16*u**6/45 - 3*u**5/20 - 5*u**4/36 + u**3/9 - 5*u. Let a(n) = 0. Calculate n.
-2/5, 0, 1/2, 1
What is x in 0 - x - 1/2*x**2 + 1/2*x**3 = 0?
-1, 0, 2
Let b(p) be the third derivative of p**5/240 - p**4/48 + 13*p**2. Factor b(a).
a*(a - 2)/4
Suppose 0 = 5*o + 3*b - 16, -b - 1 + 5 = o. Let v(g) be the second derivative of -o*g + 0 - 2/3*g**3 - 1/12*g**4 - 2*g**2. Determine z so that v(z) = 0.
-2
Let w = 316 - 316. Solve w + 2/15*x**2 - 2/15*x = 0 for x.
0, 1
Let u = -32833/14 + 4637/2. Let q = u - -27. Solve 0*m**2 + q*m**3 - 6/7*m + 4/7 = 0.
-2, 1
Solve -2/3*g**3 - 1/3*g**5 + g - 2/3*g**2 + g**4 - 1/3 = 0 for g.
-1, 1
Let b(r) be the second derivative of -r**4/3 + 4*r**3/3 + 4*r. Determine c so that b(c) = 0.
0, 2
Factor 19*w**4 - 9 + 2*w**4 - 27*w + 3 + 13*w**3 + 14*w**3 - 15*w**2.
3*(w - 1)*(w + 1)**2*(7*w + 2)
Factor -1/9*i**3 + 4/9*i + 1/9*i**4 - 4/9*i**2 + 0.
i*(i - 2)*(i - 1)*(i + 2)/9
Let z(q) be the third derivative of -7*q**7/50 - 7*q**6/20 + 3*q**5/100 + q**4/2 - 2*q**3/5 + 4*q**2. Let z(t) = 0. Calculate t.
-1, 2/7
Let x be 2/5*14/(-8). Let t = -1/5 - x. Factor -2*k**3 - 1/2 - 2*k - t*k**4 - 3*k**2.
-(k + 1)**4/2
Let x = 172 + -502/3. Factor 0*b + 0*b**3 + 4/3*b**4 + 0 + x*b**5 + 0*b**2.
2*b**4*(7*b + 2)/3
Let z be ((-1)/(-2))/((-3)/(-252)). Let w = -290/7 + z. Factor 0 + 2/7*i - 4/7*i**4 + 0*i**3 - 2/7*i**5 + w*i**2.
-2*i*(i - 1)*(i + 1)**3/7
Factor -8*f - 5*f**2 - 9 + 5 + f**2.
-4*(f + 1)**2
Let v = 50 - 48. Factor -1/2*o**3 + 1/2*o + 2*o**4 + 0 - 2*o**v.
o*(o - 1)*(o + 1)*(4*o - 1)/2
Let r(s) be the second derivative of 2*s**6/45 - s**5/5 + 13*s**4/36 - s**3/3 + s**2/6 + 5*s. Factor r(p).
(p - 1)**2*(2*p - 1)**2/3
Let z(f) be the second derivative of -f**10/30240 + f**9/15120 + f**8/6720 - f**7/2520 + f**4/4 - 3*f. Let y(a) be the third derivative of z(a). Factor y(x).
-x**2*(x - 1)**2*(x + 1)
Let r(o) = o**4 - o**2 + 1. Let t(n) = -18*n**4 - 6*n**3 + 18*n**2 + 6*n - 15. Let s(j) = -15*r(j) - t(j). Factor s(u).
3*u*(u - 1)*(u + 1)*(u + 2)
Let x(p) be the third derivative of p**10/529200 - p**9/70560 + p**8/23520 - p**7/17640 + p**5/30 - p**2. Let r(y) be the third derivative of x(y). Factor r(t).
2*t*(t - 1)**3/7
Let q(x) be the second derivative of -x**4/4 + 10*x. Determine f so that q(f) = 0.
0
Let n(m) be the first derivative of 2*m**6/3 + 12*m**5/5 - 16*m**3/3 + 26. Factor n(p).
4*p**2*(p - 1)*(p + 2)**2
Let x be 1 - (2 + (-27)/15). Let r(f) be the first derivative of 3/5*f**2 - x*f - 2/15*f**3 - 1. Find w, given that r(w) = 0.
1, 2
Suppose 4/13*c**3 + 2/13*c**2 - 4/13*c + 0 - 2/13*c**4 = 0. What is c?
-1, 0, 1, 2
Let b(k) = -5*k**2 - 2*k. Let g(z) = -5*z**2 + z**2 - 10*z**2 - 6*z. Let a(j) = -8*b(j) + 3*g(j). Suppose a(p) = 0. Calculate p.
-1, 0
Let w(t) be the first derivative of 3*t**5/25 - 9*t**4/20 + 3*t**3/5 - 3*t**2/10 - 35. Solve w(u) = 0.
0, 1
Let r(t) be the third derivative of t**8/1344 - t**7/840 - t**6/240 + 3*t**2. Solve r(s) = 0.
-1, 0, 2
Let d = 225 + -673/3. Factor -d*t + 2*t**2 + 2/3*t**4 + 0 - 2*t**3.
2*t*(t - 1)**3/3
Let b(c) be the first derivative of c**4/36 + 52. Factor b(z).
z**3/9
Let w = -19 - -18. Let s = w + 5. Factor -4/7*f**2 + 4/7*f**3 + 2/7*f**5 - 2/7 + 6/7*f**s - 6/7*f.
2*(f - 1)*(f + 1)**4/7
Find p such that 3*p**2 - 10*p - p**2 + 22 - 22 = 0.
0, 5
Let q(x) = -x**2 + 1. Let u(c) = c**3 + 6*c**2 - 5. Let y(h) = 5*q(h) + u(h). Let y(o) = 0. Calculate o.
-1, 0
Solve -18*x**2 + 2*x - 6*x**3 + 3*x**5 + 9*x**4 + 9 + 0*x + x = 0.
-3, -1, 1
Let n(f) = -9*f**3 + 7*f**2. Let l(x) = 12*x - 5*x + x**2 - 1 - 10. Let c be l(-9). Let z(p) = 13*p**3 - 10*p**2. Let r(t) = c*n(t) + 5*z(t). Factor r(s).
s**2*(2*s - 1)
Factor -5*h**2 + 5*h**3 - 5*h + 397 - 397 + 5*h**4.
5*h*(h - 1)*(h + 1)**2
Let w(y) be the first derivative of -y**6/420 + y**5/105 - y**4/84 - 3*y**2/2 + 1. Let a(m) be the second derivative of w(m). Factor a(d).
-2*d*(d - 1)**2/7
Let n(k) be the third derivative of -k**8/1008 - k**7/630 + k**6/120 + k**5/36 + k**4/36 - 10*k**2. What is l in n(l) = 0?
-1, 0, 2
Determine j so that -7/4*j - 1/2*j**4 + 1/4*j**5 + 1/2 + 2*j**2 - 1/2*j**3 = 0.
-2, 1
Let g(s) = -s + 24. Let i be g(21). Let p(k) be the first derivative of 0*k**5 - 1/27*k**6 + 0*k**3 + 1/9*k**4 - i - 1/9*k**2 + 0*k. Factor p(w).
-2*w*(w - 1)**2*(w + 1)**2/9
Let a be (3 - (-42)/(-15))/((-27)/(-180)). Factor 4/3*y**2 - 4/3*y**4 + 0 + 4/3*y - a*y**3.
-4*y*(y - 1)*(y + 1)**2/3
Suppose 5*t + 34 = r, r + 3*t + 82 = 6*r. Let j be (2/(-7))/((-12)/r). Suppose -1/6*g - j + 1/6*g**2 = 0. Calculate g.
-1, 2
Let w be 1/(-3) + (-6)/(432/(-42)). Suppose 0 = -4*d + 10 + 2. Suppose -w*c + 0 - 1/2*c**2 + 1/4*c**5 + 1/2*c**4 + 0*c**d = 0. What is c?
-1, 0, 1
Suppose 1526 = 3*n + 1517. Factor 27/4*u**5 - 15*u**2 + 111/4*u**n + 3*u + 0 - 45/2*u**4.
3*u*(u - 1)**2*(3*u - 2)**2/4
Let p(d) be the second derivative of -d**5/5 - d**4/6 + 2*d**3/3 + d**2 + 7*d. Let p(g) = 0. What is g?
-1, -1/2, 1
Let t(j) be the third derivative of j**8/10080 + j**7/840 + j**6/180 + j**5/15 + j**2. Let u(h) be the third derivative of t(h). Suppose u(m) = 0. Calculate m.
-2, -1
Suppose -2*h = 3*s - 5 - 3, 4 = 5*s + h. Let 1/2*g**2 + s - 1/2*g = 0. Calculate g.
0, 1
Suppose -3*u + 24 = -2*u. Factor 2*o**3 + 4*o**2 + 9*o**2 + u*o + 16 - o**2.
2*(o + 2)**3
Let n(k) be the third derivative of -9*k**8/112 + 33*k**7/280 + 17*k**6/160 - 17*k**5/80 + 3*k**4/32 - 3*k**2. Determine d so that n(d) = 0.
-3/4, 0, 1/3, 1
Let y(r) be the first derivative of 2*r**3/3 + 4*r**2 + 8*r + 6. Factor y(z).
2*(z + 2)**2
Let l(g) be the third derivative of g**8/336 - g**7/210 - g**6/120 + g**5/60 + 2*g**2 + 2*g. Factor l(s).
s**2*(s - 1)**2*(s + 1)
Suppose 0 = 8*c - 10*c. Determine n, given that 2/3*n**5 + 0 + 0*n**4 + 2/3*n + c*n**2 - 4/3*n**3 = 0.
-1, 0, 1
Let n(i) be the first derivative of -4 + 1/16*i**4 + 0*i - 1/20*i**5 + 0*i**2 + 0*i**3. Factor n(h).
-h**3*(h - 1)/4
Let c(t) be the second derivative of 0 + 1/9*t**3 - 1/36*t**4 + 0*t**2 + 2*t - 1/60*t**5. Let c(h) = 0. Calculate h.
-2, 0, 1
Let g be 2 + (-4 - (-210)/91). Factor 10/13*p + 8/13*p**2 + g + 2/13*p**3.
2*(p + 1)**2*(p + 2)/13
Let a = -2 + 1. Let v be (5/(-2))/(a/2). Determine h so that 2 - 3 - h**2 - 3*h + v*h = 0.
1
Suppose 2*i - 10 = -2*p + 3*p, -5*p + 25 = 5*i. Determine a so that 2/9*a + p - 2/3*a**3 + 4/9*a**2 = 0.
-1/3, 0, 1
Let o be ((-6290)/40)/((-11)/4). Let x = o - 57. Determine i so that x*i**3 - 6/11*i**2 + 0*i + 8/11 = 0.
-1, 2
Let a(l) = -l**2 + 4*l + 1. Let f be a(4). Let i = -1 + f. Factor 2*h**3 - 2*h**4 + i*h**4 - 2*h + 2*h**2 + 0*h.
-2*h*(h - 1)**2*(h + 1)
Let z(l) be the first derivative of -1/2*l**2 + 1/3*l**3 + 0*l + 1/4*l**4 - 4 - 1/5*l**5. Factor z(s).
-s*(s - 1)**2*(s + 1)
Let c(b) be the third derivative of 1/10*b**5 + 0 + 0*b - 1/35*b**7 - 1/112*b**8 + 4*b**2 + 0*b**3 + 1/8*b**4 + 0*b**6. Factor c(i).
-3*i*(i - 1)*(i + 1)**3
Let x(d) be the second derivative of -d**6/45 + d**4/6 - 2*d**3/9 - 47*d. Factor x(h).
-2*h*(h - 1)**2*(h + 2)/3
Let u be -2 + 1 + 3/3. Suppose -5*q = -u*q. Factor -2*i + q*i**2 + 3*i**4 - 3*i**3 + 5*i - 3*i**2 + 0*i**3.
3*i*(i - 1)**2*(i + 1)
Let 4*b**2 + 22*b**2 + 33*b + 3*b**3 + 15 - 5*b**2 = 0. Calculate b.
-5, -1
Let z = -13 - -16. Factor 0 + 2/5*j**4 + 0*j**2 + 0*j + 0*j**z.
2*j**4/5
Let g be -1 - (1/(-1) - 3). Let c(z) be the second derivative of 1/3*z**7 + 2*z**2 + 2/15*z**6 + 2*z - 2/3*z**4 - 7/5*z**5 + 0 + 7/3*z**g. Solve c(r) = 0 for r.
-1, -2/7, 1
Let j be 24/30 - 16/20. Factor -2/5*y**2 + 2/5*y + j - 4/5*y**3.
-2*y*(y + 1)*(2*y - 1)/5
Let m(u) be the second derivative of u**4/12 - u**3/3 + u**2/2 - 5*u. Determine q so that m(q) = 0.
1
Let -3/4*s**2 + 1/4*s - 1/4*s**3 + 3/4 = 0. What is s?
-3, -1, 1
Factor 15*q**2 - 4*q + 3*q - 3 + 14*q - q.
3*(q + 1)*(5*q - 1)
Factor 3/2*g**3 + 15/4*g**2 + 3*g + 3/4.
3*(g + 1)**2*(2*g + 1)/4
Let k(i) = 2*i + 6. Let m be k(-3). Let g(s) be the second derivative of -1/20*s**5 + m*s**2 + 0 + 0*s**3 + 2*s - 1/12*s**4. Solve g(n) = 0 for n.
-1, 0
Let k(f) = 3*f**3 + 5*f**2 - 3*f. Let q(g) = g**3 + 2*g**2 - g. Let l(y) = 3*k(y) - 8*q(y). Let s(a) = 2*a**3 + a**2. Let j(u) = 2*l(u) - 2*s(u). Factor j(w).
-2*w*(w + 1)**2
Factor 2/3*p**2 - 1/6*p**3 + 1/2*p - 3.
-(p - 3)**2*(p + 2)/6
Let t(y) = -y**2 - y. Let a(x) = 3*x**2 + 25*x + 72. Let k(i) = a(i)