r -o - 1/2 + 0*o**2 + o**3 + 1/2*o**4.
(o - 1)*(o + 1)**3/2
Let u(x) be the second derivative of x**4/96 + 7*x**3/24 + 49*x**2/16 - 5*x. Suppose u(n) = 0. Calculate n.
-7
Suppose -a - 6 = -5*m - 0*a, 5*m - 2 = 2*a. Let d be (12/(-105))/(m/(-5)). Determine n, given that -d*n**3 - 2/7 - 6/7*n**2 - 6/7*n = 0.
-1
Let g(b) be the second derivative of 11*b**4/30 - b**3/15 + 17*b. Factor g(a).
2*a*(11*a - 1)/5
Let i = 451/2740 + -3/20. Let d = i - -256/1233. Factor -2/9*a**4 + 0 - 2/3*a**2 + 2/3*a**3 + d*a.
-2*a*(a - 1)**3/9
Solve -2/11*c**4 + 2/11*c**5 + 10/11*c**2 + 0 - 4/11*c - 6/11*c**3 = 0.
-2, 0, 1
Suppose 9*x - 36 = 3*x. Let b(u) be the third derivative of -1/30*u**5 - 1/60*u**x + 0 + 2*u**2 + 0*u**4 + 0*u**3 + 0*u. Let b(w) = 0. Calculate w.
-1, 0
Suppose 0*o**2 + 0*o + 0*o**3 + 2/3*o**4 + 0 + 2/3*o**5 = 0. What is o?
-1, 0
Find z such that 2/5*z**2 + 0 + 2/15*z**4 + 2/5*z**3 + 2/15*z = 0.
-1, 0
Let f(z) be the third derivative of -z**7/210 - z**6/40 - z**5/20 - z**4/24 + 3*z**2. Factor f(p).
-p*(p + 1)**3
Let c(v) be the first derivative of 8*v**3/3 - 6*v**2 + 4*v + 12. Factor c(o).
4*(o - 1)*(2*o - 1)
Let b = 329 - 329. Solve 0*l**2 + 0*l**3 + 0*l + 2/11*l**4 + b = 0.
0
Suppose 0 = b + b - 10. Suppose -y - 2 = -b. What is p in y*p + 2*p**4 - p**3 - 3*p**3 - 2 + p = 0?
-1, 1
Let f be (-4 - -3)/((-1)/2). Let d be 3 + (-2)/(-8)*f. Determine w so that d*w + 4*w**2 + 1 + 3/2*w**3 = 0.
-1, -2/3
Let x = -3/28 + 19/28. Suppose x*c - 2/7 - 4/7*c**3 + 2/7*c**2 = 0. Calculate c.
-1, 1/2, 1
Let l(k) = -4*k**2 - k + 1. Let w be l(-3). Let g = -29 - w. Factor 2/7*i - 12/7*i**2 + 24/7*i**g + 0 + 6/7*i**5 - 20/7*i**4.
2*i*(i - 1)**3*(3*i - 1)/7
Let b(h) be the second derivative of 3*h**5/70 - 3*h**4/7 + 12*h**3/7 - 24*h**2/7 - 15*h. Determine r, given that b(r) = 0.
2
Suppose 5*u - 16 = -1. Let s be (-9)/(-4) + 3/(-12). Factor -q**s - q**3 + q**5 + u*q**5 - 3*q**5 + q**4 + 0*q**4.
q**2*(q - 1)*(q + 1)**2
Let r(o) = o**3 - 6*o**2 - 5*o - 11. Let l be r(7). Factor 0*k**2 - 2/3*k**5 + 0 + 0*k**4 + 0*k + 2/3*k**l.
-2*k**3*(k - 1)*(k + 1)/3
Solve 18*u - 37*u + 2*u**3 + 13*u + 4 = 0 for u.
-2, 1
Factor -1/3*x**2 - 48 - 8*x.
-(x + 12)**2/3
Suppose -b - 3*u + 6 = 0, 3*u - 2 = -5*b + 16. Suppose 4*n = -4*r + 12, n = -0*n + 1. Factor 12*c**b - 4*c**2 - 10*c**3 + 4*c**r.
2*c**3
Let j(k) be the second derivative of k**6/10 - 3*k**5/10 - k**4/4 + k**3 + 5*k. Factor j(z).
3*z*(z - 2)*(z - 1)*(z + 1)
Suppose -4*n = -2*c - 8, c + 4 + 0 = n. Let b = 11 - 19/2. Find d, given that n + d - b*d**2 - 5/2*d**3 = 0.
-1, 0, 2/5
Let n(p) be the second derivative of p**4/3 + 2*p**3 + 4*p**2 - 3*p. Let n(x) = 0. What is x?
-2, -1
Let b = 2 - -13. Let y be 6/b - (-4)/15. Solve -y*l**2 - 2/3 - 4/3*l = 0.
-1
Let c(n) = -n**2 + 6*n - 5. Let r(l) = -6*l + 6. Let t(b) = -4*c(b) - 6*r(b). Let t(m) = 0. What is m?
-4, 1
Let u(z) be the second derivative of -z**5/40 - 7*z**4/24 - z**3/2 + 2*z. Factor u(h).
-h*(h + 1)*(h + 6)/2
Suppose -5*b - 31 = -2*p, p = 6*p + 4*b + 5. What is d in 15*d**3 - 4*d + d**2 - 1 - 14*d**3 + p*d = 0?
-1, 1
Let u(d) = -3*d - 3. Let k be u(-2). Let -6*l**3 + 2 + 2*l**4 - 4*l**2 + 6*l**k = 0. What is l?
-1, 1
Let l be 4/((-32)/12)*-4. Let b(y) be the second derivative of 1/10*y**l + 2/5*y**5 + 0*y**2 + 7/12*y**4 - 2*y + 0 + 1/3*y**3. Factor b(u).
u*(u + 1)**2*(3*u + 2)
Let g be ((-6)/(-5))/(6/20). Let n(b) = -9*b + 3 + 0 + b**2 + 7*b - 2*b. Let x(j) = -3*j**2 + 11*j - 8. Let y(a) = g*x(a) + 11*n(a). Factor y(l).
-(l - 1)*(l + 1)
Let p(r) be the third derivative of r**7/840 - r**6/240 - r**5/80 + r**4/12 - r**3/6 - r**2 + 26*r. Factor p(v).
(v - 2)*(v - 1)**2*(v + 2)/4
Let o = -992/7 - -142. Determine m, given that 0 - 4/7*m - 8/7*m**3 + o*m**4 + 10/7*m**2 = 0.
0, 1, 2
Let t(m) be the first derivative of 1/12*m**4 - 2/9*m**3 - 7 + 0*m**2 + 0*m. Factor t(n).
n**2*(n - 2)/3
Suppose 1 = t - 0*t - 2*q, t = 4*q - 3. Let m be (t/15)/((-5)/(-6)). Solve -m*u**2 - 2/5*u + 0 = 0.
-1, 0
Let o(z) be the first derivative of 3*z**5/35 - z**3/7 + 10. Factor o(x).
3*x**2*(x - 1)*(x + 1)/7
Let i(t) be the third derivative of t**5/20 + t**4/4 - 3*t**3/2 + 12*t**2. Factor i(k).
3*(k - 1)*(k + 3)
Solve 9*f**2 + 3 + 14*f - 3*f**3 + 13*f + 6 + 6 = 0.
-1, 5
Let z(g) = g**3 + g**2 + g + 1. Let w(h) = 7*h**3 + 10*h**2 + 7*h + 4. Let x(n) = -w(n) + 4*z(n). Factor x(p).
-3*p*(p + 1)**2
Let l be 24/10 - (-6)/(-15). Let h be (-2)/(-2) - l/(-1). Factor -3*u**h - u**4 - u**3 + 2*u**3 - u**2.
-u**2*(u + 1)**2
Let r(t) = 2*t**4 + t**3 + t. Let u(j) = 11*j**4 + 2*j**3 + 3*j**2 + 4*j. Let k(b) = 5*r(b) - u(b). Find y, given that k(y) = 0.
0, 1
Suppose -5*a + 4*b + 11 = 0, -2*a + 3*b = -3*a + 6. Suppose -4*n + a*s = 3, -n = 2*s + 2 - 4. Factor n + 2/9*v + 2/9*v**2.
2*v*(v + 1)/9
Let u = -81 - -121/3. Let b = 41 + u. Find v, given that 1/3*v**4 + v**2 + v**3 + b*v + 0 = 0.
-1, 0
Factor -4*w - 65*w**2 + 12*w + 67*w**2.
2*w*(w + 4)
Let i(c) be the second derivative of -c**4/3 + 2*c**3/3 + c. What is d in i(d) = 0?
0, 1
Let f = 14 + -6. Let n = 10 - f. Find z, given that n + 2*z + 1/2*z**2 = 0.
-2
Suppose -16 = 4*b, 4*j + 4*b + 0*b + 24 = 0. Let g = j - -4. Suppose i + 4 + 2*i**2 - i**g - 5*i = 0. What is i?
2
Factor -6/5*h**2 - 3/5*h**3 - 12/5 + 21/5*h.
-3*(h - 1)**2*(h + 4)/5
Let h(x) be the second derivative of -x**5/10 + x**4/6 + 5*x**3/3 + 3*x**2 + 5*x. Find n such that h(n) = 0.
-1, 3
Let m(c) be the second derivative of -c**7/5040 - c**6/720 - c**5/240 - c**4/12 - 3*c. Let r(p) be the third derivative of m(p). Factor r(u).
-(u + 1)**2/2
Let c(v) be the first derivative of -6/35*v**5 + 0*v + 2/7*v**2 + 2/7*v**3 - 1/14*v**4 - 1/21*v**6 + 3. Find d, given that c(d) = 0.
-2, -1, 0, 1
Suppose -p + 12 = 3*j + 2*j, j = p. Suppose -p*g + 3 = -g. Find v, given that -8/11*v**2 - 12/11*v**g + 0 - 2/11*v**5 - 2/11*v - 8/11*v**4 = 0.
-1, 0
Let r(n) = n**4 - 8*n**3 - 9*n**2 + 12*n + 10. Let h(q) = -9*q**3 - 9*q**2 + 12*q + 9. Let i = 6 + -9. Let f(j) = i*r(j) + 2*h(j). Determine g so that f(g) = 0.
-1, 2
Let x(z) be the first derivative of -7/30*z**4 + 1 + 19/15*z**3 + 6/5*z**2 + 5*z. Let b(l) be the first derivative of x(l). Determine o so that b(o) = 0.
-2/7, 3
Let k be ((-9)/(-108))/((-2)/(-6)). Factor -k + 1/4*w**3 - 3/4*w**2 + 3/4*w.
(w - 1)**3/4
Suppose f = -5, -29 = 5*z + 4*f - 9. Factor p**2 - 2*p**2 + p - 2 + 2*p + z*p.
-(p - 2)*(p - 1)
Suppose -546/5*f**2 - 147/5*f**5 + 84/5*f**4 + 204/5*f - 24/5 + 429/5*f**3 = 0. What is f?
-2, 2/7, 1
Let g be 25/50*(2 + -1). Find d, given that -g*d**2 + 0*d + 0 = 0.
0
Suppose 0 = 2*c - 3*c - 1, 5*c + 11 = 3*b. Let i(s) = -s**2 + 4. Let o be i(b). Factor -1/5*d**3 + 0*d**2 + 1/5*d**5 + o*d**4 + 0 + 0*d.
d**3*(d - 1)*(d + 1)/5
Let j(g) be the first derivative of -g**7/3360 - g**6/360 - g**5/96 - g**4/48 + 2*g**3/3 + 2. Let f(n) be the third derivative of j(n). Factor f(v).
-(v + 1)**2*(v + 2)/4
Let n(v) = -v**2 - v - 1. Let i(p) = -p**2 + 9*p - 12. Let t be i(8). Let f(q) = -q**3 - 5*q**2 - 5*q - 3. Let s(u) = t*n(u) + 2*f(u). Factor s(x).
-2*(x + 1)**3
Let s be (6/(-9))/((-14)/3 + 3). Suppose s*v + 0 - 2/5*v**2 = 0. Calculate v.
0, 1
Suppose -2*q - 1/2*q**3 + 0 + 2*q**2 = 0. What is q?
0, 2
Suppose -4*d = -j + 6*j, 5 = 5*j + 3*d. Let j*u**4 - 1/4*u**2 + 1/2*u + 12*u**5 + 0 - 35/4*u**3 = 0. What is u?
-1, -1/4, 0, 1/4, 2/3
Let u(p) be the first derivative of p**4/4 - p**2/2 + 6. Factor u(a).
a*(a - 1)*(a + 1)
Factor 17*o**2 + 2*o**4 - o**2 - 11*o - 11*o**3 + o**3 + 3*o.
2*o*(o - 2)**2*(o - 1)
Let w be 6/4*(-2)/(-3). Let s = w - -3. Suppose -y**s + 5/2*y**3 + 1/2*y - 2*y**2 + 0 = 0. What is y?
0, 1/2, 1
Solve 4/7 - 4/7*o - 11/7*o**2 + 9/7*o**4 + 6/7*o**3 = 0.
-1, 2/3
Let g(p) = 2*p**2. Let j be g(1). Determine b, given that -b**2 + b + 3*b**j + 2*b**3 + b**2 + b**3 + b**4 = 0.
-1, 0
Let d be (4/15)/(24/9 + -2). Find p such that 0 + 1/5*p + 0*p**3 + d*p**4 - 1/5*p**5 - 2/5*p**2 = 0.
-1, 0, 1
Let h(i) be the second derivative of -1/5*i**4 - 8/5*i**2 + 5*i - 4/5*i**3 - 1/50*i**5 + 0. Determine d so that h(d) = 0.
-2
Suppose 2*v + 4 = 4*v - 2*a, -5*v - 5*a - 10 = 0. Solve -2/3*w**4 - 2/3*w**2 - 4/3*w**3 + v*w + 0 = 0.
-1, 0
Let o = -11 + 34/3. Factor 1/3*y**5 + 0 - y**4 + y**3 + 0*y - o*y**2.
y**2*(y - 1)**3/3
Suppose -3*r + r + 48 = 0. Let m be 3 + -1 + r/(-21). Suppose