- 6*f**2 - 4 - 3*f**3 + 4 + 0*f**2 = 0 for f.
-1, 0
Let u(t) be the second derivative of -t**5/10 - t**4/2 + 4*t**3/3 + 14*t + 1. Factor u(z).
-2*z*(z - 1)*(z + 4)
Solve -9*z**3 + 0*z + 0 - 25*z**5 - 105/4*z**4 - z**2 = 0 for z.
-2/5, -1/4, 0
Suppose -5*s = 5*s. Let -1/4 + s*g + 1/4*g**2 = 0. Calculate g.
-1, 1
Let j(s) be the first derivative of 5*s**4/4 - 3*s**3 + 3*s**2/2 + s - 18. Factor j(u).
(u - 1)**2*(5*u + 1)
Let u(w) be the third derivative of w**7/90 + 2*w**6/45 + 11*w**5/180 + w**4/36 - 12*w**2. Solve u(a) = 0.
-1, -2/7, 0
Let u(z) be the first derivative of 2*z**4/3 - 2*z**3/9 + 23. Factor u(l).
2*l**2*(4*l - 1)/3
Let y(u) be the third derivative of u**2 + 0 - 1/27*u**3 + 0*u - 1/54*u**4 - 1/270*u**5. Factor y(r).
-2*(r + 1)**2/9
Let x be (-8 + 11 - 5)/((-2)/4). Factor 8/3 + 38/3*v**2 + 1/3*v**5 + 28/3*v + 25/3*v**3 + 8/3*v**x.
(v + 1)**2*(v + 2)**3/3
Let p be (2/5)/((16/(-4))/(-60)). Let c(g) be the second derivative of 0 - 1/30*g**p + 2*g**2 - 1/4*g**4 + 1/5*g**5 - 2/3*g**3 - g. Factor c(t).
-(t - 2)**2*(t - 1)*(t + 1)
Let x(i) = i**3 + 4*i**2 - 5*i - 12. Let c(m) = -3*m**3 - 7*m**2 + 11*m + 25. Let r(o) = -6*c(o) - 15*x(o). Factor r(l).
3*(l - 5)*(l - 2)*(l + 1)
Let s(l) = -2*l - 7. Let a be s(-6). Factor -2*m + 4*m - 2*m**4 - 8*m**2 + 12*m**3 + 6*m**5 - 6*m**4 - 4*m**a.
2*m*(m - 1)**4
Let d be (-60)/24*64/(-30). Suppose 0 = 2*f - 0*f - 8. Factor -d*w**f + 4*w**3 + 0 - 2/3*w**2 + 0*w.
-2*w**2*(2*w - 1)*(4*w - 1)/3
Let u(a) be the first derivative of a**7/21 + 2*a**6/15 - a**5/10 - a**4/3 - a + 1. Let v(p) be the first derivative of u(p). Let v(n) = 0. What is n?
-2, -1, 0, 1
Let t(h) be the first derivative of -h - 1. Let y = -1 + 4. Let z(n) = n**2 - 2*n - 4. Let i(b) = y*z(b) - 15*t(b). Factor i(j).
3*(j - 1)**2
Let f(o) be the second derivative of -o**4/4 - 3*o**3/2 - 3*o**2 - 11*o. Factor f(g).
-3*(g + 1)*(g + 2)
Let u(c) be the first derivative of c**8/8400 + c**7/4200 - c**6/600 - c**5/600 + c**4/60 + c**3/3 + 2. Let h(g) be the third derivative of u(g). Factor h(y).
(y - 1)**2*(y + 1)*(y + 2)/5
Factor 0 + 4*o**4 + 0*o**2 + 2/3*o**5 + 0*o + 16/3*o**3.
2*o**3*(o + 2)*(o + 4)/3
Let h be 2/((-3)/(9/6)). Let m be (h/3)/(2/(-3)). Factor -1/2*c**5 + 0*c + 1/2*c**3 - m*c**2 + 0 + 1/2*c**4.
-c**2*(c - 1)**2*(c + 1)/2
Let c(j) be the first derivative of 0*j**2 + 2*j + 1 - 1/90*j**5 + 1/135*j**6 - 1/27*j**4 + 0*j**3. Let d(k) be the first derivative of c(k). Factor d(h).
2*h**2*(h - 2)*(h + 1)/9
Factor 10*a**3 + 5*a**4 - 8*a**5 + 7*a**5 - 4*a**5.
-5*a**3*(a - 2)*(a + 1)
Factor -2/7*q + 2/7*q**2 - 4/7.
2*(q - 2)*(q + 1)/7
Solve 5/7*x**2 + x - 4/7*x**3 - 2/7 = 0.
-1, 1/4, 2
Let k be (1/6)/(1/(-2)) + 3. Suppose 2/3*h**2 + 8/3*h + k = 0. What is h?
-2
Let x = -8 + 11. What is n in -3*n**3 - n - n**x - 6*n**2 - n**3 = 0?
-1, -1/5, 0
Let 8*s**2 - 7 - 9 - 54*s + 86*s - 20*s**2 = 0. What is s?
2/3, 2
Suppose v - 4 = -4*s, 5*s - 3*v - 2 = -14. Suppose s = 6*j - 9*j + 12. Solve 0 + 0*m**3 - 1/3*m**2 + 1/3*m**j + 0*m = 0.
-1, 0, 1
Let z(g) be the second derivative of 2/3*g**3 + g**2 - 1/15*g**6 - 1/5*g**5 - 5*g + 0 + 0*g**4. Factor z(w).
-2*(w - 1)*(w + 1)**3
Let v(p) be the third derivative of -p**6/540 - p**5/9 - 25*p**4/9 - 1000*p**3/27 - 43*p**2. Factor v(c).
-2*(c + 10)**3/9
Let b(y) be the first derivative of 2*y**3/3 + 8. Suppose b(l) = 0. What is l?
0
Let z(x) = -6*x**4 - 36*x**3 - 24*x**2 - 6*x + 51. Let i(b) = -b**4 - 7*b**3 - 5*b**2 - b + 10. Let u(m) = 21*i(m) - 4*z(m). Factor u(w).
3*(w - 2)*(w - 1)*(w + 1)**2
Let u(c) be the first derivative of -2*c**2 + 19/10*c**5 + 2*c - 6 - 23/6*c**3 + 1/8*c**4 + 7/12*c**6. Find x, given that u(x) = 0.
-2, -1, 2/7, 1
Let t be (2 + (-11)/6)*15/30. Let f(v) be the third derivative of 1/120*v**5 + 0 - 3*v**2 - 1/240*v**6 + 0*v - t*v**3 + 1/48*v**4. Factor f(k).
-(k - 1)**2*(k + 1)/2
Let w be 15/(-25) + (-76)/(-60). Factor -1/3*d**4 - 1/3*d**2 + 0*d + 0 + w*d**3.
-d**2*(d - 1)**2/3
Let v = -1438/9 - -160. Let 0*t - 2/3*t**3 - 4/9*t**2 + v*t**5 + 0 + 0*t**4 = 0. What is t?
-1, 0, 2
Let g(q) = -q + 7. Let y = 10 - 5. Let n be g(y). Suppose 2/5*m**3 + 2/5*m**5 + 0*m**n + 4/5*m**4 + 0 + 0*m = 0. Calculate m.
-1, 0
Let z(a) be the first derivative of 0*a + 0*a**2 + 3 + 3/2*a**4 + 2/3*a**3. Determine u, given that z(u) = 0.
-1/3, 0
Solve 5*z**2 - 6*z**2 - 1 - z**3 + 2*z**2 + 0*z**2 + z = 0.
-1, 1
What is m in -2*m**2 - 4*m + 3*m**2 - 5*m + 0*m = 0?
0, 9
Let u be (-6)/10*(-1 + -4). Let m be 1/(-2*(-1)/4). What is i in -i**m + i + 3*i**u + 8*i**2 - 3*i**2 = 0?
-1, -1/3, 0
Let q(f) be the first derivative of -5/12*f**4 - 1/18*f**6 + 0*f**2 - 2 + 2/9*f**3 + 4/15*f**5 + 0*f. What is g in q(g) = 0?
0, 1, 2
Let y = 4 + 0. What is t in -2*t**2 + 2 - 2*t**3 + t**3 + 5*t**3 - y*t = 0?
-1, 1/2, 1
Factor 5 - 4*n**3 + 8*n**3 - 2*n**4 - 3 - 6*n**2 + n - 11*n**3.
-(n + 1)**2*(n + 2)*(2*n - 1)
Factor 1/3*z + 1/3*z**2 - 2/3.
(z - 1)*(z + 2)/3
Let q(c) be the second derivative of c**7/420 + c**6/90 + c**5/60 + 2*c**3/3 + 2*c. Let m(d) be the second derivative of q(d). Suppose m(o) = 0. What is o?
-1, 0
Let p = -8638 + 34297/4. Let k = p - -64. Suppose 1/4 + 1/2*x + k*x**2 = 0. Calculate x.
-1
Let 12/5*d**2 + 22/5*d + 2/5*d**3 + 12/5 = 0. Calculate d.
-3, -2, -1
Suppose 32/7*a**2 - 30/7*a**3 - 20*a**5 + 0 - 194/7*a**4 + 8/7*a = 0. What is a?
-1, -1/2, -2/7, 0, 2/5
Let w(h) = -h**3 - 3*h**2 + 5*h + 4. Let l be w(-4). Let i be (-6)/(-10) - 7/(-105). Factor 0*d**4 + 0*d + 0 - 2/3*d**3 + i*d**5 + l*d**2.
2*d**3*(d - 1)*(d + 1)/3
Suppose 5*o + 4 = -3*n, -5*n + 1 = o - 7. Factor 0*k**2 + 3*k**2 - k**2 - n*k**4.
-2*k**2*(k - 1)*(k + 1)
Let d(a) be the third derivative of 3*a**6/80 - a**5/8 + a**4/16 + a**3/4 - 41*a**2. Let d(s) = 0. Calculate s.
-1/3, 1
Factor -2/5*l - 4/5*l**2 + 0 + 4/5*l**4 + 2/5*l**5 + 0*l**3.
2*l*(l - 1)*(l + 1)**3/5
Let d = -104/7 - -534/35. Let n = 5/32 - -39/160. Factor n - 2/5*x**2 + 2/5*x - d*x**3.
-2*(x - 1)*(x + 1)**2/5
Let a(p) be the third derivative of -p**5/30 - p**4/2 - 3*p**3 - 6*p**2. Determine q, given that a(q) = 0.
-3
Let o(k) be the second derivative of 0*k**5 + 3/2*k**2 + 0 + 1/180*k**6 - 1/36*k**4 + 0*k**3 + 2*k. Let r(p) be the first derivative of o(p). Factor r(x).
2*x*(x - 1)*(x + 1)/3
Let z(u) = u**2 - 16*u + 20. Let i be z(15). Let s(h) be the third derivative of 1/24*h**4 + 1/36*h**i + 0 - 1/9*h**3 + 0*h - h**2. Factor s(r).
(r + 1)*(5*r - 2)/3
Suppose 0 = -5*f + f + 12. Suppose 29 - 17 = f*c. Suppose 2*p**5 + 0 + 0*p + 3*p**c + 3/2*p**3 + 1/4*p**2 = 0. What is p?
-1/2, 0
Solve -7*d**4 + 25*d**2 + 5*d**3 - 319*d + 334*d + 2*d**4 = 0.
-1, 0, 3
Let p(m) be the second derivative of -1/3*m**2 + 1/9*m**4 + 0*m**3 + 0 + m + 0*m**5 - 1/45*m**6. Factor p(s).
-2*(s - 1)**2*(s + 1)**2/3
Let o be (-246)/123*(-1 + (-1)/2). Solve 4/3*t**o + 2/3*t**4 + 2/3*t**2 + 0*t + 0 = 0.
-1, 0
Suppose -34 = -6*b - 22. Let 0 - 4/5*u + 6/5*u**3 - 2*u**b = 0. Calculate u.
-1/3, 0, 2
Let g(s) be the third derivative of -3*s**2 + 0 + 2/9*s**3 - 1/90*s**5 + 1/36*s**4 + 0*s. Factor g(v).
-2*(v - 2)*(v + 1)/3
Let d(m) be the third derivative of -m**7/42 - 5*m**6/12 - 11*m**5/4 - 25*m**4/3 - 40*m**3/3 + 10*m**2. Solve d(z) = 0 for z.
-4, -1
Let c(w) = -13*w**2 - 6*w - 11. Let q(v) = -7*v**2 - 3*v - 6. Let y(z) = -6*c(z) + 11*q(z). Factor y(d).
d*(d + 3)
Let w(d) = 7*d**4 - 5*d**3 + 5*d**2 + 5*d - 6. Let c(h) = -h**4 + h**3 - h**2 - h + 1. Let i(s) = 6*c(s) + w(s). Factor i(a).
a*(a - 1)*(a + 1)**2
Let w = -3 + 8. Let q(x) = -x**3 - x**2 + 6*x. Let c(z) = -3*z**2 + z**2 + 3*z**2 + z**3 - 5*z. Let h(g) = w*q(g) + 6*c(g). Factor h(b).
b**2*(b + 1)
Suppose -r + 4*r = 6. Suppose -v = r*v. Factor -1/2*j**2 + v*j - 1/2*j**3 + 0.
-j**2*(j + 1)/2
Suppose -2*z + 5*v = 16, 0 = 5*v + 6 - 26. Let -2/9*u + 0 + 2/9*u**z - 2/9*u**4 + 2/9*u**3 = 0. Calculate u.
-1, 0, 1
Let i be 1*2/2084*4. Let h = 2094/2605 - i. Suppose -4/5*m**3 + 2/5*m**4 + h*m + 0*m**2 - 2/5 = 0. What is m?
-1, 1
Let n(b) = -17*b**3 + 32*b**2 - 12*b - 8. Let l(z) = 52*z**3 - 96*z**2 + 36*z + 24. Let f(k) = 5*l(k) + 16*n(k). Factor f(o).
-4*(o - 2)*(o - 1)*(3*o + 1)
Suppose 126 - 18 = 4*m. Determine w so that 0*w**3 - m + 27*w - 8*w**2 - w**2 + w**3 = 0.
3
Let u(b) = 2*b - 26. Let d be u(14). Let n(t) be the second derivative of -3/5*t**5 + 13/6*t**4 + 4*t**