23 = -5*h - 2*w, 4*h + 4*w = k*w + 20. Factor 3*x**4 + 3*x**4 - x**3 + h*x**3 - 6*x**2 - 4*x + 2*x**5.
2*x*(x - 1)*(x + 1)**2*(x + 2)
Let y(c) be the third derivative of 0*c**3 + 0*c - 1/720*c**6 + 1/1260*c**7 + 0 - 1/360*c**5 + 1/144*c**4 + 45*c**2. Factor y(u).
u*(u - 1)**2*(u + 1)/6
Suppose o - 3*o + 3*f + 179 = 0, f - 3 = 0. Determine t, given that -o*t + 1452 - 38*t + 5*t**2 - 2*t**2 = 0.
22
Determine f so that 38 - 84*f + 90*f**2 - 26*f**3 + f**4 + 14*f**3 - 11*f**3 - 13*f - 9*f**2 = 0.
1, 2, 19
Let z be ((-15)/((-1050)/(-20)))/((-15)/105). Solve -16/5 + 4/5*a + 2/5*a**z = 0.
-4, 2
Let a(l) = -5*l**2 + 11*l - 6. Let j(n) be the first derivative of 16*n**3/3 - 17*n**2 + 18*n - 68. Let o = -1 + -9. Let s(g) = o*a(g) - 3*j(g). Factor s(h).
2*(h - 3)*(h - 1)
Let x be 10/8*112*(-15)/(-1050) - 15/8. Factor -57/8*l**2 + 105*l + x*l**3 - 98.
(l - 28)**2*(l - 1)/8
Let x(u) = -2*u**3 + 21*u**2 + 12*u - 9. Let b be x(11). Let 2*l**3 + 524*l - 136*l**2 - 89*l**2 - 260 - 29*l**b + 2*l**3 - 14*l**2 = 0. Calculate l.
1, 65
Let h = 2 - -2. Suppose -l - 3*l + 6 = -5*d, 4*d = 2*l. Let -4*w**5 - 15*w**3 + 2*w**2 - 33*w**3 - 34*w**d - 24*w**h = 0. What is w?
-2, 0
Suppose -5 = 3*n - 14. Suppose -51 = n*v - 20*v. Factor 6*r**2 - 627*r + v*r**2 - 3*r**4 + 3*r**3 - 6 + 624*r.
-3*(r - 2)*(r - 1)*(r + 1)**2
Let x be 20/(6*9/(-1647)). Let a = x - -612. Factor -22/9*j - 4/9 - a*j**2.
-2*(j + 1)*(9*j + 2)/9
Suppose 3848*z - 925444 + 70*z**2 - 39*z**2 - 35*z**2 = 0. What is z?
481
Let v(f) = 4*f**4 - 8*f**2 - 4. Let j be (13/(-3) + 3)/(4/12). Let s(y) = -4*y**4 + 9*y**2 + 5. Let n(a) = j*s(a) - 5*v(a). Factor n(h).
-4*h**2*(h - 1)*(h + 1)
Suppose 4*a = 5*v + 8, -a = 2*a - 4*v - 6. Determine r, given that -7*r**a + 11*r**2 - 3*r**2 - 3*r + 2 = 0.
1, 2
Let j(g) be the first derivative of g**4/42 - 86*g**3/63 - 142*g**2/21 + 368*g/21 + 3230. Find k such that j(k) = 0.
-4, 1, 46
Let u(i) be the second derivative of -i**4/90 - 29*i**3/15 - 84*i**2/5 + 3639*i. Solve u(o) = 0 for o.
-84, -3
Let v(k) be the second derivative of k**5/210 - k**4/6 + 8*k**3/7 + 167*k**2/2 - 11*k. Let t(i) be the first derivative of v(i). Suppose t(a) = 0. Calculate a.
2, 12
Let g(i) be the third derivative of -1/112*i**8 + 17/280*i**7 + 0 - 64*i**2 + 11/40*i**5 - 1/4*i**4 + 0*i + 1/8*i**3 - 7/40*i**6. Solve g(y) = 0 for y.
1/4, 1
Let f(a) be the third derivative of -11/120*a**5 + 1/1344*a**8 + 7/160*a**6 + 40*a**2 + 1/12*a**4 + 0*a + 0*a**3 + 0 - 1/105*a**7. Let f(m) = 0. What is m?
0, 1, 2, 4
Suppose 38 = -87*s + 91*s - 3*n, -3*s - 4*n = 9. Factor -3*d**4 - 1/3*d**s + 2/3*d**2 - 14/3*d**3 + 5*d + 7/3.
-(d - 1)*(d + 1)**3*(d + 7)/3
Let k(n) be the third derivative of -1/24*n**4 + 69 + 1/60*n**6 - 1/2*n**3 - 1/70*n**7 - 1/336*n**8 + 0*n - n**2 + 1/10*n**5. Factor k(v).
-(v - 1)**2*(v + 1)**2*(v + 3)
Let w = -584 - -202. Let o = w + 1531/4. Let 0 + b**2 + 1/4*b**3 + o*b = 0. What is b?
-3, -1, 0
Suppose 4*n = -0 - 4, 0 = -5*z + 2*n + 12. Suppose 5*g - 2*g + 4*x = 4, 0 = -3*g + 2*x - z. Factor 2/7*s**2 + 4/7*s**3 + g + 2/7*s**4 + 0*s.
2*s**2*(s + 1)**2/7
Let -4/7 + 34/7*u + 4/7*u**2 - 34/7*u**3 = 0. What is u?
-1, 2/17, 1
Let i(s) be the first derivative of 4/5*s**5 + 0*s**2 + 8*s**4 + 0*s - 75 + 64/3*s**3. Factor i(u).
4*u**2*(u + 4)**2
Let i(z) be the first derivative of 9/2*z - 3*z**2 - 1 + 1/2*z**3. Factor i(k).
3*(k - 3)*(k - 1)/2
Suppose -98/3 - 77/3*s + 1/3*s**4 + 13/3*s**3 + 11*s**2 = 0. Calculate s.
-7, -1, 2
Suppose 816 = 2*r + 2*s + 822, -2*r = -s - 12. Let c(w) be the second derivative of -20*w + 0 + 1/2*w**r + 3/4*w**4 - 3*w**2. Factor c(n).
3*(n + 1)*(3*n - 2)
Let q be (30/20)/(3/4)*1. Find j such that 15*j - 45 - 20*j**3 - 7*j**2 + 28*j + 17*j + 17*j**q - 5*j**4 = 0.
-3, 1
Let o be (1/(-6))/((-13)/78)*0. Let x be (-2)/(-9) - (-8)/36. Find h, given that 2/9*h**5 + o + 2/3*h**4 - 2/3*h**2 - x*h + 2/9*h**3 = 0.
-2, -1, 0, 1
Factor -100*p**3 + 0 + 35/2*p**4 + 1/2*p**5 + 0*p**2 + 0*p.
p**3*(p - 5)*(p + 40)/2
Let m = 4/2897 - -150632/8691. Let w(r) be the first derivative of -96*r**2 - 144*r - m*r**3 - r**4 - 29. Factor w(q).
-4*(q + 1)*(q + 6)**2
Let d = -1086 - -1089. Let u(r) be the second derivative of -5*r + r**2 - 1/8*r**4 + 0*r**d - 1/40*r**5 + 0. Factor u(l).
-(l - 1)*(l + 2)**2/2
Let r(p) be the first derivative of -p**5/10 + 23*p**4/30 - 9*p**3/5 + 9*p**2/5 - 28*p - 38. Let s(h) be the first derivative of r(h). Factor s(q).
-2*(q - 3)*(q - 1)*(5*q - 3)/5
Let n(m) be the second derivative of m**2 + 6*m - 5/12*m**5 + 5/2*m**4 - 10/3*m**3 + 0. Let j(h) be the first derivative of n(h). Solve j(i) = 0 for i.
2/5, 2
Let y be -2*(0 - -2 - 3). Let c be (-82)/4*40/(-410). What is f in 0 + y*f**4 - 4/9*f**3 - 8/9*f**5 + 0*f + 0*f**c = 0?
0, 1/4, 2
Let b(l) = -72*l**3 - 36*l**2 - 12*l + 168. Let o(t) = -10*t**3 + t. Let n(p) = -b(p) + 8*o(p). Determine u so that n(u) = 0.
-2, 3, 7/2
Let c be 100/(-6) + (14 - (-40 + 37)). Factor -7/3 - 2*u + c*u**2.
(u - 7)*(u + 1)/3
Let o be 1/(-1)*(-4)/28. Let v be -3 + (-10)/14 - (-11 + 7). Factor -3/7*j + 3/7*j**3 + 1/7*j**2 + o*j**4 - v.
(j - 1)*(j + 1)**2*(j + 2)/7
Let n = -476656 + 476658. Factor z + 9/5*z**n + 3/5*z**3 - 1/5*z**4 + 0.
-z*(z - 5)*(z + 1)**2/5
Let s = -1/97882 - -73412/48941. Suppose 15*v + s*v**2 + 63/2 = 0. Calculate v.
-7, -3
Suppose 4*s**2 + 3 + 65*s**4 - 6*s**4 - s**2 + 18*s - 11*s**4 - 72*s**3 = 0. What is s?
-1/4, 1
Solve 28/5*y**2 + 1/5*y**3 + 141/5*y + 198/5 = 0.
-22, -3
Factor -2465*a + 165 + 5*a**2 - 46 + 2570*a + 71.
5*(a + 2)*(a + 19)
Let z(h) be the first derivative of 2*h**3/33 + 71*h**2/11 + 810. Factor z(o).
2*o*(o + 71)/11
Let b(h) be the third derivative of -h**6/120 + h**5/6 + 19*h**4/2 + 132*h**3 + h**2 + 14*h + 12. Solve b(k) = 0.
-6, 22
Suppose -14 = 3*p + 4*m, -p + 4*m + 28 - 6 = 0. Suppose p + 158 = 4*t. Let -12*u**2 + u - t*u**4 - 16*u**5 - 64*u**3 + 7*u - 20*u**4 = 0. Calculate u.
-2, -1, 0, 1/4
Let t(j) be the first derivative of 6*j - 2*j**3 + j**2 - 1/2*j**4 + 77. Factor t(v).
-2*(v - 1)*(v + 1)*(v + 3)
Let b be (-2 - -3)/((-2)/(-46)). Suppose 22*w + 2 = b*w. Factor 6*d - 15*d + 24*d + 5*d**w + 10.
5*(d + 1)*(d + 2)
Let w(m) be the third derivative of -m**7/210 - 7*m**6/30 - 23*m**5/12 + 399*m**2 + 3. Suppose w(b) = 0. What is b?
-23, -5, 0
Let z be (-15)/65 + (3819/494 - 6). Let -1/2*c**5 - c**3 + z*c**4 + 0 + 0*c + 0*c**2 = 0. Calculate c.
0, 1, 2
Suppose -17 - 11/2*b**2 - 45/2*b = 0. What is b?
-34/11, -1
Let r(i) = -5*i**2 + 52*i + 100. Let x(p) = 6*p**2 - 53*p - 100. Let f(t) = 5*r(t) + 4*x(t). Factor f(q).
-(q - 50)*(q + 2)
Find h such that 160/3 - 12*h**2 - 712/3*h = 0.
-20, 2/9
Let l = 6869235/4 - 1717308. Factor l*g**2 + 7/4*g - 1/2*g**4 + 3/4 - 3/4*g**3.
-(g + 1)**3*(2*g - 3)/4
Let v(y) be the third derivative of 4*y**2 - 3/4*y**3 - 1/672*y**8 + 0 + 5/16*y**4 + 3*y + 1/60*y**7 + 1/60*y**5 - 7/120*y**6. Find f such that v(f) = 0.
-1, 1, 3
Let q be (21/(-35))/((-11)/5 - -2). Suppose -13*t**q + 21*t - 3*t**4 - 4*t - 47 + 53 - 7*t**2 = 0. Calculate t.
-3, -2, -1/3, 1
Let o be 29/58*(-2 + -322). Let u be (0 - -2)*(-36)/o. Factor 2/9*j - 2/9*j**5 + 0*j**3 + 4/9*j**2 + 0 - u*j**4.
-2*j*(j - 1)*(j + 1)**3/9
Let a(n) be the first derivative of n**6/15 + 8*n**5/25 - 8*n**4/5 - 128*n**3/15 - 524. Suppose a(i) = 0. Calculate i.
-4, 0, 4
Let i(u) be the second derivative of -u**4/12 + 19*u**3/6 - 30*u**2 + 70*u - 3. Factor i(d).
-(d - 15)*(d - 4)
Let f = -6483 + 6486. Let b(h) be the third derivative of -1/330*h**5 + 0*h + 1/66*h**4 + 0 - 1/33*h**f - 23*h**2. Factor b(g).
-2*(g - 1)**2/11
Let u be (5 - 1)*((-293832)/(-352))/159. Determine f, given that -3/2*f**3 - u*f**2 + 3/2*f + 21 = 0.
-14, -1, 1
Factor 6903/5*d**3 + 6348/5*d + 12972/5*d**2 + 0 + 282/5*d**4 + 3/5*d**5.
3*d*(d + 1)**2*(d + 46)**2/5
Let m be (-139106)/15270 + (-52 - -63). Let r = m - 12/509. Let 2*z + 6/5*z**4 - 2/15*z**5 - r*z**3 - 14/15 - 4/15*z**2 = 0. Calculate z.
-1, 1, 7
Let v = 6968 - 20903/3. Let w(t) be the third derivative of 0*t - 1/60*t**5 + 0 - v*t**4 - 13*t**2 - 8/3*t**3. Factor w(z).
-(z + 4)**2
Let d(f) be the second derivative of f**5/4 - 35*f**4/12 + 35*f**3/6 + 75*f**2/2 + 5196*f. Let d(m) = 0. What is m?
-1, 3, 5
Suppose -2*w + 11*w = 90. Let -9*l**3 + 20*l**2 + 5*l**3 + w*l**2 - 60*l + 28 + 6*l**2 = 0. Calculate l