+ y**5/3 - 2*y**4/3 + y**3/9 + 23. Factor k(c).
c**2*(2*c + 1)*(5*c - 1)**2/3
Let g(x) be the first derivative of -2*x**3/39 + 2*x/13 - 16. Factor g(z).
-2*(z - 1)*(z + 1)/13
Let l be 0/(-4 - -6 - 5). Factor l + 1/3*n**2 - 1/3*n.
n*(n - 1)/3
Let i(s) be the first derivative of -4*s**3/9 - s**2 + 4*s/3 + 1. Determine v, given that i(v) = 0.
-2, 1/2
Suppose 7 = 4*q - 9. Let g be (-24)/(-36)*2/q. Factor -g*x**3 - 2/3 + 0*x**2 + x.
-(x - 1)**2*(x + 2)/3
Let d(s) be the first derivative of 15/14*s**4 + 15/7*s**5 - 2 + 0*s**2 + 0*s + 1/7*s**3. Determine f so that d(f) = 0.
-1/5, 0
Let x(q) be the third derivative of -q**7/525 - q**6/100 - q**5/150 + q**4/20 + 2*q**3/15 - 24*q**2. Solve x(w) = 0.
-2, -1, 1
Let o be 0 + 1 - 9/45. Factor 2/5*j**2 - o*j + 0.
2*j*(j - 2)/5
Let o(d) be the first derivative of -2*d**5/5 + 5*d**4/2 - 16*d**3/3 + 4*d**2 + 6. Factor o(m).
-2*m*(m - 2)**2*(m - 1)
Suppose -s + 4*v - 10 = s, -v - 8 = s. Let h(y) = -y**3 - 7*y**2 - y - 5. Let k be h(s). Factor -3*z + 3*z**2 - 3*z**k + z - 2*z**2.
-2*z*(z + 1)
Let r(h) = h**3 + 3*h**2 + 2*h - 2. Let c(x) = 3*x**3 + 7*x**2 + 5*x - 5. Let z = -16 - -12. Let f(w) = z*c(w) + 10*r(w). Factor f(j).
-2*j**2*(j - 1)
Let w(l) be the second derivative of l**7/252 - l**6/36 + 3*l**5/40 - 7*l**4/72 + l**3/18 - 2*l. What is s in w(s) = 0?
0, 1, 2
Let v be (-125)/(-10) - 3/2. Let j = -7 + v. Factor 7 + 1 + w**2 - 4 - j*w.
(w - 2)**2
Suppose 2*z - 5*w - 7 = -4*w, 0 = -3*z + 5*w + 21. Suppose -6*k**4 + 2*k**z - 4*k + 4*k + 4*k**4 = 0. What is k?
-1, 0, 1
Let x(q) be the first derivative of 3/25*q**5 + 4/15*q**3 - 1/2*q**4 + 4/5*q**2 + 0*q + 3. Suppose x(y) = 0. Calculate y.
-2/3, 0, 2
Suppose -1 = l - 2*z + z, -l + 5*z - 5 = 0. Suppose l*t**2 - 1/2*t**3 - t**4 - 1/2*t**5 + 0*t + 0 = 0. What is t?
-1, 0
Factor -8/11*m**4 - 8/11 - 25/11*m**3 - 1/11*m**5 - 28/11*m - 38/11*m**2.
-(m + 1)**2*(m + 2)**3/11
Let a = 29125 + -1223191/42. Let k = a - -2/21. Determine b, given that -k*b**2 - b + 1/2 = 0.
-1, 1/3
Suppose -4*u - u - 26 = -3*z, -z + 6 = -u. Solve -l + 50 - l**z - 50 = 0.
-1, 0
Let j = 117/8 - 3509/240. Let s(v) be the third derivative of 1/120*v**5 + 0*v + j*v**6 + v**2 + 0 - 1/48*v**4 - 1/12*v**3. Factor s(a).
(a - 1)*(a + 1)**2/2
Let d(v) be the first derivative of -v**5/10 + v**3/3 + 3*v + 3. Let n(t) be the first derivative of d(t). Factor n(c).
-2*c*(c - 1)*(c + 1)
Let t be (5/25 + 0)*1003. Let h = t + -200. Factor -h - 3/5*m**3 + 3/5*m + 3/5*m**2.
-3*(m - 1)**2*(m + 1)/5
Let a(x) be the first derivative of x**3/15 + 3*x**2/5 + 9*x/5 + 3. Determine r, given that a(r) = 0.
-3
Suppose -63 - 1 = -16*f. Factor 0 + 1/4*r**2 - 1/4*r**f - 1/4*r**3 + 1/4*r.
-r*(r - 1)*(r + 1)**2/4
Suppose 4*k**2 + 2*k + 4*k**3 + 2/5 + 2*k**4 + 2/5*k**5 = 0. What is k?
-1
Suppose 27/2*x + 6 + 9*x**2 + 3/2*x**3 = 0. What is x?
-4, -1
Let s(k) = 9*k**2 - k + 4. Let i(q) = 18*q**2 - 3*q + 7. Let m(g) = 6*i(g) - 11*s(g). Factor m(t).
(t - 1)*(9*t + 2)
Let t = 295 - 291. Suppose 6/7*c**t + 0*c**2 + 0 + 4/7*c**3 + 0*c = 0. What is c?
-2/3, 0
Let w(z) be the first derivative of -z**9/4536 - z**8/2520 + z**7/1260 + z**6/540 + z**3 + 2. Let a(t) be the third derivative of w(t). Let a(l) = 0. What is l?
-1, 0, 1
Solve 4/13 + 2/13*s**3 - 4/13*s**2 - 2/13*s = 0 for s.
-1, 1, 2
Suppose 3*j + j + m = 19, 9 = 3*m. Let f(q) be the second derivative of -q + 0*q**2 + 0*q**3 + 0 + 0*q**5 + 1/60*q**6 - 1/24*q**j. Let f(c) = 0. Calculate c.
-1, 0, 1
Let c = -5 + 12. Let 44*f**3 - c*f**4 - 18*f**2 - 32*f**3 + 2*f**4 + 3*f**4 = 0. Calculate f.
0, 3
Let n(c) = -3*c**2 + 6*c + 105. Let z be n(-5). Factor -2/5*s**2 + z + 2/5*s.
-2*s*(s - 1)/5
Let x be (-12)/(-15)*(-1 - 14/(-4)). Solve 2/7*o**x + 2/7 - 4/7*o = 0.
1
Let f be 6/(-3 - -6) - 3. Let l = 3 - f. Let -2*x**l + 0*x**2 + 2*x**2 - x + 3*x - 2*x**3 = 0. Calculate x.
-1, 0, 1
Let r(p) = p. Let z(a) = a**3 + 9*a**2 - 9*a + 8. Let l be z(-10). Let m(d) = -12*d + 0*d + 3*d + d**2. Let v(t) = l*m(t) - 18*r(t). Factor v(u).
-2*u**2
Let n(d) = d + 4. Let f be n(5). Factor 0*q**3 - 2*q**3 + 4*q**4 + f*q**5 - 11*q**5.
-2*q**3*(q - 1)**2
Let g(l) = 6*l**4 - 22*l**3 - 16*l**2 + 22*l + 10. Let b(z) = 2*z**4 - 7*z**3 - 5*z**2 + 7*z + 3. Let s(q) = -10*b(q) + 3*g(q). Factor s(k).
-2*k*(k - 2)*(k - 1)*(k + 1)
Let t(k) be the first derivative of k**4/20 - k**3/5 + k**2/5 - 18. Factor t(c).
c*(c - 2)*(c - 1)/5
Let a(t) be the third derivative of -1/12*t**3 + 0*t - 1/240*t**6 + 1/48*t**4 + 1/120*t**5 - t**2 + 0. Find m, given that a(m) = 0.
-1, 1
Suppose -30 = -4*h + 6. Let g(a) = a**2 + 2. Let x(y) be the third derivative of y**5/12 + 3*y**3/2 + y**2. Let d(b) = h*g(b) - 2*x(b). Solve d(t) = 0 for t.
0
Let a(j) = -j**2 + j. Let r(p) = 4*p**2 - 7*p. Let m = -8 - -5. Let z be m - (-1*2 - 0). Let u(g) = z*r(g) - 5*a(g). Factor u(h).
h*(h + 2)
Factor -j**4 - 3*j**3 + 2 - j**2 - 2 + 3*j + 2.
-(j - 1)*(j + 1)**2*(j + 2)
Suppose -3*u + 0 = 4*x - 3, -3*u = -3. Suppose x + 15 = 5*q. Let 10*b**2 + 6*b**q + 3*b + 3*b**3 + 3*b**4 + 0*b - b**2 = 0. What is b?
-1, 0
Factor 6/13 - 2/13*u**2 - 4/13*u.
-2*(u - 1)*(u + 3)/13
Let a(j) be the first derivative of j**4/2 - 6*j**3/5 + 3*j**2/5 + 2*j/5 + 5. Factor a(c).
2*(c - 1)**2*(5*c + 1)/5
Let r(h) be the third derivative of -h**9/13608 + h**8/2520 - h**7/1260 + h**6/1620 + h**3/3 + 3*h**2. Let s(z) be the first derivative of r(z). Factor s(t).
-2*t**2*(t - 1)**3/9
Let f(h) be the first derivative of 0*h**3 - 1 + 0*h**2 + 0*h**4 - 1/70*h**5 + 2*h. Let p(u) be the first derivative of f(u). Factor p(t).
-2*t**3/7
Let n(q) be the second derivative of 0 + 2/105*q**7 - 13/150*q**6 - 7/60*q**4 + q + 1/30*q**3 + 0*q**2 + 3/20*q**5. Let n(l) = 0. Calculate l.
0, 1/4, 1
Let p be -3*(-14)/18 + -1. Factor -4/3 - p*t - 1/3*t**2.
-(t + 2)**2/3
Let c be -2 + (0 - 1) + 4 + 1. Factor 0*w**3 + 0*w + 0*w**c + 2/5*w**4 + 0 - 2/5*w**5.
-2*w**4*(w - 1)/5
Suppose -3*t - 4 = -i + 4, t - 8 = 3*i. Let c(y) = 2*y + 28*y - 11 - 21*y**2 - 5*y. Let h(g) = 11*g**2 - 13*g + 6. Let r(z) = t*c(z) - 7*h(z). Factor r(m).
(m - 1)*(7*m - 2)
Let a(w) be the third derivative of -5*w**8/336 - w**7/21 + w**5/6 + 5*w**4/24 - 7*w**2. Suppose a(y) = 0. Calculate y.
-1, 0, 1
Let r(j) = 2*j**5 - 2*j**4 - 2*j**3 - 4*j**2 - 3*j - 3. Let q(t) = t**5 - t**4 - t**3 - t**2 - t - 1. Let v = -1 - 0. Let s(g) = v*r(g) + 3*q(g). Factor s(i).
i**2*(i - 1)**2*(i + 1)
Let m(b) be the first derivative of 9*b**4/2 + 23*b**3 + 21*b**2 - 9*b + 38. Factor m(c).
3*(c + 1)*(c + 3)*(6*c - 1)
Factor 0*c + 1/4 - 1/4*c**2.
-(c - 1)*(c + 1)/4
Let v(o) = o**5 + 8*o**4 + 3*o**3 - 8*o**2 - 7*o + 3. Let g(z) = 8*z**4 + 4*z**3 - 8*z**2 - 8*z + 4. Let m(j) = 3*g(j) - 4*v(j). Factor m(u).
-4*u*(u - 1)*(u + 1)**3
Let n be 2/(-8)*0 + 3. Solve 3*a + 10*a**5 + a**2 + a + 5*a**2 - 14*a**n - 6*a**4 = 0.
-1, -2/5, 0, 1
Let p(g) be the first derivative of -g**5/5 - g**4/6 + g**3/3 + g**2/3 - 45. Determine n so that p(n) = 0.
-1, -2/3, 0, 1
Let c = 11 - 7. Let s(x) be the first derivative of 6*x**2 + 18/5*x**5 - 3*x**c - 2*x - 16/3*x**3 - 2. What is t in s(t) = 0?
-1, 1/3, 1
Let r(q) be the first derivative of 1/12*q**3 + 1/24*q**4 - 2 - 1/40*q**5 - 2*q - 1/4*q**2. Let k(a) be the first derivative of r(a). Factor k(v).
-(v - 1)**2*(v + 1)/2
Let o be (-2 + 0 - 2) + 2. Let j be o/(-6) + (-56)/(-21). Factor p**3 + p**j - 1 + 4*p**2 + 2*p + 1.
2*p*(p + 1)**2
Suppose -r = d - 4*r - 18, 0 = 2*d - 5*r - 34. Suppose -n = -4*n + d. Suppose t**4 + 0*t**n + t**2 - t**3 + t - 2*t**2 = 0. What is t?
-1, 0, 1
Let t(f) = 5*f**2 + 7*f + 6. Let i(d) = 11*d**2 + 14*d + 13. Let k(s) = 4*i(s) - 9*t(s). Let y be k(-6). Factor 8 - 2*b**2 - 8 - y*b.
-2*b*(b + 2)
Let v(d) be the first derivative of -d**7/280 + d**5/40 + d**3/3 - 4. Let p(b) be the third derivative of v(b). Factor p(x).
-3*x*(x - 1)*(x + 1)
Let -3/2*t**3 + 0 + 3*t**2 + 0*t = 0. Calculate t.
0, 2
Suppose -p - p = 4*v - 790, 5*v - 987 = -2*p. Let d = 1383/7 - v. Factor -d*t**2 + 2/7*t**4 - 4/7*t**3 + 2/7*t + 2/7*t**5 + 2/7.
2*(t - 1)**2*(t + 1)**3/7
Let u(n) be the second derivative of -n**8/23520 + n**7/4410 - n**6/2520 - n**4/12 + 3*n. Let i(w) be the third derivative of u(w). Find h, given that i(h) = 0.
0, 1
Let u = -30 - -91/3. Let r be (-108)/(-162) + 0/2. Let 14/3*d**3 + 3*d - r - 2*d**4 - 16/3*d**2 + u*