(-6*(-4)/(-8))/((-195)/52). Determine c, given that 0*c**2 - 6/5*c + i + 2/5*c**3 = 0.
-2, 1
Let j be 2/((-24)/(-9))*-4. Let r = 3 + j. Suppose k**2 + r*k**2 + 0 + 1 - 2*k = 0. Calculate k.
1
Let a be 166/63 + 12/(-42). Let l = 18/7 - a. Solve -l*s - 2/9*s**2 + 0 = 0 for s.
-1, 0
Let q be 2 - (-3 + 51/12). Determine t, given that q*t**4 + 4*t + 7/2*t**3 + 23/4*t**2 + 1 = 0.
-2, -1, -2/3
Factor 4 + 2*d**2 - 2*d**3 + 3*d - 6*d**2 - d.
-2*(d - 1)*(d + 1)*(d + 2)
Let x = -73 - -76. Let g(o) be the first derivative of -1/8*o**2 - 1/12*o**3 + x + 0*o. Suppose g(h) = 0. What is h?
-1, 0
Let f = 7 - 5. Suppose 0*g - 12 = -5*g + i, 0 = g + i. Factor g*j**4 - 4*j**2 - f*j**3 - 2*j**2 + 4*j**2 + 2*j.
2*j*(j - 1)**2*(j + 1)
Let m be (-35)/77*8/(-20). Factor 0 + 0*l**4 + 4/11*l**3 + 0*l**2 - m*l - 2/11*l**5.
-2*l*(l - 1)**2*(l + 1)**2/11
Let r(o) be the first derivative of 9*o**4 - 11*o**3 + 0*o + 2 + 3*o**2 + 33/5*o**5 - 7*o**6. Solve r(q) = 0.
-1, 0, 2/7, 1/2, 1
Let a(m) be the first derivative of m**4/18 + m**3/9 - m - 1. Let b(d) be the first derivative of a(d). Factor b(c).
2*c*(c + 1)/3
Let z(j) be the first derivative of -3 + 1/25*j**5 + 1/20*j**4 + 0*j + 0*j**3 + 0*j**2. Factor z(h).
h**3*(h + 1)/5
Suppose -w = -5*w + 60. Suppose 0 = 2*d + 3*d - w. Factor 0*h**d - h**3 + 3*h**3 - 2*h.
2*h*(h - 1)*(h + 1)
Let j(c) be the first derivative of 3/5*c**2 + 4/5*c - 2 - 2/3*c**3. Factor j(k).
-2*(k - 1)*(5*k + 2)/5
Factor 0 + 7/2*c**4 + 3*c - 25/2*c**2 + 6*c**3.
c*(c - 1)*(c + 3)*(7*c - 2)/2
Let z(l) be the second derivative of 1/3*l**3 + 0 + 0*l**4 - 2*l + 1/150*l**5 - 1/900*l**6 + 0*l**2. Let b(f) be the second derivative of z(f). Factor b(n).
-2*n*(n - 2)/5
Let x be ((-1)/3)/(1/(-30)). Let u = 11 - x. Factor 0*s**2 + 0 + 3*s + 3 - u + s**2.
(s + 1)*(s + 2)
Suppose 4*h = 12*h - 16. Factor -8/3*z + 2/3*z**h + 8/3*z**3 - 2/3.
2*(z - 1)*(z + 1)*(4*z + 1)/3
Let w be -2 + 6/2 + 1. Let -4*l**4 - l + l + 4*l**2 + 2*l - w*l**5 = 0. What is l?
-1, 0, 1
Let d(w) = -2*w - 10. Let c be d(-5). Factor 13*g + c*g**3 - 13*g + g**3.
g**3
Let v be (-1)/((-2)/24) + 2. Let m be (-2)/(1 - (v - 3)). Let 0*u**2 + 0 + m*u**3 + 0*u + 2/5*u**4 + 1/5*u**5 = 0. What is u?
-1, 0
Let p = -6 - -7. Let s(k) = -k**3 + k**2 - k + 1. Let b(c) = 2*c**2 - 4*c + 2. Let j(u) = p*b(u) - 2*s(u). Factor j(l).
2*l*(l - 1)*(l + 1)
Suppose 4*i = -4*v - 0*v + 8, 5*i + 17 = 4*v. Factor 10*g**v + 2 - 3*g - 3*g**5 - 4*g**3 - 2.
-3*g*(g - 1)**2*(g + 1)**2
Factor 0 - 13/5*n**4 + 11/5*n**3 + 2/5*n**2 + 0*n.
-n**2*(n - 1)*(13*n + 2)/5
Let v(f) be the first derivative of 3*f**6/20 - f**5/10 - 2*f**4/3 + 4*f**3/3 + 2*f**2 - 3. Let x(y) be the second derivative of v(y). Solve x(h) = 0.
-1, 2/3
Let d = -16 - -146/9. Suppose -2/9*b**5 - d*b**4 + 2/9*b**3 + 0*b + 0 + 2/9*b**2 = 0. Calculate b.
-1, 0, 1
Let z(s) = -s**3 + 15*s**2 - 13*s - 16. Let y be z(14). Let o(q) = q**3 + 2*q**2 - q. Let h be o(y). What is b in 3/2*b**3 - 3/4*b**4 - 3*b + 9/4*b**h - 3 = 0?
-1, 2
Factor 4/5*j - 4/5*j**3 + 4/5*j**2 - 4/5.
-4*(j - 1)**2*(j + 1)/5
Let q(d) be the first derivative of 1/105*d**7 + 0*d + 0*d**6 + 0*d**4 + 2 + 0*d**5 + 0*d**3 - 1/2*d**2. Let a(j) be the second derivative of q(j). Factor a(i).
2*i**4
Let b(i) = -6*i**3 - i**2 + 1. Let o be b(-1). Let l(u) be the first derivative of 0*u - 1 - 6/5*u**5 - 8/3*u**3 + 0*u**2 + 3*u**4 + 1/6*u**o. Factor l(c).
c**2*(c - 2)**3
Let u(y) be the third derivative of -y**5/80 + 5*y**4/16 - 25*y**3/8 + 13*y**2. Solve u(l) = 0 for l.
5
Let s(u) be the third derivative of 0 + 1/36*u**3 + 3*u**2 - 1/360*u**6 + 0*u - 1/36*u**4 + 1/72*u**5. Suppose s(x) = 0. What is x?
1/2, 1
Let l(v) be the second derivative of -v**5/140 + v**3/42 + 19*v. Solve l(z) = 0 for z.
-1, 0, 1
Suppose -5*d = -4*y - d - 4, d = 5*y - 11. Solve -8*v**2 - 6*v + 5*v**5 + 4*v**4 - y*v**5 + 0*v**5 + 8*v - 4*v**3 + 4 = 0.
-2, -1, 1
Suppose -4 = -q - i - 3, 2*i = 0. Suppose 2*j - q = -4*o + 3, -2*j + 6 = 5*o. Factor -4*p**3 - 3*p**5 - 2*p**5 + o*p + 4*p**5 + 3*p**5.
2*p*(p - 1)**2*(p + 1)**2
Let h be (-38)/171 - (-2)/9. Let k(u) be the third derivative of 0*u + 1/30*u**5 + 1/60*u**6 - 1/6*u**4 + h*u**3 + u**2 + 0. Solve k(b) = 0.
-2, 0, 1
Suppose -2*j = l + l - 26, 2 = 2*j. Determine c, given that l*c**4 + 314*c**3 - 2*c + 2*c - 299*c**3 + 3*c**2 = 0.
-1, -1/4, 0
Let d = -202 + 3637/18. Let v(c) be the first derivative of 1/6*c**2 + 0*c**5 + 2 - 1/6*c**4 + 0*c**3 + d*c**6 + 0*c. Let v(b) = 0. What is b?
-1, 0, 1
Let d be (-9)/(-504)*108 + 6/(-4). Factor -d*q**2 + 15/7*q - 12/7.
-3*(q - 4)*(q - 1)/7
Let c(o) = -144*o**5 - 60*o**4 + 72*o**3 - 9*o**2 + 3*o + 3. Let j(g) = -g**5 - g**4 - g**2 - g - 1. Let t(s) = c(s) + 3*j(s). Factor t(q).
-3*q**2*(q + 1)*(7*q - 2)**2
Let c(x) be the second derivative of -1/9*x**2 + 0 + 4*x + 1/27*x**3 - 1/90*x**5 + 1/54*x**4. Let c(y) = 0. Calculate y.
-1, 1
Let -3*u**3 - 3*u**2 + u**2 + 11*u**2 = 0. What is u?
0, 3
Factor -2*q**2 - 10 - 7*q**2 + 25*q - 6*q**2.
-5*(q - 1)*(3*q - 2)
Let y = -26 + 28. Find f, given that 2/3*f + 4/3*f**y + 2/3*f**3 + 0 = 0.
-1, 0
Let r = -366 + 368. Determine j, given that 2/3 - 3*j**3 + 0*j - 17/6*j**r - 5/6*j**4 = 0.
-2, -1, 2/5
Let z(b) be the third derivative of 0 + 2*b**2 + 3/20*b**5 + 1/40*b**6 + 0*b**3 + 0*b + 0*b**4. What is q in z(q) = 0?
-3, 0
Suppose 2*t - 4*o + 14 = 0, 0*t - 4*t - 50 = 3*o. Let h be (t + 11)/(0 - -1). Factor 1/3*p**2 + 0 + h*p**3 + 0*p - 1/3*p**4.
-p**2*(p - 1)*(p + 1)/3
Let x = -27 - -31. Let o(g) be the third derivative of 0 + 0*g + 0*g**x + g**2 - 1/3*g**3 + 1/30*g**5. Solve o(h) = 0 for h.
-1, 1
Solve -10/13 + 12/13*s - 2/13*s**2 = 0.
1, 5
Suppose 3/2*r**5 + 9/2*r**4 + 0*r + 0*r**2 + 0 + 3*r**3 = 0. Calculate r.
-2, -1, 0
Factor -2/5 - 9/10*c**3 - 21/10*c**2 - 8/5*c.
-(c + 1)*(3*c + 2)**2/10
Let k(p) = -p**4 - p**3 + p**2 - p. Suppose -6*n = -n + 30. Let x(d) = -3*d**4 - 3*d**3 - 3*d**2 - 21*d - 6. Let a(m) = n*k(m) + x(m). Factor a(q).
3*(q - 2)*(q + 1)**3
Let g(p) = -54*p**5 + 51*p**4 + 52*p**3 - 55*p**2 - 7*p - 5. Let x(b) = -b**4 + b**2 - b - 1. Let k(z) = -2*g(z) + 18*x(z). Solve k(w) = 0.
-1, -2/9, 1/3, 1
Let m(v) be the first derivative of -v**7/35 - v**6/15 - v**5/50 + v**4/30 + v + 7. Let n(q) be the first derivative of m(q). Factor n(d).
-2*d**2*(d + 1)**2*(3*d - 1)/5
Let y(l) be the first derivative of l**6/720 - l**5/240 + 8*l**3/3 - 7. Let s(p) be the third derivative of y(p). Factor s(x).
x*(x - 1)/2
Let l(h) be the third derivative of h**8/448 - h**7/56 + h**6/80 + 7*h**5/40 - 3*h**4/32 - 9*h**3/8 + 15*h**2. Suppose l(s) = 0. Calculate s.
-1, 1, 3
Let v(o) be the third derivative of 10*o**7/21 - 17*o**6/3 + 349*o**5/15 - 34*o**4 + 24*o**3 + 12*o**2. Factor v(g).
4*(g - 3)**2*(5*g - 2)**2
Let b(t) = t**2 + t + 2. Let f be b(0). Factor f*m**2 + 5*m - 2 - 5*m.
2*(m - 1)*(m + 1)
Let u = 19463 - 95441/5. Let w = 376 - u. Solve 4/5*s**5 - 2/5*s**2 + 2/5*s - w*s**3 + 0 + 2/5*s**4 = 0.
-1, 0, 1/2, 1
Let s(n) be the second derivative of -n**7/98 - n**6/70 + 3*n**5/140 + n**4/28 + 8*n. Factor s(u).
-3*u**2*(u - 1)*(u + 1)**2/7
Let l(n) be the second derivative of n**6/70 - n**4/28 + 8*n. Determine k, given that l(k) = 0.
-1, 0, 1
Let k(x) be the third derivative of -x**6/480 + x**5/48 - x**4/32 - 3*x**3/8 - 31*x**2. Determine m so that k(m) = 0.
-1, 3
Let s(r) = -r**2 - r + 3. Suppose 0 = -2*u + 6*u. Let v be s(u). Factor 1/4*a**v + 1/2*a**2 + 1/4*a + 0.
a*(a + 1)**2/4
Let j(z) = -6*z**3 - 13*z**2 - 17*z - 1. Let d(m) = -18*m**3 - 40*m**2 - 50*m - 4. Let n(u) = 3*d(u) - 8*j(u). Factor n(h).
-2*(h + 1)**2*(3*h + 2)
Factor -17*p**2 + 10*p**4 - 9*p**4 + 12*p**3 - 5*p**4 + 4*p + 5*p**2.
-4*p*(p - 1)**3
Suppose -3*o = -5*o + 4. Factor o + 44*r + 2 + 196*r**3 + 76*r**2 + 85*r**2.
(4*r + 1)*(7*r + 2)**2
Factor 6*x**3 - 10*x**5 - 13*x**5 + 20*x**5 - 3*x.
-3*x*(x - 1)**2*(x + 1)**2
Let s(k) = -31*k**2 - k. Let w be s(1). Let g = w - -133/4. Find t such that 5/2*t**3 + 5/4*t - 1/4 + 1/4*t**5 - 5/2*t**2 - g*t**4 = 0.
1
Let d(a) be the third derivative of -a**8/560 + a**7/280 - 2*a**3/3 - 2*a**2. Let s(h) be the first derivative of d(h). Find n, given that s(n) = 0.
0, 1
Suppose -5*h + 4*i - 10 = -i, 4 = -h + 2*i. Factor -2/7*s**3 + h + 0*s**2 + 2/7*s.
-2*s*(s - 1)*(s + 1)/7
Let h be 1/45*(-21)/(-28). Let i(c) be the third deri