r(s) = -6*s**2 - 246*s - 249. Let z(o) = -o**2. Let g(i) = -r(i) - 3*z(i). Let v(f) = -8*f**2 - 247*f - 248. Let q(b) = 3*g(b) + 4*v(b). Factor q(a).
-5*(a + 1)*(a + 49)
Let m(l) be the first derivative of 0*l**2 + 5/6*l**6 + 10/3*l**3 + 0*l - 15/4*l**4 - 120 + 0*l**5. Let m(i) = 0. Calculate i.
-2, 0, 1
Let g(c) be the second derivative of -c**5/70 + 131*c**4/42 - 130*c**3/21 - 2*c + 272. Factor g(q).
-2*q*(q - 130)*(q - 1)/7
Solve -22 - 40*x**3 - 33 - 905 - 95*x**2 - 60 + 860*x = 0 for x.
-51/8, 2
Let z(d) be the first derivative of -d**6/90 - 7*d**5/30 + 3*d**4 - 88*d**3/3 - 52. Let l(f) be the third derivative of z(f). Find u such that l(u) = 0.
-9, 2
Let g(h) be the third derivative of -h**6/1980 - h**5/220 + 7*h**4/33 - 34*h**3/3 + 2*h**2 + 106*h. Let a(z) be the first derivative of g(z). Factor a(k).
-2*(k - 4)*(k + 7)/11
Let k(r) be the first derivative of -2*r**5/35 + 5*r**4/7 + 110*r**3/21 + 20*r**2/7 - 24*r - 4463. Let k(m) = 0. What is m?
-3, -2, 1, 14
Suppose h - 57 = 5*s + 34, -4*h - 4*s + 364 = 0. Suppose 0 = -4*t + h - 79. Factor -4/7*c**4 + 0*c**2 + 0 + 6/7*c**t + 0*c - 2/7*c**5.
-2*c**3*(c - 1)*(c + 3)/7
Suppose -2/11*h**4 - 84/11*h**3 - 384/11*h**2 - 524/11*h - 222/11 = 0. Calculate h.
-37, -3, -1
Let u = 53366 - 160088/3. Factor 0 - 2/3*h**3 - u*h + 4*h**2.
-2*h*(h - 5)*(h - 1)/3
Factor 2/21*o**2 + 2856050/21 + 4780/21*o.
2*(o + 1195)**2/21
Let l = -2/172871 + 172877/518613. Let 1/6 - 1/6*j - l*j**2 = 0. What is j?
-1, 1/2
Let t(r) = 35*r + 273. Let a be t(-5). Factor 12*m + 3 + 117*m**2 - a + 16*m**3 - 64*m**3 + 3*m**4 - 61.
3*(m - 13)*(m - 2)**2*(m + 1)
Let o = -103577/5 - -20723. Factor 66/5*p**2 + 6/5*p**4 + 0 - o*p**3 - 18/5*p.
2*p*(p - 3)**2*(3*p - 1)/5
Let i(d) be the third derivative of 41/27*d**4 + 0*d - 16*d**2 + 22/27*d**5 + 1 + 32/27*d**3 + 5/108*d**6. Factor i(z).
2*(z + 8)*(5*z + 2)**2/9
Let q be -1*3/((-15)/10). Suppose -4 - q = -3*k. Factor -59 + 3*g**5 - 6*g**k - 3*g**3 + 59 + 6*g**4.
3*g**2*(g - 1)*(g + 1)*(g + 2)
Factor -60*o + 0 + 3/5*o**2.
3*o*(o - 100)/5
Let p(c) = -10*c**3 - 2*c**2 + 4*c + 4. Let t(y) = y - 3*y**2 + 63 - 24 - 2*y**3 + 2*y**2 - 38. Let b(n) = -p(n) + 4*t(n). Determine j so that b(j) = 0.
0, 1
Let q(n) = -756*n - 49137. Let d be q(-65). What is y in 3/4*y**d - 9/2*y**2 + 33/4*y - 9/2 = 0?
1, 2, 3
Factor 174/5*u**2 - 2/5*u**3 + 0 - 1264/5*u.
-2*u*(u - 79)*(u - 8)/5
Determine c so that -1/7*c**2 - 351/7 - 120/7*c = 0.
-117, -3
Factor -35*n**2 + 1/2*n**4 + 0 + 69/2*n**3 + 0*n.
n**2*(n - 1)*(n + 70)/2
Let v(d) be the first derivative of -4/45*d**5 + 0*d**2 + 4/27*d**3 - 1/9*d**4 - 32 + 0*d + 2/27*d**6. Factor v(g).
4*g**2*(g - 1)**2*(g + 1)/9
Let l(q) be the third derivative of 0 + 1/360*q**6 + 1/9*q**4 + 2/9*q**3 + 1/36*q**5 + 0*q + 64*q**2. Factor l(z).
(z + 1)*(z + 2)**2/3
Let o be (-105)/(-40) - 228/(-608). Let h(s) be the first derivative of -8/5*s + 1/10*s**4 + 8/5*s**2 - 2/3*s**o + 4. Factor h(d).
2*(d - 2)**2*(d - 1)/5
Let z = -136 - -211. Suppose -5*j**3 + 11*j**2 - 24 - 11 - 56*j**2 - z*j = 0. What is j?
-7, -1
Let c(b) be the second derivative of b**6/210 - 9*b**5/20 + 107*b**4/84 + 305*b**3/14 + 2009*b. Factor c(p).
p*(p - 61)*(p - 5)*(p + 3)/7
Factor 1/2*y**2 - 22*y - 46.
(y - 46)*(y + 2)/2
Let f be (-21)/(-9) + ((-19999)/(-14285))/((-3)/(-14)*-4). Suppose -2*h**3 + f + h**2 - 17/10*h**4 + 11/5*h - 1/5*h**5 = 0. What is h?
-7, -1, -1/2, 1
Let l(v) be the first derivative of 7/6*v**2 + 0*v - 1/2*v**3 - 318 + 1/24*v**4. Suppose l(z) = 0. Calculate z.
0, 2, 7
Suppose -2*o + 34*n = -173 - 173, -4*o + n = -22. Suppose 0 + 0*d**2 + 1/2*d + d**4 - 3/2*d**o = 0. What is d?
-1/2, 0, 1
Let i(m) be the third derivative of m**5/450 - 31*m**4/180 + 56*m**3/15 + 243*m**2. Factor i(y).
2*(y - 24)*(y - 7)/15
Let f(r) be the third derivative of 11*r**6/60 - 19*r**5/30 - 7*r**4/6 + 16*r**3/3 + 315*r**2 - 1. Factor f(n).
2*(n - 2)*(n + 1)*(11*n - 8)
Let g be 4*10/(-8) + 26/5. Let v be ((-1)/4)/(60/(-48)). Factor v*w**3 - g*w**2 + 0*w - 1/5*w**5 + 1/5*w**4 + 0.
-w**2*(w - 1)**2*(w + 1)/5
Let q be 224/(-128) + (-12)/(-16). Let c be (-7 + (-2 - q))/(-2). Factor -4/7*r**2 - 3/7*r + 5/7*r**3 + 0 + 2/7*r**c.
r*(r - 1)*(r + 3)*(2*r + 1)/7
Let i(r) = -3*r**4 + 18*r**3 + 69*r**2 + 42*r + 6. Let x(v) = -4*v**4 + 16*v**3 + 69*v**2 + 42*v + 7. Let l(b) = -7*i(b) + 6*x(b). Solve l(z) = 0 for z.
-7, -2, -1, 0
Let o(i) = -3*i**2 - 3*i. Let z(t) = -55*t**2 + 1110*t + 460. Let x(n) = -10*o(n) + z(n). Factor x(y).
-5*(y - 46)*(5*y + 2)
Let i(h) be the first derivative of 39/2*h**2 - 12*h + 90 - 4*h**3 - 9*h**4. Factor i(o).
-3*(2*o - 1)**2*(3*o + 4)
Let f = 5799/22 - 28731/110. Determine j, given that 0*j**2 + 0 + 8/5*j**3 + 0*j + 4/5*j**5 - f*j**4 = 0.
0, 1, 2
Let l(q) be the second derivative of q**5/30 + 1565*q**4/18 - 3133*q**3/9 + 1567*q**2/3 - 109*q - 45. Factor l(u).
2*(u - 1)**2*(u + 1567)/3
Let 0 - 27/2*n + 9/4*n**2 - 1/4*n**5 - 1/4*n**4 + 15/4*n**3 = 0. What is n?
-3, 0, 2, 3
Let q be (0 - 1 - -4)/(6/10). Factor -10*z**2 - 4*z**2 + 15*z**2 - q*z.
z*(z - 5)
Let p = 91584 + -91580. Find k such that 0*k**3 + 2/3*k - 2/3*k**5 - 8/3*k**p - 4 + 20/3*k**2 = 0.
-3, -2, -1, 1
Let p(x) be the third derivative of -x**5/450 - x**4/6 - 224*x**3/45 + 35*x**2 - 7*x. Factor p(a).
-2*(a + 14)*(a + 16)/15
Let h(f) = 3*f + 70. Let x be h(-16). Let a(v) = v**3 - 31*v**2 + 80*v. Let l(j) = 6*j**2 - 16*j. Let k(i) = x*l(i) + 4*a(i). What is z in k(z) = 0?
-4, 0, 2
Let l = 358222/156723 - -2/156723. Solve 0 + 4/7*g**3 - 16/7*g - 4/7*g**4 + l*g**2 = 0 for g.
-2, 0, 1, 2
Let k(l) = 19*l**2 + 186*l + 180. Let r(n) = -9*n**2 - 93*n - 90. Suppose 35*g + 70 = -140. Let z(m) = g*k(m) - 13*r(m). Factor z(a).
3*(a + 1)*(a + 30)
Let g be ((-4)/8)/((-1)/18). Suppose -5*r = -6 - g. Factor 2*c**4 - 2*c**r - 4*c**4 + 9*c**5 + 2*c**2 - 7*c**5.
2*c**2*(c - 1)**2*(c + 1)
Suppose 185*x - 156*x - 116 = 0. Let u(k) be the first derivative of 14/27*k**3 + 1/18*k**x + 0*k - 35 + 0*k**2. Factor u(c).
2*c**2*(c + 7)/9
Suppose 3 - 476*h**2 - 2*h + 5 + 475*h**2 = 0. What is h?
-4, 2
Let b be (2*149/(-4) - 3)*(-68)/(-4590)*-72. Suppose -98*o**2 - b - 488/3*o - 52/3*o**3 + 2/3*o**4 = 0. What is o?
-2, -1, 31
Let j = 4 + -1. What is c in -20*c - 24*c**4 + 2*c**2 + 22*c**4 + 8*c**j + 0*c**3 - 16 + 4*c**2 = 0?
-1, 2, 4
Let g = 53617/3 + -17872. Solve -3 - 8/3*j + g*j**2 = 0 for j.
-1, 9
Let q(x) be the first derivative of -18*x**2 - 38*x + 2/3*x**3 - 180. Factor q(w).
2*(w - 19)*(w + 1)
Let t(i) = -2*i + 1. Let l = 367 - 366. Let f(b) = 26*b**2 - 12*b + 4. Let m(p) = l*f(p) - 4*t(p). Suppose m(a) = 0. What is a?
0, 2/13
Let o(j) = -3*j**2 + j + 4. Let z be o(0). Factor -91*w**2 + 4*w - 57*w**2 + 24*w + 13*w + z*w**5 - 44*w**4 + 132*w**3 + 15*w.
4*w*(w - 7)*(w - 2)*(w - 1)**2
Factor -8/3*d**2 - 28/3 + 2/9*d**3 + 82/9*d.
2*(d - 7)*(d - 3)*(d - 2)/9
Let o(b) = b + 5. Let u(n) = n + 4. Let c(t) = 5*o(t) - 6*u(t). Let s be c(-2). Suppose -10*f**2 - 2 - 6*f**3 - 2*f**s + 4*f + 6*f**4 + 2 = 0. What is f?
-1, 0, 1/3, 2
Let j = -892 - -6254/7. Let p = j - -1/14. Determine g so that 1/2*g - 5/2*g**3 - 3/2*g**4 + 2*g**5 + p*g**2 + 0 = 0.
-1, -1/4, 0, 1
Let o(b) = -b**5 - b**3 + 3*b**2 + 2*b + 1. Let l(z) = 20*z**5 + 16*z**4 - 88*z**3 - 176*z**2 + 68*z + 96. Let t(v) = -l(v) - 16*o(v). Let t(d) = 0. What is d?
-7, -1, 1, 4
Let i(k) = 2*k**3 - 31*k**2 - 12*k - 14. Let t be i(16). Suppose -2 + t = 16*p. Solve 3/2*z**3 - 3/2*z + p*z**2 - 3 = 0.
-2, -1, 1
Factor 34/7*n - 1/7*n**3 - n**2 + 40/7.
-(n - 4)*(n + 1)*(n + 10)/7
Let r = -144952/7 + 289911/14. Let -2*u**2 + 0 - 6*u + r*u**3 = 0. Calculate u.
-2, 0, 6
Let a(c) = 2*c**2 + 3*c + 2. Let l(q) = 5*q**3 + 27*q**2 + 48*q - 8. Let d(n) = 4*a(n) + l(n). Solve d(x) = 0 for x.
-4, -3, 0
Let z(c) be the first derivative of -5/4*c**4 - 15 + c**5 - 1/6*c**6 + 3*c**2 + 0*c - 5/3*c**3. Let z(f) = 0. Calculate f.
-1, 0, 1, 2, 3
Let p(l) = 18*l**3 + 313*l**2 - 197*l + 20. Let n be p(-18). Factor 0*h + 0 - 2/5*h**3 - 6/5*h**n.
-2*h**2*(h + 3)/5
Let j(k) = -5*k**2 + 25*k + 34. Let a(i) = 14*i + 32*i + 182 - 79 + 27*i - 14*i**2. Let g(h) = -4*a(h) + 11*j(h). Factor g(p).
(p - 19)*(p + 2)
Let p(h) be the first derivative of -3*h**5/35 - 3*h**4 - 195*h**3/7 - 174*h**2/7 + 1020*h/7 + 867. What is o in p(o) = 0?
-17, -10, -2, 1
Suppos