1
Suppose 4*x = 2*r + 8, 4*r = 3*x - 7 + 1. Let p(k) be the first derivative of -k + 9/4*k**x + 1 - 7/6*k**3. What is q in p(q) = 0?
2/7, 1
Suppose -2*x + k + 3*k = 8, 2*x - 8 = -4*k. Suppose -4*h - w + 10 = x, -2*h - 3*w + w + 8 = 0. What is o in -9*o + 2*o + 2 + 2*o**h + 3*o = 0?
1
Let n(d) be the second derivative of -2/15*d**3 + d - 1/100*d**5 + 0 + 1/15*d**4 + 0*d**2. Let n(h) = 0. What is h?
0, 2
Let o = 149/399 - 5/57. Factor 2/7 + o*a**4 - 4/7*a**2 + 0*a**3 + 0*a.
2*(a - 1)**2*(a + 1)**2/7
Factor 25*p**4 + 25*p**3 + 5*p**2 - 10*p**4 + 257*p - 262*p.
5*p*(p + 1)**2*(3*p - 1)
Suppose -2*t - 2*z = 2, -z + 8 = z. Let x be -1 + 1 + (-20)/t. Suppose -1 + 2*q**2 - 5*q**4 + 2*q**4 + 2*q**x = 0. What is q?
-1, 1
Let d be (16/18)/((-392)/(-252)). Find w, given that -36/7*w**3 - 24/7*w**2 - d*w + 0 = 0.
-1/3, 0
Find q, given that 11/3*q**3 - 4*q**4 + 46/3*q**2 + 8/3 + 12*q - 5/3*q**5 = 0.
-2, -1, -2/5, 2
Let o(z) be the second derivative of -z**5/15 + 2*z**3/9 + 5*z. Factor o(k).
-4*k*(k - 1)*(k + 1)/3
Let s(y) be the first derivative of y**5/120 - y**4/8 + 3*y**3/4 + 3*y**2/2 - 8. Let p(f) be the second derivative of s(f). Find h such that p(h) = 0.
3
Let m(x) be the first derivative of 0*x - 7 - x**2 + 5/3*x**3 + 1/2*x**6 - 1/4*x**4 - x**5. Solve m(j) = 0 for j.
-1, 0, 2/3, 1
Let h(f) be the second derivative of -3*f**5/40 + 3*f**4/8 - 3*f**3/4 + 3*f**2/4 + 7*f. Factor h(k).
-3*(k - 1)**3/2
Let w(k) be the second derivative of k**8/8400 + k**7/1400 + k**6/900 + k**3 - k. Let c(r) be the second derivative of w(r). Factor c(m).
m**2*(m + 1)*(m + 2)/5
Let r(o) be the first derivative of -5*o**6/12 - o**5 + 15*o**4/8 + 10*o**3/3 - 5*o**2 - 16. Factor r(u).
-5*u*(u - 1)**2*(u + 2)**2/2
Let s(b) be the third derivative of 0*b + 1/120*b**5 + 1/6*b**3 + 0 - 2*b**2 - 1/16*b**4. Factor s(q).
(q - 2)*(q - 1)/2
Let v(i) be the first derivative of 3*i**5/35 - 15*i**4/28 + 4*i**3/7 - 25. Factor v(o).
3*o**2*(o - 4)*(o - 1)/7
Let f(u) = 3*u**3 + 18*u**2 + 6*u - 9. Let t(y) = -2*y**3 - 9*y**2 - 3*y + 4. Let w(z) = 3*f(z) + 7*t(z). Factor w(i).
-(i + 1)**2*(5*i - 1)
Factor 106 + 38 - 44*g - 12*g + 4*g**2 + 52.
4*(g - 7)**2
Factor 2*f**2 + 0*f + 1/2*f**3 + 0.
f**2*(f + 4)/2
Let i(m) be the third derivative of m**8/448 + 3*m**7/280 + m**6/80 - m**5/40 - 3*m**4/32 - m**3/8 + 8*m**2. Factor i(d).
3*(d - 1)*(d + 1)**4/4
Factor 7/3*x**3 + 5/3*x**4 + 2/3*x**2 + 0*x + 0.
x**2*(x + 1)*(5*x + 2)/3
Let j = 910 - 3637/4. Factor 3/4*m**3 + 3/4*m**2 + 0 - 3/4*m - j*m**4.
-3*m*(m - 1)**2*(m + 1)/4
Let d(w) be the third derivative of w**7/350 + w**6/200 - w**5/100 - w**4/40 + 2*w**2. Solve d(y) = 0.
-1, 0, 1
Let w(t) be the first derivative of -t**6/1440 + t**5/240 + t**3/3 - 4. Let r(c) be the third derivative of w(c). Determine d, given that r(d) = 0.
0, 2
Let f(i) = -1. Let v(u) = -u**2 + 6*u - 7. Let h(z) = -6*f(z) - 3*v(z). Factor h(y).
3*(y - 3)**2
Let u(z) be the second derivative of -z**5/10 - z**4/6 - 18*z. Factor u(j).
-2*j**2*(j + 1)
Let i(q) be the first derivative of 10/3*q**3 - 3 - 2*q**4 - q**2 + 0*q. Determine c, given that i(c) = 0.
0, 1/4, 1
Let z(f) be the second derivative of f**7/1260 + f**6/180 + f**5/60 + f**4/4 - 3*f. Let v(n) be the third derivative of z(n). Factor v(a).
2*(a + 1)**2
Suppose 3 = x - 2*l, -x - 5*l = 3*x - 25. Suppose -3*a + 15 = a + 3*b, -b + x = 5*a. Let a + 1/6*m**2 + 1/3*m - 1/6*m**3 = 0. What is m?
-1, 0, 2
Let i(c) be the first derivative of 1/3*c**3 - 1/3*c**2 - 1/15*c**5 + 2 + 0*c + 0*c**4. Find l, given that i(l) = 0.
-2, 0, 1
Let s = 20 - 2. Let u be (-4)/6 + 66/s. Let -1/3*y**2 + 2*y**u - 3*y**4 + 4/3*y**5 + 0 + 0*y = 0. Calculate y.
0, 1/4, 1
Let i(n) be the second derivative of n**4/48 - n**2/8 - 5*n. Factor i(f).
(f - 1)*(f + 1)/4
Let j(x) = -x**2 - 8*x - 10. Let w be j(-7). Let l be -1 + 3/(w/(-4)). Find t such that -4 - l*t - 2*t**2 - t - 2*t = 0.
-2, -1
Let p(q) = -q**3 + q**2 + q + 1. Let r be p(-1). Find x, given that -7*x**3 - 2*x**2 - x**2 + 11*x - r + 5*x**2 - 4*x = 0.
-1, 2/7, 1
Let b(w) = -w**2 + 24*w + 25. Let s be b(25). Factor s + 4/7*f**2 + 2/7*f + 2/7*f**3.
2*f*(f + 1)**2/7
Let h(n) be the first derivative of -n**9/10584 + n**8/2940 - n**7/2940 + n**3/3 - 4. Let b(p) be the third derivative of h(p). Factor b(c).
-2*c**3*(c - 1)**2/7
Solve 4/3*t + 1/3*t**4 - 2*t**2 - 4/3*t**3 + 5/3 = 0 for t.
-1, 1, 5
Let b(o) = -6*o - 15. Let q be b(-5). Determine f, given that 360*f**4 - 129*f**2 - 215*f**5 + 72*f**3 + 12 - q*f**3 - 85*f**5 = 0.
-2/5, 1/2, 1
Factor 3*y**2 + y**3 + y**2 - 5*y**2 + 8*y + y**4 - 9*y.
y*(y - 1)*(y + 1)**2
Suppose 2/7*z**2 + 0*z - 2/7 = 0. What is z?
-1, 1
Suppose 3 = -2*f + 5, -4*f + 13 = 3*d. Suppose -2*u + 6/5*u**2 + 2/5*u**d - 2/5*u**4 + 4/5 = 0. Calculate u.
-2, 1
Let c(u) be the third derivative of 0*u + 1/30*u**6 - 1/105*u**7 + 0 + 0*u**4 - 4*u**2 - 1/30*u**5 + 0*u**3. Factor c(g).
-2*g**2*(g - 1)**2
Let f = -5 + 14. Let r be 35/15 + 4/6. Factor 7*y**3 - 14*y**4 - y**5 - r*y**3 + f*y**5 + 2*y**2.
2*y**2*(y - 1)**2*(4*y + 1)
Factor 1/4*l**2 - 1/4*l - 3/2.
(l - 3)*(l + 2)/4
Let l(n) be the third derivative of -n**6/100 - 11*n**5/150 - n**4/5 - 4*n**3/15 - 9*n**2. Find y such that l(y) = 0.
-2, -1, -2/3
Factor -5 - 15/2*o - 5/2*o**2.
-5*(o + 1)*(o + 2)/2
Factor -1/4*i**4 + i - 2*i**2 + 5/4*i**3 + 0.
-i*(i - 2)**2*(i - 1)/4
Suppose -5*p + p = -12. Factor -26 - 6 - q - 24*q**2 + 10*q**p - 46*q**3 + 81*q.
-4*(q + 2)*(3*q - 2)**2
Factor -578/9 - 2/9*p**2 + 68/9*p.
-2*(p - 17)**2/9
Let f(s) be the third derivative of -s**6/120 - s**5/24 - s**4/12 + s**3 - 3*s**2. Let q(j) be the first derivative of f(j). Factor q(y).
-(y + 1)*(3*y + 2)
Let l(u) be the second derivative of u**6/165 - 3*u**5/110 + 4*u**3/33 - 4*u. Factor l(v).
2*v*(v - 2)**2*(v + 1)/11
Let t(a) = a**2 + a - 4. Let b be t(-3). Find d, given that 2*d**3 - 4 - 5*d + 3*d - 8*d**4 + 10*d**2 + b*d**4 = 0.
-1, -2/3, 1
Factor 0 - 1/7*v + 0*v**2 + 1/7*v**3.
v*(v - 1)*(v + 1)/7
Let i(n) be the second derivative of 0 + 0*n**6 + 1/105*n**7 + 0*n**2 + 1/15*n**3 - 1/25*n**5 + 0*n**4 - 6*n. Factor i(w).
2*w*(w - 1)**2*(w + 1)**2/5
Factor 0*n - 4/5*n**2 + 6/5*n**3 + 0.
2*n**2*(3*n - 2)/5
Let c = -8330/33 - -1904/11. Let u = c - -80. Factor 0*n + u*n**4 + 4/3*n**3 + 2/3*n**2 + 0.
2*n**2*(n + 1)**2/3
Let v(u) = -u**2 + u + 22. Let f be v(5). Determine x, given that 0 + 1/2*x**3 - x**f + 1/2*x = 0.
0, 1
Suppose 0 + 2/11*u**3 - 4/11*u**4 + 4/11*u**2 - 2/11*u = 0. Calculate u.
-1, 0, 1/2, 1
Let f be 3/50*17 + -1. Let g(y) be the second derivative of 0 + y + f*y**5 + 0*y**4 - 1/15*y**3 + 0*y**2. Let g(s) = 0. What is s?
-1, 0, 1
Suppose 2*f + 7 = -0*f + 5*d, -2*f + 2*d + 2 = 0. Suppose -3/4*w**5 + 0*w**f + 3/2*w**3 + 0 + 0*w**2 - 3/4*w = 0. What is w?
-1, 0, 1
Let q = -7866 + 31681/4. Let o = -54 + q. What is b in -1/4*b**3 + 0*b**2 + o*b + 0 = 0?
-1, 0, 1
Let d(c) be the second derivative of c**5/240 + 7*c**4/144 + 11*c**3/72 + 5*c**2/24 - c - 10. Let d(v) = 0. What is v?
-5, -1
Suppose 0*u = 5*m - 5*u, -m = 3*u. Determine p so that 1/2*p**4 + 1/2*p**5 + m - p**3 + 0*p + 0*p**2 = 0.
-2, 0, 1
Let w be (-6)/(-33) + (-56)/(-176). Solve w*g**4 - 1/2*g**3 + 1/2*g - 1/2*g**2 + 0 = 0 for g.
-1, 0, 1
Let u(x) = -4*x**3 - x**2 - x + 1. Let w(d) = -d**3. Let p(a) = -u(a) + 5*w(a). Factor p(f).
-(f - 1)**2*(f + 1)
Suppose -b + 0*b + 5 = 0. Suppose b*i + 16 + 4 = -5*d, -20 = 4*d + 5*i. Solve d + 0*p + 2/7*p**2 = 0 for p.
0
Let r = 67 - 45. Suppose -r = -5*j + 3*m, 0*j - 3 = -j + 2*m. Let 24/5*o**2 + 0 + 38/5*o**3 + 18*o**j - 144/5*o**4 - 8/5*o = 0. Calculate o.
-2/5, 0, 1/3, 2/3, 1
Let n = 70 + -137/2. Factor 0 - n*j**4 - 3*j**2 + 0*j - 9/2*j**3.
-3*j**2*(j + 1)*(j + 2)/2
Let m(s) = s**3 + s**2 + s - 1. Let n(v) = 5*v**3 + 2*v**2 - v - 2. Let t(d) = -2*m(d) + n(d). Find j, given that t(j) = 0.
-1, 0, 1
Suppose 0*t + 12 = -4*t. Let d = 0 - t. Let 5*w**2 + 0*w + 2*w - 2*w**d - 3*w**2 - 2*w**4 = 0. What is w?
-1, 0, 1
Let t(c) = -c**2 + 4*c + 21. Let i be t(7). Determine f, given that 0*f + 0*f**2 + 1/3*f**3 + 1/3*f**4 + i = 0.
-1, 0
Let h(m) = -m**5 + 11*m**4 + 25*m**3 - 11*m**2 - 53*m - 24. Let y(b) = -b**5 + 5*b**4 + 13*b**3 - 5*b**2 - 26*b - 12. Let a(n) = -2*h(n) + 5*y(n). Factor a(r).
-3*(r - 2)**2*(r + 1)**3
Find x such that -18/11 - 2/11*x**2 + 12/11*x = 