12/5 - 21/5*n**2.
-3*(n + 2)*(7*n - 2)/5
Factor 6/5 + 3*s + 3/5*s**3 + 12/5*s**2.
3*(s + 1)**2*(s + 2)/5
Let a = 18841/120 + -157. Let u(f) be the third derivative of a*f**4 + 1/150*f**5 + 0*f + f**2 + 1/600*f**6 + 0*f**3 + 0. Let u(v) = 0. What is v?
-1, 0
Let z(w) = w + w - 6 - 1 - 4. Let c be z(7). Factor -s - 2/5 - 4/5*s**2 - 1/5*s**c.
-(s + 1)**2*(s + 2)/5
Suppose 11*f = 2*f + 27. Find d such that 1/2*d**4 + 1/2*d**5 + 1/2*d - d**f + 1/2 - d**2 = 0.
-1, 1
Factor -6 + 24*n - 39/2*n**2 + 9/2*n**3.
3*(n - 2)**2*(3*n - 1)/2
Suppose 2*v - 3*h + 7 + 4 = 0, -4*v = -4*h + 12. Factor 1/5*l**5 + 0*l**3 - 1/5*l - 2/5*l**v + 2/5*l**4 + 0.
l*(l - 1)*(l + 1)**3/5
Suppose j - n - 4 = 0, 2*n - 5 + 1 = -j. Determine b so that 0 + j - 4 - 2*b + 3*b**2 = 0.
0, 2/3
Let l = 11 + -9. Factor -2*o**l - 6*o + 2*o**2 - 2*o**2.
-2*o*(o + 3)
Suppose 0 = 3*l - 0*l - 30. Factor -8*h**3 - h**3 + l*h**3.
h**3
Let d(w) be the third derivative of -w**10/50400 + w**9/10080 - w**5/15 - 5*w**2. Let l(m) be the third derivative of d(m). Solve l(c) = 0 for c.
0, 2
Let x(f) be the first derivative of -2/3*f**3 + 2/5*f**5 - 1/6*f**6 + 1/2*f**2 + 0*f**4 + 0*f - 1. Let x(v) = 0. Calculate v.
-1, 0, 1
Let r(y) be the third derivative of y**5/15 - y**4/6 - 10*y**2. Factor r(c).
4*c*(c - 1)
Let j(v) = -v**3 - 6*v**2 + 5*v + 3. Let u be j(-7). Suppose 4*d + 16 = q - 8, -d - u = -3*q. Find r, given that -q*r**3 + 4*r**3 + 8*r**3 - 2*r = 0.
-1/2, 0, 1/2
Let h(k) = 3*k + 6*k - 6*k - 5 - k**2. Let v(z) = -1. Let w(p) = -h(p) + 3*v(p). Suppose w(b) = 0. Calculate b.
1, 2
Suppose -v = 2*v - 30. Let o be (-4)/v - 17/(-5). Let -o - t**2 + 0 + 3 = 0. What is t?
0
Let m(k) be the second derivative of 0 + 2/5*k**2 + 1/15*k**4 + 8*k - 1/3*k**3. Solve m(z) = 0.
1/2, 2
Solve 1/2*o**3 + o**2 - 1/2*o - 1 = 0 for o.
-2, -1, 1
Let u(s) = -5*s**4 - 3*s + 3. Let j(h) = 5*h**4 + 4*h - 4. Let n(w) = 3*j(w) + 4*u(w). Determine o so that n(o) = 0.
0
Let u = -6 - -3. Let g(f) = 2*f**5 + 2*f**4 + 4*f**3 + 2*f. Let k(h) = -2*h**5 - h**4 - 5*h**3 - 3*h. Let i(l) = u*g(l) - 2*k(l). Determine t so that i(t) = 0.
-1, 0
Let y(m) be the second derivative of m**7/189 + m**6/27 + 7*m**5/90 - m**4/54 - 8*m**3/27 - 4*m**2/9 - 7*m. Let y(n) = 0. Calculate n.
-2, -1, 1
Let f(a) be the second derivative of -64*a**7/189 + 112*a**6/135 - 2*a**5/3 + 13*a**4/54 - a**3/27 - 7*a. Factor f(u).
-2*u*(u - 1)*(4*u - 1)**3/9
Let x(h) be the second derivative of -1/3*h**4 + 0*h**2 + 2/3*h**3 + 1/20*h**5 - h + 0. Factor x(f).
f*(f - 2)**2
Let w(s) = -2*s**2 + 5*s + 4. Suppose 50 = v + v. Suppose v + 5 = -5*h. Let y(t) = 5*t**2 - 11*t - 9. Let i(j) = h*y(j) - 14*w(j). Let i(q) = 0. Calculate q.
-1
Let q(a) be the third derivative of -a**6/96 + 7*a**5/240 + a**4/12 - a**3/6 - 2*a**2. Factor q(l).
-(l - 2)*(l + 1)*(5*l - 2)/4
Suppose 8 = 2*i + 2*i. Solve -2*t**5 + 6 - 3*t**i + 3*t**4 - 3*t**3 + 5*t**5 - 6 = 0.
-1, 0, 1
Let y(u) be the second derivative of 1/16*u**4 + 0*u**2 + 0 + 1/40*u**6 + 0*u**3 - 6*u + 3/40*u**5. Factor y(n).
3*n**2*(n + 1)**2/4
Let v(d) be the second derivative of d**4/72 + d**3/18 - d**2/4 - d. Suppose v(l) = 0. Calculate l.
-3, 1
Let s(w) = -w**3 - w**2 + 5. Let r be s(0). Let j(t) be the third derivative of -1/12*t**4 + 0*t**3 + 0*t + 0 - 1/30*t**r - 3*t**2. Solve j(v) = 0 for v.
-1, 0
Let i(v) = -5*v**4 - 6*v**3 - 5*v**2 - 4*v - 4. Let g(s) = 14*s**4 + 24*s**2 + 11 - 10*s**2 - 2*s + 17*s**3 + 13*s. Let j(x) = -4*g(x) - 11*i(x). Factor j(h).
-h**2*(h + 1)**2
Let -8/5*k**2 - 2/5*k**3 - 12/5 + 22/5*k = 0. What is k?
-6, 1
Suppose 9*m = -36 + 54. Factor -6/5*k + 9/5 + 1/5*k**m.
(k - 3)**2/5
Let g(n) be the first derivative of 2*n**3/33 + 5*n**2/11 + 8*n/11 + 5. Find f, given that g(f) = 0.
-4, -1
Let p(f) = -f**2. Let y(u) = 4*u**2 - 6*u - 2. Let t(k) = -5*p(k) - y(k). Let b be t(-6). Let -2*s**4 + s**5 + 3*s**4 - b*s**4 = 0. What is s?
0, 1
Let f be ((-18)/(-8))/((-3)/12). Let m be f/(-6)*(-3)/(-18). Let -3/2*g + m*g**2 + 9/4 = 0. What is g?
3
Let i(j) be the first derivative of -2*j**4/3 + j**2/3 + 10. Solve i(f) = 0.
-1/2, 0, 1/2
Let j be 8/10*(-15)/(-6). Suppose -j*l - 3 = -l - 3*m, -3*l = 2*m - 2. Let -1/4*a + 1/4*a**3 + l + 0*a**2 = 0. Calculate a.
-1, 0, 1
Suppose 8*g - 10 = 3*g. Let d be (g - 1) + (-10)/50. Determine x, given that -14/5*x**2 + d + 2*x = 0.
-2/7, 1
Find k, given that 3/2*k**3 + 6 + 15/2*k**2 + 12*k = 0.
-2, -1
Let g be 30/(-35) - 125/(-105). Determine m, given that -4/3*m - g*m**2 - 4/3 = 0.
-2
Let q(v) = -36*v**2 - 10*v - 8. Let c(x) = 12*x**2 + 3*x + 3. Let p(o) = 17*c(o) + 6*q(o). Factor p(s).
-3*(s + 1)*(4*s - 1)
Let m(p) = -13*p**2 - 13*p - 9. Suppose -2*z = -z - 9. Let f = 5 - z. Let n(h) = -6*h**2 - 6*h - 4. Let w(o) = f*m(o) + 9*n(o). Factor w(g).
-2*g*(g + 1)
Let n(z) = z**2 + 10*z + 27. Let r be n(-6). Solve -159/2*b**2 + 15/2*b**5 + 36*b - 81/2*b**4 - 6 + 165/2*b**r = 0.
2/5, 1, 2
Factor -2*j**3 - 5*j**5 - 2*j**4 - 6*j**4 - 2*j**3 + j**5.
-4*j**3*(j + 1)**2
Let z(l) = 22*l**4 - 30*l**3 - 45*l**2 + 113*l - 60. Let b(g) = -7*g**4 + 10*g**3 + 15*g**2 - 38*g + 20. Let m(n) = -7*b(n) - 2*z(n). Factor m(t).
5*(t - 2)*(t - 1)**2*(t + 2)
Let d = 13 - 4. Let h(y) = -y**2 + 9*y. Let g be h(d). Factor g*s**2 - 2/7*s + 0 + 2/7*s**3.
2*s*(s - 1)*(s + 1)/7
What is t in 0 + 1/3*t**5 + 4/3*t**2 + 1/3*t + 4/3*t**4 + 2*t**3 = 0?
-1, 0
What is t in -3*t**2 - t**3 - 2 + 5*t**2 + 2*t - t**3 = 0?
-1, 1
Let t(c) = -c**2 + 18*c + 186. Let d be t(-6). Determine b, given that 0 - 27*b + d*b**3 - 15/2*b**4 - 99/2*b**2 = 0.
-2/5, 0, 3
Let l(n) be the third derivative of -1/120*n**6 - 1/120*n**5 + 1/24*n**4 + 0*n + 1/280*n**7 + 0 - 1/24*n**3 - 3*n**2. Factor l(c).
(c - 1)**2*(c + 1)*(3*c - 1)/4
Suppose 7/3*u**2 + 1/3*u**4 + 5/3*u**3 + u + 0 = 0. What is u?
-3, -1, 0
Let n(k) be the first derivative of 0*k + k**3 + 0*k**2 + 3/4*k**4 + 2. Factor n(c).
3*c**2*(c + 1)
Let p = 18 - 16. Determine t so that 4*t**2 + 6*t**p + 6*t + 5*t**2 = 0.
-2/5, 0
Factor 6 + 15 + 3*x**2 - 6*x - 30.
3*(x - 3)*(x + 1)
Let i(o) be the second derivative of -2*o**2 - o - 1/2*o**5 + 5/3*o**3 - 1/6*o**4 + 0 + 1/5*o**6. Factor i(c).
2*(c - 1)**2*(c + 1)*(3*c - 2)
Let n(h) be the second derivative of -2*h**6/15 + h**4/3 + h. Solve n(r) = 0.
-1, 0, 1
Suppose -4 + 34 = 5*k. What is f in 8 - 1 + f**2 - 1 + 3 - k*f = 0?
3
Suppose 5 = k - 0*p - p, -p = -3*k + 13. Factor -1/4*f**k - 1/4*f**3 + 0 + 1/4*f**2 + 1/4*f.
-f*(f - 1)*(f + 1)**2/4
Let q(k) be the second derivative of k**6/6 + k**5/2 - 5*k**4/3 - 5*k**3/3 + 15*k**2/2 - 2*k - 10. Factor q(l).
5*(l - 1)**2*(l + 1)*(l + 3)
Let o(p) be the first derivative of 1/3*p**4 - 1/15*p**5 - 1/3*p**3 + 0*p - 2 + 0*p**2 + 1/180*p**6. Let x(v) be the third derivative of o(v). Factor x(c).
2*(c - 2)**2
Let f(a) be the second derivative of -a**7/105 - a**6/25 - a**5/25 + 20*a. Determine b so that f(b) = 0.
-2, -1, 0
Let t(x) = -1. Let z(c) = -c - 4. Let n(f) = 6*t(f) - z(f). Let d be n(6). Factor -2/3*a + 7/3*a**2 + a**d + 0 - 8/3*a**3.
a*(a - 1)**2*(3*a - 2)/3
Let t(k) be the second derivative of -k**6/1620 + k**3/2 - 4*k. Let b(m) be the second derivative of t(m). Find r such that b(r) = 0.
0
Factor 20*k**2 + 28*k**4 + 80*k**3 + 45*k**5 + 0*k**4 + 77*k**4.
5*k**2*(k + 1)*(3*k + 2)**2
Let v = 12 + -10. Factor -v*y - 8*y + 4*y + 4 + 2*y**2 + 0*y**2.
2*(y - 2)*(y - 1)
Let u be (-2)/16 + (60/(-32))/(-5). Solve -1/4*v + 3/4*v**2 + u*v**4 - 3/4*v**3 + 0 = 0.
0, 1
Let f be -1*3 - (1 - 8). Let w(j) be the third derivative of 0 - 1/60*j**5 - 1/40*j**6 + 2*j**2 + 0*j + 1/6*j**3 + 1/8*j**f. Factor w(b).
-(b - 1)*(b + 1)*(3*b + 1)
Let s(y) be the second derivative of -y**4/15 + 26*y**3/15 - 37*y. Factor s(p).
-4*p*(p - 13)/5
Let h(s) = -7*s + 28. Let j be h(4). Factor -2/3*y + j + 1/3*y**2.
y*(y - 2)/3
Let y(q) be the first derivative of 1/21*q**6 + 6/35*q**5 + 8 + 0*q**2 + 3/14*q**4 + 2/21*q**3 + 0*q. Factor y(z).
2*z**2*(z + 1)**3/7
Let x(g) = 5*g**5 + 2*g**4 - 5*g**3 + 4*g**2 + 6. Let h(v) = -v**4 - 1 + 4*v**5 - v**5 - v**2 - 4*v**5. Let c(q) = -6*h(q) - x(q). Suppose c(s) = 0. What is s?
-2, -1, 0
Let a(j) be the second derivative of j**4/3 - 2*j**3/3 + 6*j. Factor a(b).
4*b*(b - 1)
Let j(o) be the first derivative of -2*o**6/3 + 12*o**5/5 - 3*o**4 + 4*o**3/3 - 30. Factor j(w).
-4*w**2*(w - 1)**3
Suppose 5*w 