et n(a) be the first derivative of 11*a**4/28 - 3*a**3/7 - a**2/7 - 7. Suppose n(m) = 0. Calculate m.
-2/11, 0, 1
Let u = 1 - 1. Let o(d) be the third derivative of -2/21*d**3 + u*d - 1/70*d**5 - 2*d**2 + 5/84*d**4 + 0. Find h, given that o(h) = 0.
2/3, 1
Suppose 0 = -3*l - 3*d - 6, 5*l + d + 1 = 7. Suppose 4*q - 28 = -12. Find h such that 3/2*h**3 + 3/2*h**q + 0*h**l + 0 + 0*h = 0.
-1, 0
Let r(h) be the second derivative of 1/60*h**5 + 1/6*h**3 - 3*h + 1/6*h**2 + 1/12*h**4 + 0. Factor r(j).
(j + 1)**3/3
Let d(b) = -6*b**2 + 5*b. Let t be 170/(-4)*(-12)/15. Let x(r) be the second derivative of -r**4/12 + r**3/6 + 3*r. Let l(f) = t*x(f) - 6*d(f). Factor l(i).
2*i*(i + 2)
Let s(d) = 6*d**2 + 2*d + 1. Let o be s(-3). Let u be 84/o + 2/7. Factor -3*h + 2 - h + h**u + h.
(h - 2)*(h - 1)
Let 2/13 + 8/13*h**2 + 10/13*h = 0. Calculate h.
-1, -1/4
Factor -96 - 72*p - 3/2*p**3 - 18*p**2.
-3*(p + 4)**3/2
Suppose 4*q - q + 4*w = 1, 5*w = -2*q + 3. Let u = q + 3. Solve 2/9*y**3 - 2/9*y + 0 + 0*y**u = 0 for y.
-1, 0, 1
Let l(x) be the third derivative of x**8/504 - x**7/63 + 2*x**6/45 - 2*x**5/45 - 8*x**2. Factor l(s).
2*s**2*(s - 2)**2*(s - 1)/3
Let u(g) be the first derivative of 1 - 1/20*g**5 + 3/8*g**2 + 1/2*g - 1/12*g**3 - 3/16*g**4. Suppose u(m) = 0. Calculate m.
-2, -1, 1
Let k(z) be the third derivative of -z**5/20 + z**4/4 - z**3/2 + 2*z**2. Factor k(f).
-3*(f - 1)**2
Let t(p) be the first derivative of p**5/120 + p**2 - 3. Let b(q) be the second derivative of t(q). Determine y, given that b(y) = 0.
0
Let b(k) be the second derivative of -3*k**5/4 + 25*k**4/12 + 5*k**3/3 + 20*k. Factor b(w).
-5*w*(w - 2)*(3*w + 1)
Let z(g) be the first derivative of -2/15*g**3 - 1/15*g**6 - 6/25*g**5 + 0*g**2 + 0*g - 3/10*g**4 - 1. Factor z(y).
-2*y**2*(y + 1)**3/5
Suppose -2*o - 2*o + 16 = 0. Let d = 1 + o. Factor 0*y - 2/5*y**2 + 0 - 6/5*y**4 - 2/5*y**d - 6/5*y**3.
-2*y**2*(y + 1)**3/5
Factor 12*y**2 + 11/2*y**3 + 1 + 15/2*y.
(y + 1)**2*(11*y + 2)/2
Let -2 - 5/2*p**2 + 1/2*p**3 + 4*p = 0. What is p?
1, 2
Let y(k) be the first derivative of -k**4/2 - 14*k**3/3 - 4*k**2 + 24*k - 24. Solve y(o) = 0 for o.
-6, -2, 1
Suppose 2*c + 1 - 5 = 0. Suppose -4*p - 2*m - m = -12, c*p - 2*m = -8. Factor 4*f**2 - f - 5*f**2 + 0*f + f**3 + 1 + p*f**3.
(f - 1)**2*(f + 1)
Let k(y) be the third derivative of y**6/1080 - y**4/72 + y**3/2 + 3*y**2. Let r(g) be the first derivative of k(g). Factor r(b).
(b - 1)*(b + 1)/3
Suppose -4*x + 4 - 6 = k, -x = 4*k - 7. Factor -3*f**3 - 15*f**2 + 6*f**k + 0*f**3 - 2 - 9*f - 1.
-3*(f + 1)**3
Let b(r) be the third derivative of r**7/840 - r**5/60 + 2*r**2. Find t such that b(t) = 0.
-2, 0, 2
Solve 0*o**4 - 80 - 5*o**2 - 30*o**3 - 5*o**4 + 60*o + 60*o = 0.
-4, 1
Suppose 7*p - 4*p = 0. Let s = 57/4 - 14. Let 1/2*u**2 - s*u**5 + p + 0*u**3 + 1/4*u - 1/2*u**4 = 0. Calculate u.
-1, 0, 1
Let a(r) be the first derivative of 7*r**5/5 + 5*r**4/4 - 2*r**3/3 + 11. Determine g, given that a(g) = 0.
-1, 0, 2/7
Let d(t) = 5. Let b(w) = 1. Let z(u) = 6*b(u) - d(u). Let h(o) = -o**2 + 2*o + 2. Let f(v) = h(v) - 3*z(v). Let f(y) = 0. Calculate y.
1
Suppose -61 = -5*w - 51. Let d(p) be the second derivative of -1/24*p**4 + 1/12*p**3 - 1/40*p**5 - 2*p + 0 + 1/4*p**w. Let d(f) = 0. What is f?
-1, 1
Let x(h) be the first derivative of h**6/2 + 9*h**5/5 + 3*h**4/4 - 3*h**3 - 3*h**2 + 49. Factor x(j).
3*j*(j - 1)*(j + 1)**2*(j + 2)
Let o(s) = 45*s - 133. Let j be o(3). Factor -6/11*l**3 + 0*l + 4/11*l**j - 10/11*l**4 + 0.
-2*l**2*(l + 1)*(5*l - 2)/11
Let 0*w + 0 + 0*w**2 - 6/7*w**4 + 2/7*w**3 = 0. What is w?
0, 1/3
Suppose i - 3 = -0*i. Let c(z) = z**2 - z - 2. Let t be c(i). Factor -q - 7/2*q**3 - 7/2*q**2 + 0 - q**t.
-q*(q + 1)*(q + 2)*(2*q + 1)/2
Let w(l) be the third derivative of l**5/210 - l**4/84 - 2*l**3/21 + 2*l**2. Solve w(f) = 0.
-1, 2
Let q(h) = h**5 + h**4 - h**3 - h**2 - h. Let a(l) = 5*l**5 + 9*l**4 - 5*l**3 - 9*l**2 - 6*l. Let o(f) = a(f) - 6*q(f). Find i, given that o(i) = 0.
-1, 0, 1, 3
Let v(g) be the second derivative of -1/8*g**5 + 3*g + 1/24*g**4 + 1/20*g**6 + 0 + 0*g**2 + 1/12*g**3. Solve v(q) = 0 for q.
-1/3, 0, 1
Factor -2/9 - 2/9*x + 2/9*x**2 + 2/9*x**3.
2*(x - 1)*(x + 1)**2/9
Suppose -6*v + 54*v - 240 = 0. Suppose -23/2*l**3 + 13/2*l**2 + 3/2*l**4 + 0 - l + 9/2*l**v = 0. What is l?
-2, 0, 1/3, 1
Let n(k) be the second derivative of k**6/60 + k**5/20 - k**4/24 - k**3/6 - 6*k. Factor n(r).
r*(r - 1)*(r + 1)*(r + 2)/2
Let m(a) be the second derivative of 2*a**2 + 0 - a + 2/3*a**3 + 1/12*a**4. Let m(q) = 0. What is q?
-2
Let u(r) be the first derivative of 4/7*r + 2/21*r**3 - 3/7*r**2 - 5. Factor u(w).
2*(w - 2)*(w - 1)/7
Let t(s) be the second derivative of 1/24*s**4 + 0 + 1/12*s**3 - 1/40*s**5 - 1/4*s**2 + 5*s. Solve t(g) = 0 for g.
-1, 1
Solve -7*a**2 + 2*a**2 + a**2 + 2*a**4 + 2 = 0.
-1, 1
Let t = 431 + -6457/15. Let m(w) be the second derivative of -t*w**3 - 2*w - 3/25*w**5 - 2/5*w**4 + 0 + 0*w**2 - 1/75*w**6. Factor m(c).
-2*c*(c + 2)**3/5
Let f(q) = -5*q**4 - 8*q**3 - 8*q**2 - 5*q - 7. Let i(w) = -w**2 - w - 1. Let c(s) = 3*f(s) - 21*i(s). Solve c(g) = 0 for g.
-1, 0, 2/5
Suppose 8/3*d - 2 - 2/3*d**2 = 0. Calculate d.
1, 3
Let g(x) be the first derivative of -2*x**5/65 - 5*x**4/26 - 16*x**3/39 - 4*x**2/13 - 1. What is s in g(s) = 0?
-2, -1, 0
Let d(j) be the first derivative of j**7/1260 - j**5/180 - j**3 + 3. Let u(w) be the third derivative of d(w). Let u(a) = 0. What is a?
-1, 0, 1
Let u be (1 + -3 + 1)/(-1). Find t such that -4*t**2 + 14*t + 3*t**3 - 2*t**5 + 4*t**4 - 12*t**2 + u + t**3 - 5 = 0.
-2, 1
Let j(a) be the second derivative of a**5/45 - 2*a**3/9 - 4*a**2/9 - 2*a. Find k such that j(k) = 0.
-1, 2
Let f(x) be the third derivative of -1/210*x**5 + 3*x**2 + 0*x - 1/42*x**4 + 0 - 1/21*x**3. Factor f(s).
-2*(s + 1)**2/7
Suppose 32*b - 34*b + 8 = 0. Suppose 2*a - 5*a + 1 = -4*x, -4*x = -8. Suppose 2*i**b + 2/3 - 4*i - 20/3*i**a + 8*i**2 = 0. What is i?
1/3, 1
Let l(c) be the first derivative of 1/6*c**2 + 0*c + 0*c**3 - 1/12*c**4 - 3. Factor l(t).
-t*(t - 1)*(t + 1)/3
Let u(y) be the third derivative of y**5/100 - y**4/20 + y**3/10 - y**2. Let u(k) = 0. Calculate k.
1
Let t = 19979/709680 - -3/2957. Let h(d) be the third derivative of 1/120*d**7 - t*d**5 + 0*d**3 + 1/48*d**4 - 1/240*d**6 + 0*d - 2*d**2 + 0. Factor h(u).
u*(u - 1)*(u + 1)*(7*u - 2)/4
Suppose s + s - 8 = 0. Let f be (s - 5)*8/(-2). Factor 5*p**4 + 5*p**2 - 7*p**4 - 2*p**3 - p**f - 2 + p + p**3.
-(p - 1)*(p + 1)**2*(3*p - 2)
Let h be ((-3)/4)/((-39)/104). Find c such that -4*c**4 + 3*c**3 + 109*c**2 - 2*c**5 - c**3 - 105*c**h = 0.
-2, -1, 0, 1
Factor 3/2*q**3 - 15/8*q**2 + 0 + 3/8*q.
3*q*(q - 1)*(4*q - 1)/8
Let p(s) = 5*s**2 + 6*s + 3. Let k(r) = -19*r**2 - 24*r - 11. Let i(m) = 6*k(m) + 22*p(m). Solve i(u) = 0.
-3, 0
Let d(l) = -l**2 - 10*l - 7. Let y be d(-8). Suppose 5*w**3 + y*w**3 - 20*w + 5 - 1 + 17*w**2 = 0. Calculate w.
-2, 2/7, 1/2
Let g(i) be the third derivative of i**7/8820 - i**5/420 + i**4/12 + 4*i**2. Let n(s) be the second derivative of g(s). Let n(w) = 0. Calculate w.
-1, 1
Let -1/6*q**3 + 1/3*q + 0 - 1/2*q**2 - 1/6*q**5 + 1/2*q**4 = 0. What is q?
-1, 0, 1, 2
Let o = 0 + 3. Let d = 5 - o. Find h such that 4*h**2 - 2*h**4 - 2*h**5 - 2*h + 0*h**4 + 8*h**3 - d - 4*h**3 = 0.
-1, 1
Let v be ((-2)/7)/((-4)/28). Let b(h) be the second derivative of 13/30*h**4 + 4/5*h**v + 4/5*h**3 + 3*h + 1/75*h**6 + 0 + 3/25*h**5. Factor b(g).
2*(g + 1)**2*(g + 2)**2/5
Let d(n) = -2*n**2 - 3*n - 1. Suppose -2*m + 3 = 9. Let q(t) = 4*t**2 + 6*t + 2. Let c(h) = m*q(h) - 5*d(h). Let c(i) = 0. What is i?
-1, -1/2
Let g(l) = l**5 + l**4 + l**3 - l - 1. Suppose -1 = r - 0. Let c(o) = 2*o**5 - 4*o**4 - 2*o**3 + 8*o**2 + 4*o - 4. Let a(h) = r*c(h) + 4*g(h). Factor a(x).
2*x*(x - 1)*(x + 1)*(x + 2)**2
Let m be (2 + (-16)/9)/((-14)/(-28)). Factor 2/9*f**3 - m + 0*f**2 - 2/3*f.
2*(f - 2)*(f + 1)**2/9
Suppose -2*a = -p + 19 + 27, a = -3*p + 110. Let 12*u**3 + 20*u**5 - 5*u**2 - u - 3*u - p*u**4 + 15*u**2 = 0. Calculate u.
-1/2, 0, 2/5, 1
Let z(k) = -4*k - 1. Let g be z(-4). Suppose 5*j = -0*j + g. Factor -6*i + 0 - 2*i**j + 3*i**2 + 3*i**2 + 2.
-2*(i - 1)**3
Let p(d) be the first derivative of -2*d**6/15 + 9*d**5/25 - d**4/10 - 8*d**3/15 + 3*d**2/5 - d/5 + 1. Find c such that p(c) 