erivative of k**6/120 - k**5/15 - 11*k**4/24 - k**3 + 11*k**2. Factor q(s).
(s - 6)*(s + 1)**2
Suppose -6*u + 93 = -3*u. Let g = 97/3 - u. Factor -g*y + 4/3 + 1/3*y**2.
(y - 2)**2/3
Solve -v - 22*v + 4*v**2 + v**2 + 8*v = 0 for v.
0, 3
Suppose 6/17*o**2 - 16/17*o**3 + 0 + 0*o = 0. What is o?
0, 3/8
Let y(s) be the first derivative of -1 + 3/2*s**2 - 3*s - 1/4*s**3. Factor y(w).
-3*(w - 2)**2/4
Let n(f) = 11 - 11 + f**2 + f. Let r be n(0). Factor -1/3*s + 1/3*s**2 + r.
s*(s - 1)/3
Let n(q) be the first derivative of 9*q**4/2 - 10*q**3 + 7*q**2 - 2*q - 15. Solve n(l) = 0.
1/3, 1
Let z(y) = -y**2 - 3. Let s(v) = 1. Let u(m) = 20*s(m) + 5*z(m). Factor u(h).
-5*(h - 1)*(h + 1)
Let u(v) be the third derivative of -v**7/210 + v**5/10 - v**4/3 + v**3/6 - 10*v**2. Let h(x) be the first derivative of u(x). Factor h(a).
-4*(a - 1)**2*(a + 2)
Factor 0 + 4/7*g**3 + 2/7*g**4 + 0*g + 0*g**2.
2*g**3*(g + 2)/7
Let j(a) be the first derivative of 3*a**5/5 - 15*a**4/4 + 7*a**3 - 9*a**2/2 + 17. What is c in j(c) = 0?
0, 1, 3
Let i be -5*(3 - 12/3). Let t(j) = 2*j**2 - 4*j + 2. Let o(u) = -u**2 + 2*u - 1. Let f(m) = i*o(m) + 2*t(m). Factor f(n).
-(n - 1)**2
Let g(u) be the first derivative of -3*u**5/10 + 3*u**4/4 + 3*u**3/2 - 3*u**2 - 7*u + 7. Let o(m) be the first derivative of g(m). Determine h so that o(h) = 0.
-1, 1/2, 2
Suppose 3*b - 5*k = 32 - 9, 0 = -5*b + 2*k + 32. Suppose 0 = b*j - 2*j - 8. Suppose j*n + 2*n**3 - n**2 - 2*n**4 + 3*n**2 - 4*n = 0. Calculate n.
-1, 0, 1
Let d(x) be the third derivative of x**8/336 - x**7/70 - x**6/60 + x**5/10 + x**4/24 - x**3/2 - 17*x**2. Factor d(p).
(p - 3)*(p - 1)**2*(p + 1)**2
Let q(w) be the first derivative of 0*w - 3/8*w**2 + 0*w**3 + 2 + 3/16*w**4. Factor q(y).
3*y*(y - 1)*(y + 1)/4
Let g(w) be the first derivative of -2*w**3/3 + 2*w**2 - 3. Factor g(d).
-2*d*(d - 2)
Determine t, given that -2*t**3 + 4/3*t**2 + 0 - 1/3*t + 4/3*t**4 - 1/3*t**5 = 0.
0, 1
Suppose 0*l + 4*l - 1 = -5*k, -19 = -4*l + k. Let b(j) be the first derivative of -1/2*j**l + 0*j**2 + 0*j + 2/3*j**3 + 3. Let b(n) = 0. What is n?
0, 1
Let q be (2 - -10)*3/2. Suppose -4*k - 20 = -9*k. Factor x**k + 11*x**2 + 41*x**4 - q*x**5 - 3*x**2 - 32*x**3.
-2*x**2*(x - 1)*(3*x - 2)**2
Let s(m) be the first derivative of 2*m**6/9 + 4*m**5/5 - 4*m**4/3 + 20. Factor s(c).
4*c**3*(c - 1)*(c + 4)/3
Suppose -4*h + 33 = 17. Let f(s) be the third derivative of 0*s**h + 0*s - 1/180*s**6 + 1/90*s**5 + 0*s**3 - 2*s**2 + 0. Find v, given that f(v) = 0.
0, 1
Suppose 2/5*y + 3/5*y**4 + 14/5*y**3 - 3/5 + 16/5*y**2 = 0. Calculate y.
-3, -1, 1/3
Let d(z) = -3*z - 6. Let h(u) = -u**2 - u + 1. Let v = -16 + 13. Let q(r) = v*h(r) - d(r). Factor q(c).
3*(c + 1)**2
Let t(f) be the first derivative of 6 - 2/7*f**3 + 0*f - 5/14*f**4 + 2/7*f**2. What is g in t(g) = 0?
-1, 0, 2/5
Let o(z) = -11*z**4 - 8*z**3 - z**2 - 21*z + 2. Let k(m) = 5*m**4 + 4*m**3 + 10*m - 1. Suppose q = 2*q - 13. Let d(i) = q*k(i) + 6*o(i). Factor d(t).
-(t - 1)**4
Let i(l) = 2*l**2 - 34*l + 62. Let h(k) = -k**2 - k - 1. Let s(o) = 2*h(o) - i(o). Factor s(a).
-4*(a - 4)**2
Let a be 1/3*(-1 - -4). Suppose -13 = -6*b - a. Factor 2*n**4 + 0*n + 8/3*n**5 + 0 - 2/3*n**3 + 0*n**b.
2*n**3*(n + 1)*(4*n - 1)/3
Let k(l) be the second derivative of l**5/10 + 7*l**4/6 + 5*l**3 + 9*l**2 + 3*l. Find w, given that k(w) = 0.
-3, -1
Let p(r) = -11*r**3 - 10*r**2 + 11*r + 16. Let m(x) = 155*x**3 + 140*x**2 - 155*x - 225. Let s(b) = 6*m(b) + 85*p(b). Factor s(y).
-5*(y - 1)*(y + 1)*(y + 2)
Let i(b) be the second derivative of b**6/1080 + b**5/360 + b**3/3 + 3*b. Let f(s) be the second derivative of i(s). Suppose f(u) = 0. Calculate u.
-1, 0
Suppose -2*o + 15 = 3*o. Let f be 3/(o - -3)*1. Determine g, given that 1 - 1/2*g**2 + f*g = 0.
-1, 2
Factor a - a**5 + 3*a**2 - 5*a**2 + 0*a**5 + 2*a**4 + 0*a**2.
-a*(a - 1)**3*(a + 1)
Let w(j) = -13*j**2 + 45*j - 27. Let y(m) = 72*m**2 - 248*m + 148. Let a(k) = -28*w(k) - 5*y(k). Determine c, given that a(c) = 0.
1, 4
Let c(y) be the third derivative of -1/3*y**3 - 1/8*y**4 - 1/60*y**5 - 3*y**2 + 0*y + 0. Determine n, given that c(n) = 0.
-2, -1
Solve 8/11 + 8/11*r + 2/11*r**2 = 0 for r.
-2
Let x(w) be the second derivative of -w**5/5 + w**4 - 2*w**3 + 2*w**2 + 6*w. Solve x(g) = 0 for g.
1
Let b be (-2)/(-2) + (4 - 5). Factor -a - 1 + a + b*a + a**2.
(a - 1)*(a + 1)
Let c(b) be the first derivative of -2*b**2 + 8/3*b + 1/2*b**3 - 4. Factor c(z).
(3*z - 4)**2/6
Factor -44/7*w**3 - 5324/7*w + 1/7*w**4 + 726/7*w**2 + 14641/7.
(w - 11)**4/7
Let c(o) be the first derivative of -5*o**6/6 - o**5 + 5*o**4/2 + 1. Factor c(u).
-5*u**3*(u - 1)*(u + 2)
Let s be (((1 + -1)/1)/(-3))/1. Factor -3/5*c**5 + 0 + 6/5*c**3 - 3/5*c + 0*c**4 + s*c**2.
-3*c*(c - 1)**2*(c + 1)**2/5
Let p(m) be the third derivative of -m**6/80 - m**5/18 - 13*m**4/144 - m**3/18 + 28*m**2. Solve p(h) = 0.
-1, -2/9
Let t(k) = 6*k**3 + 30*k**2 + 13*k - 49. Let i(j) = -3*j**3 - 15*j**2 - 6*j + 24. Let a(p) = -5*i(p) - 3*t(p). Find c, given that a(c) = 0.
-3, 1
Let w**2 + 1/3*w**4 + w**3 + 0 + 1/3*w = 0. What is w?
-1, 0
Let t(g) = 2*g - 34. Let o be t(18). Let n(a) be the third derivative of 0*a**3 + 1/60*a**4 + 1/150*a**5 + 0 - 2*a**o + 0*a. Factor n(d).
2*d*(d + 1)/5
Let p(q) be the first derivative of 5*q**3/3 - 5*q**2/2 - 10*q + 13. Let p(k) = 0. Calculate k.
-1, 2
Suppose 6*g = -12*g. Find v such that -v + g*v**3 - 3/2*v**2 + 1/2*v**4 + 0 = 0.
-1, 0, 2
Let o(c) be the first derivative of 3*c**4/4 + 5*c**3 + 6*c**2 + 6. Factor o(d).
3*d*(d + 1)*(d + 4)
Let d(f) be the third derivative of -3*f**2 + 0 - 25/24*f**6 + 0*f - 5/2*f**4 - 5/2*f**5 - 4/3*f**3. Factor d(v).
-(5*v + 2)**3
Let k(m) be the first derivative of 0*m**4 + 4/15*m**5 + 1/3*m**2 - 4 - 4/9*m**3 + 0*m - 1/9*m**6. Factor k(s).
-2*s*(s - 1)**3*(s + 1)/3
Let b be 0 - (-1 + (5 - 6)). Factor 1/2 + 1/2*a**b + a.
(a + 1)**2/2
Let h(m) be the third derivative of m**5/60 - m**4/24 - m**3/3 - 5*m**2. Determine w, given that h(w) = 0.
-1, 2
Let l(g) = -g**4 - g**3 - g**2 + 1. Let t(x) = -12*x**4 + 28*x**3 - 51*x**2 + 12*x + 13. Let f(y) = 5*l(y) - t(y). Suppose f(h) = 0. Calculate h.
-2/7, 1, 2
Let p(j) = 5*j**4 + 5*j**3 - 4*j**2 - 3*j + 3. Let g(k) = k**4 + k**3 - k + 1. Suppose 0*v - 12 = 4*v. Let w(q) = v*g(q) + p(q). Factor w(z).
2*z**2*(z - 1)*(z + 2)
Determine c, given that -4/3*c**2 + 1/3*c**5 + 1/3*c + 2/3*c**4 + 2/3 - 2/3*c**3 = 0.
-2, -1, 1
Let r = -3/26 - -113/78. Determine y, given that 2*y**2 - 7/3*y**3 + 7/3*y - r*y**4 - 2/3 = 0.
-2, -1, 1/4, 1
Let q(b) = 2*b**2 - 10*b**2 + 3*b**2 - 14 - 10*b. Let g(o) = -36*o**2 - 69*o - 99. Let m(f) = 2*g(f) - 15*q(f). Factor m(d).
3*(d + 2)**2
Let x(v) be the second derivative of v**6/30 - 7*v**5/30 + 23*v**4/36 - 8*v**3/9 + 2*v**2/3 - 3*v. Suppose x(b) = 0. What is b?
2/3, 1, 2
Let h be (-20)/(-6) - (-4)/(-12). Suppose y = w + h*w - 6, -2*w = 5*y - 14. Factor -1/2*d - 1/2*d**y + 0.
-d*(d + 1)/2
Let g(b) be the second derivative of b**4/12 + b**3/3 - 9*b. Factor g(h).
h*(h + 2)
Solve -9/4*b + 7/4*b**2 + 1/2 = 0.
2/7, 1
Let n(v) be the second derivative of 1/6*v**4 + v - 1/10*v**6 - 1/10*v**5 + 1/2*v**3 - 1/42*v**7 + 0 + 1/2*v**2. Factor n(c).
-(c - 1)*(c + 1)**4
Let y = -1431/7 - -205. Factor 0 + y*a - 6/7*a**2.
-2*a*(3*a - 2)/7
Let g be 6*(-6)/9 - -2. Let v = 1 - g. Factor -5*b**3 + 4*b**v + b**2 + 0 + 0.
-b**2*(b - 1)
Let o(h) be the third derivative of -h**11/1496880 - h**10/340200 - h**9/272160 + h**5/15 - 3*h**2. Let g(b) be the third derivative of o(b). Factor g(y).
-2*y**3*(y + 1)**2/9
Suppose 21 = -8*r + 15*r. Let -t**2 + 0 - 5/2*t**r + 0*t = 0. What is t?
-2/5, 0
Suppose z**3 - 3*z + 4*z + z**2 - 2*z - 1 = 0. What is z?
-1, 1
Let h(l) be the first derivative of -l**4/36 + 5*l - 5. Let t(s) be the first derivative of h(s). Factor t(j).
-j**2/3
Suppose 0 = -3*x + 6*x - 33. Suppose 2*q - x = 5*f + 18, 3*f = 3*q - 21. Factor 1/4*k**q + 1/2 + 3/4*k.
(k + 1)*(k + 2)/4
Let k = -4 + 17. Find o, given that -4*o**4 + k*o**4 + o**4 + 6*o + 11*o**4 - 36*o**3 + 9*o**2 = 0.
-2/7, 0, 1
Let v(q) = q + 6. Let n be v(-9). Let f be (-2)/1 + (1 - n). Solve -6*h**3 + 6*h**f + 0*h**4 - 2*h - 4*h**4 + 6*h**4 = 0 for h.
0, 1
Let k(r) be the first derivative of 2/27*r**3 + 0*r - 2 + 0*r**2. Suppose k(c) = 0. Calculate c.
0
Let f = 65/297 - 1/2