t(w) be the second derivative of 2*w**7/147 + 8*w**6/35 + 8*w**5/5 + 6*w**4 + 90*w**3/7 + 108*w**2/7 + 527*w. Factor t(i).
4*(i + 1)*(i + 2)*(i + 3)**3/7
Let y(b) = b**4 - 7*b**3 + 24*b**2 - 2*b - 30. Let c(w) = 2*w**4 - 13*w**3 + 49*w**2 - 5*w - 59. Let o(z) = 6*c(z) - 15*y(z). Factor o(l).
-3*(l - 4)**2*(l - 2)*(l + 1)
Suppose -5*q = -13*q. Let s(p) be the third derivative of 0*p - p**2 + q - 1/80*p**5 - 1/32*p**4 + 1/4*p**3. Factor s(m).
-3*(m - 1)*(m + 2)/4
Let b(a) be the third derivative of -a**5/390 - 4*a**4/13 - 192*a**3/13 - 8*a**2 + 4*a. Determine c, given that b(c) = 0.
-24
Let a(l) = 2*l**2 - 2*l + 2. Suppose 2*d = -3*k - 2, -k + 3 = -3*d - 0*d. Let b(y) = -33*y**2 + k*y - y + 35*y**2 + 3. Let r(p) = -3*a(p) + 2*b(p). Factor r(w).
-2*w*(w - 2)
Let 0*p - 11/5*p**3 + 0 + 1/5*p**4 - 12/5*p**2 = 0. What is p?
-1, 0, 12
Suppose o + 18*w + 7 = 16*w, -5*w = 5*o + 10. Factor 1/4 - 1/4*u**o - 3/4*u + 3/4*u**2.
-(u - 1)**3/4
Suppose 6*b + 64/5*b**3 - 4*b**4 + 0 - 76/5*b**2 + 2/5*b**5 = 0. Calculate b.
0, 1, 3, 5
Suppose d + 14 = -2*u + u, 0 = 4*u + 20. Let p be (18/4)/d*-46. Solve -2*w**2 + p*w - 12*w - 7*w = 0 for w.
0, 2
Let n(f) = -7*f**2 + 63*f + 657. Let w(a) = -3*a**2 + 32*a + 328. Let y(h) = -4*n(h) + 9*w(h). Let y(v) = 0. What is v?
-18
Let j be (-42)/77 + (1266/(-462) - -5). Let j*l**2 + 2/7*l**3 + 8/7 + 18/7*l = 0. What is l?
-4, -1
Let g = -5/2706 - -1819/8118. Let -2/9*t**2 - g*t**4 + 0*t - 4/9*t**3 + 0 = 0. What is t?
-1, 0
Suppose -2*j - 3*c + 5*c - 8 = 0, -5*c = 4*j - 20. Suppose 4*u = 2*s + 8, -20 = -s - 16. Factor -1/2*r**u + r**3 + 0 + j*r - 1/2*r**2.
-r**2*(r - 1)**2/2
Let u be 1 - (-2)/(-1) - -4. Suppose 3*s + 8*s = 88. Factor -35*v**u + 16*v**3 + 21*v**3 + s*v**4.
2*v**3*(4*v + 1)
Let r(d) = -4*d - 21. Let g be r(-6). Factor -g*l**3 + 0*l**3 + 3*l**4 + 0 + 0.
3*l**3*(l - 1)
Let o(n) be the third derivative of -n**5/120 - 31*n**4/24 - 61*n**3/12 - 202*n**2. Factor o(y).
-(y + 1)*(y + 61)/2
Suppose 22/3 - 16/9*r - 2/9*r**2 = 0. Calculate r.
-11, 3
Let c(k) be the second derivative of 2*k**7/231 + k**6/60 - k**5/330 - k**4/66 + 10*k**2 - 26*k. Let x(g) be the first derivative of c(g). Solve x(z) = 0 for z.
-1, -1/2, 0, 2/5
Factor 54*k**2 - 190*k**3 + 55*k**2 + 25 + 61*k**4 + 24*k**4 + 101*k**2 - 15*k**5 - 115*k.
-5*(k - 1)**4*(3*k - 5)
Let p be 2/(-16)*(-67)/((-1608)/(-32)). Factor b**3 - p*b**4 - 2*b**2 - 1/2 + 5/3*b.
-(b - 3)*(b - 1)**3/6
Let y = -48 + 52. Suppose -4*n + 4 + y = 3*f, -f = 2*n - 4. Find i, given that 28/3*i**4 + 4/3 + 29/3*i**3 - 19*i**n - 4/3*i = 0.
-2, -2/7, 1/4, 1
Let c(t) = t**5 - t**4 + t**2 + t - 1. Let j(y) = 2*y**5 - 8*y**4 - 7*y**3 + 3*y - 3. Let z(a) = -15*c(a) + 5*j(a). Find k such that z(k) = 0.
-3, -1, 0
Let q(k) be the first derivative of -k**5/25 - k**4/20 + 2*k**3/15 + 208. Solve q(l) = 0.
-2, 0, 1
Let o = 374 - 374. Let a(k) be the second derivative of 0*k**4 - 1/33*k**3 - 4*k + o*k**2 + 0 + 1/110*k**5. Factor a(r).
2*r*(r - 1)*(r + 1)/11
Determine c so that 21 - 37*c**3 + 3*c**4 + 135*c**3 - 24*c**2 + 18*c - 37*c**3 - 40*c**3 - 39*c**3 = 0.
-1, 1, 7
Factor -1/9*v**2 + 23/9*v - 14/3.
-(v - 21)*(v - 2)/9
Let x(k) be the first derivative of -4*k**3/21 + 2*k**2 - 48*k/7 + 79. Factor x(d).
-4*(d - 4)*(d - 3)/7
Let m be ((-1)/9)/(29 - 12 - 18). Let -m*a**3 + 0 + 0*a**2 + 1/9*a**4 + 0*a = 0. What is a?
0, 1
Suppose -m + 5*j + 31 = 0, -4*m - j + 82 = -0. Let o be (-3)/(2 + -4 + 1). Let 4*i**4 + 48*i**2 - m*i - 24*i**o - 11*i + 0*i**4 = 0. What is i?
0, 2
Let g = -1 + 31. Let l = g - 30. Factor l + 0*x + 1/5*x**5 + 0*x**3 + 1/5*x**4 + 0*x**2.
x**4*(x + 1)/5
Suppose 5*p = -27*q + 28*q, -4*p - 4*q = 0. Factor p - 1/3*o**3 + 1/3*o**2 + 2/3*o.
-o*(o - 2)*(o + 1)/3
Let j be (1/3)/(1/3). Let t(p) be the first derivative of p**2/2 + p + 6. Let x(i) = 4*i**2 + 6*i + 2. Let a(f) = j*x(f) - 6*t(f). Determine s so that a(s) = 0.
-1, 1
Let d be (-4757)/284 - (-13 + -4). Solve d*t**2 + 0 + 1/4*t = 0 for t.
-1, 0
Suppose 17*p = 16*p - 1. Let s(r) = -r**3 + r**2 + r. Let g(m) = -3*m**3 + 9*m**2 + 10*m. Let k(q) = p*g(q) + 4*s(q). Suppose k(j) = 0. Calculate j.
-3, -2, 0
Let h(v) be the second derivative of -v**6/255 - v**5/17 - 16*v**4/51 - 38*v**3/51 - 15*v**2/17 - 74*v. Determine p, given that h(p) = 0.
-5, -3, -1
Let o(n) = 2*n**2 - 9*n + 13. Let a be o(4). Let c be 5/((-90)/(-16)) - 6/a. Let 4/9 - 2/3*t**2 - 2/9*t + c*t**4 + 2/9*t**3 = 0. Calculate t.
-2, -1, 1
Let r(v) = 3*v - 100. Let s be r(35). Let z(k) be the first derivative of -1/6*k**3 + 0*k**4 - 1/8*k**2 + 1/24*k**6 + 4 + 0*k + 1/10*k**s. Factor z(w).
w*(w - 1)*(w + 1)**3/4
Suppose 4*k + 134 = 5*s - 2, 0 = -s + k + 28. Let n = s - 21. Factor 11*v - 2*v**2 - 2*v**3 - 3*v + 4 + 3*v**n + 7*v**2.
(v + 1)*(v + 2)**2
Let k(n) = 42*n**3 - 103*n**2 + 23*n + 3. Let s(c) = 85*c**3 - 205*c**2 + 45*c + 5. Let w(o) = 5*k(o) - 3*s(o). Factor w(t).
-5*t*(t - 2)*(9*t - 2)
Let p(h) be the first derivative of -3/2*h**2 + 1/2*h**3 + 14 - 9/2*h. What is b in p(b) = 0?
-1, 3
Let y(h) be the third derivative of h**5/20 - 33*h**4/2 + 2178*h**3 + 34*h**2. Let y(w) = 0. Calculate w.
66
Let m(j) be the third derivative of -j**5/20 - 3*j**4/2 - 10*j**3 + 65*j**2. Solve m(g) = 0.
-10, -2
Let c(b) = b**2 + 22*b + 24. Let j(x) = -3*x - 27. Let l be j(-2). Let f be c(l). Factor -5/3*n**f + 5/3*n + 5/3*n**4 - 5*n**2 + 10/3.
5*(n - 2)*(n - 1)*(n + 1)**2/3
Let u be 4/(-8) - ((-5681)/38)/(2 - -9). Let 14/11*q**4 + u*q**2 - 32/11 + 64/11*q + 80/11*q**3 = 0. Calculate q.
-2, 2/7
Let k be ((-384)/39 + 10)/((-1)/(-13)). Determine x, given that -2/5*x**2 - 6/5 + 2/5*x**3 - k*x = 0.
-1, 3
Let a(q) be the third derivative of -5/336*q**8 + 5*q**3 + 17/6*q**5 - q**6 + 0 - 115/24*q**4 + 22*q**2 + 4/21*q**7 + 0*q. Factor a(s).
-5*(s - 3)*(s - 2)*(s - 1)**3
Let u be ((-6)/9)/((-102)/(-27) + -4). Let x be ((u/(-2))/(-4 + 7))/(-1). Find c, given that 1/2*c**3 - x*c**2 - 1/2*c + 1/2 = 0.
-1, 1
Let q(b) be the second derivative of 0 + 1/12*b**3 + 32*b - 1/48*b**4 + 0*b**2. Factor q(y).
-y*(y - 2)/4
Let t(b) = 8*b**3 - 20*b**2 + 4*b - 4. Let g(m) = 9*m**3 - 22*m**2 + 3*m - 5. Let h(q) = -4*g(q) + 5*t(q). Let h(a) = 0. What is a?
0, 1, 2
Factor -106/7 - 1/7*k**2 - 107/7*k.
-(k + 1)*(k + 106)/7
Let a = 30673/61354 + 2/30677. Find m, given that a*m + 1/10*m**3 - 2/5*m**2 - 1/5 = 0.
1, 2
Let 168/5 - 8*q + 2/5*q**2 = 0. Calculate q.
6, 14
Determine d, given that -164/3*d**2 + 0 - 68/3*d**3 + 76*d + 4/3*d**4 = 0.
-3, 0, 1, 19
Let p be 7896/560 - (-6)/(-10). Find n, given that 69*n**2 + 3/2*n**5 + 99/2*n + p*n**4 + 27/2 + 45*n**3 = 0.
-3, -1
Suppose 1/4*a**3 - 9/2 + 37/4*a - 5*a**2 = 0. What is a?
1, 18
Let p be 6/4*(-224)/(-84). Let r be 5/p - ((-105)/(-14) - 7). Factor -9/4 - r*f**2 - 3*f.
-3*(f + 1)*(f + 3)/4
Let v = 13 - 10. Suppose c = -o + 3, 4*o + 6 = v*c + 2*c. Factor -30*b**3 + 4*b + 22*b**3 - c*b**5 + 6*b**5.
4*b*(b - 1)**2*(b + 1)**2
Let c(j) = 25*j**2 - 2065*j + 106085. Let o(r) = -14*r**2 + 1033*r - 53042. Let s(l) = 3*c(l) + 5*o(l). Suppose s(g) = 0. Calculate g.
103
Let h(y) = 4*y**2 - 87*y + 140. Let p be h(20). Factor 8/13*t**3 + p - 2/13*t**2 + 0*t.
2*t**2*(4*t - 1)/13
Let f(u) be the first derivative of 1/2*u**2 + 1/15*u**5 - 1/4*u**4 - 8 + 1/9*u**3 - 2/3*u. Find a, given that f(a) = 0.
-1, 1, 2
Let t be 6/(-15) - 4/(-10). Let d(f) be the third derivative of 0*f + 0*f**3 + f**2 + t*f**4 + 0 + 1/150*f**5. Find u such that d(u) = 0.
0
Let -2/11*m**5 + 54/11*m + 12/11*m**3 + 18/11 + 52/11*m**2 - 6/11*m**4 = 0. What is m?
-3, -1, 3
Let s = -28/359 - -802/1077. Let 0 - 4/3*o + 2*o**2 - s*o**3 = 0. What is o?
0, 1, 2
Let k be 5 + (36/16)/((-6)/8). Suppose 9*p**3 + 9*p**4 + 3/2*p**5 - 117/2*p - 27 - 30*p**k = 0. Calculate p.
-3, -1, 2
Let x(q) be the third derivative of -1/1020*q**6 - 2/51*q**3 - 9*q**2 + 1/204*q**4 + 0 - 1/1785*q**7 + 0*q + 1/170*q**5. Determine i, given that x(i) = 0.
-2, -1, 1
Let a = 2/815 - -487/815. Factor -3*w + 12/5 + a*w**2.
3*(w - 4)*(w - 1)/5
Let l be ((-19)/(-76))/(18/8). Let m(p) be the first derivative of -2 + 1/2*p**2 - l*p**3 - 2/3*p. Solve m(u) = 0.
1, 2
Let d be -3*120/(-18)*(-12 + 0). Let q be (4/(-35))/(8/d). Factor -q*n**4 - 18/7*n**3 - 10/7*n**5 - 4/7*n**2 + 0 + 0*n.
-2*n**2*(n + 1)**2*(5*n + 2)/7
Find p, given that -26*p + 3128 - 31*p**2 - 3134 + 5*p*