1
Let q = 7 - 19. Let p be (-6)/q*(-6)/(-5). Find s, given that 0 + 3/5*s**5 - p*s**3 + 0*s + 0*s**4 + 0*s**2 = 0.
-1, 0, 1
Let c(o) be the second derivative of -2*o**7/21 - 14*o**6/15 - 2*o**5 + 89*o. Factor c(t).
-4*t**3*(t + 2)*(t + 5)
Let h(m) be the third derivative of 7*m**2 - 18*m**3 + m**4 + 0 + 0*m - 1/45*m**5. Factor h(b).
-4*(b - 9)**2/3
Let h(q) = 8*q**2 + 52*q - 26. Let b be h(-7). Suppose 0 = 3*r - r. Solve 6/7*u**b - 2/7*u**4 + r + 4/7*u + 0*u**3 = 0.
-1, 0, 2
Let t be 3 + (-194)/80 + -6 + (-435)/(-75). Factor -t*m**5 + 3/2*m**4 + 0 - 9/2*m**2 + 3/4*m**3 - 27/8*m.
-3*m*(m - 3)**2*(m + 1)**2/8
Let x(l) be the third derivative of l**5/600 + 37*l**4/240 - 863*l**2. What is k in x(k) = 0?
-37, 0
Let r(c) = 14*c + 11. Let o be r(7). Suppose 3*b + 2*b - o = 4*y, -3*y = b - 18. Solve 3*l**2 + b*l - l**2 + 0*l**2 - 20*l = 0 for l.
-1/2, 0
Let b(a) = 3*a**2 + 28*a - 20. Let v be b(-10). Let g(d) be the second derivative of -1/36*d**4 - 1/18*d**3 + 0 + 2*d + v*d**2. Find i such that g(i) = 0.
-1, 0
Let o(t) = -2*t**2 + 11*t + 45. Let d be o(8). Let c(b) be the first derivative of b + 1/5*b**d - 2*b**2 - b**4 - 4 + 2*b**3. Factor c(m).
(m - 1)**4
Suppose -25 = -4*z - 37. Let b be ((-1)/(-2))/(z/(-4)). Find k such that 2/3*k**4 + 1/3*k**5 - b*k**2 + 0*k + 0 - 1/3*k**3 = 0.
-2, -1, 0, 1
Let z(c) = -2*c**2 + 2*c + 6. Let n(f) = -2*f + 0*f - 14*f**2 + f + 1 + 13*f**2. Let b(w) = -6*n(w) + z(w). Solve b(y) = 0.
-2, 0
Let b(m) = 12*m**4 + 6*m**3 - 2*m**2 + 4*m + 30. Let l(i) = -i**4 - i**3 - 3*i**2. Let v(u) = -b(u) - 10*l(u). Find j, given that v(j) = 0.
-3, -1, 1, 5
Let g(z) = 3*z**2 - 6*z + 2. Let a be g(4). Suppose -4*m = -4*c + 8, -3*c + a - 5 = 2*m. Factor -4*l**3 + 7*l**3 + 0*l**m + 4*l + 10*l**2 + 3*l**3.
2*l*(l + 1)*(3*l + 2)
Let v = 5 - 1. Factor -12*h**3 + h**2 + 20*h**v - 18*h**4 + 17*h**2.
2*h**2*(h - 3)**2
Suppose 152*d - 163*d = -33. Let y(q) be the first derivative of 2*q + 10/9*q**d + 4 - 1/6*q**4 - 7/3*q**2. Solve y(m) = 0 for m.
1, 3
Let v(n) be the third derivative of -n**7/1050 + 3*n**6/100 - 97*n**5/300 + 6*n**4/5 - 32*n**3/15 + 12*n**2. Determine l so that v(l) = 0.
1, 8
Suppose -r = -4*i - 18, 6*r - 3*i - 14 = 5*r. Suppose -s + 15 = -r*f - f, -f + 55 = 3*s. Solve -26*c**3 - 12*c**2 + s*c**3 + 12*c**3 + 16 = 0.
-1, 2
Let -16 - 169/2*v**3 - 4*v**5 + 27*v**2 + 209/6*v**4 + 128/3*v = 0. What is v?
-2/3, 3/8, 1, 4
Factor 21*l**2 - 7*l**2 + 20 - 5*l**2 - 2*l**2 - l**3 - 15*l**2 - 11*l.
-(l - 1)*(l + 4)*(l + 5)
Let k(o) be the first derivative of 8 + 0*o + 0*o**2 + 4/15*o**3 + 1/5*o**4. Factor k(j).
4*j**2*(j + 1)/5
Factor 2/7*a**3 - 12/7*a**2 + 0*a + 0 + 2/7*a**4.
2*a**2*(a - 2)*(a + 3)/7
Let x(y) be the third derivative of y**6/210 - y**5/21 - y**4/42 + 10*y**3/21 - 67*y**2. Factor x(o).
4*(o - 5)*(o - 1)*(o + 1)/7
Let w(j) be the first derivative of -5*j**4/12 - 5*j**3/2 + 24*j - 20. Let g(z) be the first derivative of w(z). Let g(t) = 0. What is t?
-3, 0
Let g(n) be the first derivative of n**4/2 - 28*n**3/3 + 25*n**2 - 24*n + 41. Let g(o) = 0. What is o?
1, 12
Let h(m) be the second derivative of 1/180*m**5 + 0 - 11*m - 1/18*m**2 + 1/18*m**3 - 1/36*m**4. Factor h(i).
(i - 1)**3/9
Let q(c) = -c**2 + 22*c - 38. Let z be q(20). What is y in -6*y**3 - 8*y**z + 5*y - 30*y + 13*y - 13*y**2 + 3*y**4 = 0?
-1, 0, 4
Factor 151 + 19*k - 4*k + 2*k**2 - 145 + 7*k**2.
3*(k + 1)*(3*k + 2)
Let z(y) be the first derivative of y**2 - 5/2*y + 1/6*y**3 + 23. Factor z(i).
(i - 1)*(i + 5)/2
Let b(n) be the first derivative of 5*n**6/2 + 8*n**5 - 145*n**4/4 - 290*n**3/3 + 210*n**2 + 360*n - 80. Suppose b(d) = 0. Calculate d.
-3, -2/3, 2
Let y(j) be the second derivative of j**5/70 - 5*j**4/7 + 51*j**3/7 + 1156*j**2/7 - 184*j. Factor y(m).
2*(m - 17)**2*(m + 4)/7
Let d(v) be the first derivative of 5*v**4/12 + 5*v**3/2 - 28*v - 2. Let k(q) be the first derivative of d(q). Factor k(x).
5*x*(x + 3)
Let k be (-16)/(-480)*-2*-48. Factor 1/5*j**2 + k*j + 64/5.
(j + 8)**2/5
Let i = -14 + 24. Factor -2*u + 20*u**2 - 8 - i*u + 0*u.
4*(u - 1)*(5*u + 2)
Determine u so that 348*u + 20184 + 3/2*u**2 = 0.
-116
Let b(q) be the third derivative of 0*q**3 + 2/65*q**5 - 21*q**2 + 0*q - 4/1365*q**7 + 0 + 1/390*q**6 - 1/2184*q**8 - 3/52*q**4. Find k, given that b(k) = 0.
-3, 0, 1
Let s(y) be the third derivative of y**7/120 - 19*y**6/240 - 3*y**5/20 - y**4/2 - 20*y**2. Let i(x) be the second derivative of s(x). Factor i(l).
3*(l - 3)*(7*l + 2)
Let s(o) be the second derivative of 8*o**6/15 - 7*o**5/5 - 7*o**4/3 + 20*o**3/3 + 159*o. Factor s(n).
4*n*(n - 2)*(n - 1)*(4*n + 5)
Let o(m) be the first derivative of -1/5*m**5 + 7*m**4 - 90*m**3 - 729*m + 486*m**2 - 11. Factor o(w).
-(w - 9)**3*(w - 1)
Factor -26*g - 4*g**3 + 3 - 2*g**4 + 6*g**3 + 14*g**2 - 1 + 10.
-2*(g - 2)*(g - 1)**2*(g + 3)
Let a(n) be the first derivative of 25*n**4/4 - 110*n**3/3 + 115*n**2/2 - 30*n + 486. What is u in a(u) = 0?
2/5, 1, 3
Let z(t) be the third derivative of -t**8/70560 - t**7/1960 + t**6/252 + t**5/30 + 31*t**2. Let r(v) be the third derivative of z(v). Factor r(q).
-2*(q - 1)*(q + 10)/7
Let o(b) be the third derivative of 5*b**4/24 - 7*b**3/2 + b**2. Let l be o(5). Factor 0*i + 0 + 1/2*i**5 + 0*i**l - 1/2*i**3 + 0*i**2.
i**3*(i - 1)*(i + 1)/2
Let w(b) be the second derivative of -1/4*b**5 - 14*b + 5/2*b**3 + 5*b**2 + 0*b**4 + 0. Factor w(h).
-5*(h - 2)*(h + 1)**2
Let s be ((-4 - -3)/10)/(((-4)/30)/1). Find h, given that 6*h**2 - 12*h + 0 - s*h**3 = 0.
0, 4
Let q(a) be the first derivative of 11*a**6/540 + a**5/135 - a**2 - 5*a - 32. Let y(v) be the second derivative of q(v). Let y(j) = 0. Calculate j.
-2/11, 0
Let h(q) be the third derivative of q**8/5040 + 13*q**4/24 + 20*q**2. Let l(f) be the second derivative of h(f). What is d in l(d) = 0?
0
Let f be (-1569)/(-55) - (-10)/50. Let x = f + -1228/55. Factor 4/5 - x*r**2 + 2*r + 18/5*r**3.
2*(r - 1)**2*(9*r + 2)/5
Let d(s) = -s**3 + s**2 - 1. Let o(c) be the first derivative of -c**2 + 3. Let i(z) = -2*d(z) + o(z). Let i(v) = 0. Calculate v.
-1, 1
Determine v, given that -101*v - 220 + 2*v**2 + 207*v + 112*v = 0.
-110, 1
Let j(s) = -s**3 - s**2 + 2*s + 1. Let g(y) = -y**4 - 9*y**3 + 16*y**2 + 6*y - 23. Let k(a) = g(a) - 5*j(a). Factor k(f).
-(f - 2)**2*(f + 1)*(f + 7)
Let d(l) = -42*l**3 + 94*l**2 - 294*l + 194. Let k(j) = 8*j**3 - 19*j**2 + 59*j - 39. Let v(f) = -3*d(f) - 16*k(f). Factor v(w).
-2*(w - 7)*(w - 3)*(w - 1)
Let q = -15 + 19. Let m = q + -2. Factor m*b**2 - 14/9*b + 4/9 - 10/9*b**3 + 2/9*b**4.
2*(b - 2)*(b - 1)**3/9
Let x be (3/(-8))/(-1) - (-52)/32. Let z(s) be the second derivative of -3/20*s**5 + 0*s**x - 2*s + 0 - 7/20*s**4 - 1/5*s**3. Let z(m) = 0. What is m?
-1, -2/5, 0
Let f be -2*6/(-3) - 8/8. Let 64*v**4 + 68*v**4 - 2*v**2 + f*v**5 + 9*v**3 - 142*v**4 = 0. What is v?
0, 1/3, 1, 2
Let f = -8/81 - -704/567. Let 32/7*l**2 - f*l + 0 - 2*l**3 = 0. Calculate l.
0, 2/7, 2
Suppose 2*t - 80 = -5*l, 0 = l - 3*t - 2 - 14. Determine f, given that 2 + 20*f - 16*f**3 + 12*f**2 - l*f**4 + 2 - 4*f**2 - 4*f**5 + 4 = 0.
-2, -1, 1
Suppose -3*n + 2*s = s - 14, s = -2*n + 6. Factor 0*j + 0 + 0*j**2 + 4/7*j**3 - 2/7*j**5 - 2/7*j**n.
-2*j**3*(j - 1)*(j + 2)/7
Let l be ((-6)/(-9))/((-2)/(-24)). Factor -b - 2*b - l + 6*b**2 - 2*b**4 - 2*b - 3*b + 4*b**3.
-2*(b - 2)**2*(b + 1)**2
Let c(y) be the second derivative of -3*y**6/2 + 35*y**5/2 - 160*y**4/3 - 80*y**3/3 - 2*y + 762. Factor c(a).
-5*a*(a - 4)**2*(9*a + 2)
Solve -3*p**2 + 15*p**3 - 60 + 25*p**3 + 48*p - 43*p**3 = 0 for p.
-5, 2
Let m be (-1476)/1230 - 12/(-5). Let 0*u**2 - m + 3/5*u**3 - 9/5*u = 0. Calculate u.
-1, 2
Let g = 11074/45 + -2186/9. Factor 4/5*s**4 + 4/5 + 16/5*s + g*s**3 + 24/5*s**2.
4*(s + 1)**4/5
Let u(q) be the second derivative of q**7/1260 + q**6/720 - q**5/360 - q**4/144 + 11*q**2 + q. Let z(y) be the first derivative of u(y). Solve z(a) = 0 for a.
-1, 0, 1
Let w(j) = -129*j**3 - 348*j**2 - 201*j - 18. Let p(h) = -51*h**3 - 139*h**2 - 80*h - 7. Let z(u) = -12*p(u) + 5*w(u). Determine c so that z(c) = 0.
-1, -2/11
Let z(y) = -y**2 + y + 3. Let a(l) = l**2 - l - 4. Let d(r) = 4*a(r) + 5*z(r). Let f(q) = q**2 + 2*q - 2. Let w(v) = 2*d(v) - f(v). Factor w(m).
-3*m**2
Factor -50*r**2 + 40*r**2 + 1 - 24 + 3 + 45*r.
-5*(r - 4)*(2*r - 1)
Let r(k) be the first deriv