2
Suppose 5*c = 4*r - 4, -5*r - 6*c + 5 = -c. Let i = 2 + r. Determine g so that 4 + g**i + 0*g**2 + g**2 - 4 = 0.
-1, 0
Solve 6 + 3*k**3 + 13*k**2 - 3*k - 4*k - 10*k + 2*k**5 - 7*k**4 = 0 for k.
-3/2, 1, 2
Let v(p) be the third derivative of -p**8/112 - p**7/70 + p**6/20 + 7*p**2. Determine g so that v(g) = 0.
-2, 0, 1
Suppose -3*s - 5*m + 29 = 0, 4*m - 9 = s + 4. Solve -5*f**2 + 5*f**2 - s*f**3 - 3 - 3 + 9*f = 0.
-2, 1
Let n(p) be the first derivative of -p**7/63 + p**5/15 - p**3/9 - 4*p - 1. Let d(q) be the first derivative of n(q). Find s, given that d(s) = 0.
-1, 0, 1
Let i(z) be the second derivative of z**5/15 - 5*z**4/18 + 2*z**3/9 + 5*z. Suppose i(m) = 0. What is m?
0, 1/2, 2
Let r(f) be the first derivative of 1/12*f**4 + 3 + 0*f**2 - 1/15*f**5 + 0*f + 0*f**3. Solve r(t) = 0.
0, 1
Suppose -2*u + 4*q + 36 = 0, 23 = 2*u + 5*q - 13. Let -2/3*z**5 + 20/3*z**4 + 0 + 36*z**2 - 24*z**3 - u*z = 0. What is z?
0, 1, 3
Let n(c) be the first derivative of 2*c**3/21 + 2*c**2/7 - 32. Factor n(j).
2*j*(j + 2)/7
Let t be 4/(-8) + (-11)/(-2). Let i be (4/t)/(2/25). Factor 0*l + 1 - 2 + 4*l**2 + 10*l**3 - i*l - 3.
2*(l - 1)*(l + 1)*(5*l + 2)
Let f = -2 - -2. Suppose f = -5*n + 10, 2*n - 13 = -5*b + 1. Factor -8*l**b + 3*l - 2 + 0*l - 8*l - 5*l.
-2*(l + 1)*(4*l + 1)
Let g(f) = f + 8. Let d be g(-4). Suppose 9*l - 10 = d*l. Factor 0*j - 1/4*j**3 + 0 + 1/4*j**l.
-j**2*(j - 1)/4
Let k(w) be the second derivative of 1/3*w**2 - 1/18*w**4 + 0*w**3 - 2*w + 0. Factor k(q).
-2*(q - 1)*(q + 1)/3
Let k(b) = -10*b**5 + 16*b**4 - 8*b**3 + 28*b**2 + 2*b - 28. Let l(r) = -3*r**5 + 5*r**4 - 3*r**3 + 9*r**2 + r - 9. Let x(f) = 5*k(f) - 16*l(f). Factor x(n).
-2*(n - 1)**3*(n + 1)*(n + 2)
Let a(q) = 5*q**2 - 20*q - 45. Let j(u) = -u**2 - 2*u + 1. Let k(r) = a(r) + 30*j(r). Factor k(o).
-5*(o + 3)*(5*o + 1)
Let s(t) be the first derivative of -t**3/9 - 11. Factor s(z).
-z**2/3
Suppose -4*l + 3*y = -23, 0 = -2*l + l - 3*y + 17. Let s = l + -6. Let -t**2 + 0*t**s + 3*t**2 - 2 = 0. Calculate t.
-1, 1
Factor 6 - 20/3*a + 2/3*a**2.
2*(a - 9)*(a - 1)/3
Let t = 3/12888298 - 23959349477/15014867170. Let c = 1/233 - t. Solve -c*f + 8/5 + 2/5*f**2 = 0.
2
Let r(u) = -u**2 - 9*u - 14. Let c be r(-7). Determine j, given that 0*j**2 + c*j - 2/3*j**4 + 0 + 1/3*j**3 = 0.
0, 1/2
Suppose g + 5*u = 11 + 2, -3*u = -2*g. Suppose 0 = 2*s - k - 113, -g*k + 222 = 4*s - k. Solve -s*v + 125/2*v**4 - 120*v**2 - 8 - 50*v**3 = 0 for v.
-2/5, 2
Let k = -15 + 7. Let r be (-15)/(-6)*k/(-5). Factor -h + h**3 - h**4 + 4 - r + h**2.
-h*(h - 1)**2*(h + 1)
Let d = 1 - -3. Factor 0*z**4 - 2*z**2 - 2*z - 2*z**4 + 2*z + d*z**3.
-2*z**2*(z - 1)**2
Let o(a) be the first derivative of -3*a**4/5 + 52*a**3/15 - 32*a**2/5 + 16*a/5 + 8. Factor o(h).
-4*(h - 2)**2*(3*h - 1)/5
Factor 8*a + 0 + 13 + 4*a**2 - 4 - 5.
4*(a + 1)**2
Let q(h) be the third derivative of h**8/784 - 3*h**6/280 + h**5/70 + 46*h**2 - 2. Factor q(r).
3*r**2*(r - 1)**2*(r + 2)/7
Let l = 190 - 187. Factor 1/5*r**2 - 4/5*r**4 + 0 + 0*r + 3/5*r**l.
-r**2*(r - 1)*(4*r + 1)/5
Let n = -12 - -21. Let s = n - 7. Find c, given that c + 3*c + s*c + 3*c**2 = 0.
-2, 0
Determine v so that 18/5 + 2/5*v**4 - 4/5*v**2 - 24/5*v + 8/5*v**3 = 0.
-3, 1
Let w(h) be the first derivative of -h - 2 + 0*h**2 + 0*h**4 - 1/120*h**6 + 1/80*h**5 + 0*h**3. Let k(c) be the first derivative of w(c). Factor k(t).
-t**3*(t - 1)/4
Let n(v) be the second derivative of v**6/75 - 4*v**5/25 + v**4/5 + 8*v**3/3 + 5*v**2 + 3*v. What is p in n(p) = 0?
-1, 5
Let m(h) be the second derivative of -h**6/75 - 2*h**5/25 + h**4/15 + 4*h**3/5 - 9*h**2/5 + h. Let m(w) = 0. Calculate w.
-3, 1
Let l(z) be the third derivative of z**7/630 + z**6/120 + z**5/60 + z**4/72 + 7*z**2. Factor l(t).
t*(t + 1)**3/3
Factor 2/9*w**2 - 4/9*w - 2/9 + 4/9*w**3.
2*(w - 1)*(w + 1)*(2*w + 1)/9
Let c(q) be the third derivative of q**5/210 - q**4/21 + q**3/7 + 4*q**2. Determine r so that c(r) = 0.
1, 3
Let j be (-1)/((-8)/(-4)*-1). Let l(m) be the first derivative of 0*m - 1 + 1/4*m**4 + 1/5*m**5 - 1/3*m**3 - j*m**2. What is g in l(g) = 0?
-1, 0, 1
Let r(w) be the third derivative of -w**10/453600 + w**9/60480 - w**8/30240 + w**5/15 - 4*w**2. Let n(c) be the third derivative of r(c). Factor n(s).
-s**2*(s - 2)*(s - 1)/3
Suppose 0*j + 4*j + 4*h = 12, 0 = 2*j - 3*h + 9. Suppose -4*x + 14 - 2 = j. Factor -5*q + q + 5*q**2 - x*q**2.
2*q*(q - 2)
Let -3/2*n**2 - 15*n - 75/2 = 0. Calculate n.
-5
Suppose 2*v = -w, 5*w + 21 = v - 1. Suppose 10 = 3*u - c, u - v*c = -3*c + 6. Factor 0*p**u - p**4 - 3*p**2 + 4*p**2.
-p**2*(p - 1)*(p + 1)
Let o be 400/160*((-1)/5 - -1). Factor -2/7*w - 6/7*w**3 + 0 - 2/7*w**4 - 6/7*w**o.
-2*w*(w + 1)**3/7
Factor 2 - 3*f**2 + 7 + 8*f - 2*f + 0*f**2.
-3*(f - 3)*(f + 1)
Let i(c) be the third derivative of -c**8/1176 - c**7/245 - c**6/210 + c**5/105 + c**4/28 + c**3/21 + 4*c**2. Let i(h) = 0. What is h?
-1, 1
Let y(g) be the second derivative of -2*g**5/5 - g**4/2 + g**3/3 + 10*g. Factor y(u).
-2*u*(u + 1)*(4*u - 1)
Let y be (-8)/(-4) - -3 - 2. Let s(z) be the first derivative of -2 + 2*z - 5/3*z**y + 3/2*z**2. Factor s(c).
-(c - 1)*(5*c + 2)
Suppose -8*d + 3*d - 15 = 0. Let q be (d/(-12))/(1/1). Suppose 1/4*r**2 + 0*r - q = 0. Calculate r.
-1, 1
Let y(i) = -9*i**4 + 6*i**3 + 3*i**2 + 3*i. Let n(x) = x**5 - 10*x**4 + 7*x**3 + 2*x**2 + 4*x. Let j(t) = -3*n(t) + 4*y(t). Solve j(m) = 0 for m.
-2, -1, 0, 1
Factor 1/2 + 1/6*x**2 - 2/3*x.
(x - 3)*(x - 1)/6
Suppose 2*t = 5*u - 12, -3*t - 5*u + 21 = -11. Suppose -2/3*c**5 + 0*c**t + 0*c**2 + 0 + 4/3*c**3 - 2/3*c = 0. Calculate c.
-1, 0, 1
Solve -3/5*h**2 + 3*h - 9/5 - 3/5*h**3 = 0 for h.
-3, 1
Let k(r) be the first derivative of 4*r**3/3 + 45*r**2/2 + 41*r - 7. Let u(q) = q**2 + 9*q + 8. Let v(p) = -2*k(p) + 11*u(p). Factor v(y).
3*(y + 1)*(y + 2)
Let i(n) = n**2 + 4*n - 2. Let y be i(-5). Let r(a) be the first derivative of 1/4*a - 3 + 1/3*a**y - 5/8*a**2. Factor r(j).
(j - 1)*(4*j - 1)/4
Suppose -3*v - 2 - 1 = 0, -7 = -3*g + v. Solve 4*t**3 + 2*t**4 + 3*t**2 + 5*t**4 - 5*t**4 - t**g = 0 for t.
-1, 0
Let x = 18 - 13. Let s be 1 - 6/(2 - x). Factor 2*i**2 + 6*i**s + 2*i**4 + i**5 + i**5 + 4*i**4.
2*i**2*(i + 1)**3
Suppose 5*i = -5*q + 13 + 12, 3*q + 5*i - 21 = 0. Suppose z = q*z. Find u such that u + 1/2*u**2 - u**3 - 1/2*u**4 + z = 0.
-2, -1, 0, 1
Let t(h) be the third derivative of h**8/3360 - h**7/630 + h**6/360 + h**4/12 + 4*h**2. Let r(n) be the second derivative of t(n). Factor r(d).
2*d*(d - 1)**2
Let w(p) be the third derivative of 7*p**6/2 - 23*p**5/15 - 8*p**4/3 + 8*p**3/3 + 7*p**2. Solve w(g) = 0.
-2/5, 2/7, 1/3
Let q = 30 + -59/2. Factor q*v**3 + 1/6*v + 0 + 1/2*v**2 + 1/6*v**4.
v*(v + 1)**3/6
Let o(k) = k + 7. Let b be o(-7). Suppose -3*v + 4*v = b. Factor 0 + v*d**3 + 4/5*d**4 - 2*d**5 + 0*d**2 + 0*d.
-2*d**4*(5*d - 2)/5
Let l(i) be the first derivative of -4*i**5/5 - i**4 + 4*i**3 + 2*i**2 - 8*i + 9. Factor l(q).
-4*(q - 1)**2*(q + 1)*(q + 2)
Solve 30 - 5 + 5*z**2 - 279*z + 249*z = 0.
1, 5
Let i(m) = -35*m**3 - 9*m**2 + 27*m + 17. Let a(k) = -12*k**3 - 3*k**2 + 9*k + 6. Let x(w) = -8*a(w) + 3*i(w). Solve x(q) = 0 for q.
-1, -1/3, 1
Suppose 24 = 4*x - 4*k, 2*x = -4*k - 12 - 0. Let n(f) = -f + 7. Let z be n(7). Suppose 1/4*h**4 - 1/4*h - 1/4*h**x + 1/4*h**3 + z = 0. Calculate h.
-1, 0, 1
What is z in z**2 + 2 - 4*z - 4 + 7 - 1 = 0?
2
Let n(o) be the third derivative of -o**7/2940 + o**3/3 + o**2. Let s(w) be the first derivative of n(w). Find r, given that s(r) = 0.
0
Let l(i) be the first derivative of 1 - 1/12*i**2 + 1/24*i**4 + 1/18*i**3 - 1/6*i. Factor l(b).
(b - 1)*(b + 1)**2/6
Suppose -3*q + 1 = -62. Suppose 3*w - 3*f - q = 0, 5*w + 3*f - 8 = -f. Solve -2/5*u**3 + 0*u + 1/5*u**2 + 0 + 1/5*u**w = 0.
0, 1
Let s be (-6)/(-7 - -5 - (-1 - -1)). Let a(u) be the second derivative of 0*u**2 + 0 - 1/10*u**4 + 1/50*u**5 + 2/15*u**s + 2*u. Let a(z) = 0. Calculate z.
0, 1, 2
Let l be (-9)/8*-2*(-10)/(-90). Find m such that -13/4*m**3 + 0 - l*m**5 + 3*m**2 + 3/2*m**4 - m = 0.
0, 1, 2
Suppose -12*x + 12 = -6*x. Find h such that 3*h - 3*h**x + 3*h**3 + 4*h**2 + 5*h**2 = 0.
-1, 0
Let x(h) be the second derivative of -1/2*h**3 - 3*h + 0*h**4 + 0*h**2 + 0 + 1/240*h**5 + 1/360*h**6. Let p(v) be the second derivative of x(v). Factor p(d).
d*(2*d + 1)/2
Let r(