1
Suppose 0 = -3*z + 2 - 26. Let t = 10 + z. Factor 0 + 0*o**t - 2/9*o**3 + 0*o.
-2*o**3/9
Let q be (-9)/36*1*-12. Let a(o) be the second derivative of 0 + 0*o**q + 1/6*o**2 - 1/36*o**4 - o. Let a(n) = 0. Calculate n.
-1, 1
Let d be (-2)/(-7) - 400/(-3108). Let y = d + -3/37. Determine b so that y*b**3 + b**2 + b + 1/3 = 0.
-1
Factor -4*i**3 - 8*i + i**3 + 11*i**3 + 4*i**4 - 4*i**2.
4*i*(i - 1)*(i + 1)*(i + 2)
Factor -20/3*h**2 - 2/3*h**3 + 0 + 22/3*h.
-2*h*(h - 1)*(h + 11)/3
Let g = -18 + 31. Suppose 3*r = -2*t + g, 2 = 4*r + 5*t - 13. Factor 4 + 2*z**4 - 2*z**r - 4.
-2*z**4*(z - 1)
Let m(o) be the first derivative of -1/24*o**4 - 1/60*o**5 + 0*o + 0*o**3 + 3/2*o**2 - 2. Let x(k) be the second derivative of m(k). Find r such that x(r) = 0.
-1, 0
Let h(c) = -16*c**3 - 23*c**2 - 29*c - 11. Let u(f) = 9*f**3 + 12*f**2 + 15*f + 6. Let a(q) = -6*h(q) - 11*u(q). Factor a(s).
-3*s*(s - 3)*(s + 1)
Factor 0 + 43*m + m**2 - 41*m - 3.
(m - 1)*(m + 3)
Let a(v) be the third derivative of v**8/20160 - v**7/5040 - v**6/360 - v**5/60 + 3*v**2. Let c(w) be the third derivative of a(w). Suppose c(g) = 0. What is g?
-1, 2
Let j(h) = h**3 + h**2 - h. Let k be j(0). Let t(u) be the second derivative of -1/3*u**4 - u - 1/10*u**5 + k*u**2 - 1/3*u**3 + 0. Factor t(b).
-2*b*(b + 1)**2
Let h(r) be the first derivative of r**3/12 + r**2 + 4*r - 7. Factor h(b).
(b + 4)**2/4
Let j = 15 - 31. Let k be (j/(-12))/((-6)/(-9)). Factor -6/11*r + 2/11*r**k + 4/11.
2*(r - 2)*(r - 1)/11
Let m be -3*(744/126 - 6). Factor -m*h**3 + 4/7*h**2 + 0 - 2/7*h.
-2*h*(h - 1)**2/7
Let y(f) be the first derivative of f**3/9 - 2*f**2/3 + f + 5. Solve y(l) = 0 for l.
1, 3
Let i be 2 + -9*(-1)/(-5). Let x be (-3)/15 - (-16)/20. Factor x*y + 1/5*y**3 + 3/5*y**2 + i.
(y + 1)**3/5
Let k = -459 - -462. What is j in 0*j**4 - 1/2*j - 1/2*j**5 + 0 + j**k + 0*j**2 = 0?
-1, 0, 1
Let x = 28/39 - 2/39. Factor 2/3*d**3 - 2/3 - x*d + 2/3*d**2.
2*(d - 1)*(d + 1)**2/3
Suppose -8*s = -3*s - 10. Factor -3 + 1 + h**s + 1.
(h - 1)*(h + 1)
Let y = 13 + -1. Suppose 0 = -u - 2*u + y. Find s, given that -2/9 + 0*s - 2/9*s**u + 4/9*s**2 + 0*s**3 = 0.
-1, 1
Let t = 3/19 + -11/190. Let x(k) be the second derivative of 1/6*k**4 - 1/15*k**6 + 1/3*k**3 + 0 + 2*k - t*k**5 + 0*k**2. Factor x(a).
-2*a*(a - 1)*(a + 1)**2
Let s(u) = 3*u - 9. Let j be s(3). Suppose -15*a + 13*a = j. Determine m, given that -2/9*m**4 + 2/9*m**3 + a + 2/9*m**2 - 2/9*m = 0.
-1, 0, 1
Let w(u) = u**2 - 1. Let h(p) = -p**3 + 6*p**2 - 5. Suppose -5*q + 4*b + 12 + 3 = 0, -2*q + 13 = -3*b. Let y(v) = q*h(v) + 5*w(v). Find m, given that y(m) = 0.
0, 1
Let c be 3 - (3/(-3) + 2). Factor -3*p**c + 3*p**2 + 2*p**2 + 2*p.
2*p*(p + 1)
Let k be -2*(1 - 10/4). Suppose 3*f**2 + 7*f**3 - 4*f**2 - 7*f + k*f**2 - 2 = 0. Calculate f.
-1, -2/7, 1
Let f be (-2)/(-3)*((-15)/(-5) + 0). Solve 0*z - 1/5 + 1/5*z**f = 0.
-1, 1
Let y(b) be the third derivative of 1/36*b**3 + 1/315*b**7 - 1/180*b**6 - 1/120*b**5 + 1/72*b**4 + 0 + 2*b**2 + 0*b. Factor y(l).
(l - 1)**2*(2*l + 1)**2/6
Let k(d) be the third derivative of d**7/7560 - d**6/1080 + d**5/360 - d**4/216 + 5*d**3/6 - 4*d**2. Let p(y) be the first derivative of k(y). Factor p(f).
(f - 1)**3/9
Let d(i) be the first derivative of -i**4 + 20*i**3/9 + 32*i**2/3 - 16*i - 22. Find o, given that d(o) = 0.
-2, 2/3, 3
Let u(o) = 164*o**2 + 256*o + 64. Let x(d) = -33*d**2 - 51*d - 13. Let c(i) = -3*u(i) - 16*x(i). Factor c(h).
4*(3*h + 2)**2
Find h, given that -h**2 - h**2 - h**2 + h**2 + 2*h**3 = 0.
0, 1
Let r(n) = 2*n**5 - 2*n**4 - 4*n**3 + 4*n**2 - 3*n - 7. Let s(c) = c + 1. Let z(j) = -r(j) - 5*s(j). Factor z(k).
-2*(k - 1)**3*(k + 1)**2
Let a(h) be the third derivative of -h**5/20 + 3*h**4/8 - h**3 - 5*h**2. Factor a(p).
-3*(p - 2)*(p - 1)
Let t(y) = 21*y**4 - 5*y**3 - 16*y**2 + 6*y + 6. Let d(w) = 125*w**4 - 30*w**3 - 95*w**2 + 35*w + 35. Let u(r) = 6*d(r) - 35*t(r). Factor u(f).
5*f**2*(f - 1)*(3*f + 2)
Let v be (6 - 3)*-1*6/(-120). Let k(w) be the first derivative of 1/5*w**3 + 1/10*w**2 + v*w**4 + 1/25*w**5 + 0*w + 2. Let k(n) = 0. What is n?
-1, 0
Let x(a) = 2*a**3 - 2*a**2 + a - 1. Let w(t) = -t + 1. Let q(n) = -6*w(n) - 2*x(n). Factor q(c).
-4*(c - 1)**2*(c + 1)
Let y(b) = -b + 13. Let f be y(7). Let r(l) be the third derivative of 0*l + 0*l**3 + 0 + 3/20*l**f + 1/3*l**4 - 2/5*l**5 - 2*l**2. What is u in r(u) = 0?
0, 2/3
Let i = 2209/3073 - 2/439. Let w(x) be the first derivative of 1/21*x**6 - 2/7*x + i*x**4 + 5/7*x**2 - 1 - 20/21*x**3 - 2/7*x**5. Find n, given that w(n) = 0.
1
Let a(r) = -2*r**3 + 8*r**2 + 11*r - 1. Let q be a(5). Let k(l) be the second derivative of 2*l + 0 + 0*l**2 + 1/12*l**3 + 1/24*l**q. Factor k(m).
m*(m + 1)/2
Let p(z) be the second derivative of z**6/45 - z**4/18 + z. Solve p(g) = 0 for g.
-1, 0, 1
Suppose 2 = -2*z + 20. Determine m so that 1 - 4 - z*m - 3*m**2 - 3 = 0.
-2, -1
Let p(i) = -i**3 + 34*i**2 + 72*i + 2. Let q be p(36). Suppose 0 - 3/4*d**3 - 1/4*d - d**q = 0. Calculate d.
-1, -1/3, 0
Let f(b) = -b**2 + b. Let l(w) = -3*w**2 + 3 - 7 - 15*w**2 - 2 + 21*w + 3*w**3. Let q(z) = 6*f(z) - l(z). Let q(v) = 0. What is v?
1, 2
Let w(u) = -5*u**5 + 3*u**4 - 3*u**3 - 3*u - 3. Let x(f) = 9*f**5 - 5*f**4 + 5*f**3 + 5*f + 5. Let j(v) = -5*w(v) - 3*x(v). Factor j(k).
-2*k**5
Let k(w) be the first derivative of -w**6/180 + w**5/90 + 4*w**3/3 + 3. Let z(s) be the third derivative of k(s). Factor z(j).
-2*j*(3*j - 2)/3
Let g be 2*((4 - 7) + 5). Factor 2/11*x - 2/11*x**2 + 0 - 2/11*x**3 + 2/11*x**g.
2*x*(x - 1)**2*(x + 1)/11
Let j(w) = -w - 6. Let d be j(-14). Factor -4*l**2 + 0*l + l + d + 3*l.
-4*(l - 2)*(l + 1)
Let x(s) be the first derivative of 0*s**2 - 4/3*s**3 + 0*s + 5. Suppose x(f) = 0. Calculate f.
0
Let v(k) be the third derivative of k**7/70 - k**6/40 - k**5/10 + 31*k**2. Let v(i) = 0. Calculate i.
-1, 0, 2
Let s = 19 - 15. Factor 5*w**s - w**3 - 7*w**4 + w**4.
-w**3*(w + 1)
Let t be ((-3)/4)/(69/(-46)). Solve 1/2 + q + t*q**2 = 0.
-1
Let u(c) be the third derivative of -9/4*c**3 + 0 + 3*c**2 - 1/40*c**5 + 3/8*c**4 + 0*c. Factor u(m).
-3*(m - 3)**2/2
Let f(g) be the third derivative of g**5/180 + g**4/36 + g**3/18 - 2*g**2. Determine w so that f(w) = 0.
-1
Let w be ((4 - 8) + (-13)/(-3))*1. Let p = -13/2 - -43/6. Factor h**2 - p + w*h.
(h + 1)*(3*h - 2)/3
Let -h**4 - h**3 - 17*h + 0 + 6*h**2 + 22*h - 3*h**2 + 2 = 0. Calculate h.
-1, 2
Let z(s) be the first derivative of 0*s**2 + s + 1/12*s**4 - 1/6*s**3 + 2. Let w(v) be the first derivative of z(v). Find y such that w(y) = 0.
0, 1
Suppose -4*t + 528 = 4*y, 0 = -4*t - y - 2*y + 528. Let v = 400/3 - t. Factor 0 - v*x**2 - 2/3*x**3 - 2/3*x.
-2*x*(x + 1)**2/3
Let s(r) be the second derivative of r**7/21 - r**5/5 + r**3/3 + 36*r. Factor s(i).
2*i*(i - 1)**2*(i + 1)**2
Suppose 0 = -4*d + 4*f + 64, -2*f - 8 = d + 3*f. Factor -11 + 3*g**2 - 6*g**2 + 2 + d*g.
-3*(g - 3)*(g - 1)
Let m be 1 + -3 + 492/205. Factor -m*w**3 + 2*w - 4/5 - 6/5*w**2 + 2/5*w**4.
2*(w - 1)**3*(w + 2)/5
Let a(d) = d - 3. Let c be a(0). Let t be (-3)/(c/(1 - -2)). Solve -t*k**3 + 2*k**3 - 2*k**4 + 3*k**4 = 0.
0, 1
Let y(w) be the second derivative of -5*w**7/42 + 2*w**6/5 - 9*w**5/20 + w**4/6 - 8*w. Find g, given that y(g) = 0.
0, 2/5, 1
Let g(z) = -z**5 + z**4 + z**3 - z**2 + z + 1. Let i(f) = -16*f**5 + 42*f**4 - 54*f**3 + 50*f**2 - 16*f + 14. Let b(x) = 10*g(x) - i(x). Factor b(j).
2*(j - 2)*(j - 1)**3*(3*j - 1)
Let l(b) = b**2 + 13*b + 10. Let h be l(-12). Let g(p) = -4*p**2 + 26*p - 36. Let d(m) = -4*m**2 + 27*m - 36. Let i(o) = h*d(o) + 3*g(o). Solve i(t) = 0 for t.
3
Let k = 4/7 - 1/14. Find d, given that -k*d + 3/4*d**2 + 0 + 1/2*d**3 - 3/4*d**4 = 0.
-1, 0, 2/3, 1
Let p(l) = -l**2 + 7*l + 6. Let m be p(7). Factor -m*w**3 - 6*w - 9*w**2 + 0*w + 3*w**3 + 0*w**3.
-3*w*(w + 1)*(w + 2)
Let x(t) be the second derivative of t**7/168 + t**6/120 - t**5/80 - t**4/48 - 7*t. Factor x(p).
p**2*(p - 1)*(p + 1)**2/4
Find b such that -1/7*b**2 + 0 + 4/7*b = 0.
0, 4
Find r such that 0*r - 2/15*r**4 - 2/15*r**3 + 4/15*r**2 + 0 = 0.
-2, 0, 1
Let v(m) be the third derivative of m**7/840 - m**6/96 + 3*m**5/80 - 7*m**4/96 + m**3/12 - 7*m**2. Suppose v(q) = 0. What is q?
1, 2
Suppose 0 = 7*j + 68 - 82. Factor 0 + 4/5*x**3 - 2/5*x**5 + 0*x**j + 0*x**4 - 2/5*x.
-2*x*(x - 1)**2*(x + 1)**2/5
F