Find s, given that s**5 + s + 0*s**5 + l*s**3 - 2*s**3 = 0.
-1, 0, 1
Let u(y) be the third derivative of 0 + 1/60*y**5 - 1/6*y**4 + 2/3*y**3 - 2*y**2 + 0*y. Determine w so that u(w) = 0.
2
Let a(z) = 2*z**3 + 48*z**2 + 48*z + 50. Let g be a(-23). Factor -1/3*q**2 - 1/6 + 1/3*q**3 + 1/2*q**g + 1/6*q**5 - 1/2*q.
(q - 1)*(q + 1)**4/6
Let u be (5/(-430))/((-1)/(-47)). Let b = -2/43 - u. Solve -1/2 - b*g + g**2 = 0.
-1/2, 1
Let s be (-1)/(10/20*-1). Solve -4/7 - 18/7*p**s - 22/7*p = 0.
-1, -2/9
Suppose y - 6*y - 19 = -2*p, 0 = 2*y + 6. Let l(o) be the first derivative of 1 + 70/27*o**3 - 25/18*o**4 - 11/9*o**p + 2/9*o. Factor l(c).
-2*(c - 1)*(5*c - 1)**2/9
Let k be (-25)/(-5) - (-1 - -4). Let d(a) = 4*a**2 - 3*a**k + 0*a**3 - a**3. Let f(s) = -10*s**3 + 13*s**2 + s. Let q(g) = -22*d(g) + 2*f(g). Solve q(l) = 0.
-1, 0
Let x be -5*(-6)/(-30)*(-1)/12. Let f(b) be the first derivative of x*b**3 + 1/16*b**4 + 0*b**2 + 1 + 0*b. Factor f(u).
u**2*(u + 1)/4
Let m(q) = -q**2 - q. Suppose 2*p - 3*p + 2 = 0. Let k(r) = 6*r**2 - 10*r + 2. Let a(h) = p*m(h) - k(h). Factor a(b).
-2*(2*b - 1)**2
Let o = 317/235 + -7/47. Factor o - 8/5*j + 2/5*j**2.
2*(j - 3)*(j - 1)/5
Let a = 111 - 77. Let c = -34 + a. Factor 0*k + c + k**2 + 1/2*k**3.
k**2*(k + 2)/2
Let t be 8/(-28) - (-44)/7. Suppose o + t = 9. What is u in 0 + 1/3*u - 1/3*u**o + 0*u**2 = 0?
-1, 0, 1
Suppose -2/7*j**3 + 0*j + 16/7*j**2 + 0 = 0. What is j?
0, 8
Let p(q) be the second derivative of 0*q**3 + 0 + 0*q**4 + 1/170*q**5 + 8*q + 0*q**2. What is m in p(m) = 0?
0
Suppose -y + 3*n = 6, 3*y + 5*n = -24 - 22. Let f = -9 - y. Solve 0*i**3 + 2*i**f + i**2 + i**3 - 8*i**3 + 4*i**4 = 0.
0, 1/4, 1
Let o(j) be the second derivative of 0 + 1/48*j**4 + 1/8*j**2 + 1/12*j**3 + 5*j. Factor o(y).
(y + 1)**2/4
Let m(u) = 7*u**2 + 7*u - 4. Let w(n) = 4*n**2 + 4*n - 2. Let f(s) = 3*m(s) - 5*w(s). Factor f(p).
(p - 1)*(p + 2)
Find z such that 1/5*z**3 - z**2 + 0 + 3/5*z + 1/5*z**4 = 0.
-3, 0, 1
Suppose -h = 2*h - 6. Suppose 0 = -3*r + h*r + 3. Factor 2*x**5 - x**2 - 2*x + 4*x**4 - 4*x**2 - r*x**2 + 4*x**2.
2*x*(x - 1)*(x + 1)**3
Let c(y) = -2*y - 7. Let z be c(-5). Factor 3*q**2 - 1 + z*q - 2 - 3.
3*(q - 1)*(q + 2)
Factor -4*w - 1 + 10*w**2 + 1 - 12*w**2.
-2*w*(w + 2)
Let d = -14 - -25. Suppose 5*y = 4 + d. Factor 4/9 - 10/9*l**y - 2/9*l - 16/9*l**2.
-2*(l + 1)**2*(5*l - 2)/9
Let r(w) be the first derivative of w**4/4 + w**3 + 3*w**2/2 + w - 40. Factor r(f).
(f + 1)**3
Suppose -4*b - b = -180. Suppose -5*i - 5*s + 18 = -22, 0 = -4*i - 5*s + b. Factor -4/7*h**2 + 4/7*h**3 + 2/7 - 2/7*h + 2/7*h**i - 2/7*h**5.
-2*(h - 1)**3*(h + 1)**2/7
Let z be (-1)/3 + 8/15. Find n such that 2/5*n + 0 + 4/5*n**5 - n**2 - 12/5*n**3 - z*n**4 = 0.
-1, 0, 1/4, 2
Let s(l) = -20*l**3 - 100*l**2 + 150*l - 35. Let h(z) = -20*z**3 - 101*z**2 + 151*z - 36. Let r(t) = 5*h(t) - 6*s(t). Find q such that r(q) = 0.
-6, 1/4, 1
Let z(j) be the second derivative of -j**6/210 - 9*j**5/70 - 61*j**4/84 + 30*j**3/7 - 50*j**2/7 - 4*j - 7. Factor z(q).
-(q - 1)**2*(q + 10)**2/7
Let f(l) be the third derivative of 0*l**7 + 0*l - 1/336*l**8 + 0*l**4 + 0*l**5 + 0 + 0*l**6 + 0*l**3 + 3*l**2. Factor f(u).
-u**5
Let c be 2 - (0 + 0/(-2)). Factor -1 + y - 1/4*y**c.
-(y - 2)**2/4
Let h(c) = -c**2 + 2*c - 6. Let z(b) be the third derivative of -b**5/60 + b**4/12 - 7*b**3/6 + 4*b**2. Let v(a) = 6*h(a) - 5*z(a). Suppose v(f) = 0. What is f?
1
Let t = -67/2 - -302/9. Let s(j) be the second derivative of -1/45*j**5 + 0 + 0*j**2 + t*j**4 - 1/27*j**3 - 2*j. Solve s(n) = 0 for n.
0, 1/2, 1
Let w(i) = i**2 - i. Let l(v) = 11*v**2 - 13*v. Let j(t) = 21*t**2 - 27*t. Let k(y) = 4*j(y) - 9*l(y). Let b(c) = k(c) + 6*w(c). Factor b(s).
-3*s*(3*s - 1)
Let z(a) be the first derivative of -a**6/120 + a**5/15 - a**4/6 - a**2/2 + 3. Let s(k) be the second derivative of z(k). Factor s(h).
-h*(h - 2)**2
Suppose -3*f + 5*g = 19, -f - 3*f = 2*g - 18. Solve 0 - 2/7*l**5 + 0*l**f - 2/7*l + 4/7*l**3 + 0*l**4 = 0 for l.
-1, 0, 1
Suppose 2*y + 2*y + 4 = 0, -4*y - 4 = -5*x. Suppose -10/3*h**2 - 2/3*h**5 + 2*h**3 + 2/3*h**4 + x + 4/3*h = 0. What is h?
-2, 0, 1
Let u be (-27)/2*(-30)/36. Let r = u - 11. Solve 0 + 1/4*v**2 + r*v = 0 for v.
-1, 0
Let c(t) be the first derivative of -t**6/40 - 3*t**5/20 - t**4/4 - t**2 + 1. Let d(p) be the second derivative of c(p). Solve d(g) = 0.
-2, -1, 0
Let o(k) be the third derivative of -k**7/210 + k**6/60 - k**5/60 + 6*k**2. Factor o(c).
-c**2*(c - 1)**2
Let r(p) be the third derivative of -p**6/480 + p**5/80 - p**4/32 + p**3/2 - 6*p**2. Let u(w) be the first derivative of r(w). Determine x, given that u(x) = 0.
1
Let c(x) be the second derivative of x**5/80 - x**4/16 + x**3/12 - 7*x. Find f, given that c(f) = 0.
0, 1, 2
Let w(u) = u**2 - 6*u + 2. Let p be 24/9*(-9)/(-4). Let n be w(p). Factor -3*q**2 + n - 2*q - 7*q**2 - 2*q**2.
-2*(2*q + 1)*(3*q - 1)
Factor 7*r**2 + r**3 + 24 - 4*r**3 + 12*r + 12*r**2 - 25*r**2.
-3*(r - 2)*(r + 2)**2
Let m be ((-28)/9 + 3)*21/(-2). Let i(b) be the first derivative of 3 - 2/3*b + 1/4*b**4 - m*b**2 - 2/9*b**3. Factor i(c).
(c - 2)*(c + 1)*(3*c + 1)/3
Let i = -6 - -9. Suppose -j + i*j = 4. Factor 18*d**3 + 2 - 2*d - 4 + 16*d - 30*d**j.
2*(d - 1)*(3*d - 1)**2
Let y = -9 + 4. Let w(m) = -m**3 - 2*m**2 + 2*m + 3. Let l(t) = 2*t**3 + 4*t**2 - 3*t - 5. Let k(b) = y*w(b) - 3*l(b). Determine c, given that k(c) = 0.
-1, 0
Let q = -12 - -21. Let h be q/(-21)*(-14)/2. Factor -1/4*g**2 + 1/4 + 1/4*g**h - 1/4*g.
(g - 1)**2*(g + 1)/4
Suppose 82 = 6*o + 70. Solve -1/10*z**5 + 3/10*z**3 + 1/5*z + 1/2*z**o + 0 - 1/10*z**4 = 0.
-1, 0, 2
Let h be (0 - 2/(-4))*7/7. Factor -1/2*i**2 + 0 - h*i.
-i*(i + 1)/2
Let o(s) be the third derivative of s**6/180 + s**5/90 - 19*s**2. What is p in o(p) = 0?
-1, 0
Let m = 7 - 11. Let w = m + 6. Let -w*b**2 + b + 3*b**2 - 2*b = 0. Calculate b.
0, 1
Let p(u) = -u**2 + 45*u - 126. Let n be p(42). Determine q so that n*q**2 + 0*q - 2/5*q**3 + 0 = 0.
0
Let t = 28 - 28. Determine n so that 2/3*n + 8/3*n**2 + 8/3*n**3 + t = 0.
-1/2, 0
Let r(h) = h + 4. Let u be r(-2). Factor -u*x**3 - 2*x**5 - x**5 + 0*x**5 + 5*x**5.
2*x**3*(x - 1)*(x + 1)
Let i = 3/2 - 7/6. Factor 0*x + i*x**4 - 1/3*x**3 + 0*x**2 + 0.
x**3*(x - 1)/3
Suppose -2*m = -4*v - 22, 8*m - 3*m + 3*v - 3 = 0. Solve 2*g**2 + 8*g**4 + g**m + 2*g**3 - 2*g**3 + 6*g**3 + 3*g**5 = 0.
-1, -2/3, 0
Let z(x) be the third derivative of -4*x**2 + 0*x**4 + 0*x**3 + 1/120*x**6 + 0*x + 1/30*x**5 + 0. Find o, given that z(o) = 0.
-2, 0
Determine i so that 11/10*i + 4*i**2 - 13/5 + 3/10*i**3 = 0.
-13, -1, 2/3
What is y in -3/2*y**2 - 5/4*y**3 + 2 - 1/4*y**4 + y = 0?
-2, 1
Let c = -50 + 28. Let q be c/(-42) + 4/12. Suppose 2/7*x**2 - 4/7*x**4 + 6/7*x**3 + 2/7 - q*x = 0. Calculate x.
-1, 1/2, 1
Let d = 10 - 8. Let p(v) be the second derivative of -1/9*v**4 + 0 + v + 1/3*v**d - 1/9*v**3. Determine x so that p(x) = 0.
-1, 1/2
Let o = 4 - 1. Factor 7*b**3 + o*b**2 - 1 - 4*b**3 - 3*b - 2.
3*(b - 1)*(b + 1)**2
Let t be (-1)/4 - 6/(-24). Let f = t + 0. Factor -1/2*d**2 + 0 - 1/2*d**5 - 3/2*d**3 - 3/2*d**4 + f*d.
-d**2*(d + 1)**3/2
Let d(j) be the first derivative of j**3/6 + j**2/2 + j/2 - 12. Factor d(f).
(f + 1)**2/2
Let f = 41/17 + 3/34. Factor 1/4 - 5/2*i**3 - 5/4*i + 5/4*i**4 - 1/4*i**5 + f*i**2.
-(i - 1)**5/4
Let p(u) = 60*u**2 + 25*u - 35. Let d(s) = 5*s**2 + 2*s - 3. Let y(q) = -35*d(q) + 3*p(q). Factor y(v).
5*v*(v + 1)
Let n(j) be the third derivative of -j**7/630 + j**6/360 + j**5/180 - j**4/72 + 6*j**2. Factor n(c).
-c*(c - 1)**2*(c + 1)/3
Let i = -1/6 - -2/3. Factor 1/2*q - i*q**4 - 1/2*q**3 + 0 + 1/2*q**2.
-q*(q - 1)*(q + 1)**2/2
Suppose 0 = -5*a + 2*k, -a - 3*k = a + 19. Let v = 4 + a. Suppose 1/4*y**v + 1 - y = 0. Calculate y.
2
Let x(n) be the first derivative of -n**3/2 - 9*n**2/4 - 3*n + 15. Factor x(c).
-3*(c + 1)*(c + 2)/2
Let m = 104 + -351. Let s = -2221/9 - m. Factor -2/9*k**2 + 0*k - s*k**4 + 4/9*k**3 + 0.
-2*k**2*(k - 1)**2/9
Determine q, given that -2/3*q**2 + 2/3*q**4 + 4/3*q + 0 - 4/3*q**3 = 0.
-1, 0, 1, 2
Factor 9*s**4 + 4*s - 8*s**4 - s**3 - 7*s**2 + s**2 + 2*s**2.
s*(s - 2)*(s - 1)*(s + 2)
Let r = -22 - -31. Find m, given that 8*m + 3*m**2 - 11*m + r*m = 0.
-2, 0
Let r(i) be the second derivative of -3*i**5/20 - 3*i**4/4 - 3*i**3/2 - 3*i**2/2 - 38*i + 2.