 + s**2 - 1/2 + 0*s**3 = 0.
-1, 1
Let v(l) = -l**4 + l**3 - l**2. Let k(u) = -5*u**5 - 40*u**4 + 30*u**3 - 20*u**2 + 5*u. Let w(d) = -k(d) + 30*v(d). Let w(t) = 0. Calculate t.
-1, 0, 1
Suppose 0 = -19*r + 29*r - 50. Solve 1/2*d**2 + 0*d - 1/2*d**4 + 5/4*d**3 - 5/4*d**r + 0 = 0 for d.
-1, -2/5, 0, 1
Let a be 1 + 4*(-2)/(-4). Let b = a - 1. Let -u**2 + u**2 + 0*u**b - u**3 = 0. What is u?
0
Suppose -5*l = -3*t - 9, 3*t = -4*l + 3*l + 9. Suppose -5*d + 3 = -2. Solve -2 - 24*q**4 - 18*q**3 + l - 4*q**2 - 10*q**5 - d = 0 for q.
-1, -2/5, 0
Suppose -5*g + 2*v = 0, 3*g + 7*v - 4*v = 0. Determine m, given that 2*m**3 + 2*m + 2*m**3 - 6*m**2 + g*m**3 - 6*m**3 + 6 = 0.
-3, -1, 1
Let j(a) be the second derivative of 0 + 1/48*a**4 + 1/24*a**3 - 3*a - 1/4*a**2. Factor j(g).
(g - 1)*(g + 2)/4
Let j(m) be the first derivative of 1/21*m**6 - 6/35*m**5 + 0*m + 2 + 0*m**3 + 1/7*m**4 + 0*m**2. Factor j(x).
2*x**3*(x - 2)*(x - 1)/7
Let z(f) = -101*f**4 - 79*f**3 - 15*f**2 - f. Let g(v) = v**4 - v**3 - v**2 + v. Let d(s) = -g(s) - z(s). Let d(b) = 0. Calculate b.
-2/5, 0
Let a(r) = 6*r**3 + 2*r**3 - 1 - 4*r**3. Let i be a(1). Factor m**4 + 0*m + 0*m - i*m**3 - m + 3*m**2.
m*(m - 1)**3
Factor 4/9*j**2 + 22/9*j**3 - 4/9 - 22/9*j.
2*(j - 1)*(j + 1)*(11*j + 2)/9
Factor -2/21*f**2 - 4/3*f - 14/3.
-2*(f + 7)**2/21
Suppose 4 - 21 + y**2 + 11 - y + 4 = 0. Calculate y.
-1, 2
Let d(r) be the third derivative of r**6/420 + r**5/105 - r**4/84 - 2*r**3/21 - 5*r**2. Suppose d(x) = 0. What is x?
-2, -1, 1
Let f be -2 - (-3 - (1 - 2)). Let i be (0/1)/(2 - f). Suppose 3/4*r**2 - 3/4*r + i = 0. What is r?
0, 1
Factor -2/5*y**3 - 2*y - 8/5*y**2 - 4/5.
-2*(y + 1)**2*(y + 2)/5
Let f(o) be the first derivative of o**5/20 + o**4/12 + 4*o + 2. Let h(c) be the first derivative of f(c). Determine n, given that h(n) = 0.
-1, 0
Let i = 19 - 14. Suppose i*z + 15 = 0, 0 = 5*s + 3*z + z + 2. Factor 1/4*t - 1/4*t**s + 1/4 - 1/4*t**3.
-(t - 1)*(t + 1)**2/4
Let d = -18 + 12. Let n = 6 + d. Factor 0*j + 0*j**2 - 2/9*j**3 + n.
-2*j**3/9
Let d(y) be the second derivative of -3/40*y**5 + 1/4*y**3 + y + 0 + 1/40*y**6 - 3/8*y**2 + 0*y**4. Factor d(n).
3*(n - 1)**3*(n + 1)/4
Let 0*q + 85/3*q**4 + 25/3*q**5 + 0 + 20/3*q**2 + 80/3*q**3 = 0. Calculate q.
-2, -1, -2/5, 0
Suppose -3/2*u**2 - 12*u - 24 = 0. Calculate u.
-4
Let g = -8 - -8. Let m(f) be the third derivative of 1/24*f**8 - f**2 + 0 + g*f**3 - 11/105*f**7 + 0*f**4 + 0*f - 2/105*f**5 + 8/105*f**6. Factor m(x).
2*x**2*(x - 1)*(7*x - 2)**2/7
Let i be (14 + 0)/((-22)/(-11)). Let c(n) = 28*n**2 - 13*n - 7. Let k(s) = 9*s**2 - 4*s - 2. Let l(d) = i*k(d) - 2*c(d). Determine z so that l(z) = 0.
0, 2/7
Let z = -3 - -6. Suppose z*t - 2 = 16. Factor j**4 + 1 - t*j**2 + 4*j**3 + 3*j**4 - j - 3*j**5 + 1.
-(j - 1)**3*(j + 1)*(3*j + 2)
Let z = -11 + 13. Suppose z*b = -5*i + 6, i = -0*i. Solve -2*p**2 + 5*p**5 - 16*p**3 + b*p**3 - 20*p**4 - 14*p**5 = 0.
-1, -2/9, 0
Let v be (1 + 5/(-7))/((-104)/(-52)). Let -v*k**2 + 1/7 - 1/7*k + 1/7*k**3 = 0. Calculate k.
-1, 1
Factor 2/7 - 2/7*h**2 + 2/7*h**3 - 2/7*h.
2*(h - 1)**2*(h + 1)/7
Factor 4/5*b + 4/5 + 1/5*b**2.
(b + 2)**2/5
Let t(v) be the first derivative of -v**4/8 - 5*v**3/3 - 7*v**2 - 12*v + 27. Let t(f) = 0. What is f?
-6, -2
Let z(s) be the second derivative of -s**5/20 + 3*s**4/8 - s**3 + 3*s**2/2 + s. Let w(b) be the first derivative of z(b). Factor w(j).
-3*(j - 2)*(j - 1)
Factor -16*j + 7*j**2 + 3*j**2 + 10 - 5*j**2 + j.
5*(j - 2)*(j - 1)
Let c(r) be the third derivative of -1/60*r**6 + 0*r**4 + 0*r**3 - 2*r**2 + 1/105*r**7 + 0 + 0*r - 1/15*r**5. Factor c(i).
2*i**2*(i - 2)*(i + 1)
Suppose 0 = -2*z + 3*z + 4*j + 16, 0 = -2*z + j + 13. Let -4/5*k**3 + 2/5*k + 2/5*k**5 - 2/5 + 4/5*k**2 - 2/5*k**z = 0. What is k?
-1, 1
Factor -21/4*t + 3/4*t**3 + 0 + 9/2*t**2.
3*t*(t - 1)*(t + 7)/4
Let m(x) = -x + 1. Let t(p) be the third derivative of -p**5/60 - p**4/12 + p**3/2 - 2*p**2. Let n(v) = -2*m(v) + t(v). Factor n(z).
-(z - 1)*(z + 1)
Let s(y) be the third derivative of -y**7/21 - y**6/24 + y**5/6 + 5*y**4/24 - y**2. Let s(r) = 0. Calculate r.
-1, -1/2, 0, 1
Let q(c) = c**3 + c**2 - c + 1. Let z(p) = -3*p**3 + 5*p**2 - 12*p + 6. Let w(k) = 2*q(k) + z(k). Factor w(n).
-(n - 4)*(n - 2)*(n - 1)
Let x(t) be the second derivative of -t**7/840 + t**6/180 + t**5/120 - t**4/12 - t**3/3 - 2*t. Let y(o) be the second derivative of x(o). Factor y(q).
-(q - 2)*(q - 1)*(q + 1)
Let b(t) = -2*t**3 - 2*t**2 + 3*t + 2. Let k be b(-2). Let c**3 - c**5 + 0*c**5 + c**k + 4*c**2 - 5*c**2 = 0. Calculate c.
-1, 0, 1
Find h such that 0*h + 87*h**2 - 3*h - 84*h**2 = 0.
0, 1
Let l(k) = -4*k**3 + 7*k**2 - 2*k + 6. Let v(p) = p**3 - 2*p**2 + p - 2. Let z(u) = 2*l(u) + 7*v(u). Let z(i) = 0. What is i?
-2, 1
Let n(r) be the second derivative of -r**7/840 + r**5/120 + 5*r**3/6 + 4*r. Let u(c) be the second derivative of n(c). Determine d, given that u(d) = 0.
-1, 0, 1
Let t(p) be the first derivative of p**7/3780 - p**6/1620 - p**5/540 + p**4/108 - p**3 + 2. Let y(u) be the third derivative of t(u). Factor y(s).
2*(s - 1)**2*(s + 1)/9
Let o(c) = 12*c**4 + 29*c**3 - 33*c**2 - 17*c + 9. Let x(n) = 12*n**4 + 28*n**3 - 34*n**2 - 16*n + 10. Let d(g) = 2*o(g) - 3*x(g). Solve d(a) = 0.
-3, -2/3, 1/2, 1
Let z = 6 + -4. Factor -2*p**2 + z + 0 + 0*p**2.
-2*(p - 1)*(p + 1)
Let m(b) be the third derivative of 0*b**3 + 1/12*b**4 + 0*b + b**2 - 1/210*b**7 + 1/40*b**6 - 1/336*b**8 + 1/12*b**5 + 0. Solve m(x) = 0.
-1, 0, 2
Let o(t) be the third derivative of 0 - 3/10*t**6 + 9/20*t**5 + 0*t + 0*t**3 + 1/14*t**7 - 1/4*t**4 + 3*t**2. Solve o(n) = 0 for n.
0, 2/5, 1
Let c = 603 + -4213/7. Let p = 103/84 - 1/12. Suppose -c*u + p + 2/7*u**2 = 0. What is u?
2
Let j(r) = -r**5 + 5*r**4 - 4*r**3 - 4. Let p(d) = -d**5 + 6*d**4 - 5*d**3 - 5. Let y(a) = 5*j(a) - 4*p(a). Factor y(v).
-v**4*(v - 1)
Suppose -1284*k = -1281*k. Let s be (1/7)/(1/2). Factor k*p + s*p**3 + 0 + 0*p**2 + 2/7*p**5 - 4/7*p**4.
2*p**3*(p - 1)**2/7
Factor 2/3*y - 2/3 + 2/3*y**2 - 2/3*y**3.
-2*(y - 1)**2*(y + 1)/3
Let t(s) = 3*s + 12 - s - s. Let i be t(0). Factor -i*a**2 + 7*a**4 + 3*a**2 + 3*a - 5*a - 3*a + 2 + 5*a**3.
(a - 1)*(a + 1)**2*(7*a - 2)
Factor -10/11*w - 2/11*w**3 + 8/11*w**2 + 4/11.
-2*(w - 2)*(w - 1)**2/11
Let t(a) be the third derivative of 1/90*a**5 - 4*a**2 + 1/60*a**6 + 0 - 2/315*a**7 + 0*a + 1/9*a**3 - 1/12*a**4. Find m such that t(m) = 0.
-1, 1/2, 1
Let i(y) = -y - 3. Let p be i(-7). Suppose 0 = 2*g - g - 4*w + 4, p*g - 3*w = -3. Solve 3/4*l**3 + g*l - 1/4*l**4 + 0 - 1/2*l**2 = 0 for l.
0, 1, 2
Let a(z) be the third derivative of 0 + 6*z**2 - 1/15*z**5 + 1/12*z**4 + 1/60*z**6 + 0*z**3 + 0*z. Factor a(x).
2*x*(x - 1)**2
Let x be 3 - ((-12)/18)/((-14)/35). Suppose 0 = -6*t + 2*t + 8. Factor x - 14/3*c + 10/3*c**t.
2*(c - 1)*(5*c - 2)/3
Let k(g) be the third derivative of g**7/1260 + g**6/180 + g**5/60 + g**4/6 - 2*g**2. Let b(z) be the second derivative of k(z). Factor b(l).
2*(l + 1)**2
Suppose 0*y = 4*y - 12. Let s(a) be the second derivative of -1/5*a**6 + 0*a**y + 0*a**2 + 4/5*a**5 - a - 2/3*a**4 + 0. Factor s(o).
-2*o**2*(o - 2)*(3*o - 2)
Suppose 0*v - v - 28 - 3*v + 8 + 4*v**3 + 20*v**2 = 0. What is v?
-5, -1, 1
Let p(f) = f**3 + 6*f**2 + 3. Let z be p(-6). Suppose 4*o**4 + 0*o**3 - o**4 - 6*o**4 - z*o**3 + 15*o + 9*o**2 + 6 = 0. Calculate o.
-1, 2
Let m(q) be the third derivative of q**6/180 + q**5/30 - q**4/36 - q**3/3 - 20*q**2. Factor m(s).
2*(s - 1)*(s + 1)*(s + 3)/3
Let d(g) be the third derivative of g**5/30 - g**4/3 + 4*g**3/3 - 6*g**2. Factor d(h).
2*(h - 2)**2
Suppose 4*r - 58 = 30. Let f be ((-8)/(-20))/(r/20). Factor 2/11*v**2 + f - 6/11*v.
2*(v - 2)*(v - 1)/11
Let q(j) be the third derivative of j**6/900 + j**5/150 - j**3/3 + j**2. Let x(n) be the first derivative of q(n). Suppose x(h) = 0. What is h?
-2, 0
Factor 1/2 + 2*j + 2*j**3 + 1/2*j**4 + 3*j**2.
(j + 1)**4/2
Let s(k) be the second derivative of k**5/20 - k**4/4 + 2*k**2 - 4*k. Find a such that s(a) = 0.
-1, 2
Suppose -4/7 - 2/7*m**2 - 6/7*m = 0. What is m?
-2, -1
Let q(d) = d**2 + 4*d - 7. Let h be q(-6). Let s = -8 + 14. Factor 0*p + s*p**3 - 3*p - 8*p**h + 5*p**5.
-3*p*(p - 1)**2*(p + 1)**2
Let b(g) be the second derivative of 8*g**6/135 - 7*g**5/15 + 11*g**4/9 - 38*g**3/27 + 2*g**2/3 - 39*g. What is k