c) + r(c). Let h be l(6). Find g such that 1/2*g**4 + 1/4*g - 1/4*g**h + 0 - 1/2*g**2 = 0.
-1, 0, 1/2, 1
Let d(x) be the third derivative of x**6/120 + 11*x**5/360 + 5*x**4/144 + 21*x**2. Factor d(a).
a*(a + 1)*(6*a + 5)/6
Let g(u) be the first derivative of u**4 - 28*u**3/3 + 20*u**2 - 766. Factor g(p).
4*p*(p - 5)*(p - 2)
Factor 7*v**3 - 6*v**3 - 2*v + 5*v - 3*v**2 - v**2.
v*(v - 3)*(v - 1)
Let c(x) = -x**2 + x + 3. Let v be c(0). Suppose 0 = -z - v*z + 16. Find y, given that 18*y**2 - z + 2*y**3 + 12 + 16*y - 8*y**2 = 0.
-2, -1
Factor 0 + 4/3*u**3 + 2/9*u**5 - 10/9*u**4 + 8/9*u**2 - 16/9*u.
2*u*(u - 2)**3*(u + 1)/9
Let x = -20 - -23. Suppose 22*m**4 - 4*m**4 - 4*m**2 - 7*m**4 + 2*m**x - 7*m**4 - 2*m**5 = 0. Calculate m.
-1, 0, 1, 2
Suppose -3/2*i + 27/8*i**3 + 0 - 15/8*i**2 = 0. Calculate i.
-4/9, 0, 1
Let -94/3*l**4 + 128/3*l - 110/3*l**3 + 70/3*l**2 - 6*l**5 + 8 = 0. Calculate l.
-3, -2, -1, -2/9, 1
Let p(g) be the first derivative of -32/65*g**5 - 20/13*g**4 - 35/13*g**2 + 58/13*g**3 + 22 + 8/13*g. Suppose p(a) = 0. Calculate a.
-4, 1/4, 1
Let t(n) be the second derivative of -n**10/75600 - n**9/5400 - n**8/1120 - n**7/700 + 7*n**4/4 + n. Let v(k) be the third derivative of t(k). Solve v(x) = 0.
-3, -1, 0
Factor 747*c**4 - 2 + 4 + 8 + 35*c**3 - 15*c - 762*c**4 - 15*c**2.
-5*(c - 1)**3*(3*c + 2)
Let u(h) be the third derivative of 22*h**2 - 1/36*h**3 + 1/360*h**5 + 0*h**4 + 0*h + 0. Suppose u(q) = 0. Calculate q.
-1, 1
Let s be 8/5 - 6/10. Suppose -4*x - s = -17. Find t, given that 5*t**3 - 9*t**4 + 2*t**2 + x*t**2 - 2*t**3 + 0*t**4 = 0.
-2/3, 0, 1
Factor -2/5*l**4 + 8/5*l**2 - 8/5*l + 0 + 2/5*l**3.
-2*l*(l - 2)*(l - 1)*(l + 2)/5
Let d(o) be the second derivative of -o**6/210 + 9*o**5/140 - o**4/7 - 40*o**3/21 + 96*o**2/7 + 97*o. Factor d(p).
-(p - 4)**3*(p + 3)/7
Let q be -4*(1 - 18/8). Let c be (7 + (-160)/24)*(2 - 2). Factor -3/4*b**q + c + 0*b - 5/4*b**4 + 0*b**2 - 1/2*b**3.
-b**3*(b + 1)*(3*b + 2)/4
Suppose 0 = 4*t - 4*r - 32, 2 = 188*t - 184*t + r. Factor 0*n + 0*n**t + 16/9*n**3 + 0 - 4*n**4 + 2*n**5.
2*n**3*(3*n - 4)*(3*n - 2)/9
Let 95*t**2 + 5/4*t**3 + 745/4*t + 185/2 = 0. What is t?
-74, -1
Let w(c) be the first derivative of -3*c**4/32 - 3*c**3/4 - 27*c**2/16 - 3*c/2 - 54. Factor w(x).
-3*(x + 1)**2*(x + 4)/8
Let p(s) be the first derivative of -4*s**5 - 105*s**4/4 - 145*s**3/3 - 15*s**2 - 495. Find j such that p(j) = 0.
-3, -2, -1/4, 0
Suppose 5*h - 130*o + 129*o - 17 = 0, 5*h + 5*o = 35. Let t(i) be the first derivative of -1/2*i**h - 2/3*i**3 + i**2 + 2*i - 7. Factor t(a).
-2*(a - 1)*(a + 1)**2
Let d(i) be the third derivative of -i**8/224 - i**7/70 + i**6/16 + i**5/4 - i**4/4 - 2*i**3 + 3*i**2 - 11*i. Let d(y) = 0. Calculate y.
-2, -1, 1, 2
Let g = -32482 + 163401/5. Let c = g + -197. Determine l so that -14/5*l**2 + 6/5*l**4 + 1/5*l**3 + 1/5*l + c = 0.
-3/2, -2/3, 1
Let f(x) be the first derivative of 3*x**4/20 + 2*x**3/5 - 3*x**2/10 - 6*x/5 - 44. Find h, given that f(h) = 0.
-2, -1, 1
Let h = 73/222 - 6/37. Let k(w) be the second derivative of 1/36*w**4 + h*w**3 + 1/3*w**2 + 0 - 5*w. Let k(a) = 0. Calculate a.
-2, -1
Let c(a) be the second derivative of 0*a**3 + 1/300*a**5 + 1/2*a**2 - 1/40*a**4 + 0 - 7*a. Let l(d) be the first derivative of c(d). Let l(q) = 0. What is q?
0, 3
Let c = 26 + -21. Let -23*k + 29*k + c + 4 - 3*k**2 = 0. What is k?
-1, 3
Let q(p) be the third derivative of p**8/84 - 22*p**7/105 + 43*p**6/30 - 73*p**5/15 + 28*p**4/3 - 32*p**3/3 - 139*p**2 + p. Factor q(g).
4*(g - 4)**2*(g - 1)**3
Suppose 2*c - 2 = 0, -4*b + 9*b + 4*c - 29 = 0. Find l such that -20 + 65*l**2 + 5*l**4 - 95*l**3 - 50*l**4 + 25*l + 35*l + 35*l**b = 0.
-1, 2/7, 1, 2
Let z(o) be the first derivative of 2/15*o**5 + 0*o - 1/18*o**6 + 0*o**3 - 1/12*o**4 - 5 + 0*o**2. Determine p so that z(p) = 0.
0, 1
Factor 12/5*k**2 + 2/15*k**3 + 32/15 + 22/5*k.
2*(k + 1)**2*(k + 16)/15
Let 27*i**4 + 21*i**4 + 13*i**2 - 13*i**3 - 15*i**3 - 9*i**2 = 0. Calculate i.
0, 1/4, 1/3
Let u(x) be the second derivative of -161/18*x**3 - 36*x + 0 + 49/6*x**2 + 95/18*x**4 - 47/30*x**5 - 1/126*x**7 + 17/90*x**6. Let u(k) = 0. Calculate k.
1, 7
Let q(b) = -b**3 + 3*b**2 + 5*b + 2. Let w be q(4). Suppose -5*u**3 - w + 75 - 95*u - 24 + 55*u**2 = 0. Calculate u.
1, 9
Suppose -5*p = d - 52, 2*p - 7*p = -5*d - 70. What is z in -16*z + p*z - 5*z**2 + 2*z + 13*z = 0?
0, 2
Let m(i) be the second derivative of 0*i**2 + 1/3*i**6 + 0 + 4/21*i**7 - i + 1/10*i**5 + 0*i**3 + 0*i**4. Suppose m(r) = 0. What is r?
-1, -1/4, 0
What is b in 11 + 7*b**3 - 145*b - 10 - 14*b**3 - 60*b**2 - 91 + 2*b**3 = 0?
-9, -2, -1
Let r(o) = 3*o + 9 + 50*o**2 - 49*o**2 - 4. Let h be r(0). Suppose -2/9*y**4 + 2/9*y**h + 0*y**3 + 0 + 0*y + 0*y**2 = 0. What is y?
0, 1
Let z(l) be the second derivative of 2 - 8/3*l**3 + 5/12*l**4 - 32/3*l**2 + 11*l - 1/60*l**5. Factor z(w).
-(w - 8)**2*(w + 1)/3
Suppose 3*v - 25 = -3*t + 11, 0 = -5*v + t + 30. Factor 6*c**2 - 10 - v*c**2 + 6*c**2 + 5*c.
5*(c - 1)*(c + 2)
Let j(w) be the second derivative of -3*w + 0 + 0*w**3 - 1/56*w**7 + 0*w**4 + 0*w**2 + 1/20*w**6 - 3/80*w**5. Factor j(b).
-3*b**3*(b - 1)**2/4
Let i = 29/4 + -133/20. Find y, given that -i*y + 0 - 12/5*y**4 - 18/5*y**2 - 27/5*y**3 = 0.
-1, -1/4, 0
Let j(a) = 4*a**2 + 2*a. Let s be j(-2). Suppose -2*k + 3*k + 10 = -4*m, 4*m + s = 0. Determine f so that 2*f**2 + f**4 + 5/2*f**5 + 0 + k*f - 15/2*f**3 = 0.
-2, -2/5, 0, 1
Let t(l) = -l**2 + l. Let q(s) be the first derivative of -16/3*s**3 + 12 + 16*s**2 - 16*s. Let i(u) = q(u) - 20*t(u). Find w, given that i(w) = 0.
-4, 1
Solve -240*k**3 - 8*k**5 + 217*k**2 - 512*k + 295*k**2 + 15*k**5 - 6*k**5 + 192 - 5*k**5 + 52*k**4 = 0 for k.
1, 2, 6
Let f(z) be the first derivative of -3/8*z**3 + 0*z**2 + 3/16*z**4 - 1/40*z**5 + 0*z - 4. Factor f(n).
-n**2*(n - 3)**2/8
Let a = 30402 + -30402. Determine z, given that -11/2*z**3 + 0 + 7*z**5 + 39/2*z**4 + a*z - 3*z**2 = 0.
-3, -2/7, 0, 1/2
Let h = 8 - 5. Let x be 104/(-672) + (0 - -1)*(-25)/(-100). Factor 0*a + 0*a**2 + 2/21*a**5 - 4/21*a**h + 0 + x*a**4.
2*a**3*(a - 1)*(a + 2)/21
Factor -6 + 7/3*g + 1/3*g**2.
(g - 2)*(g + 9)/3
Factor 1/5*p**4 - 9/5 + 8/5*p**2 - 2*p**3 + 2*p.
(p - 9)*(p - 1)**2*(p + 1)/5
Let d = -224 + 222. Let n be (d/(-5) - 1)*(-40)/48. Suppose -3/2*y**2 + 1/2*y**3 - n*y + 3/2 = 0. What is y?
-1, 1, 3
Let k = -4/149 + 161/447. Let d(v) be the second derivative of k*v**4 - 8*v + 0*v**2 + 0 + 2/3*v**3. Factor d(f).
4*f*(f + 1)
Let q = -40 - -95. Factor -108 - 6*m + 53 - m**2 + q.
-m*(m + 6)
Let -7*v**4 + 5*v**2 + 2 + 33/4*v - 15/2*v**3 - 3/4*v**5 = 0. What is v?
-8, -1, -1/3, 1
Let c(y) be the third derivative of 0*y - 1/720*y**6 - 1/6*y**3 + 0 - 1/48*y**4 + 1/120*y**5 + 4*y**2. Let f(u) be the first derivative of c(u). Factor f(l).
-(l - 1)**2/2
Suppose -4*f + 2*w + 16 = 0, 0 = f - 2*w + 12 - 19. Determine q, given that 10/21*q**2 + 4/21 + 6/7*q - 6/7*q**f - 2/3*q**4 = 0.
-1, -2/7, 1
Let h(o) = -2*o**3 + 31*o**2 - 115*o + 178. Let a be h(11). Factor -2/3*t**3 - 4*t**a - 2/3*t - 32/3*t**5 + 16*t**4 + 0.
-2*t*(t - 1)**2*(4*t + 1)**2/3
Let m = 1028/5 - 7166/35. Factor 3/7*b**2 + 0 - m*b + 3/7*b**3.
3*b*(b - 1)*(b + 2)/7
Solve -278*f**3 + 142*f**3 - 24*f + 20*f**2 + 140*f**3 = 0.
-6, 0, 1
Let j(r) = -8*r - 125. Let t be j(-16). Let w(v) be the first derivative of t*v**2 - 5 - 1/2*v**3 - 9/2*v. Solve w(d) = 0 for d.
1, 3
Factor -1/3*j**2 + 22/3 + 3*j.
-(j - 11)*(j + 2)/3
Let n(d) be the first derivative of -d**7/840 - d**6/360 + d**5/60 + d**3 - 14. Let m(u) be the third derivative of n(u). Factor m(t).
-t*(t - 1)*(t + 2)
Let w = -1/4 + 1/2. Let b be (-6)/21 + 25*(-1)/(-14). Factor w*y + y**4 + b*y**2 + 0 + 9/4*y**3.
y*(y + 1)**2*(4*y + 1)/4
Let o(m) = m**2 - m - 3. Let s be o(3). Suppose -6*c + s*c + 6 = 0. Factor 5*f - f**5 - 25*f**c + 2 - 4*f**3 + 12*f**2 + 15*f**2 - 4*f**4.
-(f - 1)*(f + 1)**3*(f + 2)
Let d(a) = 9*a**2 + 47*a - 151. Let c(v) = -6*v**2 - 31*v + 101. Let u(s) = 7*c(s) + 5*d(s). Factor u(y).
3*(y - 2)*(y + 8)
Suppose 48*y - 27 = 39*y. Solve 12*u + 4*u**2 + 5 - 2 - y = 0.
-3, 0
Let x(w) = 29*w**5 - 51*w**4 - 2*w**3 - 16*w + 8. Let v(r) = 20*r**5 - 34*r**4 - r**3 - 10*r + 5. Let h(s) = -8*v(s) + 5*x(s). Suppose h(o) = 0. What is o?
0, 2/15, 1
Let v = 80 + -53. Find y such that 7*y**4 + 1