). Let t(d) = s*q(d) - 2*c(d). Factor t(h).
-2*h*(h - 1)*(h + 1)**3
Suppose -2159 = 26*r - 2211. Let t(k) be the first derivative of -32 - 14/57*k**3 - 8/19*k**r + 8/19*k + 5/38*k**4. Suppose t(u) = 0. What is u?
-1, 2/5, 2
Let a(r) be the third derivative of -r**8/560 + r**7/70 - 9*r**6/200 + 7*r**5/100 - r**4/20 - 2026*r**2. Let a(b) = 0. Calculate b.
0, 1, 2
Let m(g) be the first derivative of g**4/34 - 26*g**3/51 + 14*g**2/17 + 176*g/17 + 10896. Find x, given that m(x) = 0.
-2, 4, 11
Let l(z) = -6325*z - 25297. Let a be l(-4). Solve 114/13*n**2 - 2/13*n**a + 1568/13 - 1680/13*n = 0 for n.
1, 28
Find j such that 1/3*j**5 - 13/2*j**3 + 56/3*j - 13/6*j**4 + 0 + 104/3*j**2 = 0.
-4, -1/2, 0, 4, 7
Let v(t) be the first derivative of 3/4*t**4 + 75*t**3 + 2052*t**2 + 78 - 4332*t. What is c in v(c) = 0?
-38, 1
Let g = 565 - 564. Let d be (-1 + 3)*g - (33 + -33). Factor 6/11*u + 0 + 10/11*u**d + 2/11*u**3 - 2/11*u**4.
-2*u*(u - 3)*(u + 1)**2/11
Let r = -125 - -127. Factor -4*c**r + 48 - 30*c - 16*c + 2*c.
-4*(c - 1)*(c + 12)
Let y(l) = -11*l**2 - 25*l + 30. Let b(x) = 9 + 5*x + 3*x**2 - 4 - 3 - x - 3*x. Let i(v) = 4*b(v) + y(v). Let i(p) = 0. Calculate p.
2, 19
Let i(u) be the second derivative of u**5/90 + 4*u**4/27 + 5*u**3/9 - 7*u - 83. Determine o so that i(o) = 0.
-5, -3, 0
Let f = -9 - -12. Suppose 9*w - 12*w = -6. Solve -11*a - 5*a + f*a + 3*a + 5*a**w = 0 for a.
0, 2
Let x(i) be the third derivative of 0*i**4 + 0 + 118*i**2 + 0*i**3 - 1/1680*i**8 - 1/150*i**5 + 1/200*i**6 + 0*i**7 + 0*i. Suppose x(y) = 0. What is y?
-2, 0, 1
Let p(n) be the first derivative of -5*n**6/3 - 242*n**5/5 - 1077*n**4/5 - 392*n**3/3 + 1976*n**2/5 - 192*n + 512. Suppose p(d) = 0. Calculate d.
-20, -3, -2, 2/5
Let h be 1491/630 + (671/(-66) - -11). Factor 26/5*g**2 + 4/5*g**3 + 44/5*g + h.
2*(g + 2)*(g + 4)*(2*g + 1)/5
Let f(o) = 5*o**2 + 75*o + 138. Let k(v) = -22*v**2 - 299*v - 546. Let z(y) = -9*f(y) - 2*k(y). Solve z(p) = 0.
-75, -2
Let x = 160662 - 160660. Factor 12*f + 5/2 + 15/2*f**x - 2*f**3.
-(f - 5)*(f + 1)*(4*f + 1)/2
Suppose 1 = -3*v + 4. Let b(r) = 2*r**3 + r**2 - r + 1. Let l(h) = 22*h**3 + 24*h**2 + 20*h + 12. Let i(s) = v*l(s) - 12*b(s). Let i(z) = 0. What is z?
-2, 0, 8
Solve 925/8*n + 231/4 + 58*n**2 + 1/8*n**3 = 0 for n.
-462, -1
Let l(q) = -q**2 - 12*q - 3. Let s(o) = 0*o**2 + 315 + o**2 - 311 + 11*o. Let p(u) = -4*l(u) - 3*s(u). Factor p(x).
x*(x + 15)
Let n(c) be the second derivative of -c**6/30 + 13*c**5/20 - 5*c**4/2 - 2*c**3/3 + 20*c**2 - 520*c. Factor n(l).
-(l - 10)*(l - 2)**2*(l + 1)
Let c(z) be the first derivative of -2*z**3/27 + 1676*z**2/9 - 3350*z/9 + 4098. Find g, given that c(g) = 0.
1, 1675
Suppose -35 = -3*n + 40. Let k be (n/(-20))/(-6 + 1). Factor -k + 3/4*z + 1/4*z**3 - 3/4*z**2.
(z - 1)**3/4
Factor 0 - 1018/7*u + 1/7*u**2.
u*(u - 1018)/7
Let i(f) be the first derivative of 10 + f**3 + 1/4*f**4 + 0*f**2 - 8*f. Let z(a) be the first derivative of i(a). Factor z(x).
3*x*(x + 2)
Let m be 6/(-16) + -6 + 2/((-400)/(-1307)). Let n(j) be the first derivative of 1/5*j**4 - 1/15*j**6 + m*j**5 - 16/15*j**3 - 4/5*j - 15 + 7/5*j**2. Factor n(s).
-2*(s - 1)**4*(s + 2)/5
Let i be (-5)/(-3)*(-3)/(-1). Suppose -6*l = -i*l - 12. Factor -l*a**4 + 25*a**3 + 2*a**5 - 7*a**3 - 24*a - 45*a**2 + 53*a**2.
2*a*(a - 3)*(a - 2)**2*(a + 1)
Suppose 3*o = -9, -4*o - 5 - 19 = -3*x. Let t(r) be the third derivative of 5/48*r**x + 1/18*r**5 + 0 + 0*r - 15*r**2 + 0*r**3 + 1/144*r**6. Factor t(k).
5*k*(k + 1)*(k + 3)/6
Let l be 8760/(-2044) - 15/(6/(-2)). Suppose x - 3 = -0*x. Factor 0 - 1/7*r**x - l*r + 6/7*r**2.
-r*(r - 5)*(r - 1)/7
Let u(k) be the second derivative of 0*k**6 + 3*k - 1/98*k**7 - 4 + 0*k**3 + 1/14*k**4 + 0*k**2 + 9/140*k**5. Solve u(q) = 0 for q.
-1, 0, 2
Let d = -74120/3 - -296615/12. Factor -d - 605/4*s**2 + 165/2*s.
-5*(11*s - 3)**2/4
Let b(h) = h**2 - 5*h + 2. Let g be b(5). Determine a so that -g*a**3 + 654*a + 8*a**4 - 26*a**3 + 28*a**2 - 662*a = 0.
0, 1/2, 1, 2
Let s(c) be the second derivative of -1 + 1/150*c**6 + 2/5*c**3 - 1/30*c**4 + 9/10*c**2 - 1/25*c**5 - 29*c. Factor s(u).
(u - 3)**2*(u + 1)**2/5
Let v = 15280/17 - 45721/51. Solve x - 1/3*x**4 + 5/3*x**3 - v*x**2 + 0 = 0.
0, 1, 3
Let f(b) = b**2 - 4*b - 488. Let h be f(-20). Let a(g) = -64*g - 509. Let d be a(h). Find k such that 3/2*k**2 + 0*k**d + 3/4*k**5 - 3/4*k + 0 - 3/2*k**4 = 0.
-1, 0, 1
Factor -2/5*f**4 - 8/5*f**3 + 4/5 + 1/5*f**5 + 7/5*f - 2/5*f**2.
(f - 4)*(f - 1)*(f + 1)**3/5
Let 736 + 364*w - 1/4*w**3 + 44*w**2 = 0. Calculate w.
-4, 184
Let n(y) = -y**2 + y - 1. Let k(m) = 9*m**4 + 39*m**3 + 43*m**2 + 5*m + 4. Let x = 240 + -244. Let t(p) = x*n(p) - k(p). Determine w, given that t(w) = 0.
-3, -1, -1/3, 0
Let m = 11406 + -2690. Factor 5*y**4 + 10*y**3 - 4349 - 4412 + m - 40*y**2 - 90*y.
5*(y - 3)*(y + 1)**2*(y + 3)
Let b(x) be the third derivative of -36*x**2 + 4/15*x**3 + 0*x + 0 + 1/30*x**5 + 1/300*x**6 + 2/15*x**4. Determine j so that b(j) = 0.
-2, -1
Let q = 306 + -597/2. Let l = 1/85 + 763/170. Let -3 - 39/2*c**3 + 27/2*c**4 - 3*c**5 + l*c + q*c**2 = 0. What is c?
-1/2, 1, 2
Let g(m) be the first derivative of 1/4*m**3 + 5/8*m**4 - 4*m**2 - 32 + 5*m - 1/20*m**5. Factor g(u).
-(u - 10)*(u - 1)**2*(u + 2)/4
Let k be (28/(-7))/(-1 + -13). Suppose 116*l - 20 = 112*l. Suppose -k*p**3 + 3/7*p**4 + 1/7*p + 1/7*p**l - 6/7*p**2 + 3/7 = 0. What is p?
-3, -1, 1
Let u = 179/1336 + -3/334. Let o(p) be the first derivative of 14 + u*p**2 - 1/4*p**3 - 1/16*p**4 + 3/4*p. Factor o(j).
-(j - 1)*(j + 1)*(j + 3)/4
Let x be (11/((-88)/80))/((-4)/6). Suppose 3*u - x = -c, 2*c + u - 16 + 11 = 0. Suppose c - 4/7*r**2 + 2/7*r - 2/7*r**5 + 0*r**3 + 4/7*r**4 = 0. Calculate r.
-1, 0, 1
Suppose -113*a - 382*a = 0. Factor 12/7*p**2 - 2/7*p + a.
2*p*(6*p - 1)/7
Let n be 3/(-3)*0 + 0. Suppose n = -w + 62 - 60. Factor 2*i**2 + 3*i**w - 2*i**2 - 3*i - 2*i**2.
i*(i - 3)
Let w(h) be the third derivative of h**7/2520 + h**6/216 - h**5/45 - h**4/6 - 104*h**3/3 + 13*h**2 - 1. Let c(a) be the first derivative of w(a). Factor c(f).
(f - 2)*(f + 1)*(f + 6)/3
Suppose -48*j - 814 = -53*j - 3*k, -338 = -2*j + 5*k. Suppose 84*y - j = 2*y. Factor 0 + 3*c**4 + 0*c**y + 0*c - 2/3*c**3.
c**3*(9*c - 2)/3
Let o be (-28 - -10) + (0 - 2). Let w be (-48)/(-10) - 4/o. Factor -2*b**4 + b**5 + w*b**2 - 44*b - 3*b**3 + 42*b + b**4.
b*(b - 1)**3*(b + 2)
Suppose -11*g - 5*g = 48. Let p(h) = 6*h**2 - 78*h + 507. Let l(r) = -5*r**2 + 78*r - 507. Let n(b) = g*l(b) - 2*p(b). Factor n(u).
3*(u - 13)**2
Suppose 3*y = 4*f - 84, 4*f = 5*f - 2*y - 26. Let t be f/((-10)/(180/(-189))). Find p, given that 10/7*p - 2/7*p**2 - t = 0.
2, 3
Let n be (-51)/(-2)*256/96. Suppose 36 - n*x - 8*x**2 - 4*x**5 - 63*x**4 + 83*x**4 + 72*x**3 - 48*x**4 = 0. What is x?
-9, -1, 1
Suppose 3*p = r, 4*r - 24 = 3*r - 3*p. Suppose r*g = 17*g - 15. Factor 1 + 6*o**3 - 6*o**g + 0*o**3 - o**2 + 4*o**3 - 4*o.
(o - 1)*(o + 1)*(4*o - 1)
Let q(f) be the first derivative of f**6/780 + 7*f**5/78 + 109*f**2/2 + 134. Let u(v) be the second derivative of q(v). Factor u(o).
2*o**2*(o + 35)/13
Let m(r) be the first derivative of 4*r**3/27 + 76*r**2/3 - 100. Determine j so that m(j) = 0.
-114, 0
Let v(u) = u**2 + 43*u - 1. Let m(t) = 3*t**2 + 141*t - 1128. Let z(o) = -m(o) + 6*v(o). Factor z(g).
3*(g + 17)*(g + 22)
Let j(s) be the third derivative of -29*s**5/60 + 5*s**4/2 - 2*s**3/3 + 16*s**2 - 29*s. Factor j(b).
-(b - 2)*(29*b - 2)
Let v be ((-17)/204)/(35/820). Let t = 134/21 - v. Solve -20/3*w**5 - 25/3*w**4 + 0 + 5*w**3 + 5/3*w + t*w**2 = 0 for w.
-1, -1/4, 0, 1
Determine h so that 5295 - 16*h**2 + 43*h**2 + 8435*h - 22*h**2 - 6655*h = 0.
-353, -3
Let j(w) be the first derivative of w**5 + w**3/3 - 5*w**2 + 233. Let d(l) = 2*l + l**3 - 3*l + 2*l. Let z(o) = -24*d(o) - 3*j(o). Factor z(x).
-3*x*(x + 1)**2*(5*x - 2)
Let o(y) = 2*y**5 - y**4 - y**3 + y**2 - 1. Let k(x) = 25*x**5 - 173*x**4 - 6084*x**3 + 26417*x**2 - 20172*x - 13. Let s(b) = -k(b) + 13*o(b). Factor s(i).
i*(i - 3)*(i - 1)*(i + 82)**2
Determine p, given that -21/5*p**2 + 153/5 + 12/5*p = 0.
-17/7, 3
Suppose -j = 2*y - 552, y + 562 = 3*y - 4*j. Suppose 273*k + 12 = y*k. Factor 7*h**3 - h**2 + 6*h + 5*h**3 - 14*h**2 - k*h**4.
-3*h*(h - 2)*(h - 1)**2
Let a be -8*2/4 - -47. Suppose -80 = -4*b + 16. Facto