g**2 - 3*g + 2. Let m(z) = 16*z**5 - 9*z**4 + 9*z**3 + 10*z**2 - 14*z + 10. Let k(h) = 2*m(h) - 11*u(h). Factor k(s).
-(s - 2)*(s - 1)**3*(s + 1)
Let t(m) be the first derivative of 2*m**5/45 - m**4/6 + 4*m**3/27 - 6. Factor t(o).
2*o**2*(o - 2)*(o - 1)/9
Solve 2*z**2 + 4/5*z + 6/5*z**3 + 0 = 0.
-1, -2/3, 0
Let v(x) be the first derivative of -x**8/9240 + x**7/2310 - x**5/330 + x**4/132 - x**3/3 - 8. Let q(f) be the third derivative of v(f). Factor q(u).
-2*(u - 1)**3*(u + 1)/11
Let x = -133 - -1199/9. Factor -2/9*o**3 + x*o + 0 - 2/9*o**4 + 2/9*o**2.
-2*o*(o - 1)*(o + 1)**2/9
Let p(q) = q**3 - q**2 + 1. Let l(w) = -w**4 - 12*w**3 - 3*w**2 - 6. Let m(o) = -5*l(o) - 30*p(o). Factor m(y).
5*y**2*(y + 3)**2
Suppose -y = 2*y - 6. Factor 3/2*m**y - 2 - m + 5/4*m**3 + 1/4*m**4.
(m - 1)*(m + 2)**3/4
Suppose 4*w - 6*w + 12 = 4*s, -s + 2 = 0. Factor -8/9*t**4 - 2/9*t - 4/3*t**w + 0 - 2*t**3.
-2*t*(t + 1)**2*(4*t + 1)/9
Let z(h) be the third derivative of h**6/480 - h**5/48 + 7*h**4/96 - h**3/8 - 17*h**2. Suppose z(y) = 0. Calculate y.
1, 3
Suppose -36 = -23*p + 10. Solve -1/3*f**3 + 1/3*f**p + 1/3*f - 1/3 = 0 for f.
-1, 1
Let p = -15 + -12. Let o be 7/4 + p/18. Find k, given that -1/4*k**2 + 0 + o*k = 0.
0, 1
Let w(m) be the second derivative of m**7/280 + m**6/60 - m**5/40 - m**4/4 + m**3/2 + 3*m. Let n(i) be the second derivative of w(i). Factor n(t).
3*(t - 1)*(t + 1)*(t + 2)
Let j(l) be the first derivative of 0*l - 1/2*l**4 + 0*l**2 + 4/5*l**5 - 4/3*l**3 + 1/3*l**6 - 2. Solve j(c) = 0.
-2, -1, 0, 1
Let a be 1 + -1 + (-17)/20. Let x = a - -11/10. Solve -x*s**2 + 0 + 0*s = 0 for s.
0
Let g = 554 - 552. Factor -12/7 - 20/7*p + 4/7*p**3 - 4/7*p**g.
4*(p - 3)*(p + 1)**2/7
Let t = -10 - -15. Let u(z) be the first derivative of -1/5*z**t + 1 - 1/4*z**4 + 1/4*z**3 - 1/4*z + 1/4*z**2. Factor u(s).
-(s + 1)**2*(2*s - 1)**2/4
Let d be 3 + ((-9)/(-3))/(-3). Let f(j) be the second derivative of -1/12*j**3 + 1/24*j**4 - d*j + 0*j**2 + 0. Factor f(p).
p*(p - 1)/2
Suppose 8 = 4*f, -2*f + 2 + 0 = -q. Let t(y) be the second derivative of -3*y + 1/20*y**5 + 1/4*y**4 + 1/2*y**3 + 0 + 1/2*y**q. Factor t(s).
(s + 1)**3
Suppose 0*t - 4*t = -2*t. Factor -2/3*r**3 + 0*r + 1/3*r**4 + 1/3*r**2 + t.
r**2*(r - 1)**2/3
Let y(g) = 22*g**3 + 6*g**2 - 10*g + 10. Let v(c) = 3 + 0*c**2 + 7*c**3 - 2*c + 4*c**2 - 2*c**2 - c. Let f(x) = 10*v(x) - 3*y(x). Factor f(l).
2*l**2*(2*l + 1)
Solve -6/5*f + 3/5*f**2 - 9/5 = 0 for f.
-1, 3
Let q(i) be the first derivative of i**4/4 - i**3/3 - i**2/2 + i - 2. Let q(w) = 0. Calculate w.
-1, 1
Solve 4/9*q + 0 - 4/9*q**2 = 0 for q.
0, 1
Factor -145 + 141 - 2*r**2 + 8*r + 4*r**2 - 6*r.
2*(r - 1)*(r + 2)
Factor g - 1/2*g**4 + 0 - 1/2*g**5 + 5/2*g**2 + 3/2*g**3.
-g*(g - 2)*(g + 1)**3/2
Suppose 4*y = -2*u - 2*u + 20, 0 = -5*y - u + 25. Find b, given that -1/4*b + b**2 - 3/2*b**3 + b**4 - 1/4*b**y + 0 = 0.
0, 1
Let g(o) be the second derivative of 0 + 0*o**2 + 4*o - 1/4*o**4 + 2/3*o**3 - 9/40*o**5 - 1/30*o**6. Let h(b) be the second derivative of g(b). Factor h(n).
-3*(n + 2)*(4*n + 1)
Let n(i) = i**3 + 13*i**2 + 3*i + 42. Let q be n(-13). Factor 1/3*b**q - 2/3 - 4/3*b**2 + 5/3*b.
(b - 2)*(b - 1)**2/3
Let a(z) be the third derivative of z**7/840 + z**6/80 + 3*z**5/80 + 6*z**2. Find f, given that a(f) = 0.
-3, 0
Let v(m) = -15*m**2 - 18*m - 21. Let j(q) = 3*q**2 + 0*q + 4*q**2 + 9*q + 2 + 8. Let f(i) = -9*j(i) - 4*v(i). Factor f(c).
-3*(c + 1)*(c + 2)
Let c(a) be the second derivative of a**7/840 - a**6/1080 - a**5/120 + a**4/72 - a**3/6 + 5*a. Let y(j) be the second derivative of c(j). Factor y(g).
(g - 1)*(g + 1)*(3*g - 1)/3
Let x(d) be the third derivative of -2/9*d**3 - 1/180*d**6 + 0*d + 1/45*d**5 + 1/36*d**4 + 2*d**2 + 0. Determine n, given that x(n) = 0.
-1, 1, 2
Suppose 3*n = -3*d - 3, -3*d + 2*n + 2 = 15. Let c be 46/14 + d + 0. Factor 2/7 - 4/7*v + c*v**2.
2*(v - 1)**2/7
Let a(i) = i**2 - 4*i + 7. Let y be a(5). Suppose 0 = -5*k + k + y. Factor -3*h**3 + 6*h**2 - 4*h + h**k + 0*h**2.
-2*h*(h - 2)*(h - 1)
Suppose 4*m - 8 - 4 = 0. Let b be -4 - (-18 + 0)/m. Solve -1/3*w**b - 1/3 + 2/3*w = 0 for w.
1
Suppose -r - 2*r = 3*r. Let v = 1 + 2. Factor 1/4*i**5 - 1/2*i**4 + 0 + r*i + 1/4*i**v + 0*i**2.
i**3*(i - 1)**2/4
Let w be (49 + -4)/3*-1. Let z = w + 15. Suppose -1/2*a**2 + 7/2*a**4 + z - 2*a**5 + 0*a - a**3 = 0. Calculate a.
-1/4, 0, 1
Let b(v) be the first derivative of 1/50*v**5 - 1/15*v**3 - 1/30*v**4 + 2 + 1/5*v**2 + 3*v. Let f(w) be the first derivative of b(w). Find g such that f(g) = 0.
-1, 1
Factor -2*d**3 + 3/2*d**2 + 1/2*d**4 + 0 + 0*d.
d**2*(d - 3)*(d - 1)/2
Let b(m) be the second derivative of m**5/35 - m**4/21 + 18*m. Find h, given that b(h) = 0.
0, 1
Suppose 6 = -3*d - 0*d + 3*v, v = 3*d + 8. Let p be d/21*1*-4. Factor 2/7 + 6/7*l + p*l**2.
2*(l + 1)*(2*l + 1)/7
Let y(n) = -4*n**4 + 4*n**3 - 9*n**2 - 9*n - 9. Let m(i) = -i**4 + i**3 - 2*i**2 - 2*i - 2. Let x(q) = 9*m(q) - 2*y(q). Find l such that x(l) = 0.
0, 1
Let z = -3 + 1. Let i be z/(-7) + (-68)/(-7). Determine d so that -i*d**5 - d**4 - 10*d - 1 + 8*d**2 - 3*d**4 - 3 + 20*d**3 = 0.
-1, -2/5, 1
Suppose -3*g - 2 = -8. Let l(x) be the first derivative of -g + 1/3*x + 0*x**2 - 1/9*x**3. Factor l(q).
-(q - 1)*(q + 1)/3
Let p be 6 + (-2 - 5 - -4). Solve 0*i**p - 4/3*i**4 + 0*i**2 + 0 + 0*i = 0.
0
Let i = 175/2 - 86. Solve 3/2 + 3/2*d**4 + 3*d**3 - 3/2*d - i*d**5 - 3*d**2 = 0.
-1, 1
Let b(d) be the second derivative of -2*d**7/21 + d**5/5 + 12*d. Let b(m) = 0. Calculate m.
-1, 0, 1
Let w(k) be the third derivative of 5/72*k**4 + 1/40*k**6 - 1/9*k**3 + 4/45*k**5 - 4*k**2 + 0 + 0*k. What is j in w(j) = 0?
-1, 2/9
Let d = 22 - 22. Let x(j) be the second derivative of d*j**4 - 1/45*j**6 + 1/15*j**5 + 2*j + 1/3*j**2 + 0 - 2/9*j**3. Find m such that x(m) = 0.
-1, 1
Suppose -1/4*o**2 - 3*o - 9 = 0. Calculate o.
-6
Let g(a) = -4*a**5 - 12*a**4 + 8*a**3 + 160*a**2 - 312*a + 184. Let c(p) = p**5 - p**4 - p**3 - p + 1. Let b(x) = -8*c(x) - g(x). Find v, given that b(v) = 0.
-3, 2
Let y be 10/30 - 113/112. Let r = -1/112 - y. Factor -r + 4*s - 6*s**2.
-2*(3*s - 1)**2/3
Let x be (-12)/21*42/(-12). Let m be (-15)/70*(-8)/6. Factor -2/7*g**x - m + 4/7*g.
-2*(g - 1)**2/7
Factor 0 + 0*o**4 + 0*o**2 + 0*o - 1/2*o**3 + 1/2*o**5.
o**3*(o - 1)*(o + 1)/2
Suppose 134*i + 48 = 158*i. Determine t so that -1/6*t**4 + 0*t**3 + 1/2*t**i + 1/3*t + 0 = 0.
-1, 0, 2
Let q(s) be the second derivative of 1/70*s**5 + 1/14*s**4 + 0*s**2 - 3*s + 0 + 2/21*s**3. Factor q(o).
2*o*(o + 1)*(o + 2)/7
Let u(f) be the first derivative of 3/4*f**2 + 1 + 0*f**3 + 1/2*f - 1/2*f**4. Factor u(l).
-(l - 1)*(2*l + 1)**2/2
Let a(l) be the second derivative of -1/189*l**7 + 5*l + 0*l**6 + 1/27*l**4 + 0*l**3 + 1/30*l**5 + 0 + 0*l**2. Find g, given that a(g) = 0.
-1, 0, 2
Let g(f) be the first derivative of -f**4/8 - f**3/3 - 21. Factor g(p).
-p**2*(p + 2)/2
Let x(c) = -11*c**2 - 6*c - 29. Let m(g) = -4*g**2 - 2*g - 10. Let r(s) = -17*m(s) + 6*x(s). Find i, given that r(i) = 0.
-1, 2
Let u(b) be the first derivative of 2/5*b + 0*b**2 + 5 - 2/15*b**3. Suppose u(a) = 0. What is a?
-1, 1
Suppose 0 = 2*q + 87 - 87. Let b(u) be the first derivative of 0*u**5 + 0*u + 1/2*u**6 + q*u**2 - 1 - 3/4*u**4 + 0*u**3. Factor b(k).
3*k**3*(k - 1)*(k + 1)
Let b(d) be the first derivative of 0*d - 2/3*d**3 + 3 - 4*d**4 - 2*d**5 + 2*d**2. Factor b(l).
-2*l*(l + 1)**2*(5*l - 2)
Let o(n) = -9*n**4 + 13*n**3 - 10*n - 6. Let d(f) = -8*f**4 + 12*f**3 - 9*f - 5. Let y(a) = 6*d(a) - 5*o(a). Factor y(i).
-i*(i - 2)*(i - 1)*(3*i + 2)
Let t = 79/332 + 1/83. Let i(p) be the second derivative of 0*p**2 + 3*p - t*p**3 + 1/16*p**4 + 0. Suppose i(x) = 0. What is x?
0, 2
Suppose 5*t + 4*q - 78 = 0, 3*q - 34 = -2*t - 0*t. Let b be 1 + (4/t - 1). Suppose 0 + b*o**2 - 2/7*o = 0. What is o?
0, 1
Let b = -26 + 30. Let r(j) be the third derivative of 0*j - 2*j**2 - 1/180*j**5 + 1/36*j**b + 0 - 1/18*j**3. Determine u, given that r(u) = 0.
1
Let b be (-56)/(-12) - (-4)/(-6). Suppose 12 = b*m + 4. Factor 0*g + 0 + 1/2*g**m.
g**2/2
What is a in -3*a**2 - a**2 - 10*a**3 + 33*a**5 - 41*a**5 + 22*a**4 = 0?
-1/4, 0, 1, 2
Let i(v) be the first derivative of -7*v**6/3 + 66*v**5/5 + 59*v**4/2 - 14*v**3 - 52*v**2 - 24*v - 65. Let i(c) = 0. Calculate c.
-1, -2/7, 1, 6
Factor 12/5*x - 9/5