0. Let a(c) be the first derivative of -4/3*c + y*c**2 + 9 + 7/9*c**3. Find m such that a(m) = 0.
-2, 2/7
Factor 166/3*w**2 + 4/3*w**3 + 176/3 - 436/3*w.
2*(w - 2)*(w + 44)*(2*w - 1)/3
Let p(i) be the first derivative of -2*i**5/85 - 61*i**4/34 - 2030*i**3/51 - 2523*i**2/17 - 1180. Determine j, given that p(j) = 0.
-29, -3, 0
Let h = 16 + -13. Suppose 6*y - 6*y + 95*y = -11*y. Let y + 16/13*t**2 + 10/13*t**h + 8/13*t + 2/13*t**4 = 0. What is t?
-2, -1, 0
Let b be (9/6)/((-3)/(-4)). Let t(u) = -76*u - 834. Let f be t(-11). What is z in -24 - 7*z**2 + 9 + b*z**f - 20*z = 0?
-3, -1
Let g(o) = 4*o**2 + 18*o - 7. Let k be g(-5). Factor -21 + k*p + 4*p**2 - 13*p**2 - 13*p + 8*p**2.
-(p + 3)*(p + 7)
Let o(v) = v. Let z = 41 - 38. Suppose z = 2*x + x. Let k(m) = 2*m**2 - 14*m + 72. Let g(r) = x*k(r) - 10*o(r). Let g(i) = 0. What is i?
6
Let u = 163927/15 - 10928. Let l(d) be the second derivative of 3/10*d**2 - u*d**3 + 40*d + 0 - 1/12*d**4. Factor l(o).
-(o + 3)*(5*o - 1)/5
Let a(g) = -10*g**3 - g**2 - g + 18. Let r(n) = 2*n**4 - n**3 + n - 3. Let v(t) = -a(t) - 6*r(t). Let v(q) = 0. Calculate q.
-1/2, 0, 5/6, 1
Suppose 95/6*y - 29/6*y**2 + 125/6 + 1/6*y**3 = 0. What is y?
-1, 5, 25
Let c be (-127)/(-6) - (29 + -34). Let d = -137/6 + c. Factor -2/3*a**5 + d*a**4 - 16/3*a**3 + 0 + 8/3*a**2 + 0*a.
-2*a**2*(a - 2)**2*(a - 1)/3
Let y be ((-12)/(-14))/((-57)/(7980/(-40))). Factor 9/4*z**y + 3/8*z**4 + 0 + 0*z - 21/8*z**2.
3*z**2*(z - 1)*(z + 7)/8
Suppose 2*j + 170 = -o + 194, 0 = j - 5*o - 12. Let q be j/594*-9 + 36/77. Factor 0 - q*w**2 + 1/7*w**3 + 1/7*w.
w*(w - 1)**2/7
Factor -1/5*j**2 + 16/5*j - 4 - 1/5*j**3.
-(j - 2)**2*(j + 5)/5
Let a be ((-12)/30)/((-2)/30). Let j be (40/(-15) - -2)/((-2)/a). Solve 44*c - 12*c + 106 + c**j + 3*c**2 - 42 = 0 for c.
-4
Let l = -3369 - -2284183/678. Let p = 5417/4746 + l. Let 4/7*g + 0 + p*g**5 - 2*g**2 + 2*g**4 - 12/7*g**3 = 0. Calculate g.
-2, -1, 0, 1/4, 1
Suppose -2*d + 0 = 6. Let c = d - -24. Factor 13*m**2 + m**3 + 5*m**2 + 2*m - c*m**2.
m*(m - 2)*(m - 1)
Suppose -3*n - 63 = 4*n. Let t be 6/(-33) + 18*n/(-594). Suppose -t*v - 2/11*v**2 - 1/11*v**3 + 0 = 0. Calculate v.
-1, 0
Factor -23*q**3 - 33*q**3 - 26*q**3 - 408*q + 108*q**2 + 107*q**3 - 27*q**3 + 400.
-2*(q - 50)*(q - 2)**2
Let c(g) = 2*g**4 + g**3 + 5*g + 1. Let v(x) = -11*x**4 + 178*x**3 - 748*x**2 + 722*x - 6. Let z(k) = 30*c(k) + 5*v(k). Factor z(d).
5*d*(d - 2)**2*(d + 188)
Let w be (-10 - (-16 + 0))*4/(-1134). Let u = w + 67/189. Solve -1/2 + 1/6*t**2 + u*t = 0 for t.
-3, 1
Let x(l) be the second derivative of l**7/42 - l**6/2 + 41*l**5/10 - 33*l**4/2 + 205*l**3/6 - 75*l**2/2 + 125*l - 3. Solve x(j) = 0 for j.
1, 3, 5
Let p(w) be the third derivative of w**7/2100 + 7*w**6/900 + w**5/50 - 2*w**3/3 - w**2 + 3*w. Let s(i) be the first derivative of p(i). Factor s(u).
2*u*(u + 1)*(u + 6)/5
Let f(q) be the third derivative of q**7/504 + 5*q**6/144 + q**5/4 + 15*q**4/4 - 8*q**2 - q. Let i(n) be the second derivative of f(n). Factor i(x).
5*(x + 2)*(x + 3)
Let c(a) = -9*a**3 - 5*a**2 + 4. Let d(m) be the second derivative of 3*m**5/20 - m**4/12 - m**2/2 + 3*m. Let y(z) = c(z) + 4*d(z). Suppose y(b) = 0. What is b?
0, 3
Let w be (32/(-24))/((-4)/6). Suppose -24 = -2*j - 5*f, -3*j + j = -w*f + 4. Factor 12*c**2 + 21*c**j - 5*c**2 + 75*c - 125 + 17*c**2 + 5*c**3.
5*(c - 1)*(c + 5)**2
Suppose -64*g = -69*g + 65. Find q, given that g*q**2 + 2*q - 3*q**2 + 754 - 7*q + 5*q**3 - 764 = 0.
-2, -1, 1
Let k be ((-42)/56)/((-27)/18). Solve 0*f + k*f**2 - 1/2*f**4 - 1/4*f**5 + 1/4*f**3 + 0 = 0.
-2, -1, 0, 1
Let j be (32/(-6))/(0 - (-8)/(-12)). Factor 336*c**4 - 12*c + 4*c**5 + 8*c**2 - 680*c**4 + j*c**3 + 332*c**4 + 4.
4*(c - 1)**4*(c + 1)
Let y(p) = 5*p**2 + p - 2. Let j(w) = 7*w**2 + 2966*w - 4. Let n(a) = j(a) - 2*y(a). Factor n(l).
-3*l*(l - 988)
Let c(h) be the third derivative of 1/80*h**5 - 1/120*h**6 - 6*h**2 + 1/24*h**4 - 1/6*h**3 + 1/840*h**7 + 0 + 0*h. Factor c(g).
(g - 2)**2*(g - 1)*(g + 1)/4
Suppose 3*b - 39 = 7*b - d, 4*d + 31 = -b. Let a(c) = -c**2 - 9*c + 24. Let i be a(b). Factor 1/7*r**5 - 2/7*r**3 + 0*r**i + 1/7*r + 0 + 0*r**4.
r*(r - 1)**2*(r + 1)**2/7
Let s(d) = d**3 - 30*d**2 - 2*d + 4. Let l(z) = -3*z**3 + 120*z**2 + 9*z - 18. Let h(m) = 2*l(m) + 9*s(m). Let h(o) = 0. What is o?
0, 10
Let u be (-5)/(-1) + (9435/(-68))/3*1/10. Find g, given that u - 5/8*g**2 - 1/4*g = 0.
-1, 3/5
Factor -48*i - 872*i**4 - 60*i**3 + 863*i**4 - 90*i**2 - 18*i**2.
-3*i*(i + 2)*(i + 4)*(3*i + 2)
Let r = 8779/3512 + 1/3512. Let h(y) be the first derivative of 1/40*y**5 - r*y**2 + 11/8*y**3 + 10 + 2*y - 5/16*y**4. Let h(z) = 0. What is z?
1, 4
Let x(m) be the second derivative of -m**6/90 + m**4/36 + m + 1. Factor x(w).
-w**2*(w - 1)*(w + 1)/3
Let g(d) be the first derivative of 5*d**6/6 - 3*d**5 - 265*d**4/4 + 185*d**3 - 140*d**2 + 1061. Factor g(q).
5*q*(q - 8)*(q - 1)**2*(q + 7)
Let i(h) be the third derivative of h**7/1260 - h**6/180 + h**5/180 + h**4/36 - h**3/12 + 9*h**2 - 207. Factor i(d).
(d - 3)*(d - 1)**2*(d + 1)/6
Let l(z) = -z**2 + 2*z - 2. Let m be l(0). Let g(t) = -11*t**2 + 33*t - 50. Let d(q) = 3*q**2 + q. Let p(s) = m*d(s) - g(s). Factor p(o).
5*(o - 5)*(o - 2)
Let r = 160 - 158. Determine d so that 8 - 17 - 365*d**r + 363*d**2 + 41 + 12*d = 0.
-2, 8
Let i(z) be the third derivative of z**4/12 - 2*z**3/3 - 21*z**2. Let k be i(17). Factor 0*y**2 + 40*y + 5*y**4 - 22*y**2 - k*y**3 + 2*y**2 + 5*y**5.
5*y*(y - 2)*(y - 1)*(y + 2)**2
Let i(t) be the third derivative of -t**5/20 + 63*t**4/8 + 32*t**3 - 229*t**2 - 2*t. Factor i(o).
-3*(o - 64)*(o + 1)
Let t(i) be the second derivative of 3*i**5/40 + 85*i**4/24 + 223*i**3/6 - 84*i**2 + 3905*i. Factor t(f).
(f + 8)*(f + 21)*(3*f - 2)/2
Let l be (-235)/(-35) + -7 - (-36474)/112. Let p = l - 325. Let -3/8*w + 0 - p*w**2 = 0. Calculate w.
-1, 0
Let d be 3 + (-14 - -13)*0. Let u(f) be the third derivative of 0*f**d - 18*f**2 + 0*f + 0 + 1/51*f**4 - 1/510*f**5. Find c such that u(c) = 0.
0, 4
Suppose -17*f + 80 = -7*f. Let k(l) = -4*l**2 + 4. Let d(b) be the first derivative of 2*b**3 - 6*b + 7. Let o(s) = f*k(s) + 5*d(s). Factor o(g).
-2*(g - 1)*(g + 1)
Let y be (-8)/(-6)*6540/2725. Find l such that 16/5*l**2 - 2/5*l**3 - y + 2/5*l = 0.
-1, 1, 8
Let l be (288/5)/((-3432)/416). Let b = -68/11 - l. Suppose 18/5*i**3 + 14/5*i**4 - 2*i**2 - 18/5*i - b = 0. What is i?
-1, -2/7, 1
Let d(k) = -7*k**3 + 132*k**2 - 316*k - 62. Let h be d(16). Determine w so that -21/5 + 24/5*w - 3/5*w**h = 0.
1, 7
Let f(k) be the third derivative of -k**7/10 - 53*k**6/4 - 9403*k**5/20 + 3003*k**4 - 3042*k**3 + k**2 + 284. Suppose f(v) = 0. Calculate v.
-39, 2/7, 2
Factor 0 - 198/5*p**2 + 2/5*p**3 + 196/5*p.
2*p*(p - 98)*(p - 1)/5
Let h(c) = 7*c**2 + 9*c + 8. Let k(a) = -21*a**2 + 8*a**2 + 9*a - 21*a - 7*a - 17. Let s(b) = 11*h(b) + 6*k(b). Determine v, given that s(v) = 0.
-14, -1
Let u(y) be the third derivative of y**5/330 + 7*y**4/132 - 98*y**3/11 - y**2 + 4415*y. Find q, given that u(q) = 0.
-21, 14
Let n(g) be the second derivative of -1/60*g**6 + 0*g**3 + 1/16*g**4 + 1/16*g**5 + 0*g**2 + 7 + 2*g. Find o such that n(o) = 0.
-1/2, 0, 3
Let c(q) = q + 1. Let r(f) = 10*f + f**2 + 6*f + 21 + 19. Suppose -4*z = 6 + 10. Let h(u) = z*c(u) + r(u). Find t, given that h(t) = 0.
-6
Let l(u) be the first derivative of 5*u**7/42 + u**6/6 - u**5 - 5*u**4/3 - 115*u - 68. Let p(m) be the first derivative of l(m). Factor p(k).
5*k**2*(k - 2)*(k + 1)*(k + 2)
Let b(r) be the first derivative of 50/3*r + 25 + 9/2*r**3 - 15*r**2. Find k, given that b(k) = 0.
10/9
Let q(u) be the first derivative of -u**4/36 - u**3/18 - 256*u - 101. Let x(r) be the first derivative of q(r). Factor x(d).
-d*(d + 1)/3
Suppose -2*l + 4*j = -18, 3*l - 22 = -5*j - 6. Suppose -l = -6*o + 23. Factor -3*i**3 + 2*i**4 - 14*i**4 - 3*i**2 - 7*i**o + 5*i**2.
-i**2*(i + 1)**2*(7*i - 2)
Let j = 88172/15 - 29384/5. Let 0 - j*f**4 + 2/3*f**5 + 0*f - 10/3*f**3 + 4*f**2 = 0. What is f?
-2, 0, 1, 3
Let u(g) = 16*g**2 - 742*g + 7. Let x(m) = 5*m**2 - 248*m + 2. Let a(k) = 2*u(k) - 7*x(k). What is o in a(o) = 0?
0, 84
Suppose 1/5*t**2 + 4/5*t - 9 = 0. Calculate t.
-9, 5
Suppose -104 = 5*j + 8*j. Let m be (90/(-210))/(j/98). Factor m*c**2 + 2*c**3 + 9/2*c + 0 + 1/4*c**4.
c*(c + 2)*(c + 3)**2/4
Le