 0, 1
Suppose 1/4*p**2 + 1/2 - 3/4*p = 0. Calculate p.
1, 2
Let u = -65 - -68. Solve 0*f - 2*f**u + 1/2*f**2 + 0 = 0 for f.
0, 1/4
Let k(o) be the second derivative of o**7/630 + o**6/90 + o**5/30 + 7*o**4/12 + 2*o. Let u(q) be the third derivative of k(q). Let u(n) = 0. What is n?
-1
Let t = -16/3 + 41/6. Let f(o) be the first derivative of 2*o**3 - 9/2*o**2 + t*o**4 + 1 + 3*o + 1/2*o**6 - 9/5*o**5. Solve f(c) = 0 for c.
-1, 1
Suppose -3*x = 3*q - 15, 4*x + 5*q - 18 = 7. Let k(s) be the third derivative of 0*s - 2*s**2 - 1/30*s**4 + 0 + x*s**3 + 1/150*s**5. Factor k(v).
2*v*(v - 2)/5
Factor 1/6*i**5 - 1/3 - 1/3*i**3 - 7/6*i + 1/3*i**4 - 4/3*i**2.
(i - 2)*(i + 1)**4/6
Let b(t) = 2*t**2 - 17*t - 7. Let s be b(9). Suppose 1/4*h**s + 0 + 1/4*h = 0. What is h?
-1, 0
Let h = 117/4 + -29. Let y(u) be the first derivative of -2 + 0*u**3 - h*u**2 + 0*u + 1/8*u**4. Solve y(j) = 0.
-1, 0, 1
Let d(b) = 4*b**4 - 8*b**3 + 6*b**2 - 2. Let x(n) = -4*n**4 + 8*n**3 - 7*n**2 + 3. Let y(m) = 3*d(m) + 2*x(m). Let y(i) = 0. Calculate i.
0, 1
Let u(g) be the first derivative of g**6/36 + g**5/10 - g**4/24 - 11*g**3/18 - g**2 - 2*g/3 - 7. Suppose u(s) = 0. Calculate s.
-2, -1, 2
Factor 2/5*o**2 + 8/5 - 2*o.
2*(o - 4)*(o - 1)/5
Let s(f) be the first derivative of 0*f + 1/16*f**4 - 3 + 0*f**2 + 1/6*f**3 - 1/20*f**5. Suppose s(a) = 0. What is a?
-1, 0, 2
Let w be 4 - (2 - (0 + 0)). Determine y so that 3*y**2 - 4*y**w + y + 2*y**3 - y**2 + 2 - 3*y = 0.
-1, 1
Let f(b) = 19*b**3 - 2*b**2 - 56*b + 28. Let y(t) = -18*t**3 + 3*t**2 + 57*t - 27. Let z(w) = 3*f(w) + 4*y(w). Solve z(i) = 0.
-2, 2/5, 2
Let a(q) be the third derivative of q**8/16800 - q**7/12600 - q**6/900 + q**5/20 - 4*q**2. Let o(i) be the third derivative of a(i). Solve o(u) = 0.
-2/3, 1
Factor 0 - m**4 + 1/4*m**2 + 0*m + 3/4*m**3.
-m**2*(m - 1)*(4*m + 1)/4
Let n be 1*3/6*0. Let v(b) be the first derivative of 1/16*b**4 + 1/12*b**3 + 0*b + 1 + n*b**2. Factor v(i).
i**2*(i + 1)/4
Let p(c) = -4*c**2 + 2*c + 6. Let f(x) = x**2 + x + 1. Let i(t) = 3*f(t) - p(t). Let a(l) = -4*l**2 - l + 2. Let w(r) = 5*a(r) + 3*i(r). Solve w(b) = 0 for b.
1
Let j(n) = -1 + 4*n**2 + 2*n - 3*n - 2*n + 0. Let q(w) = 3*w**2 - 3*w. Let p(t) = -2*j(t) + 3*q(t). Factor p(v).
(v - 2)*(v - 1)
Factor 3/4*x**2 - 3/2*x**3 + 0*x + 0.
-3*x**2*(2*x - 1)/4
Suppose 1 + 47 = 4*m. Factor 11*l - m + 0*l**2 - 3*l**2 + l + 0*l.
-3*(l - 2)**2
Let q(f) be the second derivative of -1/4*f**2 + 6*f + 1/24*f**4 + 1/80*f**5 + 0 - 1/24*f**3. Factor q(r).
(r - 1)*(r + 1)*(r + 2)/4
Let g(o) be the first derivative of -121*o**3/9 - 22*o**2/3 - 4*o/3 + 6. Factor g(v).
-(11*v + 2)**2/3
Suppose -2*q + 3*q - 5*w - 27 = 0, -2*q - 2*w - 6 = 0. Factor 0 + 2/3*h**3 + 2/3*h**q - 4/3*h.
2*h*(h - 1)*(h + 2)/3
Let j = -5/224 - -7183/672. Let a = j + -10. Determine t, given that 0 - 2/3*t + a*t**2 = 0.
0, 1
Let c be (-9)/30*(-3)/6. Let p(z) be the second derivative of 1/12*z**4 - c*z**5 + 0*z**2 + 0 - 3*z + 0*z**3. Let p(f) = 0. Calculate f.
0, 1/3
Factor -3/4*j + 1/4*j**2 + 0.
j*(j - 3)/4
Let u(a) be the third derivative of a**5/15 + a**4/6 + 20*a**2. Factor u(q).
4*q*(q + 1)
Factor 2/11 + 2/11*t**2 + 4/11*t.
2*(t + 1)**2/11
Suppose -l = -0*l. Suppose -3*h = 5*w - l*h - 16, w + 8 = 5*h. Suppose 1/4*r**w - 1/4*r**4 + 0*r**3 + 0*r + 0 = 0. Calculate r.
-1, 0, 1
Let q(l) be the second derivative of -13*l**4/6 - l**3 - 8*l**2 - 2*l. Let w = 16 + 0. Let g(u) = 5*u**2 + u + 3. Let j(r) = w*g(r) + 3*q(r). Factor j(y).
2*y*(y - 1)
Let n(l) = -103*l**3 + 154*l**2 - 64*l + 13. Let g(x) = -49*x**3 + 25*x**2 + 14 - 64*x - 42*x**3 - 13*x**3 + 129*x**2. Let q(f) = 5*g(f) - 6*n(f). Factor q(a).
2*(a - 1)*(7*a - 2)**2
Let m(r) = 7*r + 58. Let c be m(-8). Solve -4/11*x**c + 0 - 10/11*x**5 + 10/11*x**3 + 4/11*x**4 + 0*x = 0 for x.
-1, 0, 2/5, 1
Suppose 6*k + 5 = 23. Suppose -4*l - 4 + 15 = -3*u, 4*u - 37 = -5*l. Suppose 4*a + 4*a**k - 2*a**l - 5*a + a - 2*a = 0. What is a?
-1, 0, 1
Let f = 12 + -13. Let d be (3/(f - 2))/(-3). Let h**4 - h**2 + 0 - 1/3*h**3 + d*h = 0. What is h?
-1, 0, 1/3, 1
Let u(p) be the first derivative of 2/3*p**3 - 4 - 6*p**2 + 18*p. Factor u(d).
2*(d - 3)**2
Suppose -o = -6*o. Suppose 6 = -60*u + 63*u. Suppose 1/3*h**4 + 2/3*h**3 + 0 + 1/3*h**u + o*h = 0. Calculate h.
-1, 0
Let v(t) be the second derivative of -3*t**5/20 - 6*t. Determine z so that v(z) = 0.
0
Let t(d) = -23*d - 6. Let o be t(6). Let l be o/(-88)*4/6. Factor 2/11 - 8/11*w + l*w**2 + 2/11*w**4 - 8/11*w**3.
2*(w - 1)**4/11
Suppose -23 = -7*q - 2. Determine u so that -1/2*u**q - 3/2*u**2 + 0*u + 2 = 0.
-2, 1
Let h(f) be the first derivative of f**4/4 - 2*f**3/3 - 21. Factor h(k).
k**2*(k - 2)
Let l(q) be the first derivative of -28/5*q**5 + 3 - 2/3*q**3 + 0*q - 15/4*q**4 + 0*q**2. Determine a so that l(a) = 0.
-2/7, -1/4, 0
Factor 1/2*g**2 - 1/2*g**4 + 1/2*g - 1/2*g**3 + 0.
-g*(g - 1)*(g + 1)**2/2
Let g(r) be the second derivative of r**6/840 - r**5/140 + r**4/84 - 5*r**2/2 - 6*r. Let l(n) be the first derivative of g(n). Factor l(c).
c*(c - 2)*(c - 1)/7
Suppose 0 = 4*s - 4*l + 112, 5*l + 25 = 3*s + 105. Let i be s/(-6) + -1 + 0. Let -7*m**2 + i - 1 - 2*m**2 + 3*m**4 + 3*m**2 = 0. Calculate m.
-1, 1
Let b(v) be the third derivative of -5*v**8/63 - 68*v**7/105 - 349*v**6/360 + 5*v**5/36 + 3*v**4/4 + 4*v**3/9 - 33*v**2. Determine a, given that b(a) = 0.
-4, -1, -1/4, 2/5
Suppose w = 5*k + 6, -3*w = -0*w + k + 46. Let c be 11/(-22) + w/(-12). Find d such that 0*d**2 + 0 + 0*d + c*d**4 - 4/3*d**3 = 0.
0, 2
Solve 2*c**3 - c**2 - 2*c**3 + c**4 + 0*c**4 = 0.
-1, 0, 1
Let k(f) be the first derivative of 24*f + 9/5*f**5 - 51/4*f**4 + 4 - 42*f**2 + 34*f**3. Factor k(j).
3*(j - 2)**2*(j - 1)*(3*j - 2)
Let 2*s**4 - 2*s**3 + 15*s**3 - 3*s**5 + s**4 - 7*s**3 = 0. Calculate s.
-1, 0, 2
Let v = -2929/5 + 597. Solve 98/5*x**2 + 8/5 + v*x = 0.
-2/7
Let a(c) be the second derivative of -c**10/7560 + c**8/1680 - c**4/4 - 5*c. Let v(l) be the third derivative of a(l). Factor v(z).
-4*z**3*(z - 1)*(z + 1)
Let j(g) be the second derivative of 3*g - 1/12*g**4 + 0 + 0*g**2 - 1/12*g**3 - 1/40*g**5. Let j(k) = 0. Calculate k.
-1, 0
Let o(b) be the second derivative of b**7/17640 - b**6/2520 + b**5/840 - b**4/3 + 4*b. Let q(w) be the third derivative of o(w). Factor q(s).
(s - 1)**2/7
Let z(b) be the second derivative of 0 + 25/84*b**7 + 5*b + 1/2*b**6 - 9/10*b**5 + 0*b**3 + 0*b**2 + 1/3*b**4. Factor z(h).
h**2*(h + 2)*(5*h - 2)**2/2
Let q(f) be the second derivative of 0 + 1/11*f**3 + 5*f + 2/11*f**2 + 1/66*f**4. Determine i, given that q(i) = 0.
-2, -1
Suppose -4*s + 20 = s. Factor -2*g**4 + 6*g**4 - 10*g - 4*g + 2*g**5 + 12*g - s*g**2.
2*g*(g - 1)*(g + 1)**3
Suppose 0 = -p - 2*p - 6. Let v be (p + (-6)/(-3))/(-2). Factor 3*h**2 + v + 0 + 2*h - 2*h**2 + 1.
(h + 1)**2
Let t(z) be the second derivative of 0*z**2 - 1/40*z**6 + 0*z**4 - z + 0 + 0*z**5 + 0*z**3 - 1/56*z**7. Let t(y) = 0. Calculate y.
-1, 0
Let f(i) = -i**2 - 9*i - 4. Let o be f(-8). Suppose o*q - 10 = -2. Let 2/7*c**3 - 2/7*c + 0 - 2/7*c**4 + 2/7*c**q = 0. Calculate c.
-1, 0, 1
Suppose -8*s**3 - s + 3*s**2 + 5*s + 4*s**5 - 3*s**2 = 0. What is s?
-1, 0, 1
Let y(o) be the third derivative of o**7/735 - o**6/840 - 13*o**5/420 - o**4/28 + 9*o**2. Factor y(x).
x*(x - 3)*(x + 2)*(2*x + 1)/7
Suppose -4*j + 8 = -2*z, 0*j - 5*j - 3*z = -21. Let q(u) = 2*u**2 + 2*u. Let r(w) = -w**2 - 2*w. Let f(d) = j*r(d) + 2*q(d). Factor f(h).
h*(h - 2)
Let x(d) be the third derivative of d**7/42 + 31*d**6/60 + 17*d**5/5 + 3*d**4 - 2*d**2 - 4. Solve x(l) = 0.
-6, -2/5, 0
Let p(q) be the third derivative of 0*q**3 - 3*q**2 + 1/420*q**6 - 1/84*q**4 + 1/735*q**7 + 0 + 0*q - 1/210*q**5. Factor p(z).
2*z*(z - 1)*(z + 1)**2/7
Let f = -19 - -21. Let h(p) be the second derivative of 2*p**f - 5/4*p**4 + 2*p**3 + 0 - 2*p + 1/5*p**5. Factor h(n).
(n - 2)**2*(4*n + 1)
Suppose 4 - 12 = -4*b. Suppose a + f - 1 = b*f, 5 = a + 3*f. Let 4/7*l**3 + 0*l**a - 4/7*l + 2/7*l**4 - 2/7 = 0. Calculate l.
-1, 1
Let a(f) be the third derivative of -f**7/70 - f**6/100 + 11*f**2. Factor a(n).
-3*n**3*(5*n + 2)/5
Let x(z) be the third derivative of 0*z + 1/9*z**3 + 7/72*z**4 + 0 + 1/180*z**6 - 4*z**2 - 1/1008*z**8 + 2/45*z**5 - 1/315*z**7. Factor x(k).
-(k - 2)*(k + 1)**4/3
Determine x, given that 21/5*x**2 - 9*x - 3/