3*y**3. Suppose h(a) = 0. Calculate a.
-4/3, -1, 1/4, 2
Let -15901 + r**2 + 16023 - 123*r + 0*r**2 = 0. What is r?
1, 122
Let l(i) be the third derivative of 17/180*i**4 + 0 - 1/450*i**5 - 16/45*i**3 + 0*i + 130*i**2. Factor l(r).
-2*(r - 16)*(r - 1)/15
Let r(k) be the first derivative of -k**4/26 - 154*k**3/39 + 6*k**2 - 1748. Factor r(u).
-2*u*(u - 1)*(u + 78)/13
Suppose 0 = -10*d - 173*d. Let u(v) be the first derivative of 4/3*v**3 - 11 + d*v - v**2 - 1/2*v**4. Let u(c) = 0. What is c?
0, 1
Let c(r) be the first derivative of 0*r + 1/12*r**6 - 3/8*r**4 + 1/3*r**3 + 0*r**5 + 41 + 0*r**2. Factor c(l).
l**2*(l - 1)**2*(l + 2)/2
Let x = 19 + -17. Suppose 4 = 2*k + x*c, 2*c + 21 = 3*k - 10. Factor k - 1 + 4*r**2 - 7*r + 4 - 7*r.
2*(r - 1)*(2*r - 5)
Let d be -3 + 3 + 6/30*(-240)/(-168). Find k such that 0 - 24/7*k**4 - d*k**5 - 14*k - 44/7*k**3 + 24*k**2 = 0.
-7, 0, 1
Let c(k) be the third derivative of k**7/315 - k**6/90 - k**5/30 + 2*k**4/9 - 4*k**3/9 - 21*k**2 + 43. What is n in c(n) = 0?
-2, 1, 2
Let q(r) = 10*r**2 + 89*r - 68. Let p(x) = 39*x**2 + 357*x - 270. Suppose 33*l = -90 - 207. Let v(u) = l*q(u) + 2*p(u). Find y such that v(y) = 0.
-8, 3/4
Let -16/3*a**4 + 24*a + 0 - 136/3*a**2 + 2/9*a**5 + 238/9*a**3 = 0. Calculate a.
0, 1, 2, 3, 18
Factor 16*g**5 + 15*g**4 + 3*g**3 + 15*g**3 - 7*g**5 + 2*g**5 - 8*g**5 - 21*g - 6*g**2 - 9.
3*(g - 1)*(g + 1)**3*(g + 3)
Let h(x) be the third derivative of x**7/315 + 79*x**6/45 + 12482*x**5/45 - 4*x**2 + 80*x. Factor h(v).
2*v**2*(v + 158)**2/3
Let h(r) be the third derivative of r**5/105 - 54*r**3/7 - 67*r**2 - 4. Factor h(o).
4*(o - 9)*(o + 9)/7
Let c(w) be the second derivative of -49/195*w**6 + 45*w + 77/130*w**5 + 0*w**2 - 16/39*w**4 + 0 + 4/39*w**3. Let c(d) = 0. Calculate d.
0, 2/7, 1
Let c(i) be the second derivative of i**6/70 - 3*i**5/28 - i**4/2 - 322*i - 3. Determine x, given that c(x) = 0.
-2, 0, 7
Let s(r) be the second derivative of 3*r**3 - 377*r**2 - 453*r + 2. Let j be s(42). Determine t so that 5/2 + 15/2*t + 15/2*t**j + 5/2*t**3 = 0.
-1
Let i(u) = u**2 + 15*u + 23. Let z be i(-14). Let d = -1 + z. Solve 4 - 24*g + d*g**2 - 4*g**2 - 4 = 0 for g.
0, 6
Let p = -174803 - -174803. Find v such that p - 1/10*v**5 - 8/5*v**2 + 2/5*v**4 + 6/5*v + 1/10*v**3 = 0.
-2, 0, 1, 2, 3
Let t(o) be the first derivative of -2*o**6/15 + 72*o**5/25 - 61*o**4/5 + 96*o**3/5 - 56*o**2/5 + 1699. Let t(r) = 0. Calculate r.
0, 1, 2, 14
Suppose -17*x + 8 = -13*x. Factor 16*i - 4 + 6*i**3 - 213*i**2 - 4*i - i**4 + 200*i**x.
-(i - 2)**2*(i - 1)**2
Let a(q) be the second derivative of 0 - 2*q**3 - 10*q + 1/4*q**4 - 15/2*q**2. Factor a(x).
3*(x - 5)*(x + 1)
Suppose -993*i = -948*i - 180. Suppose -2*o = -7*o + 15. Factor -8/11*p**2 - 16/11*p**o + 0*p - 2/11*p**5 - 10/11*p**i + 0.
-2*p**2*(p + 1)*(p + 2)**2/11
Let r be -1*(-2526)/42 + (-1)/7. Factor 15*j**2 + 8*j**3 - r - 54*j - 3*j**3 + 34*j.
5*(j - 2)*(j + 2)*(j + 3)
Let r(m) be the first derivative of 3*m**4/4 - 127*m**3/3 + 429*m**2 - 272*m - 8024. Solve r(i) = 0 for i.
1/3, 8, 34
Let k be (1300/(-91))/25*((9 - 2) + -2 + -6). Factor -k*c**2 + 0 + 1/7*c.
-c*(4*c - 1)/7
Let g(h) = -h**2 - 14*h - 1. Let k(a) = 7*a**2 - 742*a + 170575. Let z(o) = -30*g(o) - 5*k(o). What is v in z(v) = 0?
413
Let u(s) be the third derivative of -4 - 4*s**2 + 1/20*s**5 - 3/8*s**4 + 0*s + 0*s**3. Determine q so that u(q) = 0.
0, 3
Suppose 45 = 3*k - 3*c - 18, -2*k = 3*c - 37. Let w be 19/(-57) + k/6. Suppose 112/9*n + 4*n**w - 32/9 + 136/9*n**2 = 0. Calculate n.
-2, 2/9
Let w(c) be the third derivative of -c**8/1008 + 377*c**7/630 - 3927*c**6/40 - 3969*c**5/20 + 3463*c**2. Factor w(u).
-u**2*(u - 189)**2*(u + 1)/3
Let u be (6/4)/((-15)/320). Let c(y) = -18*y**2 - 16*y. Let q(a) be the first derivative of 116*a**3/3 + 52*a**2 + 20. Let l(z) = u*c(z) - 5*q(z). Factor l(j).
-4*j*(j + 2)
Let k = 271/1632 - -1/1632. Let d(r) be the second derivative of -k*r**6 + 0*r**3 + 0*r**2 - 1/60*r**4 + 6*r + 1/10*r**5 + 0. Factor d(v).
-v**2*(5*v - 1)**2/5
Let k(f) be the second derivative of -f**7/49 + 3*f**6/2 - 2613*f**5/70 + 9633*f**4/28 - 2197*f**3/7 - 8993*f. Solve k(v) = 0.
0, 1/2, 13, 26
Let c be (155/(-2325))/((-2)/10). Factor 0 + c*z**4 - 3*z**3 - 1/3*z**2 + 3*z.
z*(z - 9)*(z - 1)*(z + 1)/3
Factor -14*j - 2/5*j**2 - 248/5.
-2*(j + 4)*(j + 31)/5
Let n(b) be the second derivative of 130*b + 0*b**2 + 0*b**3 + 0*b**4 - 1/15*b**6 + 1/40*b**5 + 0. Factor n(j).
-j**3*(4*j - 1)/2
Let v(z) = -z**3 + 2. Suppose 0 = m + p, -15*m = -13*m - 2*p + 16. Let o(b) = -b**3 - 20*b**2 + 95*b - 78. Let l(k) = m*v(k) - o(k). Factor l(j).
5*(j - 2)*(j - 1)*(j + 7)
Let v(j) be the first derivative of -11/7*j**3 - 621/14*j**2 + 114/7*j + 16. Solve v(m) = 0 for m.
-19, 2/11
Find w, given that 8/9 + 2/9*w - 8/9*w**2 - 2/9*w**3 = 0.
-4, -1, 1
Suppose 8/5*j**4 + 0 + 372/5*j**3 - 584/5*j**2 - 384/5*j = 0. What is j?
-48, -1/2, 0, 2
Let h be (-76)/(-26) + (-52)/(-676). Let g(n) be the first derivative of 0*n**2 + 8/9*n**h - 1/15*n**5 + 15 + 0*n**4 - 16/3*n. Factor g(t).
-(t - 2)**2*(t + 2)**2/3
Let i = 261190 - 261190. Let d = -21/10 - -23/10. Factor i + d*q**2 + 0*q.
q**2/5
Let 27639*u**3 + 573*u**4 - 54150*u - 77*u**5 - 64*u**5 + 206*u**5 - 62*u**5 + 25935*u**2 = 0. What is u?
-95, -2, 0, 1
Let a(u) be the first derivative of -71/24*u**3 - 1295/16*u**2 - 1225/8*u + 140 - 1/32*u**4. Factor a(v).
-(v + 1)*(v + 35)**2/8
Let d(i) be the third derivative of 0*i + 3/40*i**6 - 1/3*i**3 + 4 + 13/24*i**4 - 2/5*i**5 + 15*i**2. Factor d(h).
(h - 2)*(3*h - 1)**2
Let -1/9*w**4 - 44/3*w**2 - 320/9*w - 256/9 - 20/9*w**3 = 0. Calculate w.
-8, -2
Suppose u + 15*u = -3*u. Solve -364*g**3 - 3 - 3*g + 367*g**3 + 3*g**2 + u*g = 0.
-1, 1
Suppose -32 = -2*c - 2*t, -c - 20 - 614 = -49*t. Factor 0 + 4/7*d**c + 8/7*d**2 + 4/7*d.
4*d*(d + 1)**2/7
Factor 9/5 + 11/10*g + 1/10*g**2.
(g + 2)*(g + 9)/10
Let n(g) be the second derivative of g**7/231 - 101*g**6/165 - 3*g**5/110 + 301*g**4/66 + 202*g**3/33 - 2625*g. Determine d so that n(d) = 0.
-1, 0, 2, 101
Let n(l) = -5*l**2 + 2840*l. Let r(b) = b**2 + b. Let j(x) = n(x) + 4*r(x). Factor j(f).
-f*(f - 2844)
Let f(p) be the second derivative of 221/70*p**5 + 0 + 82/21*p**4 - 1/3*p**6 + 4/3*p**3 + 135*p + 0*p**2. Find u, given that f(u) = 0.
-2/5, -2/7, 0, 7
Let y be (2 - 1)/(6/4). Let s be 1 + (-20)/6*(29 + 472/(-16)). Factor -10/3*a + s + y*a**2.
2*(a - 4)*(a - 1)/3
Let g(d) = 2*d**3 + d**2 - 15*d + 4. Let r be g(3). Factor 720*q**2 - 233 + 54*q**3 - 145 + r*q**3 + 2*q**4 - 76*q - 344.
2*(q - 1)*(q + 1)*(q + 19)**2
Let 73*p**3 + 67*p**3 - 100*p**2 - 5*p**5 + 9*p**5 - 44*p**4 - 144*p + 80 + 88 - 24 = 0. Calculate p.
-1, 1, 2, 3, 6
Suppose 10*w = -110 + 110. Let z(f) be the first derivative of 10/3*f**3 + 0*f**2 + w*f + 1 + 5/8*f**4. Factor z(j).
5*j**2*(j + 4)/2
Let i(v) be the first derivative of -5*v**6/6 - 14*v**5 - 65*v**4/4 + 3052. Factor i(c).
-5*c**3*(c + 1)*(c + 13)
Find q, given that 14/11*q**2 + 0 - 2/11*q**5 - 14/11*q**4 + 2/11*q**3 + 0*q = 0.
-7, -1, 0, 1
Let d = 193682/25 - 7749. Let k = 163/25 + d. Determine l so that -72/5 - 2/5*l**2 + k*l = 0.
6
Let y(v) be the first derivative of -5 - 1/7*v**3 + 48/7*v + 0*v**2. Find m, given that y(m) = 0.
-4, 4
Let j(d) = 8425*d + 480227. Let n be j(-57). Determine s so that 35/2*s**3 + 0*s + 1/4*s**5 + 31/8*s**4 + 0 + 147/8*s**n = 0.
-7, -3/2, 0
Suppose 10677 = 16*l - 7403. Let b = 1132 - l. Factor -50/7 + 20/7*y - 2/7*y**b.
-2*(y - 5)**2/7
Let x be (-220)/15 - (-4)/(-12). Let p = x - -17. Suppose 4*b + b**p - 4*b + 3*b + 2 = 0. Calculate b.
-2, -1
Let d = -35 + 44. Suppose 6456 = d*n - 861. Determine g, given that -n*g**3 + 5*g**4 + 813*g**3 - 5*g**2 = 0.
-1, 0, 1
Let a(x) = -5*x**3 - 158*x**2 - 614*x + 783. Let v(t) = -10*t**3 - 315*t**2 - 1230*t + 1565. Let n(p) = -5*a(p) + 3*v(p). Solve n(w) = 0 for w.
-26, -6, 1
Let j = 64151/36644 - 6/9161. Suppose -5/4*b**2 + j*b - 3/4 + 1/4*b**3 = 0. Calculate b.
1, 3
Let a = 90 + -86. Suppose 5*x + 7 = -3, 0 = a*k - 5*x - 90. Let 17*d + 10*d**2 - 21 - d + k*d + 5 = 0. Calculate d.
-4, 2/5
Let z(d) = -17*d**2 + 2233*d + 1236463. Let k(o) = 15*o**2 - 2232*o - 1236472. Let l(c) = 9*k(c) + 8*z(c). Factor l(u).
-(u + 1112)**2
Let z(u) = -8*u**2 + 3074*u - 6149. Let l(n) = -105*n**2 + 39960*n - 79940. Let i(g)