.
-2, 1
Suppose 33*i = 68 - 2. Factor -2 + 2*f - 1/2*f**i.
-(f - 2)**2/2
Let w(o) = o**2 - o - 8. Let s(q) = -q**2 + q + 17. Suppose 0 = -2*z - 2*z + 20. Let p(l) = z*w(l) + 2*s(l). Factor p(g).
3*(g - 2)*(g + 1)
Let o(d) be the first derivative of -d**8/1680 - d**7/420 + d**6/360 + d**5/60 - d**3/3 + 2. Let m(t) be the third derivative of o(t). Factor m(i).
-i*(i - 1)*(i + 1)*(i + 2)
Let u(z) be the first derivative of -z**5 - 5*z**4/2 - 5*z**3/3 - 3. Factor u(x).
-5*x**2*(x + 1)**2
Let t(j) = -j + 6. Let c be t(4). Let x(z) be the second derivative of -1/6*z**3 - 2*z + 0*z**c + 0 - 1/12*z**4. Factor x(a).
-a*(a + 1)
Let x(l) be the third derivative of -l**5/20 + 7*l**4/8 + 24*l**2. Factor x(m).
-3*m*(m - 7)
Suppose d = -3*d. Let z be 9/(54/(-60))*2/(-4). Factor 0*h**4 - 2/7*h**z + 0*h + 0 + d*h**2 + 2/7*h**3.
-2*h**3*(h - 1)*(h + 1)/7
Factor -7/4*q**2 + 15/4*q + 1/4*q**3 - 9/4.
(q - 3)**2*(q - 1)/4
Let z(u) be the third derivative of -u**7/7560 + u**5/360 - u**4/6 - u**2. Let t(s) be the second derivative of z(s). Factor t(v).
-(v - 1)*(v + 1)/3
Let m(g) = g**2 + 7*g - 4. Let d be m(-6). Let n = -10 - d. Solve -1/2*u**5 + 1/2*u**2 + 0 + 1/2*u**3 - 1/2*u**4 + n*u = 0 for u.
-1, 0, 1
Factor -2*v**2 + v + v - 3*v - 3*v.
-2*v*(v + 2)
Let l(t) be the first derivative of -6*t**5/5 + t**4 + 8*t**3/3 - 2*t**2 - 2*t - 6. Find a such that l(a) = 0.
-1, -1/3, 1
Suppose 3*o - o - 6 = 0. Factor t**o + 3*t**2 + 0*t**3 - 4*t**2.
t**2*(t - 1)
Let j = 27 + -18. Let q = 12 - j. Let 0*i**3 + 0*i**q + 4*i**2 + 2*i**3 - 4*i**3 = 0. Calculate i.
0, 2
Let h(w) be the first derivative of -w**5/20 + w**4/8 + w**3 + w**2 - 3. Let l(b) be the second derivative of h(b). Determine i so that l(i) = 0.
-1, 2
Suppose f**5 - 11*f**4 - 2*f - 4*f**4 + 3*f**2 + f**3 + 12*f**4 = 0. Calculate f.
-1, 0, 1, 2
Let z = 49 + -49. Factor 8/3*l**2 + z*l + 0 + 20/3*l**3 + 4*l**4.
4*l**2*(l + 1)*(3*l + 2)/3
Factor 15*c**2 - 16*c + 4*c**3 - 22*c**2 + 19*c**2 + 0*c**3.
4*c*(c - 1)*(c + 4)
Let x(s) be the second derivative of s**7/84 - s**5/20 + s**3/12 - 8*s. Factor x(f).
f*(f - 1)**2*(f + 1)**2/2
Solve 0 + 3/5*s - 1/5*s**3 - 2/5*s**2 = 0.
-3, 0, 1
Let r(d) be the second derivative of -d**8/168 + d**7/840 + 7*d**6/360 + d**5/60 + 5*d**3/6 + 4*d. Let h(f) be the second derivative of r(f). Factor h(q).
-q*(q - 1)*(2*q + 1)*(5*q + 2)
Let r = 35 - 18. Suppose 2 + 0 = -a, -4*a - r = -3*x. What is v in 0 + 1/4*v + 1/4*v**x + 1/2*v**2 = 0?
-1, 0
Let y(d) be the second derivative of d**5/210 + d**4/42 + d**3/21 + 5*d**2/2 + 6*d. Let x(s) be the first derivative of y(s). Factor x(z).
2*(z + 1)**2/7
Let y = 17 + -7. Let n(s) = -s**2 + 11*s - 7. Let g be n(y). What is u in -4*u + 1/2 + 21/2*u**2 - 9*u**g = 0?
1/3, 1/2
Let c(j) = -j + 6. Let h be c(6). Let t(v) be the third derivative of 1/210*v**6 + 0*v**4 + 0*v + 0*v**3 - 1/735*v**7 - 1/210*v**5 + v**2 + h. Factor t(k).
-2*k**2*(k - 1)**2/7
Let s = 207 - 203. Factor 1/3*q - 1/3*q**2 - 1/3*q**3 + 0 + 1/3*q**s.
q*(q - 1)**2*(q + 1)/3
Let g(o) be the first derivative of -o**4/12 - 5*o**3/9 - o**2/2 + 7*o + 2. Let x(k) be the first derivative of g(k). Factor x(l).
-(l + 3)*(3*l + 1)/3
Suppose -3*l - 14 = 4*o, -5*l + 0*o = o + 12. Let t(m) = -m - 2. Let y be t(l). Factor 2/11*c**2 + y + 2/11*c.
2*c*(c + 1)/11
Let p be (-15)/6*(-54)/15. Let r = p + -8. Factor 0*k - 4*k + r - 2*k**2 - 7 + 4.
-2*(k + 1)**2
Let z(i) be the second derivative of 1/3*i**3 + 0*i**2 + 5*i + 0 + 7/10*i**6 + 1/20*i**5 - 3/4*i**4 + 3/14*i**7. Factor z(r).
r*(r + 1)*(r + 2)*(3*r - 1)**2
Let k be (5 + 0)*(-3)/(-5). Suppose -s = k*s - 12. Factor 1/4*c**s + 1/4 - 1/4*c - 1/4*c**2.
(c - 1)**2*(c + 1)/4
Let b(t) be the third derivative of -t**6/540 + t**5/360 + t**3/2 - 4*t**2. Let k(l) be the first derivative of b(l). Factor k(d).
-d*(2*d - 1)/3
Let q(w) be the first derivative of 2*w**3/3 - 9*w**2/7 + 4*w/7 + 8. What is c in q(c) = 0?
2/7, 1
Let k(s) be the third derivative of 1/90*s**5 + 4/9*s**3 + 0 + 0*s + 1/9*s**4 - 2*s**2. Determine c, given that k(c) = 0.
-2
Let v(w) be the first derivative of -4*w**5/5 + 3*w**4/2 - w**2 - 2. Factor v(h).
-2*h*(h - 1)**2*(2*h + 1)
Let k = -8495/24 - -354. Let b(x) be the third derivative of -1/8*x**6 + k*x**4 + 4/15*x**5 + 0 - 1/3*x**3 + 0*x + 4*x**2. Factor b(o).
-(o - 1)*(3*o + 1)*(5*o - 2)
Suppose -5*g + u + 17 + 0 = 0, 0 = -3*g - 3*u + 21. Solve 0*q + 0 + 6/7*q**3 - 8/7*q**g + 0*q**2 + 2/7*q**5 = 0 for q.
0, 1, 3
Solve 3*k**2 - 3*k - 3*k**4 + 3*k + 3*k - 6*k**3 + 3*k = 0.
-2, -1, 0, 1
Suppose 0 = 5*v - 4*t - 5, -4*t + 3 = 3*v + t. Let f = v + 2. Determine k, given that -3/5*k**f + 6/5*k - 3/5*k**2 + 0 = 0.
-2, 0, 1
Let b(r) = 19*r**3 + 37*r**2 + 31*r - 1. Let n = -1 - -5. Let s(x) = -10*x**3 - 19*x**2 - 16*x + 1. Let g(a) = n*b(a) + 7*s(a). Solve g(z) = 0.
-1, -1/2
Let x(p) be the second derivative of p**6/15 - p**4/3 + p**2 - p. Factor x(f).
2*(f - 1)**2*(f + 1)**2
Suppose -2*w = -5*w + 48. Solve -29*h**2 + 9*h**2 + w*h**2 + 4 = 0.
-1, 1
Factor -2/7*z**4 + 8/7*z**3 - 24/7*z - 18/7 + 4/7*z**2.
-2*(z - 3)**2*(z + 1)**2/7
Suppose -6*o + 9/7*o**2 + 24/7 = 0. What is o?
2/3, 4
Let n(u) be the third derivative of 0*u + 1/480*u**6 + 1/96*u**4 + 1/120*u**5 + 4*u**2 + 0*u**3 + 0. Determine x, given that n(x) = 0.
-1, 0
Let q(x) be the second derivative of -1/54*x**4 + 0*x**3 + 0*x**2 - 1/90*x**5 - 4*x + 0. Factor q(c).
-2*c**2*(c + 1)/9
Let m = 543 - 543. Suppose 9 = 2*y + y. Factor m*i + 0*i**2 + 0 - 3/2*i**y.
-3*i**3/2
Let m(l) = -4*l**4 + 4*l**2. Let d(o) = -o**5 - 12*o**4 + o**3 + 12*o**2. Let s(q) = -4*d(q) + 11*m(q). Factor s(w).
4*w**2*(w - 1)*(w + 1)**2
Let a(r) be the third derivative of 1/72*r**4 + 1/90*r**5 + 0 + 0*r - 2*r**2 + 1/360*r**6 + 0*r**3. Factor a(x).
x*(x + 1)**2/3
Let c(b) be the third derivative of -b**8/112 + 3*b**6/40 - b**5/10 + 10*b**2. Find l, given that c(l) = 0.
-2, 0, 1
Let i(y) be the second derivative of -y**9/12096 - y**8/3360 - y**7/3360 + y**3/3 + 3*y. Let t(g) be the second derivative of i(g). Factor t(f).
-f**3*(f + 1)**2/4
Factor 4 + 8/3*h**2 + 22/3*h - 2/3*h**3.
-2*(h - 6)*(h + 1)**2/3
Let j(k) = -10*k**2 + 2*k - 6. Let f(c) = 9*c**2 - c + 5. Let g(m) = 6*f(m) + 5*j(m). Solve g(a) = 0 for a.
-1, 0
Factor 6*t**4 + 5*t**4 - 5*t**5 - 6*t**4.
-5*t**4*(t - 1)
Suppose -3 = -3*u + 4*c, 4*c - c = 5*u - 16. Solve 7*r**4 - 3*r**3 - r**3 - 2*r**u - r**4 = 0 for r.
0, 1, 2
Let w(j) be the third derivative of -j**7/16380 - j**6/1170 - j**5/195 - j**4/12 + 6*j**2. Let v(d) be the second derivative of w(d). Let v(k) = 0. Calculate k.
-2
Let q(z) = 3*z**3 - 9*z**2 + 12. Let t(b) = 3*b**3 - 9*b**2 + 12. Let c(j) = -6*q(j) + 5*t(j). Factor c(n).
-3*(n - 2)**2*(n + 1)
Let b(i) be the third derivative of -i**7/210 - i**6/60 + i**5/20 + i**4/6 - 2*i**3/3 + 5*i**2. Solve b(y) = 0 for y.
-2, 1
Let w(z) be the second derivative of -5*z + 1/30*z**4 - 3/100*z**5 + 0*z**3 + 0 + 0*z**2. Solve w(d) = 0 for d.
0, 2/3
Let z(n) = n**3 + 3*n**2 - 4*n + 4. Let p be z(-4). Factor -4*x + 8*x - x**5 + 8*x**p - 3*x**5 - 8*x**2.
-4*x*(x - 1)**3*(x + 1)
Let l(g) = -4*g**2 - 5. Let u(n) = 5*n**2 - 2*n + 12. Let p(z) = 7*z**2 - 3*z + 18. Let b(w) = 5*p(w) - 8*u(w). Let m(x) = 3*b(x) - 4*l(x). Factor m(d).
(d + 1)*(d + 2)
Let c(d) be the second derivative of -d**4/84 - d**3/7 - 9*d**2/14 + 15*d. Factor c(y).
-(y + 3)**2/7
Suppose -1/6*p**3 + 2/3*p**2 - 2/3*p + 0 = 0. What is p?
0, 2
Suppose 20 = 3*c - 7*c. Let u = 7 + -3. Let t(f) = 3*f**3 - 3*f**2 + 2*f - 4. Let a(d) = 4*d**3 - 4*d**2 + 2*d - 5. Let s(m) = c*t(m) + u*a(m). Factor s(q).
q*(q - 2)*(q + 1)
Let z be -3 + ((-40)/(-45) - -3). Let 0 + 0*i + z*i**3 + 2/9*i**2 = 0. Calculate i.
-1/4, 0
Let w(m) be the second derivative of 0 - 5*m + 3/40*m**5 + 2*m**3 - 3*m**2 - 5/8*m**4. Let w(l) = 0. What is l?
1, 2
Let j(g) be the first derivative of -2*g**5/45 - 4*g**4/9 - 40*g**3/27 - 16*g**2/9 - 16. Determine d, given that j(d) = 0.
-4, -2, 0
Let k be 20 - (0 + 0)/(-1). Suppose 2*l = -3*l + k. Suppose -4*h**3 - h**4 - 11*h**2 - 12*h - 2*h**2 - l - 2*h**3 = 0. What is h?
-2, -1
Factor -4*x**4 + 8*x**2 + 12*x**3 - 2*x**4 - 12*x**2 - 2*x**4.
-4*x**2*(x - 1)*(2*x - 1)
Let v(q) be the third derivative of q**8/1176 - q**7/735 - q**6/210 + q**5/105 + q**4/84 - q**3/21 + q**2. Determine g so that v(g) = 0.
-1