Let g(f) = -6*i(f) - u(f). Factor g(w).
(w - 1)**2
Let c(i) be the third derivative of -i**2 - 1/10*i**6 + 0*i + 0*i**3 + 0 - 1/30*i**5 + 0*i**4 - 3/35*i**7 - 1/42*i**8. Factor c(t).
-2*t**2*(t + 1)**2*(4*t + 1)
Let x = -16 + 29. Suppose x = 4*s + 5. Determine a, given that 4/3 - 8/3*a**3 - 8/3*a**4 + 4/3*a**s - 2/3*a**5 + 10/3*a = 0.
-2, -1, 1
Suppose 5*l - 5*v + 250 = 0, l + 2*v + 28 + 37 = 0. Let j be ((-8)/(-10))/(l/(-25)). What is k in 2/11*k**2 - j*k + 2/11 = 0?
1
Let u = -19 - -21. Factor -2*g - 3*g**2 - 2*g + 8*g + 2*g**4 + g**u - 4*g**3.
2*g*(g - 2)*(g - 1)*(g + 1)
Suppose 2*g - 3*g = 3*g. Let d(h) be the second derivative of -1/18*h**4 + g*h**2 - h + 1/90*h**6 + 0*h**3 + 0 + 1/60*h**5. Find r such that d(r) = 0.
-2, 0, 1
Find k, given that 48*k**2 + 8*k - 99*k**2 + 55*k**2 = 0.
-2, 0
Suppose -4*c = 2*p + 14, 3*p - 5*p = -4*c - 26. Let g be -3 + p/9 - -3. Factor g*u**3 + 1/3*u - 2/3*u**2 + 0.
u*(u - 1)**2/3
Let a be (4*1 - 0) + -1. Let v = 127 + -505/4. Solve 1/4 + 3/4*i + v*i**2 + 1/4*i**a = 0 for i.
-1
Let u(l) be the third derivative of l**10/15120 + l**9/3780 + l**8/3360 - l**4/3 + l**2. Let w(b) be the second derivative of u(b). Factor w(s).
2*s**3*(s + 1)**2
Factor 32*n - 34*n**2 + 4 + 56*n**2 + 42*n**2.
4*(4*n + 1)**2
Factor 0 - 3/4*m + m**2 - 1/4*m**3.
-m*(m - 3)*(m - 1)/4
Let b(q) be the first derivative of -q**3/8 + 3*q**2/8 - 3*q/8 - 3. What is l in b(l) = 0?
1
Let f(a) be the first derivative of a**6/540 - a**5/90 + a**4/36 - a**3 + 1. Let d(q) be the third derivative of f(q). Factor d(n).
2*(n - 1)**2/3
Suppose 4 = -r + 2*r. Suppose -c = -r*c + 15. Determine s, given that -s**3 + 2*s**c - 4*s**5 + s**5 + 2*s**3 = 0.
-1, 0, 1
Let f = 19 - 27. Let m be 14/f + (-2)/(-1). Solve b**3 - m*b**4 - 1/4 - 3/2*b**2 + b = 0 for b.
1
Factor -3/2 + 9/4*g**3 + 9/4*g + 6*g**2.
3*(g + 1)*(g + 2)*(3*g - 1)/4
Let u(f) be the second derivative of f**7/15 + 2*f**6/75 - 7*f**5/50 - f**4/15 - 2*f. What is i in u(i) = 0?
-1, -2/7, 0, 1
Let w = -20 - -12. Let h = -5 - w. Factor 3/4*i + 1/2 - 3*i**2 + 7/4*i**h.
(i - 1)**2*(7*i + 2)/4
Let t = 57 + -54. Let h(w) be the first derivative of 0*w**2 - 3 + 0*w + 2/9*w**t. Factor h(j).
2*j**2/3
Let s(n) = -n**3 + 5*n**2 - n + 7. Let b be s(5). Let x(r) be the third derivative of b*r**2 + 0 - 1/30*r**4 + 1/300*r**5 + 0*r + 2/15*r**3. Factor x(o).
(o - 2)**2/5
Let q = 153785/7 + -22107. Let j = q - -138. Factor 4/7*v**2 + 0 - 2/7*v**3 - j*v.
-2*v*(v - 1)**2/7
Let z(a) be the first derivative of 2*a**3/3 + 6*a**2 - 14*a + 2. Determine v, given that z(v) = 0.
-7, 1
Suppose -5*u + 21 = -i, u - 3*i + 15 = 2*i. Let t = -6 - -8. Solve 3*f**4 - 3*f + 3*f + 4*f**u - t*f**4 = 0.
-1/4, 0
Let m(h) be the third derivative of h**8/840 + h**7/175 + h**6/100 + h**5/150 + 4*h**2. Factor m(x).
2*x**2*(x + 1)**3/5
Let x = -2 + 5. Suppose -a + 1 + 4 = -x*y, -4*y - 12 = -4*a. Find b such that a*b - b**3 + 0*b - b**3 = 0.
-1, 0, 1
Let k(m) be the third derivative of m**7/1680 - m**6/960 - 3*m**5/160 - 11*m**4/192 - m**3/12 + 33*m**2. What is y in k(y) = 0?
-1, 4
Let p = 57 - 33. Determine a so that -p*a**3 - 15*a**5 + 7*a**2 + 12*a**5 + 5*a**2 + 2*a**4 + 13*a**4 = 0.
0, 1, 2
Let m = -22 - -19. Let o(q) = -q**2 + q + 1. Let a(l) = 24*l**2 - 60*l - 21. Let i(y) = m*o(y) - a(y). What is w in i(w) = 0?
-2/7, 3
Let b(x) be the third derivative of x**8/1344 - x**7/840 - x**6/80 + x**5/60 + x**4/12 - 37*x**2. Factor b(j).
j*(j - 2)**2*(j + 1)*(j + 2)/4
Suppose -3*o = 4*g - 10, 3*o - 5*g = -6 - 20. Let a be o - (10 + 2)/(-2). Factor -1/2*i**2 - 1/4 + 3/4*i**a + 1/2*i**3 - 3/4*i + 1/4*i**5.
(i - 1)*(i + 1)**4/4
Let c be 0/(2 + -1 - 0). Suppose -z + 2 + 0 = c. Factor -1/3*s**4 + 0 + 1/3*s - 1/3*s**3 + 1/3*s**z.
-s*(s - 1)*(s + 1)**2/3
Let o(y) be the first derivative of -y**4/4 + y**3 + 2*y**2 - 17. Solve o(z) = 0.
-1, 0, 4
Solve 0 - 5/3*b**4 + 4/3*b**3 + 0*b - 2/3*b**5 + b**2 = 0.
-3, -1/2, 0, 1
Let w(l) = -16*l**2 + 34*l + 32. Let y(t) = t**2 - t. Let z(m) = 2*w(m) + 36*y(m). Factor z(q).
4*(q + 4)**2
Let i = 8/11 - 1275/44. Let n = -28 - i. Let -n + 0*u + 1/4*u**2 = 0. What is u?
-1, 1
Let m = -11 - -13. Suppose 5*g + g**m - 4*g - 1 - 2*g**3 + g**3 = 0. Calculate g.
-1, 1
Factor -f**3 - 62 + 62 + f**4.
f**3*(f - 1)
Let p(y) be the first derivative of y**3/27 - 11*y**2/9 + 121*y/9 - 13. Find a such that p(a) = 0.
11
Let i(f) be the third derivative of f**8/336 + f**7/210 - f**6/40 - f**5/12 - f**4/12 + 14*f**2. Factor i(h).
h*(h - 2)*(h + 1)**3
Suppose -3*f - 2*v - 3 = -7, f = -2*v. Factor -4 + 2 - 32*l**3 + 14*l + 4 + 16*l**f.
-2*(l - 1)*(4*l + 1)**2
Suppose 2*z + 27 = -61. Let t = z + 316/7. Factor 0*p - 10/7*p**3 - 2/7*p**2 + 0 - t*p**4.
-2*p**2*(p + 1)*(4*p + 1)/7
Let u be (-24)/54*12/(-40). Let a(j) be the first derivative of -u*j**3 + 3 - 18/5*j + 6/5*j**2. Factor a(m).
-2*(m - 3)**2/5
Let n(y) be the first derivative of -y**8/336 + y**7/210 + y**6/120 - y**5/60 - 5*y**2/2 - 5. Let f(o) be the second derivative of n(o). Solve f(c) = 0.
-1, 0, 1
Factor 2*b**3 - 6*b + b**2 - 9/2 - 1/2*b**4.
-(b - 3)**2*(b + 1)**2/2
Let o(a) be the second derivative of a**4/7 + a**3/2 - 3*a**2/7 - 19*a. Factor o(r).
3*(r + 2)*(4*r - 1)/7
Suppose 43 + 20 = -3*y. Let u = y + 65/3. Factor 0 + 1/3*s**3 + u*s**2 + 1/3*s.
s*(s + 1)**2/3
Let a(i) be the third derivative of -1/6*i**4 + 2*i**2 + 1/15*i**5 + 0*i**3 + 0 - 1/120*i**6 + 0*i. Suppose a(r) = 0. What is r?
0, 2
Let f(m) be the third derivative of 2*m**7/15 + 2*m**6/5 + m**5/5 - m**4/3 - 7*m**2. Factor f(r).
4*r*(r + 1)**2*(7*r - 2)
Let x(a) = -8*a**2 + 21*a + 29. Let h(g) = 9*g**2 - 21*g - 30. Let f(y) = 5*h(y) + 6*x(y). Factor f(q).
-3*(q - 8)*(q + 1)
Suppose 3*b + 81 + 9 = 0. Let s = b - -30. Factor 3/2*o**3 + 0*o**2 + s*o + 0.
3*o**3/2
Suppose 198*j - 6 = 196*j. Factor j + 16/3*h**2 + 8*h.
(4*h + 3)**2/3
Let g = 13 - 10. Determine c, given that -1 - 10*c**3 - 8*c**2 + 14*c**g - 8*c**3 + 4*c + 9 = 0.
-2, -1, 1
Let s(p) be the first derivative of -1/2*p**3 - 3/4*p**2 + 0*p + 6. Factor s(h).
-3*h*(h + 1)/2
Let m(y) = -7*y + 42. Let l be m(6). Suppose 0*v + l - 9/2*v**4 - 3/2*v**2 - 6*v**3 = 0. What is v?
-1, -1/3, 0
Suppose -4*z = 3*p - 2 - 2, -z + 2 = p. Suppose -s - 40 = -5*x - 6*s, 0 = p*s - 12. Factor -2*c**3 - 2*c**3 + c + 0*c**5 - 2*c**2 + c**x + 2*c**3 + c**4 + 1.
(c - 1)**2*(c + 1)**3
Let a(r) be the first derivative of r**8/448 - r**7/210 + r**6/480 + 3*r**2/2 - 3. Let t(s) be the second derivative of a(s). Factor t(v).
v**3*(v - 1)*(3*v - 1)/4
Let z(d) = 5*d**2 + 3*d + 7. Let j = -15 + 12. Let h(u) = 26*u**2 + 14*u + 36. Let w(g) = j*h(g) + 16*z(g). Let w(y) = 0. Calculate y.
-2, -1
Let g(w) = -w**3 + w**2. Let k(j) = -16*j**2. Let z(t) = 4*g(t) + k(t). Solve z(s) = 0 for s.
-3, 0
Let k(f) be the second derivative of -1/6*f**3 + 0 - 1/40*f**5 + 5/48*f**4 + 1/8*f**2 + 3*f. Factor k(t).
-(t - 1)**2*(2*t - 1)/4
Let k(m) be the second derivative of -2/21*m**3 + 1/42*m**4 + 0 + 1/7*m**2 + m. Solve k(t) = 0 for t.
1
Let b(n) be the first derivative of -3*n**5/5 - 3*n**4/4 + 6. Let b(l) = 0. Calculate l.
-1, 0
Let f(y) be the first derivative of -11*y**4/24 - 13*y**3/12 - y**2/2 - 4*y + 6. Let h(a) be the first derivative of f(a). Find m, given that h(m) = 0.
-1, -2/11
Let g be 4/3*3/24. Let w(t) be the first derivative of g*t**3 - 3/20*t**5 + 1/24*t**6 - 3/8*t**2 + 1/8*t**4 + 1/4*t - 1. Suppose w(s) = 0. What is s?
-1, 1
Let j = 79 + -73. Let q(m) be the third derivative of 1/6*m**4 - 1/30*m**j + 1/105*m**7 + 0*m + 3*m**2 + 0*m**5 + 0 - 1/3*m**3. Factor q(n).
2*(n - 1)**3*(n + 1)
Let k(m) = -m**4 + m**3 + m**2 - m + 1. Let z(j) = -3*j**4 + 145*j**3 - 3887*j**2 + 46655*j - 209951. Let g(w) = -2*k(w) + 2*z(w). Solve g(i) = 0.
18
Let g(s) be the first derivative of -s**7/147 - s**6/105 + s - 1. Let x(l) be the first derivative of g(l). Factor x(b).
-2*b**4*(b + 1)/7
Solve -r + r + 3*r**2 + r**4 - 4*r**4 = 0 for r.
-1, 0, 1
Determine m, given that 0*m**4 - 9*m**2 - m**4 + 195 - 7*m - 197 - 5*m**3 = 0.
-2, -1
Let i(g) be the second derivative of g**6/60 + g**5/15 + g**4/12 + 2*g**2 + g. Let m(z) be the first derivative of i(z). Factor m(d).
2*d*(d + 1)**2
Let l(x) be the third derivative of -5*x**2 + 0 + 0*x - 7/30*x**5 - 1/12*x**6 - 1/6*x**4 + 0*x**3. Factor l(j).
-2*j*(j + 1)*(5*j + 2)
Let x(