f(p) = 21*p**4 - 7878*p**3 + 986625*p**2 - 41296872*p + 11718753. Let l(k) = k**3 + k + 1. Let n(z) = -f(z) + 3*l(z). Factor n(q).
-3*(q - 125)**3*(7*q - 2)
Let v(o) = -8*o**2 + 18. Let k(b) = 4*b**2 - 10. Let d be (-14)/4*1*(-48)/56. Let u(t) = d*v(t) + 5*k(t). Find z, given that u(z) = 0.
-1, 1
Suppose 162/7*l**3 + 1/7*l**4 + 0 + 0*l + 6561/7*l**2 = 0. Calculate l.
-81, 0
Suppose -10*r + 2*r = -3872. Factor 958*w**2 - 2*w - 476*w**2 - r*w**2.
-2*w*(w + 1)
Let h = -4297401/11 + 390675. Find r, given that h - 16/11*r + 2/11*r**2 = 0.
2, 6
Suppose 6*t = t + 110. Let f(w) = w**2 - 12*w + 31. Let d be f(t). Let 224*s**4 + 16*s**2 - 151*s**4 + d*s**4 + 144*s**3 = 0. Calculate s.
-2/9, 0
Solve 4*u**2 + 4610 - 117*u + 3489 + 997*u - 9875 = 0.
-222, 2
Let o = 466 - 471. Let q be o - 65/(-30) - -4. Let 0 - w + q*w**4 + 13/3*w**3 + 13/6*w**2 = 0. Calculate w.
-3, -1, 0, 2/7
Let s(g) be the first derivative of g**3/6 + 61*g**2/2 + 3721*g/2 + 748. Factor s(a).
(a + 61)**2/2
Let o = -228 + 158. Let k be 6/(((-12)/o)/(24/42)). Factor k*b**4 - 20*b**2 + 14*b**3 - 4*b - 35*b**3 + 3*b**5 + 22*b**5.
b*(b - 1)*(b + 1)*(5*b + 2)**2
Let r(p) be the third derivative of p**7/840 - 1247*p**6/480 + 249*p**5/16 - 3733*p**4/96 + 311*p**3/6 + 5848*p**2. Factor r(x).
(x - 1244)*(x - 1)**3/4
Let k(u) be the third derivative of 0*u**4 + 0 + 0*u**5 - 186*u**2 - 1/70*u**7 + 0*u**3 - 7/5*u**6 + 0*u. What is z in k(z) = 0?
-56, 0
Let d = 36 + -32. Let y be -25*(-21)/35*(-2)/(-10). Factor -8*q**2 - 13 + 9 - d*q**y + 4.
-4*q**2*(q + 2)
Solve 2*l + 2/7*l**2 - 240/7 = 0 for l.
-15, 8
Let a(q) = -q**3 - 43*q**2 + q + 43. Let r be 3/((-12)/20) + -38. Let k be a(r). Let -4*l**5 + 0*l**3 + 40/3*l**4 - 40/3*l**2 + k + 4*l = 0. What is l?
-1, 0, 1/3, 1, 3
Suppose 2*f - 16 = -2*m - 2*f, 0 = m - f - 2. Let r be (-138)/(-648) + (3380/135 - 25). Solve 0*j**2 + 0*j - 1/4*j**m - r*j**3 + 0 = 0.
-1, 0
Suppose 7*r - 44 = 3*r. Factor 20*n**2 - r*n**2 - 18*n - 10*n**2 + 14*n.
-n*(n + 4)
Suppose -35*a + 35 + 113 = 2*a. Let k(y) be the second derivative of -22*y + 5/24*y**3 + 0 + 1/48*y**a + 3/4*y**2. Factor k(c).
(c + 2)*(c + 3)/4
Let g be (-23)/(-69) - 6/18. Let o(t) be the first derivative of -20 + 8/7*t + g*t**2 - 2/21*t**3. Factor o(y).
-2*(y - 2)*(y + 2)/7
Determine m, given that -92/21*m**2 + 2/21*m**3 - 172/21 + 262/21*m = 0.
1, 2, 43
Let s(d) = 156*d**2 - 7*d - 58. Let o(k) = -22*k**2 + k - 2. Let p(q) = 14*o(q) + 2*s(q). Determine r, given that p(r) = 0.
-6, 6
Let z = 221 - 147. Let t = z + -72. Solve 5 + 8*u**t + 1 + 34*u - 60*u = 0.
1/4, 3
Suppose -297 - 191 = 4*l - 2*a, -5*l + 2*a - 609 = 0. Let j = l + 123. Factor 2*t**2 - 661 + 661 - j*t.
2*t*(t - 1)
Suppose 76 + 29 = -15*h. Let z(f) = 3*f**2 + 16*f - 29. Let r(l) = -2*l**2 - 7*l + 15. Let k(d) = h*r(d) - 3*z(d). Factor k(v).
(v + 2)*(5*v - 9)
Let b(t) be the first derivative of t**3/12 - 5*t**2/8 - 26*t - 1439. Factor b(v).
(v - 13)*(v + 8)/4
Let h(i) be the first derivative of -38 + 1/12*i**5 + 35/2*i**2 + 10/3*i**3 + 0*i - 5/6*i**4. Let o(n) be the second derivative of h(n). Factor o(g).
5*(g - 2)**2
Let r be -4 - (-8 + 1794/453). Let k = r + 260/1057. Factor 2/7*y**3 + 0*y**2 + 0*y + 0 - k*y**4.
-2*y**3*(y - 1)/7
Suppose 40*u + 551 = 631. Factor -u*b**2 - 12/5*b + 2/5*b**3 + 0.
2*b*(b - 6)*(b + 1)/5
Let w = -208 + 228. Suppose -t + w = -5*f, 0 = -0*t + t + 4*f + 16. Solve 9/2*c**2 + 3/2*c + 9/2*c**3 + t + 3/2*c**4 = 0 for c.
-1, 0
Suppose 0 = -54*o + 181 - 73. Let b(p) be the second derivative of 0 + 13*p - 1/14*p**5 + 0*p**o - 1/21*p**4 + 0*p**3. Factor b(i).
-2*i**2*(5*i + 2)/7
Let o = 771/8 - 11561/120. Let s(i) be the third derivative of -o*i**5 + 22*i**2 + 0*i**4 + 0 + 0*i + 4/3*i**3. Solve s(p) = 0.
-2, 2
Let s be 10/65 - 1344/(-728). Let c(f) be the first derivative of -s*f**2 - 5 - 4/3*f**3 + 8*f. Factor c(r).
-4*(r - 1)*(r + 2)
Suppose o = 2*f - 6, 31*o = 3*f + 30*o - 8. Let y(l) = l**3 - 2*l**2 - 4. Let v be y(3). Factor f*x**2 - 4*x + 6 - v*x + 6*x - 5*x**2.
-3*(x - 1)*(x + 2)
Find o, given that -1/4*o**5 + 7/2*o**4 + 0 - 53/4*o**3 - 9*o + 19*o**2 = 0.
0, 1, 2, 9
Let 2648*m**2 + 2170*m - 264*m + 1910*m**3 + 1166*m**2 - 93*m**4 + 95*m**4 = 0. Calculate m.
-953, -1, 0
Factor 6612/11*n + 2/11*n**2 + 5464818/11.
2*(n + 1653)**2/11
Factor 4/7*b**4 + 0 - 124/7*b - 132/7*b**3 + 36*b**2.
4*b*(b - 31)*(b - 1)**2/7
Let p(z) be the second derivative of 250*z**7/21 - 70*z**6 - 18*z**5 + 414*z**4 + 702*z**3 + 486*z**2 - 184*z + 10. Let p(b) = 0. Calculate b.
-3/5, 3
Let f be 26/52 - 1670/4. Let r = -417 - f. Determine p so that 0 + 0*p - 3/4*p**2 + r*p**3 + 3/4*p**4 = 0.
-1, 0, 1
Let u(a) be the first derivative of a**7/42 - a**6/4 + a**5 - 5*a**4/3 + 7*a**2/2 - 5*a - 15. Let k(g) be the second derivative of u(g). Factor k(y).
5*y*(y - 2)**3
Let r be 774 - -8*(-3)/(-6). Solve -1218*b**2 + 2145*b**3 + 125*b**5 + 1150*b**4 + 500*b - r*b**2 - 304*b**2 = 0 for b.
-5, 0, 2/5
Let s(y) be the second derivative of 0*y**2 + 1/6*y**6 + 69*y + 0*y**3 - 1/3*y**4 + 0 - 2/5*y**5. Factor s(g).
g**2*(g - 2)*(5*g + 2)
Let k(w) be the second derivative of -w**6/45 - 31*w**5/10 - 46*w**4/9 + w + 380. Determine q so that k(q) = 0.
-92, -1, 0
Let u(d) = 138*d - 8418. Let m be u(61). Let k(i) be the third derivative of -20*i**2 + 3/4*i**4 + 0 + m*i - 8/3*i**3 - 1/30*i**5. Find n such that k(n) = 0.
1, 8
Factor 72529382*w**2 - 219122*w**3 + 3973195810651/5 + 331*w**4 - 1/5*w**5 - 12003612721*w.
-(w - 331)**5/5
Solve 153*y + 81 - 3/4*y**4 + 249/4*y**2 - 21/2*y**3 = 0 for y.
-18, -1, 6
Factor 1/6*s**4 - 26/3*s**2 + 0 - 3/2*s**3 + 0*s.
s**2*(s - 13)*(s + 4)/6
Let q(h) be the first derivative of -h**5/60 + 5*h**4/18 + h**3/18 - 5*h**2/3 + 51*h + 124. Let s(r) be the first derivative of q(r). Factor s(x).
-(x - 10)*(x - 1)*(x + 1)/3
Let r(p) = 3*p**2 - 2763*p**4 + 2 + 2762*p**4 + 0*p**3 + 24*p - 23*p**3 + p**3. Let x(c) = c**4 + c**3 + 1. Let v(q) = r(q) - 2*x(q). Factor v(o).
-3*o*(o - 1)*(o + 1)*(o + 8)
Suppose -7 + 9 = l. Find j such that -2*j**2 + 2*j**l + 16*j + 14 - 4*j**2 + 6*j**2 = 0.
-7, -1
Let p(f) be the first derivative of -f**6/42 + 6*f**5/35 + 15*f**4/28 + 8*f**3/21 - 4700. Determine s so that p(s) = 0.
-1, 0, 8
Let m be (1 - 3)/(1/(-7) + 0). Suppose 6 = -o - 2*n, -11*n + m*n = -2*o - 8. Determine j so that 1/3*j**3 - 2*j**o - 2 + 11/3*j = 0.
1, 2, 3
Suppose 8371 = 12*y + 3115. Let f = y - 873/2. What is p in 3/2*p**3 - 3/2 + 9/8*p**2 + 3/8*p**4 - f*p = 0?
-2, -1, 1
Let k be (-44)/(-55)*((-27)/36)/(112/(-2560)). Find z, given that 72/7 + k*z + 26/7*z**2 + 2/7*z**3 = 0.
-6, -1
Suppose -29*f + 837 = -642. Let y = 54 - f. Factor 7/3*d**3 + y*d + 5*d**2 + 1/3.
(d + 1)**2*(7*d + 1)/3
Let g be -7 - (-9910)/2580*2. Let m = g + -15/43. Factor 0 + 1/3*q**5 - 1/3*q**3 + 0*q + m*q**4 - 1/3*q**2.
q**2*(q - 1)*(q + 1)**2/3
Let v(t) be the third derivative of 9*t**2 + 8/3*t**3 + 0 + 7*t + 5/36*t**4 - 1/90*t**5. Factor v(q).
-2*(q - 8)*(q + 3)/3
Suppose -2*z - 4 = 4*o, 5*o - 7*o + 2 = 2*z. Factor 0 + 24*f + 0 + 188*f**2 - z*f**3 - 184*f**2.
-4*f*(f - 3)*(f + 2)
Let b(v) be the third derivative of -2/15*v**6 + 1/5*v**5 + 0*v + 14*v**2 + 0*v**3 + 0 + 1/6*v**4. What is n in b(n) = 0?
-1/4, 0, 1
Let r = 1375 + -1372. Suppose 0 = r*i - 2*j - 4, 42*j = 4*i + 47*j - 13. Factor -10/19*y + 8/19*y**i + 2/19*y**3 + 0.
2*y*(y - 1)*(y + 5)/19
Solve 1/5*r**2 - 297/5*r + 296/5 = 0.
1, 296
Let r(w) = w**2 + 21*w + 105. Let z be r(-9). Let b be z*(-9)/243*14. Factor -b*d + 2/9*d**2 + 4/3.
2*(d - 6)*(d - 1)/9
Let h = -402959/60 + 6716. Let y(w) be the third derivative of -2/3*w**3 + 28*w**2 + 1/6*w**4 + 0 + h*w**5 - 1/120*w**6 + 0*w. Factor y(c).
-(c - 2)*(c - 1)*(c + 2)
Factor 37277/2*y**3 - 2381045/2*y**2 - 515217625/4 - 461/4*y**4 + 1/4*y**5 + 89923925/4*y.
(y - 145)**3*(y - 13)**2/4
Let r be ((-12)/14)/(7/(-98)). Let j = -469 + 471. Factor 588*s**j + 22*s**3 + 4802 + 2*s**4 + 2744*s - r*s**3 + 46*s**3.
2*(s + 7)**4
Let d(o) = 2*o**2 - 42*o + 76. Let q be d(2). Let j(r) be the second derivative of 1/9*r**3 + 0 + 12*r + q*r**2 + 1/18*r**4. Suppose j(f) = 0. Calculate f.
-1, 0
Let i be 196/(-56)*1*(-8)/14. Factor 128 - 12*x - 4*x**4 + 28*x**3 - 116*x - 10*x**2 - 14*x**i.
-4*(x - 4)**2*(x - 1)*(x + 2)
Suppose -33*m**3 - 2*m**2 - 41*m**3 - 5844*m**4 + 74*m + 5846*m**4 = 0. 