 - 121. Let b(g) = -g**3 + 10*g**2 - 2*g + 22. Let o be b(q). Factor -18*k**3 + 63*k - 9*k**4 + 3*k**5 + 30*k**2 + 17 + 10 + 2*k**5 - o*k**5.
3*(k - 3)**2*(k + 1)**3
Suppose 24 = 9*s - 3. Determine f, given that 118*f**2 + 159*f**2 - 121*f**s + 127*f**2 - 91*f**3 - 19*f + 16*f**4 - 69*f = 0.
0, 1/4, 2, 11
Let a be (-20)/8*(-6)/5. Let n be (-2*(-51)/(-18))/(a/(-9)). Solve -6*u**3 + 0*u**5 + 9*u**2 + 3*u**4 - n*u**2 + u**5 = 0 for u.
-4, -1, 0, 2
Let b(d) be the second derivative of d**6/1620 + d**5/180 + d**4/54 + 31*d**3/3 - d + 46. Let c(j) be the second derivative of b(j). Factor c(w).
2*(w + 1)*(w + 2)/9
Suppose 7762 = -21995*y + 21999*y + x, -y - 5*x + 1874 = 0. Factor -72*g + y + 2/3*g**2.
2*(g - 54)**2/3
Let c = 493141 - 493139. Factor -20/7 - 2/7*y**3 - 34/7*y - 16/7*y**c.
-2*(y + 1)*(y + 2)*(y + 5)/7
Factor -126/11*s + 0 + 48/11*s**2 - 2/11*s**3.
-2*s*(s - 21)*(s - 3)/11
Suppose 8*j = -5*j - 10*j + 46. Let -1/5*c**3 + 57/5*c - 27/5*c**j - 29/5 = 0. What is c?
-29, 1
Factor 300*l - 209 + 148 + 85*l**2 + 61 + 5*l**3.
5*l*(l + 5)*(l + 12)
Let t(b) = b**3 + 9*b**2 - 14*b. Let g be t(4). Suppose 114 = -19*y + g. Factor -y*s + 3*s**2 + 1/3.
(3*s - 1)**2/3
Let t = -31/4 + 127/16. Let x(f) be the second derivative of 1/40*f**6 - 27*f - 3/80*f**5 + 3/4*f**2 + 1/8*f**3 + 0 - t*f**4. Find l, given that x(l) = 0.
-1, 1, 2
Suppose -l**3 - 235*l - 4*l**3 + 2127 - 1977 + 90*l**2 = 0. What is l?
1, 2, 15
Let z(j) be the first derivative of -j**5/24 + j**4/4 - 7*j**3/36 - j**2/2 - 9*j - 69. Let s(w) be the first derivative of z(w). What is f in s(f) = 0?
-2/5, 1, 3
Let x(w) = -w**3 - 3*w**2 + 3*w. Suppose 0 = 2*s - 2*o + 6*o + 12, -14 = 5*s + 2*o. Let k(b) = b**2. Let u(z) = s*k(z) - 2*x(z). Factor u(r).
2*r*(r - 1)*(r + 3)
Let z(d) = 11*d**3 - 34*d**2 + 9*d - 2. Suppose -160 + 136 = -8*o. Let c be z(o). Factor -8 + 4*y**3 - 1/2*y**4 + c*y - 12*y**2.
-(y - 2)**4/2
Let h be -6 + (4 - 18/(-8)). What is g in 1/4*g**4 - h + 0*g**2 + 1/2*g - 1/2*g**3 = 0?
-1, 1
Factor 15/2 + 1/4*g**3 + 61/4*g + 8*g**2.
(g + 1)**2*(g + 30)/4
Let o(w) be the first derivative of 18*w**5/35 + 1839*w**4/28 + 20910*w**3/7 + 358938*w**2/7 + 117912*w/7 + 641. Factor o(f).
3*(f + 34)**3*(6*f + 1)/7
Let p(v) = 64*v - 117. Let d be p(-7). Let w = d + 565. Factor t**3 + 5/4*t**2 + 1/2*t + 1/4*t**4 + w.
t*(t + 1)**2*(t + 2)/4
Suppose -57 + 101 = 11*b. Factor -5*n + 10*n - 5*n**b - 456*n**2 - 5*n**3 - 10 + 471*n**2.
-5*(n - 1)**2*(n + 1)*(n + 2)
Suppose -d - a = -552, 0 = -4*a - 8 - 4. Suppose 551*o**2 - 3 - d*o**2 + 3*o + 0*o + o**3 + 3 = 0. What is o?
0, 1, 3
Let j(a) = 11*a**2 + 85*a - 249. Let v(i) = -13*i**2 - 85*i + 246. Let r(g) = 6*j(g) + 5*v(g). Factor r(f).
(f - 3)*(f + 88)
Let i(p) be the second derivative of -p**5/25 + 83*p**4/30 + 43*p**3/5 + 7303*p. Find v, given that i(v) = 0.
-3/2, 0, 43
Suppose -44*g + 109 + 707 = 24*g. Let r(p) be the second derivative of -4/3*p**3 + g*p**2 + 0 + 4*p + 1/18*p**4. Factor r(t).
2*(t - 6)**2/3
Let i be -25*(-1 + 4 - 4). Suppose i = -3*u - 5*m, -3*u - m + 4*m + 15 = 0. Find q, given that -2/9*q**2 + 2/9*q**4 + 0*q**3 + 0*q + u = 0.
-1, 0, 1
Let l = 1383058 - 6915286/5. Factor -l*i**2 + 12/5*i**3 + 2/5*i**5 + 0*i + 0 - 9/5*i**4.
i**2*(i - 2)**2*(2*i - 1)/5
Let n(q) be the third derivative of q**8/1008 + q**7/630 - q**6/120 - q**5/180 + q**4/36 - 73*q**2. Determine m, given that n(m) = 0.
-2, -1, 0, 1
Let h(r) = 8*r**3 + 2*r**2 + 7*r + 16. Let j be h(-4). Let i = j + 496. Determine d so that 0 - 1/4*d**i - 5/4*d**2 + 1/2*d + d**3 = 0.
0, 1, 2
Let t(o) be the first derivative of 6*o - 7/6*o**2 + 157 - 1/9*o**3. Suppose t(u) = 0. What is u?
-9, 2
Let l(w) = 939*w**2 - 943*w + 16. Let y(i) = i**2 - 2*i - 1. Let r(g) = -l(g) - 6*y(g). Let r(t) = 0. What is t?
2/189, 1
Determine z, given that -25/2*z**3 - 1135/2*z - 195 - 205*z**2 = 0.
-13, -3, -2/5
Let t be -1 - (4/(-10))/((-2)/(-320)). Factor -206 + 131 + 5*s**2 - 7*s - t*s.
5*(s - 15)*(s + 1)
Let q(d) = -17*d + 60. Let g be q(-9). Let l be (g/(-21) + -1)/(6/(-42)). Factor -4*f**2 - 66*f - 10 + 2 + l*f.
-4*(f - 2)*(f - 1)
Let o = -137/7 + 141/7. Suppose 8*x - 4*t + 27 = 55, 5*t + 35 = -4*x. Factor -2/7*p**3 + 0 - o*p**2 + x*p.
-2*p**2*(p + 2)/7
Suppose -v = -7*l - 0*l + 12284, 2*l - 24616 = 2*v. Let u be (v/(-64))/(-19) + 11. What is h in -5/8*h**4 - 1/4*h**2 + 0 + 0*h - u*h**3 = 0?
-1, -2/5, 0
Suppose 22*y - 432 = 448. Let m be (-44)/(-16) + 10/y. Suppose -9/4*i**m - 3/2 + 21/4*i - 3/2*i**2 = 0. What is i?
-2, 1/3, 1
Let c(i) be the first derivative of 3*i**5/5 + 6*i**4 + 15*i**3 - 576. Let c(a) = 0. Calculate a.
-5, -3, 0
Let x be 1*-2*18/(-16). Suppose -1463*v + 1464*v = -4*i + 11, 0 = 2*i + v - 11. Factor 3/4*g**2 - 3/4*g + x*g**4 + 15/4*g**3 + i.
3*g*(g + 1)**2*(3*g - 1)/4
Suppose -47*i = 16232 + 14083. Let z = i - -649. Factor 14/5*t**z + 26/5*t + 6/5 + 44/5*t**2 + 2/5*t**5 + 36/5*t**3.
2*(t + 1)**4*(t + 3)/5
Let v(f) be the second derivative of -f**6/135 + 4*f**5/15 + 17*f**4/18 + 26*f**3/27 - 1867*f + 1. Solve v(r) = 0.
-1, 0, 26
Let x = -322979/60 + 5383. Let k(s) be the third derivative of 5/3*s**4 + 0 + 0*s - 24*s**2 - 4/5*s**5 - x*s**7 + 11/60*s**6 - 4/3*s**3. Factor k(u).
-(u - 2)**3*(7*u - 2)/2
Suppose 10498 - 10795 = -99*y. Factor 11/3*a - 4/3*a**2 - 2 - 1/3*a**y.
-(a - 1)**2*(a + 6)/3
Let l(s) = -2*s**2. Let c be l(1). Let z be (c + 14/10)*-5. Suppose v + 4 + 8*v**2 + 3*v - 6*v**2 - z*v**2 - v**3 = 0. Calculate v.
-2, -1, 2
Let t = -9039/2 - -27125/6. Let s(l) be the third derivative of 5/6*l**4 + 0 + t*l**3 + 0*l + 37*l**2 + 4/15*l**5 + 1/30*l**6. Factor s(o).
4*(o + 1)**2*(o + 2)
Determine h, given that 0*h - 36*h**4 + 0 - 110*h**3 - 10/3*h**5 - 200/3*h**2 = 0.
-5, -4/5, 0
Let t(d) be the first derivative of 3*d**4/28 - 1244*d**3/7 - 7473*d**2/14 - 534*d - 1794. Solve t(i) = 0.
-1, 1246
What is q in -35/4*q**2 - 27/2 + 123/4*q = 0?
18/35, 3
Let h be (13/(-26))/((-15)/2). Let k(c) be the third derivative of 0 - 15*c**2 + 50/3*c**3 + 0*c + h*c**5 + 5/3*c**4. Factor k(l).
4*(l + 5)**2
Let v(l) be the second derivative of 0 - 1/9*l**3 + 1/72*l**4 + 4*l + 1/180*l**5 - l**2. Let i(x) be the first derivative of v(x). Let i(b) = 0. What is b?
-2, 1
Let y(l) = l**2 - 23*l + 93. Let q be y(5). Let f be -25 - -32 - 19/q. Let 16/21*x + 2/21*x**2 + f = 0. Calculate x.
-7, -1
Let t be (12 + (14 - 8))*(-86)/(-1935). What is l in 0*l**4 + 4/5*l + 0 + t*l**5 - 8/5*l**3 + 0*l**2 = 0?
-1, 0, 1
Let n(z) be the second derivative of -10*z**3 - 1/3*z**4 + 0 - 28*z**2 + 58*z. Find o such that n(o) = 0.
-14, -1
Factor 3215*r**3 - 9636*r**3 - 2371600*r + 3080*r**2 + 3213*r**3 + 3207*r**3.
-r*(r - 1540)**2
Factor 27*t**2 - 13*t**2 - 5*t**2 - 2273*t - 7017201 - 10*t**2 - 3025*t.
-(t + 2649)**2
Suppose 806 = -6*k + 212. Let w = k + 102. Factor 3*j**5 - 9*j**w + 6*j**4 + 2542 - 2542.
3*j**3*(j - 1)*(j + 3)
Let a(l) be the second derivative of -l**5/20 + l**3/6 + 23*l + 2. Let n(i) = 4*i**3 - 3*i - i + 0*i. Let u(b) = -14*a(b) - 3*n(b). Factor u(y).
2*y*(y - 1)*(y + 1)
Let p(f) = -f**3 - 2*f**2 + f. Suppose 278 = -6*n + 266. Let g(k) = -2*k**4 + 10*k**3 - 22*k**2 - 6*k + 24. Let c(a) = n*p(a) + g(a). Factor c(o).
-2*(o - 3)*(o - 2)**2*(o + 1)
Solve 50*v**4 + 28*v**4 - 393*v + 1489876 - 232*v**2 - 1490034 - v**5 + 82*v**3 = 0.
-1, 2, 79
Let s(k) be the first derivative of k**4/8 - 13*k**3/6 - 9*k**2/4 + 405*k/2 - 900. Let s(v) = 0. Calculate v.
-5, 9
Let a(f) be the first derivative of -f**3/3 + 205*f**2 - 409*f - 53. Solve a(l) = 0.
1, 409
Determine k, given that -13184*k**2 + 353*k**3 + 39392*k - 2*k**4 + 3272*k**2 + 489*k**3 - 685717 + 633365 = 0.
4, 409
Let 8/7*u**3 + 24/7 - 8/7*u + 2/7*u**4 - 26/7*u**2 = 0. What is u?
-6, -1, 1, 2
Let y(o) be the third derivative of o**8/1064 - 11*o**7/1995 - o**6/1140 + o**5/30 + o**4/38 + 1757*o**2. Find t, given that y(t) = 0.
-1, -1/3, 0, 2, 3
Let l(a) be the first derivative of -a**6/2 + 216*a**5/5 + 477*a**4/4 - 802*a**3 - 1386*a**2 + 7992*a - 1300. Solve l(d) = 0.
-3, 2, 74
Let s be 0/3*16/64. Factor 304*f**2 + 8*f**3 + s*f**3 - 184*f**2 + 900*f - 4*f**3.
4*f*(f + 15)**2
Let r = 128646 - 128646. Factor 4/7*m**2 + 6/7*m + 2/7*m**5 - 4/7 - 8/7*m**3 + r*m**4.
2*(m - 1)**3*(m + 1)*(m + 2)/7
Let g(z) be the second derivative of z**4/20 + z**3/5 - 36*z**2 + 1537*z.