**3 + q - 1. Let o(i) = 5*d(i) + y(i). Let f(u) = 1. Let m(a) = 4*f(a) - 2*o(a). Factor m(l).
2*l**2*(l - 1)*(5*l + 1)
Suppose 3*f + 2*l + 142 = 0, -4*f - 5*l = -7*f - 149. Let h be 108/f*(-14)/6. Factor -4*t + h*t**2 - 9/4*t**3 + 1.
-(t - 1)*(3*t - 2)**2/4
Let i(f) be the first derivative of 0*f + 1/3*f**6 + 0*f**3 + 2*f**4 + 0*f**2 + 8/5*f**5 + 3. Let i(z) = 0. What is z?
-2, 0
Let f(y) be the first derivative of y**3/15 + 63*y**2/10 - 64*y/5 - 78. Factor f(r).
(r - 1)*(r + 64)/5
Let r be 6/3*(-20)/(-8) + 3. Let m(t) be the first derivative of -9/4*t**4 + r*t**3 - 9/2*t**2 - 2 - 6*t. Find s such that m(s) = 0.
-1/3, 1, 2
Let t(a) = a**2 + 9*a - 1. Let m be t(-11). Let h = 23 - m. Suppose -4*p**3 + 2*p**h + 3*p**2 - p**2 = 0. Calculate p.
0, 1
Let n(l) be the first derivative of l**4/4 - 2*l**2 - 710. Solve n(a) = 0.
-2, 0, 2
Let s(u) = 174*u + 1044. Let m be s(-6). What is p in m*p + 0 - 4/9*p**2 + 2/3*p**3 - 2/9*p**4 = 0?
0, 1, 2
Factor -1682/13 - 3248/13*d - 1452/13*d**2 + 112/13*d**3 - 2/13*d**4.
-2*(d - 29)**2*(d + 1)**2/13
Suppose -3*t = d - 33, 4*d + t + 20 = 97. Factor -3 - 3*c**2 - 10 + d*c - 14 + 0*c**2.
-3*(c - 3)**2
Let s be 6364/1332 - (-2)/9. Find i, given that -4/3*i + 5/6*i**4 - 2/3 - 1/6*i**2 + 1/6*i**s + 7/6*i**3 = 0.
-2, -1, 1
Factor -1355*w**4 + 12*w**2 + 1371*w**4 + 52*w**2 + 2*w**5 - 22*w - 60*w**3.
2*w*(w - 1)**3*(w + 11)
Let w(b) be the second derivative of b**4/138 + 22*b**3/69 - 2*b - 19. Determine t so that w(t) = 0.
-22, 0
Factor 25*r - 43*r + 16 + 16*r + 8 - 2*r**2.
-2*(r - 3)*(r + 4)
Let t(a) be the second derivative of a**6/45 - 86*a**5/15 + 1849*a**4/3 - 318028*a**3/9 + 3418801*a**2/3 + 146*a. Factor t(j).
2*(j - 43)**4/3
Let f(d) be the first derivative of 2/15*d**3 - 8 - 2/25*d**5 + 0*d**2 + 0*d + 1/15*d**6 - 1/10*d**4. Factor f(i).
2*i**2*(i - 1)**2*(i + 1)/5
Let t = 1816/85 - 336/17. Factor -36/5*y + 48/5*y**2 + t - 4*y**3.
-4*(y - 1)**2*(5*y - 2)/5
Let w(n) be the third derivative of n**5/20 + 7*n**4/4 - 3*n**2 - 5. Factor w(y).
3*y*(y + 14)
Let k(n) be the first derivative of -n**4/20 - n**3/10 + 13*n + 5. Let a(v) be the first derivative of k(v). Factor a(u).
-3*u*(u + 1)/5
Determine r so that -31 - 454*r**4 - 7*r**3 + 453*r**4 + 31 = 0.
-7, 0
Let b = 1286255647/1922393 - -3/174763. Factor -3072/11*n**4 - 5250/11*n - 1250/11 - 512/11*n**5 - b*n**3 - 800*n**2.
-2*(n + 1)*(4*n + 5)**4/11
Let i(m) = -129*m + 20*m**3 + 129*m - 29*m**3 + 9*m**2. Suppose 0 = d - 1. Let s(o) = o**3 - o**2. Let k(q) = d*i(q) + 12*s(q). Let k(p) = 0. What is p?
0, 1
Let m be 5*((-48)/(-15))/(-4). Let x be ((-18)/m)/(3/4). Let 24*p**4 - 7*p**2 - x - 14*p**2 - 18*p**3 + 3 + 18*p = 0. What is p?
-1, 1/4, 1/2, 1
Suppose -5*p = 4*o - 14, -5*p - 2*o + 4 = -4*p. Let l be 57/15 - 1 - p. Factor -2/5*t**3 - 2/5*t + 0 + l*t**2.
-2*t*(t - 1)**2/5
Let g(u) be the first derivative of -u**6/27 + 2*u**5/45 - 4. Solve g(h) = 0 for h.
0, 1
Let x(m) = -2*m**3 + 24*m**2 - 23*m + 278. Let g be x(12). Suppose -9/2*l + 0 - 3/4*l**g = 0. What is l?
-6, 0
Suppose -6 = -4*z + 6. Factor -q**4 + 262*q**z - q**2 - 258*q**3 - 3*q**2.
-q**2*(q - 2)**2
Let l = 6284/3 - 2094. Suppose 2/9 - 8/9*y**2 + l*y = 0. What is y?
-1/4, 1
Let r(y) be the first derivative of 6 - 1/60*y**5 + 0*y + 0*y**4 + 1/360*y**6 + 0*y**2 - 2/3*y**3. Let t(x) be the third derivative of r(x). Factor t(v).
v*(v - 2)
Factor 7*s - 166*s**2 - 132*s**3 - 91*s**3 - 3*s + 34*s + 10*s - 9*s**4.
-s*(s + 1)*(s + 24)*(9*s - 2)
Let m be 255/(-1870) - (-97)/66. Let 3*v**4 + m*v + 20/3*v**2 + 9*v**3 + 0 = 0. Calculate v.
-2, -2/3, -1/3, 0
Let c(u) be the third derivative of 0 - 1/1020*u**6 - 1/51*u**3 - 1/170*u**5 - 1/68*u**4 + 0*u - 16*u**2. Factor c(h).
-2*(h + 1)**3/17
Factor 751 - 58 + 210*o**3 - 279 + 5*o**4 + 1097 - 4620*o + 1985*o**2 + 909.
5*(o - 1)**2*(o + 22)**2
Suppose -3 = 4*g - 11. Factor -o**4 - 5*o**4 + 6*o + 39*o**3 + 5*o**2 + 18*o**4 + 28*o**g.
3*o*(o + 1)*(o + 2)*(4*o + 1)
Let o(i) = -17*i**2 + 40*i + 7. Let a(v) = 18*v**2 - 39*v - 6. Let q(k) = 2*a(k) + 3*o(k). Factor q(t).
-3*(t - 3)*(5*t + 1)
Let g(l) be the second derivative of -3*l**5/20 - 7*l**4/4 - 3*l**3 + 193*l. Let g(s) = 0. What is s?
-6, -1, 0
Let q(y) be the first derivative of 0*y - 5 + 5/6*y**3 + 5/16*y**4 + 5/8*y**2. Factor q(h).
5*h*(h + 1)**2/4
Let d(s) be the first derivative of -s**5/390 + 2*s**4/39 - 12*s**2 - 32. Let b(k) be the second derivative of d(k). Factor b(m).
-2*m*(m - 8)/13
Let x(i) = i**2 + 5*i + 130. Let d(q) = -9*q**2 - 36*q - 912. Let c(s) = -2*d(s) - 15*x(s). Factor c(l).
3*(l - 7)*(l + 6)
Let d be 35/140 - 366/56. Let f = 359/56 + d. Find n, given that 3/8 - f*n**2 + 1/4*n = 0.
-1, 3
Let s(r) be the second derivative of 1/60*r**4 + 2*r + 0 - r**2 + 1/150*r**5 - 2/15*r**3. Let u(i) be the first derivative of s(i). What is j in u(j) = 0?
-2, 1
Let q(m) = 2815*m + 2827. Let z be q(-1). Find x such that 3 + 15/2*x - 9/2*x**2 - z*x**3 + 6*x**4 = 0.
-1/2, 1, 2
Factor -5*t**3 + 5/4*t**4 + 5*t + 25/4 - 15/2*t**2.
5*(t - 5)*(t - 1)*(t + 1)**2/4
Let a be 9/(-6) + (-416)/320 + 5. Determine q so that -1/5 - a*q**2 - q**3 - 7/5*q = 0.
-1, -1/5
Suppose 5*n - 7 = z + 37, 4*n - 28 = -z. Factor -2*c**5 - n*c**4 - 14*c - 4*c**2 - 13*c - 10*c**3 + 27*c.
-2*c**2*(c + 1)**2*(c + 2)
Let u(v) be the second derivative of -5/24*v**4 + 5*v**2 + 5/4*v**3 - 2*v + 0. Factor u(x).
-5*(x - 4)*(x + 1)/2
Factor -1/8*i**3 - 55/2*i + 27 + 29/4*i**2.
-(i - 54)*(i - 2)**2/8
Let v be 2 + (-8)/(20/(-5)). Factor 16*j**2 + 2 - 2 + 4*j**3 - v*j**2.
4*j**2*(j + 3)
Let d(o) be the first derivative of 3/140*o**5 + 0*o**3 + 5*o + 3 - 1/14*o**4 + 0*o**2. Let a(m) be the first derivative of d(m). Factor a(h).
3*h**2*(h - 2)/7
Let n be (-1755)/540*(2/(-13))/1. Factor 1/2*g**5 + n*g**4 + 0 + 0*g - 1/2*g**2 - 1/2*g**3.
g**2*(g - 1)*(g + 1)**2/2
Let f(d) be the second derivative of 2 - 11/20*d**5 + 4*d + 5/12*d**4 + 1/10*d**6 + 1/2*d**3 + 0*d**2. Factor f(m).
m*(m - 3)*(m - 1)*(3*m + 1)
Factor -40*m**4 + 51*m**3 - 43*m**3 - 40*m**3 + 12*m**5 + 0*m**5.
4*m**3*(m - 4)*(3*m + 2)
Let q(x) be the first derivative of x**3/12 + x**2/4 - 2*x + 51. Solve q(m) = 0.
-4, 2
Factor 1/6 + 7/6*t**2 + 5/6*t + 1/2*t**3.
(t + 1)**2*(3*t + 1)/6
Find q, given that 10 - 120*q**2 + 35 - 42*q + 117*q**2 = 0.
-15, 1
Let n(p) be the second derivative of p**6/15 - p**5/10 - 5*p**4/3 - 8*p**3/3 + p - 7. Let n(w) = 0. What is w?
-2, -1, 0, 4
Suppose 0 = -4*o - 3*h - 1, -2*h + 6 = -2*o + 3*o. Let z be (-30)/(-48)*o/(-10). Factor 0 - z*m**2 + 0*m.
-m**2/4
Let o = -47 - -49. Factor -1 - 5 + 1 - 2*q**2 - 3*q**o - 10*q.
-5*(q + 1)**2
Let c(d) be the third derivative of -20*d**2 + 20/3*d**4 + 0 + 0*d - 1/6*d**6 + 1/84*d**8 - 32/3*d**3 + 2/21*d**7 - 5/3*d**5. Factor c(g).
4*(g - 1)**3*(g + 4)**2
Let t(r) = 3*r + 17. Let q be t(-5). Suppose 0 = h + 5*w - w, -q*h = -2*w. Determine i so that -2/11*i**3 + 0 + 0*i**2 + h*i = 0.
0
Suppose 110*p + 15*p**2 + 24 - 20*p**2 + 10*p**2 + 176 = 0. Calculate p.
-20, -2
Let l be (-32)/(-36)*(-3)/(-2). Suppose 5*x + 4 = -2*y, 2*y - 4*x - 16 = -2. Let -8/3*n - 4/3*n**5 + l*n**2 + 0 - 4/3*n**4 + 4*n**y = 0. Calculate n.
-2, -1, 0, 1
Suppose 50/7*x**4 + 200/7 + 460/7*x**3 - 920/7*x + 858/7*x**2 = 0. Calculate x.
-5, 2/5
Let p(v) be the second derivative of 11*v - 1/135*v**6 + 1/18*v**5 + 0 + 0*v**2 + 4/27*v**3 - 4/27*v**4. Factor p(u).
-2*u*(u - 2)**2*(u - 1)/9
Let z(i) be the first derivative of i**5/5 + 7*i**4/4 + 17*i**3/3 + 17*i**2/2 + 6*i + 22. Determine p, given that z(p) = 0.
-3, -2, -1
Find g such that 0*g**2 + g**2 + 5*g**2 + 48*g + 6*g**2 - 126 - 66 - 3*g**3 = 0.
-4, 4
Let v(c) be the first derivative of -c + 0*c**2 - 13 + 1/3*c**3. Let v(z) = 0. What is z?
-1, 1
Let y(w) be the first derivative of -22 - 1/21*w**3 - 1/7*w - 1/7*w**2. Factor y(o).
-(o + 1)**2/7
Let j = 72 - 431/6. Let y = 1/3 + j. Let 0 - b**4 - 3/2*b**5 + b**2 + 2*b**3 - y*b = 0. Calculate b.
-1, 0, 1/3, 1
Let l(b) = 687*b**4 - 1452*b**3 + 834*b**2 - 84*b + 15. Let c(m) = -m**4 + m**3 + 2*m**2 - m - 1. Let u(h) = -12*c(h) - l(h). Determine y, given that u(y) = 0.
1/15, 1
Let x(z) be the first derivative of 1/7*z**3 + 2/7*z**2 - 4/7*z + 8. Find i such that x(i) = 0.
-2, 2/3
Let j = 6/1067 - -3998/48015. Let k(b) be the second derivative of j*b**6 + 0 - 2/9*b**4 + 2/9*b**3 