
Let z(n) = -10*n**4 - 55*n**3 + 10*n**2 + 10*n. Let u(h) = h**4 + 5*h**3 - h**2 - h. Let d(v) = -45*u(v) - 4*z(v). Let d(j) = 0. Calculate j.
-1, 0, 1
Let p = -88 + 63. Let f be (p - -25)/(3 + 1). Factor 0 + 0*y - 1/2*y**3 + f*y**2.
-y**3/2
Suppose 230 = g - 3*i, -2*i + 0*i = -3*g + 725. Let s = g - 2693/11. Solve 2/11 + 0*b - s*b**2 = 0 for b.
-1, 1
Suppose -3*y - 5*r - 4 = 0, -36*y + 6 = -35*y - 2*r. Factor 0 + 8/7*d**y + 4/7*d + 4/7*d**3.
4*d*(d + 1)**2/7
Let b(g) = -g**2 + 10*g + 16. Let a be b(11). Factor 2*m**5 - 9*m**3 + m**5 - 9*m**4 - 6*m**a - 3*m**2.
-3*m**2*(m + 1)**3
Let b(h) be the first derivative of h**5/10 + 3*h**4/8 + h**3/2 + h**2/4 - 11. Let b(j) = 0. Calculate j.
-1, 0
Determine x, given that 0*x - 2*x**2 + 0 - 1/2*x**4 + 5/2*x**3 = 0.
0, 1, 4
Let i(x) be the first derivative of x**4/4 - 2*x**3 + 6*x**2 - 8*x + 11. Factor i(y).
(y - 2)**3
Let g(r) be the second derivative of 0 - 1/12*r**4 - 5*r + 0*r**3 + 0*r**2. Find s, given that g(s) = 0.
0
Let t = 1 + 6. Suppose -h - 6*c + 2*c = -16, 0 = -2*h + 5*c - t. Factor -3*y**2 - 1/2 - 2*y - 2*y**3 - 1/2*y**h.
-(y + 1)**4/2
Suppose 2*s = 5*s + 5*s. Let s - 9/5*h - 1/5*h**3 - 6/5*h**2 = 0. Calculate h.
-3, 0
Let n = 9/8 + -23/24. Let m(d) be the second derivative of 0 + 0*d**2 + 1/6*d**4 - n*d**3 + d - 1/20*d**5. Find q such that m(q) = 0.
0, 1
Let m(q) be the first derivative of -q**6/6 + q**5/5 + 5*q**4/4 + q**3 - 40. Solve m(p) = 0 for p.
-1, 0, 3
Let u(i) be the second derivative of -i**5/36 - i**4/24 + i**3/9 + i**2/2 + 3*i. Let j(a) be the first derivative of u(a). Solve j(m) = 0 for m.
-1, 2/5
Find w, given that 0*w - 32/3*w**2 + 0 - 2/3*w**4 - 16/3*w**3 = 0.
-4, 0
Factor -2*o**5 + 24*o**3 + 2*o**5 - 20*o**3 - 4*o**5.
-4*o**3*(o - 1)*(o + 1)
Let w(r) = r**3 + 8*r**2 + 5*r. Let k be w(-7). Let g = k + -10. Determine i, given that 2*i + 4*i**2 - g*i**2 - 4*i**3 - 2*i**2 + 4*i**2 = 0.
-1/2, 0, 1
Let w(u) be the second derivative of 4*u + 1/120*u**5 + 0*u**4 - 1/36*u**3 + 0 + 0*u**2. Determine k so that w(k) = 0.
-1, 0, 1
Let t(y) be the second derivative of y**6/1440 - y**5/240 - y**3/3 + 6*y. Let f(m) be the second derivative of t(m). Factor f(r).
r*(r - 2)/4
Suppose -7*d + 84 = 5*d. Let i(h) be the second derivative of 0*h**3 + 0*h**2 + 0*h**4 - 1/15*h**6 + 1/21*h**d + h - 1/5*h**5 + 0. Factor i(n).
2*n**3*(n - 2)*(n + 1)
Factor -2*d**2 + 7 + 7 - 4 - 2.
-2*(d - 2)*(d + 2)
Let p(s) be the second derivative of 3*s**5/70 - s**4/21 - s**3/7 + 2*s**2/7 - 8*s. Factor p(y).
2*(y - 1)*(y + 1)*(3*y - 2)/7
Let p be 1 + -1*(2 - -2). Let u be ((-1)/p)/(3/18). Let w**2 + 4*w**3 + u*w + 2*w**2 - 3*w**3 = 0. What is w?
-2, -1, 0
Let c = 8/5 - -4/35. Determine u so that c*u - 2/7*u**2 - 18/7 = 0.
3
Factor -5/8*u + 3/8*u**2 + 1/4.
(u - 1)*(3*u - 2)/8
Let r = 3 + 15. Let k be (r/12)/(2/4). Let 14*j**5 + 8*j**k - 12*j**3 + 10*j**4 - 2*j + 2*j = 0. Calculate j.
-1, 0, 2/7
Factor 4*y + 0*y + 8*y + 4*y**2 - 4*y.
4*y*(y + 2)
Let q(j) be the first derivative of j**6/10 - j**4/2 + 3*j**2/2 + 6*j - 5. Let w(u) be the first derivative of q(u). Determine y, given that w(y) = 0.
-1, 1
Let u be (-2 - (1 - 2)) + 1. Suppose u = 2*p - 3*l - 9, 3*l = 3*p - l - 13. Factor q**3 - 2*q**2 - 2*q**3 - 5*q**4 + 3*q**p + 7*q**4 - 2*q.
2*q*(q - 1)*(q + 1)**2
Let o(c) = -8*c**2 - 10*c - 8. Let j(l) = -7*l**2 - 9*l - 7. Let m(q) = 6*j(q) - 5*o(q). Let m(v) = 0. What is v?
-1
Let 1/10*r**5 + 0*r**2 + 1/5*r**4 + 1/10*r**3 + 0*r + 0 = 0. What is r?
-1, 0
Let g be (-6)/(6/(-2)) + (-4)/(-2). Solve -8/7*r + 2/7*r**g + 2/7*r**3 + 16/7 - 12/7*r**2 = 0.
-2, 1, 2
Let n(t) = -t**3 - 2*t**2 + 2*t + 3. Let z be 2 + -7 + 2 + 0. Let l be n(z). Factor 0*s - 16*s**3 + 1 + 18*s**2 - 9*s + l*s**2.
-(s - 1)*(4*s - 1)**2
Suppose -13 = 4*y - 5*i, 0 = -2*y - 0*i - 3*i + 21. Factor -1/5*q + 0 - 2/5*q**2 - 1/5*q**y.
-q*(q + 1)**2/5
Let c(d) be the second derivative of -d**6/360 - d**5/180 + d**4/72 + d**3/18 + 7*d**2/2 - 8*d. Let x(m) be the first derivative of c(m). Factor x(h).
-(h - 1)*(h + 1)**2/3
Let w(q) = -4*q**5 + 6*q**4 - 2*q**3. Let g(d) = d**5 - d**4. Let r(s) = -5*g(s) - w(s). Determine t, given that r(t) = 0.
-2, 0, 1
Solve 10*i**3 - 8*i**4 - 27*i + i**5 + 27 - 6*i**4 + 21*i**4 - 18*i**2 = 0 for i.
-3, 1
Factor -6*p - 15*p**2 - 37 - 3*p**4 + 37 - 12*p**3.
-3*p*(p + 1)**2*(p + 2)
Let y(r) = 4*r**4 + 2*r**2 - 3*r - 3. Let f = 6 + -4. Let k(h) = h**4 + h**2 - h - 1. Let i(a) = f*y(a) - 6*k(a). Factor i(p).
2*p**2*(p - 1)*(p + 1)
Let j(q) be the second derivative of -q**8/1680 + q**7/210 - q**6/90 + q**3/2 - 3*q. Let z(a) be the second derivative of j(a). Factor z(c).
-c**2*(c - 2)**2
Let r be 0/(-2) - (9 + -12). Factor r + 0*d + d + 0*d - 3*d**3 + 2*d - 3*d**2.
-3*(d - 1)*(d + 1)**2
Find d such that -36*d**2 + d**5 - 3*d + 11*d + 20*d**3 + 36*d**4 - 29*d**5 = 0.
-1, 0, 2/7, 1
Let r(d) be the third derivative of 2*d**2 + 0 - 1/36*d**4 - 1/18*d**3 + 0*d + 1/60*d**5. Factor r(f).
(f - 1)*(3*f + 1)/3
Factor 26*c**2 - 2*c**2 - 113 - 4*c**3 - 3 - 12.
-4*(c - 4)**2*(c + 2)
Factor 1/3*v**2 + 0*v + 0.
v**2/3
Let a be ((-6)/9 - 0)/(-14). Let b(n) be the first derivative of -2 + 3/14*n**4 + 0*n - 6/35*n**5 - 2/21*n**3 + a*n**6 + 0*n**2. Factor b(r).
2*r**2*(r - 1)**3/7
Let b = -23042090/217 - -106185. Let g = 1/31 + b. Determine y so that 0 - 2/7*y**3 + 2/7*y**5 + 0*y + 2/7*y**4 - g*y**2 = 0.
-1, 0, 1
Let g be (8/30)/(10/25). Factor -4/3*m + 0 - g*m**2.
-2*m*(m + 2)/3
Let v(x) be the first derivative of x**4/2 - 2*x**3 + 2*x**2 + 11. Factor v(h).
2*h*(h - 2)*(h - 1)
Let r be ((-2)/25)/(2/(-20)). Let f = 30 + -28. Factor r - 2/5*h**3 + 8/5*h**f - 2*h.
-2*(h - 2)*(h - 1)**2/5
Suppose -8/7 - 8/7*s - 2/7*s**2 = 0. Calculate s.
-2
Let o(n) be the second derivative of n**5/8 + 13*n**4/24 + n**3/3 - n**2 + 4*n. Factor o(c).
(c + 1)*(c + 2)*(5*c - 2)/2
Let c be (-5)/2 + 0 - 310/(-124). Find g such that c*g + 0*g**2 - 2/5*g**4 + 0 - 2/5*g**3 = 0.
-1, 0
Let c(n) be the second derivative of n - 1/6*n**5 + 1/30*n**6 + 1/3*n**4 + 0 + 1/6*n**2 - 1/3*n**3. Suppose c(w) = 0. Calculate w.
1/3, 1
Factor -4*b + 2*b**2 - 5*b**4 - b**2 + 14*b**2 - 6*b.
-5*b*(b - 1)**2*(b + 2)
What is s in -2/3*s**2 + 4/3*s - 2/3 = 0?
1
Let j be 3/(-4)*8/(-12). Determine g so that 0*g**2 + 0 + j*g**3 + 0*g - 1/4*g**4 = 0.
0, 2
Determine y so that -1/3*y**2 + 2/3 + 1/3*y = 0.
-1, 2
Let n(g) = 3*g**5 - 3*g**3 - 4*g**2 - 2. Let v(i) = -13*i**5 + i**4 + 13*i**3 + 17*i**2 + 9. Let m(r) = -9*n(r) - 2*v(r). Factor m(d).
-d**2*(d - 1)*(d + 1)*(d + 2)
Let g(p) be the first derivative of p**3 - 9/20*p**4 - 3/5*p + 2 - 3/10*p**2. Determine m so that g(m) = 0.
-1/3, 1
Determine z so that -z - z**4 - 163*z**3 - 2 + 83*z**3 + 81*z**3 + 3*z**2 = 0.
-1, 1, 2
Find p such that 25*p**4 - 5*p**3 + 3*p**2 - 5*p**3 - 28*p**2 + 10*p = 0.
-1, 0, 2/5, 1
Let f(n) be the third derivative of -n**6/30 + n**5/15 + 31*n**2. Factor f(k).
-4*k**2*(k - 1)
Let h(b) be the first derivative of -b**6/900 - b**5/300 + b**3/3 + 2. Let i(s) be the third derivative of h(s). Factor i(f).
-2*f*(f + 1)/5
Suppose -4/9*z + 2/9*z**2 + 2/9 = 0. What is z?
1
Let l(q) = q**2 - 7*q - 2. Let d be l(7). Let k be d/(-3)*(-135)/(-18). Factor -3*r**5 + r**2 + 0*r**4 + 5*r**5 - r**4 + r**3 - 3*r**k.
-r**2*(r - 1)*(r + 1)**2
Let x(j) be the first derivative of 3*j**4/8 - j**3 + 3*j**2/4 + 22. Factor x(o).
3*o*(o - 1)**2/2
Let y = -5 + 8. Let z be 2 + y + (-1)/1. Factor -3*k**4 - 2*k**4 - 4*k**3 + 3*k**3 + z*k**4.
-k**3*(k + 1)
Let a(l) = -l**2 + 3*l + 12. Let f be a(5). Factor 1/3*i**f - 1/3*i + 0 - 1/3*i**4 + 1/3*i**3.
-i*(i - 1)**2*(i + 1)/3
Let i(j) be the third derivative of 0*j**5 + 0*j**3 + 0*j**4 - 1/210*j**7 + 7*j**2 - 1/1008*j**8 + 0*j + 0 - 1/180*j**6. Suppose i(y) = 0. What is y?
-2, -1, 0
Let f = -105 - -317/3. Factor f + 2/3*p**2 - 4/3*p.
2*(p - 1)**2/3
Let k(s) be the third derivative of 0*s**5 + 0*s - 4*s**2 - 1/60*s**6 + 0 + 0*s**3 - 4/105*s**7 + 0*s**4. Let k(h) = 0. What is h?
-1/4, 0
Let f(m) = 13*m**4 + 10*m**3 + 4*m - 4. Let s(u) = -38*u**4 - 29*u**3 - 11*u + 11. Let v(j) = 11*f(j) + 4*s(j). Factor v(y).
-3*y**3*(3*y + 2)
Let x = 175 - 1223/7. Let q = -3 + 3. Let x + q*n - 2/7*n**2 = 0. What is n?
-1, 1
Factor 4*h**2 - 2*h - h**3 + 3*h + 0*h - 5*h.
-h*(h - 2)**2
Let i(v) be the third derivative of v**8/336 + v**7/