d**2 - 25*d - 21. Let m be i(5). Factor 0*p**k - 2/9*p**5 + 0 + 0*p**m + 2/9*p**3 + 0*p.
-2*p**3*(p - 1)*(p + 1)/9
Let n(d) be the second derivative of d**7/168 - d**6/40 + d**5/40 - d + 12. Factor n(k).
k**3*(k - 2)*(k - 1)/4
Let x(w) be the first derivative of 5*w**6/2 + 51*w**5/5 + 33*w**4/4 - 13*w**3 - 24*w**2 - 12*w - 104. Find q, given that x(q) = 0.
-2, -1, -2/5, 1
Let p(i) = i**3 + 38*i**2 + 38*i + 39. Let o be p(-37). Suppose -1/2*v**o - 1/4*v + 0 - 1/4*v**3 = 0. What is v?
-1, 0
Let c(f) = 2*f + 21. Let b be c(-10). Suppose -2 = -3*w + b. Let 73*l**3 + 17 + 56*l + 76*l**2 - 23*l**3 + 2*l**5 - w + 16*l**4 = 0. What is l?
-2, -1
Let t be 14/(-12) + (-3200)/(-2304). Factor -t*q + 0*q**2 + 0 + 2/9*q**3.
2*q*(q - 1)*(q + 1)/9
Factor -16/5 + 108/5*a - 26/5*a**2.
-2*(a - 4)*(13*a - 2)/5
Factor p**2 + 4*p**3 - 3 - 240*p**4 + 2*p**5 - 2 + 5 + 245*p**4.
p**2*(p + 1)**2*(2*p + 1)
Factor 3/2*p**2 + 15 + 21/2*p.
3*(p + 2)*(p + 5)/2
Let z(x) be the first derivative of -3*x**7/1540 - x**6/660 - x**3 + 22. Let l(r) be the third derivative of z(r). Find q, given that l(q) = 0.
-1/3, 0
Let w be (5/(-10))/(6/(-104)*2). Let g(p) be the first derivative of 3/2*p**4 - 4 + 1/5*p**5 + 6*p**2 + 4*p + w*p**3. Let g(t) = 0. What is t?
-2, -1
Let l(s) = s**2 - 37*s - 33. Let x(u) = u**2 - 67*u - 65. Let f(w) = -10*l(w) + 6*x(w). Let f(i) = 0. Calculate i.
-5, -3
Let u = 12 - 8. Determine a so that 0*a**2 + u*a + 6*a**2 - 3*a**3 + 11*a**3 - 6*a**3 = 0.
-2, -1, 0
Let c(u) be the third derivative of 0 + 0*u + 7/6*u**3 - 1/120*u**5 - 5*u**2 - 1/36*u**4 - 1/1080*u**6. Let n(r) be the first derivative of c(r). Factor n(o).
-(o + 1)*(o + 2)/3
Let x(n) = 43*n**3 + 53*n**2 - 14*n. Let c(g) = 21*g**3 + 26*g**2 - 8*g. Let m(w) = 13*c(w) - 6*x(w). Factor m(d).
5*d*(d + 2)*(3*d - 2)
Solve 18/5*l - 2/5*l**3 - 18/5 + 2/5*l**2 = 0 for l.
-3, 1, 3
Let 1/11 - 20/11*r**2 + 8/11*r = 0. What is r?
-1/10, 1/2
Let s = 67 - 64. Suppose 0 = -2072*d + 2074*d - 10. Factor -1/6*p**d + 0*p + 1/6*p**s + 0*p**2 + 0*p**4 + 0.
-p**3*(p - 1)*(p + 1)/6
Let v(y) be the second derivative of -y**4/48 + 2*y**3 - 72*y**2 + y + 15. Factor v(l).
-(l - 24)**2/4
Let r(z) = z**3 - z**2. Let g(t) = -9*t**3 - 12*t**2 - 3*t + 6. Suppose 2*v - 2*w - 12 = 0, 0*v - 2*w - 5 = 5*v. Let i(p) = v*g(p) + 3*r(p). Factor i(m).
-3*(m + 1)*(m + 2)*(2*m - 1)
Solve 0*b**3 + 0 + 12/5*b + 6/5*b**4 - 18/5*b**2 = 0 for b.
-2, 0, 1
Let p = 4079/19056 + 6/397. Let a = 7/16 + p. What is l in -2*l**3 - a*l + 0 - 2*l**2 - 2/3*l**4 = 0?
-1, 0
Suppose 2*k + 10 = 0, -69*k - 27 = -4*m - 66*k. Factor -4/3*j**5 - 4*j**m + 0*j - 4*j**4 - 4/3*j**2 + 0.
-4*j**2*(j + 1)**3/3
Let b(t) be the second derivative of -1/119*t**7 + 0*t**3 + 0 + 0*t**2 + 1/255*t**6 + 3/170*t**5 - 14*t - 1/102*t**4. Solve b(q) = 0.
-1, 0, 1/3, 1
Let v = -368 + 371. Let g(w) be the first derivative of 1/12*w**2 + 4 + 0*w - 1/24*w**4 + 0*w**v. Factor g(s).
-s*(s - 1)*(s + 1)/6
Let f(q) be the third derivative of -1/8*q**4 + 0 + 4*q**2 + 0*q**3 + 0*q + 0*q**6 + 1/35*q**7 + 1/112*q**8 - 1/10*q**5. What is x in f(x) = 0?
-1, 0, 1
Let b(h) = h**2 - 18*h - 401. Let u be b(31). Factor -2/5*v**3 + 4/5 - 4/5*v**u + 2/5*v.
-2*(v - 1)*(v + 1)*(v + 2)/5
Let y(w) be the first derivative of -w**3/3 - 49*w**2/3 - 64*w/3 - 120. Determine d so that y(d) = 0.
-32, -2/3
Let h(l) = -7*l**2 - 31*l + 12. Let k be h(-9). Let q = 278 + k. Factor 0*w**3 + 0*w + 0 - 2/11*w**q + 2/11*w**4.
2*w**2*(w - 1)*(w + 1)/11
Factor -352/7*c + 242/7*c**2 + 128/7.
2*(11*c - 8)**2/7
Let m(v) = v + 1. Let q be m(1). Let r be q/(-4)*-2 - -2. Suppose i**4 + 5*i**2 - 8*i**4 + 2 + 7*i - 2*i**5 + i**3 + 0*i**r - 6*i**3 = 0. Calculate i.
-2, -1, -1/2, 1
Let b be ((-54)/(-126))/((-9)/(-4)). Let p(t) be the first derivative of 5 - 1/21*t**6 + 3/7*t**2 - b*t**3 + 6/35*t**5 - 1/7*t**4 - 2/7*t. Factor p(s).
-2*(s - 1)**4*(s + 1)/7
Suppose 11*d - 8*d = 5*a + 5, 0 = -3*d + 15. Solve 10/17*x**a + 2/17*x - 10/17 - 2/17*x**3 = 0.
-1, 1, 5
Suppose 9*n - 5 = 31. Let f(d) = 3*d**5 - 7*d**4 + 4*d**2 - 4. Let v(p) = -p**5 + p**4 + 1. Let t(w) = n*v(w) + f(w). Solve t(b) = 0 for b.
-2, 0, 1
Let b(f) be the first derivative of -22 - 1/15*f**3 - 2/5*f + 3/10*f**2. What is q in b(q) = 0?
1, 2
Let j(b) be the third derivative of b**8/6 + 83*b**7/105 - 929*b**6/60 - 953*b**5/30 + 101*b**4/12 + 70*b**3/3 - 19*b**2 + 17. Solve j(f) = 0 for f.
-7, -1, -1/4, 2/7, 5
Suppose 40*u + 53*u**2 + 0*u**5 - 5*u**5 + 22*u**2 - 15*u**4 + 10*u**3 - 15*u**2 = 0. Calculate u.
-2, -1, 0, 2
Let f(q) be the second derivative of q**4/12 + 11*q**3/2 + 16*q**2 + 163*q + 2. Factor f(j).
(j + 1)*(j + 32)
Determine d, given that -8*d**4 + 0 + 15/2*d - 1/2*d**5 + 8*d**2 - 7*d**3 = 0.
-15, -1, 0, 1
Let p = -81 + 84. Let z(n) be the first derivative of 0*n - 2/13*n**2 + 11 + 6/13*n**p. Suppose z(f) = 0. What is f?
0, 2/9
Factor -16 + 2*k**4 + 27*k**2 - 12 + 22*k**2 - 30*k - 23*k**2 + 30*k**3.
2*(k - 1)*(k + 1)**2*(k + 14)
Let n(f) = -1 - 3*f**3 + 338*f - f**2 - 325*f + 2*f**3. Let p be n(3). Solve -3/4*o - 3/4*o**5 + 0*o**p + 0*o**4 + 0 + 3/2*o**3 = 0 for o.
-1, 0, 1
Let m(t) = -t**3 + 8*t**2 - 16*t + 2. Let p be m(4). Factor 0 - 2/11*b - 2/11*b**p.
-2*b*(b + 1)/11
Factor -7/3*i - 2 - 2/3*i**3 + 3*i**2.
-(i - 3)*(i - 2)*(2*i + 1)/3
Determine u, given that 2/9*u**2 + 2/9*u - 8/3 = 0.
-4, 3
Let l(r) be the first derivative of 0*r - 5/4*r**4 + 1/3*r**3 + 3/5*r**5 + 8 + 1/2*r**2. Determine o, given that l(o) = 0.
-1/3, 0, 1
Let n(a) be the third derivative of -3*a**7/175 + 151*a**6/300 - 49*a**5/30 + 73*a**4/60 + 2*a**3 - 2*a**2 + 18. Let n(f) = 0. What is f?
-2/9, 1, 15
Let o = -583 - -590. Let y(v) be the third derivative of 1/15*v**5 - 1/30*v**6 + 0 + 0*v**3 + v**2 - 2/105*v**o + 0*v + 1/6*v**4. Suppose y(c) = 0. Calculate c.
-1, 0, 1
Let m be 115*(-25)/250 + 19. Factor -3/4*i**2 - 27/4 + m*i.
-3*(i - 9)*(i - 1)/4
Let v(a) be the second derivative of 0 + 8*a - 1/50*a**5 + 0*a**2 - 1/5*a**3 + 2/15*a**4. Determine f, given that v(f) = 0.
0, 1, 3
Let c = -751 + 751. Let y(n) be the first derivative of -3 - 7/18*n**6 + 0*n**2 + c*n + 2/9*n**3 - 11/12*n**4 + 16/15*n**5. Factor y(s).
-s**2*(s - 1)**2*(7*s - 2)/3
Let s = -69 + 71. Let -6 + 129*i**3 - 3*i + 9*i**2 + s*i**4 - 126*i**3 - 5*i**4 = 0. What is i?
-1, 1, 2
Let n(f) = 4*f**3 - 6*f**2 + 2*f - 8. Let u(b) = -b**3 + b. Let d(c) = -n(c) - 10*u(c). Let o(p) = p**3 - p + 1. Let z(q) = d(q) - 8*o(q). Factor z(r).
-2*r*(r - 2)*(r - 1)
Let q be (12/270)/((-13)/(390/(-6))). Factor -242/9*z + 0 + 44/9*z**2 - q*z**3.
-2*z*(z - 11)**2/9
Let k(s) = -s - 4. Let b be k(6). Let g = b + 13. Factor -2*w**5 + w**4 - 2*w**3 - w**2 + 5*w**3 - 2*w**g + w**5.
-w**2*(w - 1)**2*(w + 1)
Let m be 1/(-4 + 3 + 0). Let y be (2 - m) + 8/(-8). Factor 144*i - 30*i**2 - 32 - y*i**2 - 34*i**2 + 8*i**3.
2*(i - 4)**2*(4*i - 1)
Let o(z) be the first derivative of -z**6/540 + z**5/135 + z**4/108 - 2*z**3/27 + 4*z**2 - 1. Let f(n) be the second derivative of o(n). Factor f(q).
-2*(q - 2)*(q - 1)*(q + 1)/9
Let a = -138 + 140. Let m(b) be the first derivative of -1 - 3/4*b**4 + 0*b + 0*b**a + 0*b**3. Factor m(x).
-3*x**3
Let p(u) be the second derivative of -u**5/5 + 359*u**4/21 - 904*u**3/21 + 200*u**2/7 + 12*u + 40. What is l in p(l) = 0?
2/7, 1, 50
Suppose 40 = 2*r - 3*o, -30 = -r - 2*r - 3*o. Solve -66*x**3 + 71*x**3 + 9 - 25*x - r*x**2 + 4*x**2 + 21 = 0.
-2, 1, 3
Let c(n) be the second derivative of n**6/480 + n**5/60 - n**4/32 - 3*n**3/4 - 8*n**2 + 3*n. Let j(q) be the first derivative of c(q). Factor j(h).
(h - 2)*(h + 3)**2/4
Let m(x) be the second derivative of x**4/6 + 10*x**3/3 + 25*x**2 + 4*x + 2. Factor m(l).
2*(l + 5)**2
Let w(l) be the second derivative of -l**4/6 - 106*l**3 - 25281*l**2 + 17*l + 14. Let w(c) = 0. Calculate c.
-159
Suppose 0 = 5*n - 6 + 1. Let z be (-11)/(110/12)*n/(-3). Factor 3/5*f**2 + 0 - 1/5*f**3 - z*f.
-f*(f - 2)*(f - 1)/5
Suppose -43 = -4*k + 5*n - 0, -k - 5*n - 8 = 0. Let w be 9 + 1 + (4 - k). Factor w*d + d - 5 + 25*d**4 + 70*d**3 + 5 + 44*d**2.
d*(d + 2)*(5*d + 2)**2
Let o(y) = y**3 - 17*y**2 - 37*y + 4. Let i be o(-2). What is l in 2/3*l**i + 1/3*l**3 - 1/3*l - 2/3 = 0?
-2, -1, 1
Let t(g) be the third derivative of g**5/80 + 7*g**4/4 + 98*g**3 + 100*g**2. Factor t(w).
3*(w + 28)**2/4
Suppose -802*y + 797*y 