6). Let 1/5*c**2 - w*c + 0 = 0. Calculate c.
0, 2
Suppose 6*a + 33 = 3*a + 4*t, -2*a - t - 33 = 0. Let k be 3/a - (-10)/50. Factor 2/13*u**2 + 0 + 150/13*u**4 + k*u - 250/13*u**5 - 30/13*u**3.
-2*u**2*(5*u - 1)**3/13
Let y(s) be the first derivative of -7/15*s**3 + 23/10*s**2 - 6 - 6/5*s. Factor y(x).
-(x - 3)*(7*x - 2)/5
Suppose 8 = t - 3*y, 5*t - 6 = t - y. Solve 0*x**3 - 2/11*x**4 + 0 - 4/11*x + 6/11*x**t = 0 for x.
-2, 0, 1
Let v(b) be the second derivative of b**5/30 - 7*b**4/9 - 68*b**3/9 - 24*b**2 - 25*b. Factor v(q).
2*(q - 18)*(q + 2)**2/3
Let c be 2/((-12)/(-9))*2. Suppose 2*x - 3*n = -8, 0 = -4*x + 3*n - 0*n - 4. Factor -4*h**3 + 3*h**x - 4*h**2 + 8*h**2 - 2*h - h**c.
-h*(h - 1)*(5*h - 2)
Factor 3/4*d**3 - 153/4*d**2 + 468*d + 507.
3*(d - 26)**2*(d + 1)/4
Let a(u) = 8*u**2 + 12*u - 95. Let g(m) = -33*m**2 - 51*m + 381. Let d(f) = 21*a(f) + 5*g(f). What is w in d(w) = 0?
-5, 6
Factor -2/3*j**4 + 80/3*j - 32/3 - 22*j**2 + 20/3*j**3.
-2*(j - 4)**2*(j - 1)**2/3
Let j(x) be the first derivative of 1/13*x**6 - 1/26*x**4 + 0*x - 2/13*x**2 - 14/39*x**3 + 14/65*x**5 - 10. Find t, given that j(t) = 0.
-2, -1, -1/3, 0, 1
Let v(p) be the first derivative of 0*p**2 + 0*p - 7/40*p**4 + 4/25*p**5 + 1/15*p**3 + 3 - 1/20*p**6. Factor v(a).
-a**2*(a - 1)**2*(3*a - 2)/10
Let z = -55 + 49. Let u(f) = -15*f**2 - 66*f - 29. Let c(l) = -15*l**2 - 66*l - 30. Let v(g) = z*u(g) + 5*c(g). Factor v(k).
3*(k + 4)*(5*k + 2)
Factor y**2 + 0*y + 0 + 1/7*y**4 - 8/7*y**3.
y**2*(y - 7)*(y - 1)/7
Let a(m) be the second derivative of 1/15*m**5 + 2*m + 0*m**2 + 1/9*m**4 + 0*m**3 + 0 + 1/90*m**6. Let a(n) = 0. What is n?
-2, 0
Let f(b) be the second derivative of 1/4*b**4 + 0*b**2 - 13*b - 1/2*b**3 + 0. Factor f(g).
3*g*(g - 1)
Solve -36*m**2 + 4*m**3 + 24*m**2 - 4*m + 2*m**4 + 10*m**2 = 0.
-2, -1, 0, 1
Let p(m) = 56*m + 284. Let g be p(-5). Let y(n) be the first derivative of -2/3*n**3 + 10 + 2/3*n**g + 1/6*n**2 + 0*n. Let y(q) = 0. Calculate q.
0, 1/4, 1/2
Let i = -32530 - -32530. Suppose 2/7*f**2 - 2/7 + i*f = 0. What is f?
-1, 1
Let t(o) = 3*o**3 - 73*o**2 + 23*o + 32. Let x(n) = 8*n**3 - 220*n**2 + 68*n + 96. Let g(j) = 16*t(j) - 5*x(j). Factor g(p).
4*(p - 8)*(p - 1)*(2*p + 1)
Suppose -7/2*a - 1/12*a**2 - 20/3 = 0. What is a?
-40, -2
Let n be 544/24*3/2. Suppose n*m = 33*m + 4. Find z such that -1/6*z**m + 0*z**3 + 0*z + 1/6*z**2 + 0 = 0.
-1, 0, 1
Factor 22/3*l**2 + 128/3*l - 8.
2*(l + 6)*(11*l - 2)/3
Let -5/12*l - 1/2 - 1/12*l**2 = 0. What is l?
-3, -2
Let c(y) be the first derivative of y**4/4 - 8*y**3/3 + 8*y**2 - 309. Find a, given that c(a) = 0.
0, 4
Solve 2/7*h**3 - 8/7*h**2 - 50/7*h + 8 = 0 for h.
-4, 1, 7
Let v(f) be the second derivative of f**5/10 + 49*f**4/6 + 208*f**3 + 576*f**2 - 6*f - 2. Let v(w) = 0. Calculate w.
-24, -1
Solve -5/4*t**2 - 380*t - 28880 = 0.
-152
Let u(p) be the second derivative of p**4/3 - 4*p**3/3 + 101*p. Factor u(w).
4*w*(w - 2)
Let f(p) be the first derivative of -p**5/60 + p**4/12 + 19*p - 19. Let w(t) be the first derivative of f(t). Determine o, given that w(o) = 0.
0, 3
Suppose 0 = 5*x - 5*t + 5, 0 = 3*x + 2*t - 4*t. Suppose -2*v**3 - 5*v**4 - 4*v - 3*v**2 - v**x + 3*v**3 + 6*v**4 = 0. What is v?
-2, -1, 0, 2
Let c(w) be the third derivative of -w**6/780 + w**4/52 - 2*w**3/39 + 213*w**2. Find j such that c(j) = 0.
-2, 1
Let z(a) be the first derivative of 2*a**4 - 212*a**3/3 + 50*a**2 + 104*a + 568. Suppose z(i) = 0. Calculate i.
-1/2, 1, 26
Let q(r) = r**3 - r**2 - 3. Let l(a) = 2*a**3 + 11*a**2 + 36*a - 3. Let i(d) = -2*l(d) + 2*q(d). Factor i(k).
-2*k*(k + 6)**2
Let u(m) = -m**2 + 4*m + 6. Let j be u(6). Let i be 156/42 - j/21. Factor -2/11*v**3 + 4/11*v**i + 0 + 0*v + 0*v**2 - 2/11*v**5.
-2*v**3*(v - 1)**2/11
Let x(p) be the second derivative of -p**6/90 + 7*p**5/30 - p**4 + 2*p**3/3 + 6*p. Let v(y) be the second derivative of x(y). Factor v(w).
-4*(w - 6)*(w - 1)
Let g(s) be the third derivative of -s**8/216 + 2*s**7/63 - 29*s**6/540 - 11*s**5/135 + s**4/3 - 8*s**3/27 - 107*s**2 + 2. Solve g(x) = 0.
-1, 2/7, 1, 2
Suppose 5*m + 135 = 5*u, 2*u - 21 = -m + 12. Factor 50/17*g**3 + 248/17*g - 48/17 - u*g**2.
2*(g - 6)*(5*g - 2)**2/17
Let y(m) be the first derivative of -3*m**5/5 + 3*m**4/4 + 4*m**3 - 6*m**2 - 27. Factor y(j).
-3*j*(j - 2)*(j - 1)*(j + 2)
Let o(d) be the first derivative of -d**4 - 20*d**3 - 150*d**2 - 500*d + 98. Find m such that o(m) = 0.
-5
Suppose 0 = 3*i + 4*x - 32, 0*i + x - 35 = -3*i. Suppose -2 = 5*v - i. Factor 4*y + 3*y**3 + 2*y**v - y - 8*y**2.
3*y*(y - 1)**2
Suppose -18 + 6 = -5*f - u, 0 = -4*f - 3*u + 14. Factor 1/2*a**3 - 3/2 - 5/2*a**f + 7/2*a.
(a - 3)*(a - 1)**2/2
Let y(n) = n**3 - 11*n**2 - n + 11. Let p be y(11). Suppose -3*h + 2*h + 8 = p. Factor -h*g - 5*g**3 + 7*g**4 - 12*g**2 + 4*g**5 + 5*g**4 + 6*g**3 + 3*g**3.
4*g*(g - 1)*(g + 1)**2*(g + 2)
Let u(m) be the first derivative of -m**6/6 - 4*m**5 - 25*m**4 + 127. Suppose u(k) = 0. What is k?
-10, 0
Let a(z) be the second derivative of z**6/45 + z**5/10 + z**4/6 + z**3/9 - 13*z - 1. Solve a(w) = 0 for w.
-1, 0
Let w = -3542/17 + 21812/51. Let s = w - 217. Let 0*c + 0 + 2/3*c**3 - 1/3*c**2 + 4/3*c**5 + s*c**4 = 0. What is c?
-1, 0, 1/4
Suppose -2*q + 3*q - 4*g = -4, 0 = -q - g - 4. Let j = 0 - q. Let -6*i**4 + i**5 + 0*i**2 + j*i**4 - i + 2*i**2 = 0. Calculate i.
-1, 0, 1
Let c(o) be the first derivative of o**5/6 - 2*o**4/9 - o**3/9 + 6*o - 2. Let l(z) be the first derivative of c(z). Find u, given that l(u) = 0.
-1/5, 0, 1
Suppose -3*c - 5*f = 14, 0 = 4*c - 3*f + 10 - 30. Let x be 1/(-9) + (3 - c). Find z such that -4/9 + x*z - 1/3*z**2 = 0.
2/3, 2
Let -20*y + 2*y**5 + 3*y + 20*y**4 + 5*y**3 + y**3 - 10*y**2 - 10*y**4 + 9*y = 0. What is y?
-4, -1, 0, 1
Let d(h) be the third derivative of 1/24*h**5 + 0*h**3 + 0 + 1/80*h**6 + 1/24*h**4 + 11*h**2 + 0*h. Factor d(t).
t*(t + 1)*(3*t + 2)/2
Suppose -5*b - 4 = -2*x, -762 = x - 5*b - 764. Determine o, given that 0 - 4/3*o + 14/3*o**x = 0.
0, 2/7
Let w(v) be the second derivative of 0 - 1/90*v**6 + 2/9*v**4 - 2/3*v**3 + 41*v + 0*v**2 + 1/60*v**5. Factor w(r).
-r*(r - 2)**2*(r + 3)/3
Let f(c) be the third derivative of 1/85*c**5 + 0 - 5/204*c**6 + 0*c + 0*c**3 + 0*c**4 + 1/408*c**8 - 9*c**2 + 4/595*c**7. Let f(u) = 0. What is u?
-3, 0, 2/7, 1
Let m be (0/2 - 3/(-6))*8. Factor -5*a**m + 140*a**3 + 7*a - 153*a**3 - 3*a - 4*a**2.
-a*(a + 1)*(a + 2)*(5*a - 2)
Let f(u) = 4*u**4 + u**3 + u + 2. Let y(p) = 4*p**3 + p + 13*p**4 + p**2 - 8 + 2*p + 15. Let b = -15 - -22. Let l(g) = b*f(g) - 2*y(g). Factor l(c).
c*(c - 1)*(c + 1)*(2*c - 1)
Let j(d) be the second derivative of -d**5/70 - d**4/6 - 2*d**3/3 - 8*d**2/7 + d + 7. What is l in j(l) = 0?
-4, -2, -1
Let z(d) be the second derivative of -d**9/3024 + d**8/448 - d**7/252 - 7*d**4/6 - 5*d. Let p(s) be the third derivative of z(s). Solve p(t) = 0 for t.
0, 1, 2
Let s be (42/9 - -2) + (-36 - -36). Suppose 7/3*h**2 + s*h + 4/3 - 3*h**3 = 0. What is h?
-1, -2/9, 2
Let q(l) be the third derivative of l**6/160 - l**5/80 - l**4/16 + 21*l**2. Factor q(w).
3*w*(w - 2)*(w + 1)/4
Suppose 5*x - 2*x = 5*d - 11, 3*d - 9 = x. Suppose 0 = 5*u + 5*h + 5, -8*u - 1 = -3*u + h. Suppose -3*a + u - 5*a**2 + 4 + 2*a**2 + x*a**3 - 1 = 0. What is a?
-1, 1
Suppose 29 = 12*v - 31. Factor 0*w**3 + 0*w**3 + 88*w - 4*w**2 + 4*w**4 - 90*w + 2*w**v.
2*w*(w - 1)*(w + 1)**3
Let y(c) be the first derivative of 7 - 1/2*c**3 + c - 3*c**2 + 1/4*c**4. Let s(f) be the first derivative of y(f). Factor s(b).
3*(b - 2)*(b + 1)
Let i(y) = y**3 - 39*y**2 + 137*y + 117. Let r be i(35). Solve r*c**3 + 0 + 14/5*c**4 + 12/5*c + 58/5*c**2 = 0 for c.
-3, -1, -2/7, 0
Let f be 1*(3 - (-2 - -3)). Suppose 0 = 2*n - n - f. Determine j, given that 16*j**5 - 13*j**3 + 24*j**n + 0*j + 48*j**4 + 65*j**3 + 4*j = 0.
-1, -1/2, 0
Let c(h) be the third derivative of 1/3*h**4 - 2*h**2 + 1/180*h**6 + 2/3*h**3 + 0*h + 0 + 1/15*h**5. Let r(i) be the first derivative of c(i). Factor r(u).
2*(u + 2)**2
Suppose 0 = -5*f - 5*m - 20, 15 + 55 = -f - 12*m. Factor 0*v - 3/5*v**f + 3/5.
-3*(v - 1)*(v + 1)/5
Let m(p) = -4*p**3 - 54*p**2 + 40*p + 6. Let r(h) = h**2 + 2*h - 1. Let o(g) = m(g) + 6*r(g). Suppose o(l) = 0. Calculate l.
-13, 0, 1
Let z be (-468)/(-63)*(-7)/(-2). Let n = z - 23. Solve -a**3 - 4*a**5 + a**5 - 12 - 9*a**