0.
-5
Let -305/2*b**3 - 2*b**4 - 184*b**2 + 75 + 527/2*b = 0. What is b?
-75, -2, -1/4, 1
Let t(v) be the third derivative of v**5/100 + 19*v**4/4 - 1073*v**2 - 1. Factor t(b).
3*b*(b + 190)/5
Factor 96 + 4*h**2 + 1553*h + 1501*h - 3098*h.
4*(h - 8)*(h - 3)
Let k(t) = -2*t**4 - 18*t**3 + 12*t**2 - 16*t - 72. Let g(v) = v**4 + 12*v**3 - 8*v**2 + 10*v + 45. Let l(u) = 8*g(u) + 5*k(u). Factor l(n).
-2*n**2*(n - 2)*(n - 1)
Let t(n) = 2*n**3 + 3*n + 2. Suppose 0 = 7*l - 2 + 37. Let a(x) = 3*x**3 + 6*x + 4. Let s(p) = l*t(p) + 3*a(p). Suppose s(v) = 0. Calculate v.
-1, 2
Let h(t) be the first derivative of -t**4 - 64*t**3/3 - 122*t**2 - 264*t + 2088. Suppose h(a) = 0. Calculate a.
-11, -3, -2
Let q(o) be the first derivative of -2*o**3/21 - 40*o**2/7 - 50*o + 94. Factor q(s).
-2*(s + 5)*(s + 35)/7
Let l(m) = 7*m**2 + 1246*m + 2458. Let d(z) = 6*z**2 + 1244*z + 2460. Let c(i) = 3*d(i) - 2*l(i). Factor c(x).
4*(x + 2)*(x + 308)
Suppose 2*c + z - 12 = 0, -579 + 639 = 3*c + 5*z. Suppose -2/7*j**3 - 8/7*j**2 - 6/7*j + c = 0. What is j?
-3, -1, 0
Let x = -663 + 667. Solve 5*m**2 - m**2 + 416*m**3 - 412*m**3 - 4*m**x - 4*m**5 = 0.
-1, 0, 1
Suppose 0 - 3*s - 7/2*s**3 + 1/2*s**5 + 13/2*s**2 - 1/2*s**4 = 0. What is s?
-3, 0, 1, 2
Let m(t) = -2*t**2 - 2. Let z(u) = 2*u**2 + 536*u + 542. Let w(i) = 4*m(i) + 2*z(i). Factor w(p).
-4*(p - 269)*(p + 1)
Let v be ((-1185)/(-25))/(255/50). Let s = v - 479/68. Let -3/4*x**3 - s*x + 3/4 + 9/4*x**2 = 0. Calculate x.
1
Suppose -4*q + 2*o = 11321 - 11315, 14 = 2*o. Let 9/2*i**q - 15*i + 0 + 3/2*i**4 + 9*i**3 = 0. What is i?
-5, -2, 0, 1
Let b be 120530/105 - 2/(-21). Let c = b - 10316/9. Suppose 2/9*o**5 - c - 16/9*o**4 - 76/9*o**2 + 50/9*o**3 + 56/9*o = 0. What is o?
1, 2
Let h = -2566 - -922. Let n = -1642 - h. Factor 2/3*p**3 + 0 - 10/3*p + 8/3*p**n.
2*p*(p - 1)*(p + 5)/3
Suppose 19 + 26 = 3*d. Let q = d - 59/5. Factor -32/5*o - 2/5*o**3 + q*o**2 + 0.
-2*o*(o - 4)**2/5
Let p be (-15835)/75 + (-28)/(-210). Let h = -209 - p. Factor -7/2 - 1/2*y**h - 4*y.
-(y + 1)*(y + 7)/2
Let x(m) be the second derivative of -m**5/80 - 105*m**4/16 - 157*m**3/12 + 1453*m. Dete