e ((-21)/(-126))/(7/p). Factor 1/7*v**3 + 0 + g*v - 2/7*v**2.
v*(v - 1)**2/7
Let n(w) be the third derivative of 0 - w**2 + 1/210*w**7 + 0*w**3 - 1/24*w**6 + 0*w**4 + 1/15*w**5 - 15*w. Find k, given that n(k) = 0.
0, 1, 4
Let w(r) = -1. Let u(k) be the second derivative of -k**4/6 - 38*k**3/3 - 725*k**2/2 + 15*k - 1. Let x(f) = u(f) - 3*w(f). Factor x(i).
-2*(i + 19)**2
Let a(p) be the second derivative of 0*p**4 + 0*p**5 - 1/20*p**6 + 0*p**3 + 6*p**2 + 2*p + 0 + 1/70*p**7. Let k(n) be the first derivative of a(n). Factor k(j).
3*j**3*(j - 2)
Let i(z) be the third derivative of -z**7/70 - 15*z**6/8 - 18*z**5/5 + 37*z**4/2 + 1380*z**2. Factor i(k).
-3*k*(k - 1)*(k + 2)*(k + 74)
Let a(g) be the third derivative of -g**6/1020 + g**5/30 + 133*g**4/204 + 115*g**3/51 + 1645*g**2. Factor a(h).
-2*(h - 23)*(h + 1)*(h + 5)/17
Let u be (31785/(-3423))/(100/(-28)). Factor -1/5*y**2 - u*y - 12/5.
-(y + 1)*(y + 12)/5
Suppose -14 = 3*f - 23. What is v in 10*v**f - 12 + 3*v + 17 - 13*v - 5*v**4 = 0?
-1, 1
Let h be (-1)/(((-88)/40)/11). Let x be (2/(-4))/(2 - h - -2). Factor -2*n**2 + x*n - 2*n**4 + 0 + 1/2*n**5 + 3*n**3.
n*(n - 1)**4/2
Let v be (-58838)/(-169) - ((-135)/(-360) + 46/(-208)). Determine o so that -54*o**3 + 16 - 440/3*o + v*o**2 = 0.
2/9, 6
Suppose 0 = 3*k - 4*c + 30, -6054*k + 6051*k = 2*c - 24. Factor -2*f + 5 - 1/4*f**k.
-(f - 2)*(f + 10)/4
Let a be -3*(-10)/6 + 18/(-2). Let s(n) = n**3 + 5*n**2 + 4*n + 4. Let l be s(a). Let 6*w**2 + 4 + 1/4*w**l - 2*w**3 - 8*w = 0. Calculate w.
2
Suppose 285357*h = 285296*h + 183. Let c = -4 + 9. Suppose q**h + 0 - 7/3*q**2 + 2/3*q - 5/3*q**c + 7/3*q**4 = 0. Calculate q.
-1, 0, 2/5, 1
Determine f so that 65*f - 636 - 258 + 0*f**2 - 153*f + 392*f - 2*f**2 = 0.
3, 149
Let x(o) be the first derivative of -2*o**3/15 - 296*o**2/5 - 43808*o/5 - 844. Factor x(u).
-2*(u + 148)**2/5
Suppose 9/2*z + 0 - 39/8*z**3 + 3/8*z**5 - 3/2*z**2 + 3/2*z**4 = 0. Calculate z.
-6, -1, 0, 1, 2
Let i be -1*((-45)/54 - 0). Let v be 9/(-6)*(-12)/27. What is x in -i*x**2 + 1/6*x**3 - v + 4/3*x = 0?
1, 2
Let c(v) be the second derivative of v**6/60 - 7*v**5/20 + 29*v**4/24 + 11*v**3/3 + v - 1591. Factor c(t).
t*(t - 11)*(t - 4)*(t + 1)/2
Factor 10290*v**3 - 12*v + v**4 - 20575*v**3 - 4*v**2 + 10288*v**3.
v*(v - 2)*(v + 2)*(v + 3)
Let u(s) = -1045*s + 313504. Let q be u(300). Factor -1/2*p**2 + 0 - q*p.
-p*(p + 8)/2
Let v = 61151 + -61148. Find n, given that -8/5*n + 0 - 46/5*n**v + 8*n**2 + 14/5*n**4 = 0.
0, 2/7, 1, 2
Let k(w) be the third derivative of -w**6/1440 + w**5/160 - 55*w**3/3 - 43*w**2 + w. Let l(o) be the first derivative of k(o). Find c such that l(c) = 0.
0, 3
Let u(b) be the third derivative of -b**5/15 + 23*b**4/3 + 170*b**3 + 7648*b**2. Factor u(h).
-4*(h - 51)*(h + 5)
Factor -27*l**2 + 26*l**3 + 28*l**3 - 82*l**3 - 124*l + 29*l**3.
l*(l - 31)*(l + 4)
Let t = 77205/8 + -77201/8. Let -25/6 + 29/6*f**2 + t*f**3 + 65/6*f = 0. Calculate f.
-5, 1/3
Let g(p) = 6*p**3 + 2*p**2 - 6*p + 8. Let w be 385/330 + (2/(-12) - 0). Let z(k) = -k**2 + k**3 - 2*k + k + 2*k**2. Let s(t) = w*g(t) - 10*z(t). Factor s(l).
-4*(l - 1)*(l + 1)*(l + 2)
Factor -6*v**3 - 540*v + 1289*v**2 - 600 - 1367*v**2 + 3*v**4 + 5*v**3 + 28*v**3.
3*(v - 5)*(v + 2)**2*(v + 10)
Let d(f) be the first derivative of f**3/18 - 122*f**2 + 89304*f + 2765. Determine h so that d(h) = 0.
732
Suppose -2*s - 5*l = 69, l + 75 = -2*s - 2*l. Let j = -14 - s. Factor -10 + 8 + 15*y - 36*y - j - 3*y**2.
-3*(y + 2)*(y + 5)
Let k(w) = 125*w**2 + 86665*w - 22108465. Let u(v) = -7*v**2 - 5098*v + 1300498. Let b(q) = -2*k(q) - 35*u(q). Solve b(x) = 0 for x.
510
Let l(o) = o**2 + 1058*o - 308. Let c(v) = 4*v**2 + 2122*v - 616. Let z(i) = 3*c(i) - 5*l(i). Factor z(x).
(x + 154)*(7*x - 2)
Suppose -160*u + 239*u**2 - 75 + 293*u**2 - 8*u**3 + u**4 - 626*u**2 = 0. What is u?
-5, -1, 15
Suppose -134*t - 112 = -162*t. Let m(c) be the first derivative of 0*c + 18 - 2/7*c**6 + 0*c**t + 0*c**2 + 2/35*c**5 + 0*c**3. Factor m(x).
-2*x**4*(6*x - 1)/7
Let h(v) be the second derivative of v**8/336 - v**6/40 + v**5/30 - 127*v**2/2 + 75*v + 2. Let y(m) be the first derivative of h(m). Factor y(d).
d**2*(d - 1)**2*(d + 2)
Let q be 18/4 + 17/(-34). Suppose 60 = 2*z + z - 5*d, 42 = 2*z - q*d. What is p in -11*p**2 + 16*p**2 - 5*p - 15*p + z = 0?
1, 3
Suppose 29 = 8*l + 5. Let c be -1 + 5 + -2 + 0. Solve -13*b**3 + 2*b - 4*b**l + 16*b**3 - 3*b - 2*b**c = 0 for b.
-1, 0
Suppose 4*h + 46 = 30*h - 3*h. Let f(t) be the second derivative of -17*t + 0 - 1/90*t**4 + 0*t**h - 2/45*t**3. Suppose f(u) = 0. What is u?
-2, 0
Let w(q) be the second derivative of -25 + q - 8*q**3 - 18*q**2 + 3/4*q**4. Factor w(v).
3*(v - 6)*(3*v + 2)
Suppose 2*i = 2*p - 102, 4*i - 8 = -12. Determine f so that -416*f**3 + 1328*f**2 + p*f**4 + f**5 - 3*f**5 + 800 - 749*f - 1011*f = 0.
1, 2, 10
Let j = -4159220/7 - -594252. Suppose 8/7*u + 276/7*u**4 - j*u**3 + 0 + 260/7*u**2 = 0. Calculate u.
-2/69, 0, 1
Let k = -157 + 157. Let r(q) be the third derivative of -1/40*q**6 + 0 + 1/5*q**5 - 5/8*q**4 + k*q + q**3 + 14*q**2. Factor r(z).
-3*(z - 2)*(z - 1)**2
Let y(u) be the second derivative of 14*u**6/5 + 5*u**5 + 4*u**4/3 + 4070*u. Find r, given that y(r) = 0.
-1, -4/21, 0
Let u(k) = -11*k**2 - 7*k - 119. Let r(v) = -3*v**2 + 1. Let p(b) = 4*r(b) - u(b). Let n be p(15). Factor -4*l**4 + 8*l**n + 0 + 2/3*l**5 + 2*l - 20/3*l**2.
2*l*(l - 3)*(l - 1)**3/3
Let c = 1822 + -1820. Suppose 5*f = -h + 17, 6*h - c*f + 12 = 9*h. What is b in 6/7*b - 4/7 - 2/7*b**h = 0?
1, 2
Let d be (0 - (-4)/(-7))/(38014/(-581) - -64). Factor 8/5*n**3 + 4/5*n**2 - 18/5 - 24/5*n - d*n**4.
-2*(n - 3)**2*(n + 1)**2/5
Let m(x) be the first derivative of -60 + 1/6*x**2 - 2/3*x + 1/9*x**3. Factor m(r).
(r - 1)*(r + 2)/3
Suppose -s = 2*t - 9, 5*t + s + 8 = 29. Let p(c) be the second derivative of -11*c - 15/4*c**t + 1/2*c**5 + 0 + 10*c**3 - 10*c**2. Factor p(q).
5*(q - 2)**2*(2*q - 1)
Let 2074*l - 824*l - 2585325 + 8414*l - 4*l**2 - 3251731 = 0. What is l?
1208
Suppose 553*j - 608*j = -110. Determine d so that 0 + 0*d - 4/9*d**j + 14/9*d**3 = 0.
0, 2/7
Let t = -37 + 1. Let x = -34 - t. Factor -5*f + 0*f - 8 - x*f**2 + 2*f - 5*f.
-2*(f + 2)**2
Let m = 13 - 11. Factor -96 + 96*t**3 + 224*t - 37*t**4 + 29*t**4 - 14*t**4 - 208*t**m + 2*t**5.
2*(t - 3)*(t - 2)**4
Let s(l) = 2*l**3 - 14*l**2 - 15*l + 13. Let p(u) = -2*u**2 - u - 1. Let y(r) = -3*p(r) + s(r). Let o be y(5). Factor -18 - 1/2*f**2 + o*f.
-(f - 6)**2/2
Let y(s) = -13*s**3 + 506*s**2 - 247*s - 256. Let w(z) = -z**3 - z**2 + 2*z + 2. Let p(i) = -5*w(i) - y(i). Let p(c) = 0. What is c?
-1/2, 1, 82/3
Let m(i) be the second derivative of -i**5/5 + 19*i**4/3 - 60*i**3 + 144*i**2 - 308*i + 1. Let m(y) = 0. Calculate y.
1, 6, 12
Let f be 260/(-16) - -3*(-1)/(-12). Let i be (f - -28) + (-30)/3. Let -8/11*u - 2/11*u**5 - 8/11 + 10/11*u**3 + 10/11*u**i - 2/11*u**4 = 0. What is u?
-2, -1, 1, 2
Let j(i) = -2*i**3 + 6. Let y(w) = 2. Suppose 37 = 20*x - 3. Let f(l) = x*j(l) - 6*y(l). Factor f(d).
-4*d**3
Let z = -979 - -453. Let y = z - -528. Factor 2/3*g**y + 8/3 + 10/3*g.
2*(g + 1)*(g + 4)/3
Let p(n) = -2*n**3 + 221*n**2 - 3176*n - 49. Let f be p(17). Factor 32/5*r + 2/5*r**3 + 0 + 34/5*r**f.
2*r*(r + 1)*(r + 16)/5
Let v be ((-6)/(-20))/(474/3160). Let g(k) be the first derivative of -4/21*k**3 + 12/7*k + 4/7*k**v - 17. Factor g(s).
-4*(s - 3)*(s + 1)/7
Suppose -33*z - 11*z + 1804 = 0. Let v be z/44 + (-22)/121. Factor 3 - 3*y + v*y**2.
3*(y - 2)**2/4
Let i(w) = -2*w**2 - 2*w + 1. Let c(g) = -3*g**2 - 3 - 5 + 8*g**2 + 2*g + 0*g + 4. Let h(l) = -c(l) - 4*i(l). Factor h(r).
3*r*(r + 2)
Suppose -3*g + q - 3 = 0, 4*q = -4*g - 9 + 21. Suppose w = -h + 5, -2*w - 5*h + 8*h = g. Find d such that 0 + 1/3*d**2 + 2/3*d - 2/3*d**w - 1/3*d**4 = 0.
-2, -1, 0, 1
Suppose 4626*w = 4669*w - 86. Let m be (-1)/4 + 66/24. Find i such that -10/3*i**3 + 55/6*i + 20/3*i**w + m = 0.
-1/2, 3
Let g be (-1095)/(-555) - 130/(-4810). Solve -4*x**g + 17/2*x**3 - x**4 + 0 + 0*x = 0 for x.
0, 1/2, 8
Let u(k) be the second derivative of -1/105*k**6 + 1/42*k**4 + 1/21*k**3 - 8 + 0*k**2 - 1/70*k**5 + 2*k. Factor u(z).
-2*z*(z - 1)*(z + 1)**2/7
Suppose -297*y + 18*y**2 + 3/4*y**3 - 7260 = 0. Calculate y.
-22, 20
Let c(j) be the third derivative of j**5/45 - 55*j*