
-4*m*(m + 1)/7
Factor 3*c + c**2 + 2*c**2 - c - 2*c**2 - 3.
(c - 1)*(c + 3)
Let m be 2/3 - (-13)/(-26). Let v(t) be the second derivative of 0 + 1/4*t**2 - m*t**3 + t + 1/24*t**4. Factor v(x).
(x - 1)**2/2
Suppose -4/13*r**2 + 6/13*r + 4/13 = 0. What is r?
-1/2, 2
Let s = 13 + -10. Let w be 0*(-2 + s/2). Determine k so that w - 1/2*k**4 + 0*k + 1/2*k**5 - 1/2*k**3 + 1/2*k**2 = 0.
-1, 0, 1
Let v(z) be the second derivative of -z**6/6 + z**5/4 + 5*z**4/4 - 5*z**3/6 - 5*z**2 + 41*z. What is m in v(m) = 0?
-1, 1, 2
Factor 0*y + 0*y**3 - 1/4*y**2 + 0 + 1/4*y**4.
y**2*(y - 1)*(y + 1)/4
Let c be (380/35)/((-30)/14). Let l = -22/5 - c. Factor -2/3*o**4 + l*o**2 - 2/3*o**3 + 2/3*o**5 + 0 + 0*o.
2*o**2*(o - 1)**2*(o + 1)/3
Let 8*d + 1/2*d**2 + 32 = 0. What is d?
-8
Let k be (22 + -2)/(-4) - 4. Let z be (6/k*12)/(-2). Determine d so that 0*d + 0*d**2 - 1/4*d**5 + 1/4*d**3 + 0*d**z + 0 = 0.
-1, 0, 1
Suppose 0 = -0*g - 4*g + 5*c + 11, g + 5*c = 9. Factor -4*d + 5*d**5 - d**3 + 12*d**4 - 12*d**2 + 4*d**5 - g*d**3.
d*(d - 1)*(d + 1)*(3*d + 2)**2
Let w be 1*(2/(-10))/(6/(-10)). Factor -1/3*b**2 + 0 + w*b.
-b*(b - 1)/3
Suppose 20*g**2 - 1024 - 4*g**3 + 20*g**2 + 2*g**2 - 896*g + 82*g**2 = 0. What is g?
-1, 16
What is p in 139 - 127 + 54*p - 18*p + 27*p**2 = 0?
-2/3
Let -h**4 + 2*h**3 - 7*h + 0 + 5*h + 1 = 0. Calculate h.
-1, 1
Factor -275/6*o + 70/3*o**2 - 125/3 - 5/2*o**3.
-5*(o - 5)**2*(3*o + 2)/6
Let 2*s**2 + 3*s**3 - 12*s**2 + 21*s - 5*s**2 - 9 = 0. Calculate s.
1, 3
Let z(q) be the third derivative of -q**6/40 + q**5/10 - 2*q**2. Factor z(n).
-3*n**2*(n - 2)
Let m be 7/21 + 5/3. Let u(n) be the first derivative of m*n**3 + 2*n**2 + n**4 + 1/5*n**5 + n - 1. What is v in u(v) = 0?
-1
Let g = 16 + -10. Suppose 2*c - g = -c. Let 2/5*z - 1/5*z**c - 1/5 = 0. What is z?
1
Let q be 14/6 + 4/(-12). Find v such that -4*v - v + 4*v + v**2 - 2*v**q = 0.
-1, 0
Let k(z) be the first derivative of z**6/540 - z**5/135 + z**4/108 - 2*z**2 - 3. Let r(l) be the second derivative of k(l). Factor r(t).
2*t*(t - 1)**2/9
Let j(g) be the first derivative of g**3 + 6*g**2 + 12*g + 60. Factor j(r).
3*(r + 2)**2
Let p = 11 - 7. Suppose -3*g = -p*g. Factor -2*n**2 + 0*n**2 + 2*n**3 + g*n**2.
2*n**2*(n - 1)
Let w(v) = -4*v**4 - 2*v**3 + 2*v**2 + 24*v + 15. Let m(g) = -7*g**4 - 5*g**3 + 3*g**2 + 47*g + 31. Let z(l) = -6*m(l) + 10*w(l). Factor z(x).
2*(x - 2)*(x + 1)*(x + 3)**2
Suppose -5*w = 2*k - 6*k + 16, 0 = 4*w. Factor 8*x**2 + k*x - 2*x**4 - 4*x**3 + 2 - 8*x**2.
-2*(x - 1)*(x + 1)**3
Let t = -5 + 6. Let w(r) be the first derivative of 1/4*r**2 + t - 1/4*r - 1/12*r**3. Solve w(m) = 0.
1
Let x(z) be the second derivative of z**5/60 + z**4/12 - 2*z**3/9 + 15*z. Factor x(l).
l*(l - 1)*(l + 4)/3
Let b(v) be the third derivative of -v**8/84 + 2*v**7/105 + v**6/30 - v**5/15 - 5*v**2. Factor b(o).
-4*o**2*(o - 1)**2*(o + 1)
Suppose -2*r = 4*r + 42. Let v = 7 + r. Factor 0*p + 2/7*p**2 - 2/7*p**4 + 0*p**3 + v.
-2*p**2*(p - 1)*(p + 1)/7
Let y(m) be the first derivative of -m**7/210 - m**6/120 + m**5/60 + m**4/24 - 3*m**2/2 + 5. Let q(n) be the second derivative of y(n). Solve q(c) = 0.
-1, 0, 1
Let g(u) be the second derivative of -1/2*u**3 + 3/20*u**5 + 1/4*u**4 + 0 - 1/10*u**6 - 7*u + 0*u**2. Determine i so that g(i) = 0.
-1, 0, 1
Let n(a) = -12*a**2 + 3*a - 11. Let w(y) = -5*y**2 + 2*y - 5. Let j(h) = -6*n(h) + 15*w(h). Factor j(g).
-3*(g - 3)*(g - 1)
Suppose t = -3*p - 1, -2*t - t - 3*p = -15. Let h be 6/t - (-39)/(-84). Suppose -4/7*q**2 - h*q**5 - 8/7*q**4 + 0*q - 10/7*q**3 + 0 = 0. What is q?
-2, -1, 0
Let v(n) = -4*n**2 + 1 - 4*n + 3*n**2 + 2. Let x be v(-4). Suppose -5 + 3*d**2 - d**2 + x = 0. What is d?
-1, 1
Let y(r) be the third derivative of -r**8/168 + 4*r**7/105 - r**6/12 + r**5/15 - 12*r**2. Factor y(h).
-2*h**2*(h - 2)*(h - 1)**2
Let h be (-2)/2*1 - -3. Let x = h - -1. Factor 1 + 4*b - 3*b**2 - x*b - b**3 + 2*b**2.
-(b - 1)*(b + 1)**2
Let a(w) = 2*w - 1. Let x be a(3). Let d be 6*((-5)/(-2))/x. Factor 6*k**2 - 10*k**d + 3*k - k + 2*k.
-2*k*(k - 1)*(5*k + 2)
Suppose 5*s + 0*s = 10. Factor -u**s + 22*u**3 + 12*u**4 - 18*u**5 - 8*u - 7*u**2 + 0*u**4.
-2*u*(u - 1)**2*(3*u + 2)**2
Let j be (-2)/(-8) - 15/(-4). Let w be 0 - -5 - (-3 + j). Factor 4*l**4 - 4*l**4 - 2*l**w.
-2*l**4
Let t = -24 - -29. Let m(v) be the second derivative of 0*v**4 + 0*v**3 + 0*v**2 + 2*v + 0 + 1/20*v**t - 1/30*v**6. Factor m(h).
-h**3*(h - 1)
Let i(b) = 2*b**4 + 3*b**3 + 2*b**2 + 5. Let x(j) = j**4 + j**2 + j + 1. Let y(s) = 4*i(s) - 12*x(s). Find d, given that y(d) = 0.
-1, 1, 2
Let c(s) be the second derivative of s**5/5 - 7*s**4/6 + 7*s**3/3 - 2*s**2 - 30*s. Factor c(p).
2*(p - 2)*(p - 1)*(2*p - 1)
Let h(v) be the third derivative of -1/60*v**6 - 1/336*v**8 + 0*v - 2*v**2 - 1/30*v**5 + 1/8*v**4 + 1/70*v**7 - 1/6*v**3 + 0. Factor h(j).
-(j - 1)**4*(j + 1)
Let t(x) = 24*x + 72. Let m be t(-3). Solve -1/2*h**4 + 0 - 1/2*h**5 + 0*h**2 + 0*h + m*h**3 = 0 for h.
-1, 0
Let z(w) be the third derivative of -1/12*w**4 + 0*w - 1/15*w**5 + 0 - 1/60*w**6 + 7*w**2 + 0*w**3. Suppose z(m) = 0. What is m?
-1, 0
Let w(j) be the first derivative of -3 + 1/3*j**2 + 0*j + 5/3*j**3 + 29/15*j**5 + 11/4*j**4 + 1/2*j**6. Factor w(l).
l*(l + 1)**3*(9*l + 2)/3
Determine d so that -3/4*d**2 + 3/4*d**4 - 3/2*d + 0 - 3/4*d**5 + 9/4*d**3 = 0.
-1, 0, 1, 2
Factor 8/5*s + 12/5*s**2 - 16/5 + 2/5*s**4 - 2*s**3.
2*(s - 2)**3*(s + 1)/5
Determine u so that 0 - 1/2*u**2 - 1/2*u = 0.
-1, 0
Let u(i) be the first derivative of -i**4/20 + i**3/15 + i**2/10 + i + 3. Let h(o) be the first derivative of u(o). Suppose h(s) = 0. Calculate s.
-1/3, 1
Let m = 5 + 17. Let j(y) = -y**2 + y - 2. Let c(o) = 6*o**2 - 6*o + 11. Let b(r) = m*j(r) + 4*c(r). Factor b(k).
2*k*(k - 1)
Let a(q) be the second derivative of -1/8*q**4 + 0 + 1/2*q**2 + 1/60*q**6 + 1/12*q**3 + q - 1/40*q**5. Factor a(i).
(i - 2)*(i - 1)*(i + 1)**2/2
Suppose -3*z + c + 13 = 0, 21 = 6*z - 2*z - 5*c. What is s in -15*s - z + 9*s + 0*s**2 - 2*s**2 = 0?
-2, -1
Suppose -6*u = -u - 2*q - 8, 0 = -4*u + q + 4. Let d = -1 - -1. Let -2/5*b**2 + d*b + u = 0. Calculate b.
0
Let w(h) be the third derivative of h**8/20160 + h**7/3780 + h**6/2160 - h**4/24 + 5*h**2. Let b(n) be the second derivative of w(n). Factor b(k).
k*(k + 1)**2/3
Suppose -108*i**4 - 188*i**3 + 108*i**2 - 163*i**3 - 12*i + 46*i**5 + 120*i**3 + 197*i**5 = 0. What is i?
-1, 0, 2/9, 1
Let j(b) be the second derivative of b**6/40 + 3*b**5/20 + 3*b**4/8 + b**3/2 - b**2/2 - 2*b. Let r(n) be the first derivative of j(n). Factor r(h).
3*(h + 1)**3
Let g = 139 - 2081/15. Let r = 23/30 - g. Factor -r*q**2 + 0*q + 1/4*q**4 + 1/4 + 0*q**3.
(q - 1)**2*(q + 1)**2/4
Solve 2*q**3 + 0*q**3 - 2*q - q**3 + q**2 = 0.
-2, 0, 1
Let c(s) be the first derivative of s**3/18 + s**2/2 + 3*s/2 + 3. Let c(q) = 0. What is q?
-3
Let f(d) be the second derivative of -1/20*d**5 + 0*d**2 - d + 1/6*d**3 - 1/30*d**6 + 1/12*d**4 + 0. Determine r, given that f(r) = 0.
-1, 0, 1
Let r(h) be the first derivative of h**6/3 - 8*h**5/5 + 3*h**4 - 8*h**3/3 + h**2 + 17. Factor r(j).
2*j*(j - 1)**4
Let a(x) be the third derivative of -x**8/21 + 2*x**7/35 + x**6/30 + 2*x**2. Solve a(s) = 0.
-1/4, 0, 1
Let z(r) be the second derivative of 0*r**2 + 0 + 1/3*r**3 + 3/20*r**5 - 3*r - 5/12*r**4. Factor z(i).
i*(i - 1)*(3*i - 2)
Let m(k) be the first derivative of k**4 + 20*k**3/3 + 6*k**2 - 36*k - 7. Factor m(c).
4*(c - 1)*(c + 3)**2
Let a(n) be the second derivative of -n**7/70 + 3*n**6/20 - 13*n**5/20 + 3*n**4/2 - 2*n**3 + n**2/2 + n. Let z(s) be the first derivative of a(s). Factor z(k).
-3*(k - 2)**2*(k - 1)**2
What is x in -3/4*x - 3/2 + 3/4*x**2 = 0?
-1, 2
Let g(s) be the second derivative of 2*s**6/135 + 7*s**5/45 + 16*s**4/27 + 8*s**3/9 + 30*s. Let g(w) = 0. Calculate w.
-3, -2, 0
Factor 0 - 1/3*u + 1/3*u**2.
u*(u - 1)/3
Let z(i) be the second derivative of -i**9/3024 - i**8/1680 - i**3/6 + 3*i. Let s(a) be the second derivative of z(a). Find g such that s(g) = 0.
-1, 0
Let m be 22/2*5/5. Let f = m - 11. Factor -1/3 - 1/3*x**4 + 2/3*x**2 + f*x + 0*x**3.
-(x - 1)**2*(x + 1)**2/3
Let z be -3 - -2*495/10. Let m = 682/7 - z. Find d such that m*d**2 - 2/7*d + 0 = 0.
0, 1/5
Let l(m) be the third derivative of -m**4/12 - 3*m**2. Let c be l(-2). Solve -18*z**4 + 7*z**c - 49