j**3/3 - 2*j**2 - 4. Let h(a) be the third derivative of u(a). Solve h(z) = 0 for z.
2/5, 1
Suppose 5*k = -5*s + 75, 1 - 16 = -5*k. Suppose -5*h - 14 = 3*l, 6*l + s = 4*l - 4*h. Factor -95*x + 36*x**l - 49*x - 77 + 140 + 129 - 3*x**3.
-3*(x - 4)**3
Let l(o) = -o**4 - o**3 - 6*o. Let j(t) = -48*t**3 - 350*t**2 - 738*t. Let a(b) = j(b) + 2*l(b). Suppose a(p) = 0. What is p?
-15, -5, 0
Let l(p) be the second derivative of 0*p**4 - 1/840*p**6 - 31/6*p**3 - 3/280*p**5 + 0 + 0*p**2 - 25*p. Let a(k) be the second derivative of l(k). Factor a(y).
-3*y*(y + 3)/7
Suppose -4*v + 2*y = 862 + 2872, -3*v - 4*y - 2828 = 0. Let p be (v/10)/((-6)/60*3). Factor -75 - 507*o**2 + p*o + 14 + 13.
-3*(13*o - 4)**2
Let m(k) be the second derivative of -11/30*k**5 - 3*k + 4/9*k**4 + 4/9*k**3 + 1/15*k**6 + 0*k**2 + 1. Solve m(p) = 0.
-1/3, 0, 2
Suppose 8*m + 193 = -23. Let d = m - -27. Factor 65*l**3 - 6*l**4 - 68*l**3 + 3*l**5 + d*l**4 + 6*l**2.
3*l**2*(l - 2)*(l - 1)*(l + 1)
Let k(a) be the third derivative of -a**6/120 - 26*a**5/15 - 745*a**2. Determine t, given that k(t) = 0.
-104, 0
Let n(i) be the first derivative of 2*i**3/3 + 696*i**2 + 1390*i + 2197. Factor n(b).
2*(b + 1)*(b + 695)
Let w(h) = h + 16. Let g be w(-13). Factor -753*p**3 + 30*p - 18*p**2 - 18 + 3*p + 756*p**g.
3*(p - 3)*(p - 2)*(p - 1)
Suppose 2*l + 2*l - 8 = 0, 2*v + l = -2. Let n(q) = 3*q**2 + 4*q. Let p be n(v). Factor 2/3 - 1/3*w**3 - w**2 + 1/3*w + 1/3*w**p.
(w - 2)*(w - 1)*(w + 1)**2/3
Let c = -1254341 - -6271706/5. Let r be (-1 - -2) + (-2)/5. Factor 2/5*b - r*b**2 + c.
-(b - 1)*(3*b + 1)/5
Let o(z) be the first derivative of 66*z**5/5 - 201*z**4/4 + 47*z**3 - 3*z**2 + 5985. Factor o(m).
3*m*(m - 2)*(m - 1)*(22*m - 1)
Let z(w) = -4*w**2 + 887*w - 904. Let a(g) = -3*g**2 + 444*g - 453. Let x(m) = -7*a(m) + 4*z(m). Let x(h) = 0. Calculate h.
-89, 1
Suppose 0 = 15*s - 8*s - 504. Factor 2*k - s - 24*k - 26*k + 22*k**2 - 2*k**3.
-2*(k - 6)**2*(k + 1)
Let v(o) be the first derivative of -1/5*o**5 + 5/4*o**4 - 112 + 0*o + 2*o**2 - 8/3*o**3. Solve v(q) = 0 for q.
0, 1, 2
Suppose 604*g - 864 = 572*g. Suppose g*o - 43*o + 32 = 0. Suppose o*h**3 + 0 + 3/2*h**4 + 1/2*h**2 + 0*h = 0. What is h?
-1, -1/3, 0
Let f be 3/(1*-14 + 30976/2178). Solve f + 3/4*x**2 + 57/4*x = 0.
-18, -1
Let k(q) = 9*q**3 - 45*q**2 - 218*q - 192. Let y(t) = 4*t**3 - 22*t**2 - 110*t - 96. Let g(p) = -6*k(p) + 14*y(p). Factor g(j).
2*(j - 24)*(j + 1)*(j + 4)
Factor 0*z**2 - 49/2*z**3 - 1/2*z**4 + 0*z + 0.
-z**3*(z + 49)/2
Let y(o) be the third derivative of o**5/510 + 91*o**4/102 + 8281*o**3/51 - 4*o**2 + 77*o. Determine k so that y(k) = 0.
-91
Let d(b) = 4*b**2 + 197*b + 809. Let v(j) = -j**2 + j + 3. Let k(r) = -4*d(r) - 20*v(r). Determine u so that k(u) = 0.
-4, 206
Suppose -5*s**5 - 15964*s**3 + 0 + 110*s**4 + 1170*s**2 + 15289*s**3 + 0 = 0. Calculate s.
0, 3, 6, 13
Let x(w) = -11*w**2 + 33*w + 374. Let h(z) = -35*z**2 + 96*z + 1121. Let s(n) = -4*h(n) + 13*x(n). Factor s(a).
-3*(a - 21)*(a + 6)
Find q such that 51656384*q - 3*q**3 + q**3 - 51656384*q + 294*q**2 = 0.
0, 147
Let p(i) be the first derivative of -16*i**5/5 + 129*i**4 + 132*i**3 + 1801. Factor p(v).
-4*v**2*(v - 33)*(4*v + 3)
Let x = 2/191543 - -1149244/1340801. Suppose -x*q**4 + 48/7*q**2 + 0 - 6*q**3 + 0*q = 0. What is q?
-8, 0, 1
Let b(w) be the first derivative of -2*w**5/75 + 19*w**4/15 - 170*w**3/9 + 1156*w**2/15 - 1226. Factor b(k).
-2*k*(k - 17)**2*(k - 4)/15
Suppose -54 = -14*f + 16. Factor -53*u**3 + 23*u**3 + f*u**2 + u - u + 25*u**4.
5*u**2*(u - 1)*(5*u - 1)
Let v = -75/6193 - -99313/18579. Factor 16/3 + 4/3*b**3 - v*b**2 - 4/3*b.
4*(b - 4)*(b - 1)*(b + 1)/3
Let t(d) = -d**3 - 9*d**2 - 23*d - 12. Let s be t(-5). Let 60*p**s - 44*p + 4*p**4 + 92*p**2 + 33*p**3 - 145*p**3 = 0. What is p?
0, 1, 11
Let a(i) be the first derivative of 2/9*i**6 - 11/3*i**4 - 32/3*i - 52/3*i**2 - 116/9*i**3 + 4/15*i**5 - 56. Factor a(r).
4*(r - 4)*(r + 1)**3*(r + 2)/3
Let h(y) be the first derivative of -y**8/175 - y**7/150 + y**6/45 - 6*y**3 - y**2 + 146. Let u(g) be the third derivative of h(g). Factor u(m).
-4*m**2*(3*m - 2)*(4*m + 5)/5
Suppose -2*s + 3*c - 2 = 0, c = -25 + 29. Factor -129*n**4 + 3*n**4 - 91767*n**3 + 3*n**s + 93090*n**3.
3*n**3*(n - 21)**2
Let m(g) = -g**2 + 11*g + 2. Let k(s) = 5*s**2 + 2740*s + 1937656. Let u(r) = k(r) + 4*m(r). Determine p, given that u(p) = 0.
-1392
Let n(m) be the second derivative of -m**7/14 + 39*m**6/10 - 477*m**5/10 - 599*m**4/2 - 1281*m**3/2 - 1323*m**2/2 - 14*m - 27. Factor n(q).
-3*(q - 21)**2*(q + 1)**3
Let w = 356217 + -356215. Let -1/8*v**4 - 1/2 + 1/2*v + 3/8*v**w - 1/4*v**3 = 0. What is v?
-2, 1
Let t = 1/97744 + 3909747/1270672. Factor t*o + 8/13*o**2 + 50/13.
2*(2*o + 5)**2/13
Let w = -38 - -40. Let m be -8*(3 - w - 2). Factor -m*z - 3*z**3 + 23*z**2 - 3*z**2 - 9*z**3 + 0*z**2.
-4*z*(z - 1)*(3*z - 2)
Let w = -49/1412 - -3461/18356. Factor 0 - 12/13*f + w*f**3 - 10/13*f**2.
2*f*(f - 6)*(f + 1)/13
Let q(v) be the second derivative of v**4/12 + 26*v**3/3 + 235*v**2/2 - 1575*v. Factor q(h).
(h + 5)*(h + 47)
Let n(z) be the third derivative of -z**8/40320 - z**7/1440 - z**6/120 - 7*z**5/60 - z**4/24 + 134*z**2. Let d(l) be the third derivative of n(l). Factor d(x).
-(x + 3)*(x + 4)/2
Let o(h) be the first derivative of -3*h**5/25 + 53*h**4/10 - 1003*h**3/15 + 578*h**2/5 + 505. Factor o(s).
-s*(s - 17)**2*(3*s - 4)/5
Suppose -4*z - a = -33, -4*z - 4*a + 21 = -3. Suppose s + z = 11. Determine k so that 4 - 10*k + 2*k**5 + 8*k**3 - 6*k**s - 8*k**4 - 3*k**2 + 13*k**2 = 0.
-1, 1, 2
Let f be (-4)/(-44) + (7 - 1752/396). Find y such that -10/3*y - f*y**2 + 0 + 2/3*y**3 = 0.
-1, 0, 5
Let y(j) be the second derivative of 3*j**6/10 + j**4/12 + 5*j**2/2 + 64*j. Let o(w) = -2*w**4 - w**3 + w**2 - 1. Let a(m) = 5*o(m) + y(m). Factor a(n).
-n**2*(n - 1)*(n + 6)
Factor -2/5*n**2 + 646/5*n - 644/5.
-2*(n - 322)*(n - 1)/5
Suppose -d - t = -134, 2*t - 44 = 4*d - 568. Suppose 5 + 167*i + d*i**2 - 968*i**3 + 14 - 10 + 7 - 23*i = 0. What is i?
-2/11, 1/2
Let c be (-24)/36 + 77/21. Solve 1/2*m**4 - 2*m**2 + 4*m - c*m**3 + 0 + 1/2*m**5 = 0 for m.
-2, 0, 1, 2
Let -142*b - 140*b**2 - 73*b**3 + 217*b**3 - 103*b**5 + 140*b**4 + 27*b**5 + 74*b**5 = 0. Calculate b.
-1, 0, 1, 71
Let v = -63499/11 - -5773. Let u(a) be the second derivative of -1/66*a**4 + 0 + 2*a - 1/11*a**3 + v*a**2. Suppose u(s) = 0. What is s?
-4, 1
Suppose 0 - 2/9*p**5 - 100/9*p**3 + 0*p**2 + 0*p - 34/3*p**4 = 0. Calculate p.
-50, -1, 0
Factor -25*z**2 - z - 31*z + 2*z**4 - 9*z**2 - 28*z**3 - 30*z**2 + 2*z**2.
2*z*(z - 16)*(z + 1)**2
What is g in 0 - 1/4*g**2 + 1/4*g = 0?
0, 1
Let c = 41/15436 - -802467/77180. Factor -c*m - 33/5 + m**2.
(m - 11)*(5*m + 3)/5
Let k = 32/9 - 134/63. Let r = 2753/14 - 391/2. Factor 0 + r*t**2 + 2/7*t**4 - k*t**3 + 0*t.
2*t**2*(t - 4)*(t - 1)/7
Let w(j) be the third derivative of j**6/480 + 73*j**5/240 + 1365*j**2. Factor w(v).
v**2*(v + 73)/4
Find w such that -132*w - 126*w**2 - 127*w**2 + 329*w**2 + 5*w**4 - w**4 + 52*w**3 = 0.
-11, -3, 0, 1
Let g(o) be the second derivative of o**4/12 + 211*o**3/6 + 105*o**2 + 2409*o. Find h, given that g(h) = 0.
-210, -1
Let n = 335 + -81. Let 1 - n*u - 35*u**2 + 72 - 3 + 19*u = 0. What is u?
-7, 2/7
Let i(p) = -43*p - 28 - 26*p + 30*p - 36*p - 50*p**2 - 19*p**3. Let b(r) = -12*r**3 - 33*r**2 - 50*r - 19. Let u(z) = 8*b(z) - 5*i(z). Factor u(w).
-(w + 1)**2*(w + 12)
Let r(v) = 361*v - 18409. Let h be r(51). Find l, given that -4/3 + 0*l + 1/3*l**h = 0.
-2, 2
Factor 10/3 - 7/4*r**2 + 3/2*r + 1/12*r**3.
(r - 20)*(r - 2)*(r + 1)/12
Let c(l) be the first derivative of -8/3*l - 56 - 1/6*l**4 - 32/9*l**2 - 46/27*l**3. Factor c(f).
-2*(f + 1)*(f + 6)*(3*f + 2)/9
Let j(f) = -7*f**4 + 784*f**3 + f**2 - 790*f + 36. Let q(d) = -5*d**4 + 785*d**3 - 790*d + 30. Let s(a) = -5*j(a) + 6*q(a). Factor s(b).
5*b*(b - 1)*(b + 1)*(b + 158)
Suppose 5*j = -10 + 25. Factor -38*m**j + 18*m - 118*m**2 - 10*m - 14*m**4 + 102*m**2.
-2*m*(m + 1)*(m + 2)*(7*m - 2)
Let d(j) = j - 1. Let c(y) be the first derivative of 4*y**3/3 + 42*y**2 + 696*y + 1169. Let o = 28 + -8. Let b(t) = o*d(t) + c(t). Factor b(v).
4*(v + 13)**2
Let n(u) be the first derivative of 2/15*u**3 - 28 + 8/5*u + u**2. What is b in n(b) = 0?
-4, -1
Factor 436*h**2 + 5*h**3 - 