r be o(-2). Factor 1/5*x**r - 1/5 + 1/5*x - 1/5*x**3.
-(x - 1)**2*(x + 1)/5
Suppose -5*w - 11 + 17 = -l, 3*l = -5*w + 22. Let p = 62 - 247/4. Factor -27/4*r**5 - 9*r**3 - 27/2*r**4 + 0 - 5/2*r**w - p*r.
-r*(r + 1)*(3*r + 1)**3/4
Factor 1/3 + 1/6*d - 1/6*d**2.
-(d - 2)*(d + 1)/6
Factor 4/5*d**4 + 0*d**3 + 0 - 16/5*d**2 - 16/5*d + 1/5*d**5.
d*(d - 2)*(d + 2)**3/5
Let v = 1247 - 122205/98. Let r = v - -389/294. Suppose n**2 - 4/3*n - 1/3*n**4 + 2/3*n**3 - r = 0. Calculate n.
-1, 2
Let r be (-108)/30 - (-2 - 0 - 2). Factor r + 4/5*n + 2/5*n**2.
2*(n + 1)**2/5
Suppose 2*c + 9 = 13. Let p(h) be the first derivative of 4/3*h**3 - h**6 + 0*h + 3/2*h**4 - 1 + 0*h**c - 4/5*h**5. Let p(w) = 0. What is w?
-1, -2/3, 0, 1
Let w be (8/7)/((-2)/(-7)). Suppose -w - 4*d**2 + 4*d**3 - 1 + 5 = 0. What is d?
0, 1
Let v(i) be the first derivative of -i**4/16 + i**3/3 + i**2/8 - i + 8. What is y in v(y) = 0?
-1, 1, 4
Suppose -a - 5*y = -2*a - 6, 3*y - 10 = -a. Let 24*k**a - 20*k**4 - 12*k**3 + 4 + k**2 + 12*k + 0 = 0. Calculate k.
-1/2, 2
Determine l so that -8/7*l + 4/7*l**2 + 4/7*l**3 + 0 = 0.
-2, 0, 1
Let n = -12 - -15. Let u(f) be the second derivative of -f**2 + 0 - 2/3*f**n - f - 1/6*f**4. Factor u(v).
-2*(v + 1)**2
Suppose 0*m = -m + 14. Determine u, given that -3*u**5 + 8 - u**5 + m*u**3 + 8*u**4 - 8*u**2 - 6*u**3 - 4*u - 8*u**2 = 0.
-1, 1, 2
Let s(x) = -x**2 + x + 1. Let j(t) = 3*t**4 + 3*t**3 - 6*t**2 - 18*t - 6. Let u(d) = -j(d) - 6*s(d). Suppose u(z) = 0. What is z?
-2, -1, 0, 2
Let l(u) = -4*u + 26. Let k be l(6). Factor 1/3*s + 1/3*s**3 + 2/3*s**k + 0.
s*(s + 1)**2/3
Let r(l) = -2*l**2 - 22*l - 53. Let a be r(-4). Suppose 0 - 8/7*q**2 + 4/7*q**a + 0*q = 0. Calculate q.
0, 2
Let i(y) be the third derivative of -y**6/120 - y**5/5 - 2*y**4 - 32*y**3/3 + 3*y**2. Let i(b) = 0. What is b?
-4
Let p(m) be the third derivative of m**9/13608 - m**8/2520 + m**7/1260 - m**6/1620 + m**3/6 + m**2. Let i(w) be the first derivative of p(w). Factor i(g).
2*g**2*(g - 1)**3/9
Let z(p) be the first derivative of -p**6/12 - p**5/5 + 3*p**4/8 + 2*p**3/3 - p**2 - 33. Suppose z(t) = 0. What is t?
-2, 0, 1
Let g = -6 - -8. Find p such that -p**g + 4*p + 4*p**2 - p**2 = 0.
-2, 0
Suppose -3 = -3*m + 6*m. Let s be (-2 - m) + 3*1. Factor -1/3*j**5 + 1/3*j**3 + 0*j**s + 0*j**4 + 0*j + 0.
-j**3*(j - 1)*(j + 1)/3
Suppose -2*m + 2 = 4*p, 4*p - 2*m - 14 = -0*m. Factor -25*o**p - 21*o**3 - 33*o + 73*o**2 + 0 + 6.
-3*(o - 1)**2*(7*o - 2)
Let m be (-190)/(-8) - (-7)/28*1. Solve -m*z**5 + 6 + 399/2*z**2 + 132*z**4 - 60*z - 507/2*z**3 = 0.
1/4, 1, 2
Let z(s) = -4*s**2 + s. Let p(m) = m**2. Let v(y) = -y**2 - 5*y - 6. Let n be v(-4). Let t be -1 + n + 5 + -3. Let u(d) = t*z(d) - 5*p(d). Solve u(c) = 0.
-1, 0
Let k(u) be the second derivative of u**5/35 + 2*u**4/21 + 2*u**3/21 - 7*u. Factor k(h).
4*h*(h + 1)**2/7
Suppose 0 = 2*r + 2*b + b + 7, 0 = 2*r + 2*b + 2. Let h = 6 - r. Solve -y**4 + 2*y**3 + 0*y**4 + h*y**4 - 1 - 2*y = 0.
-1, 1
Let m(f) be the second derivative of -f**5/20 - f**4/12 + 2*f**3/3 + 2*f**2 - 39*f. Find k, given that m(k) = 0.
-2, -1, 2
Factor x**4 + 0*x**3 + 1/2*x - x**2 + 0 - 1/2*x**5.
-x*(x - 1)**3*(x + 1)/2
Let a(f) be the first derivative of -f**7/540 - f**6/135 - f**5/180 + f**4/54 - 8*f**3/3 - 3. Let p(r) be the third derivative of a(r). Factor p(y).
-2*(y + 1)**2*(7*y - 2)/9
Let y = -3 + 6. Suppose t + 31 = 2*r, 0*r + 3*t + 65 = 4*r. What is m in -y*m + 4 + 11*m - r*m**2 + 2*m = 0?
-2/7, 1
Let v be (1 - 1)*(-2)/4. Suppose 0 = 2*k - 6, -t - 4*k = -v*t - 14. Let 0*r + 1/3*r**4 - 2/3*r**3 + 1/3*r**t + 0 = 0. Calculate r.
0, 1
Solve -1/2*l + 0 - 3/2*l**3 - 1/2*l**4 - 3/2*l**2 = 0 for l.
-1, 0
Let a(z) be the second derivative of -z**5/180 + z**4/12 - z**3/2 + z**2/2 - z. Let x(q) be the first derivative of a(q). Determine g, given that x(g) = 0.
3
Let w = -11917/3 - -4032. Let q = -59 + w. What is z in -4/3 - q*z**2 + 2*z = 0?
1, 2
Let l(f) be the first derivative of f**6/105 + 2*f + 3. Let p(w) be the first derivative of l(w). Factor p(n).
2*n**4/7
Find g such that 7*g**4 - 2*g**4 - 2*g**4 + 3*g**3 = 0.
-1, 0
Let b = 8 + -12. Let p = b - -6. Factor -5*x**3 + 4*x**p + 3*x**3 + 6*x**4 + 12*x**3.
2*x**2*(x + 1)*(3*x + 2)
Let s(k) = k**3 + 3*k**2 - 6*k - 3. Let y be s(-4). Factor -6*h**3 - 4*h**4 - h - 4*h**4 + 4*h**4 - 4*h**2 - h**y.
-h*(h + 1)**4
Factor -4 - l**3 + 7*l**5 + 7 + 3*l - 4*l**5 - 5*l**3 - 6*l**2 + 3*l**4.
3*(l - 1)**2*(l + 1)**3
Let o(w) be the first derivative of -2*w**3/15 - 3*w**2/5 - 4*w/5 + 5. Factor o(q).
-2*(q + 1)*(q + 2)/5
Solve -4*u + 4*u**2 + 2*u**2 - u**2 + 54*u + 125 = 0.
-5
Let h = -11/35 + 5/7. Solve 0 - 2/5*t + h*t**2 = 0.
0, 1
Solve -2/5*w - 1/5*w**2 + 6/5*w**4 + 7/5*w**3 + 0 = 0.
-1, -2/3, 0, 1/2
Let n(d) be the third derivative of -d**6/480 - d**5/240 + d**4/24 + d**3/6 - 5*d**2. Factor n(g).
-(g - 2)*(g + 1)*(g + 2)/4
Let y(z) be the first derivative of 3/4*z**4 - 3*z + 5 + z**3 - 3/2*z**2. Suppose y(v) = 0. What is v?
-1, 1
Let n(w) = w**4 - 6*w**4 - w + 4*w**4 - w**2. Let f(l) = -3*l**5 - 2*l**4 + 3*l**3 - 2*l**2 - 2*l. Let g(d) = f(d) - 2*n(d). Factor g(v).
-3*v**3*(v - 1)*(v + 1)
Suppose 3*a = -5*t, -2*t + 2*a + 16 = -0*t. Factor -2/3*h**4 - 2/3 + 4/3*h**2 + 0*h**t + 0*h.
-2*(h - 1)**2*(h + 1)**2/3
Let s = 24/43 - -224/215. Let o be (-2)/(-4) + 11/10. Factor 2/5 - s*a + o*a**2.
2*(2*a - 1)**2/5
Suppose 2*q + 2 - 6 = -o, 2*o - 7 = -3*q. Let d(w) be the second derivative of 0*w**2 + 2/15*w**4 - 1/15*w**3 - o*w + 0. Factor d(j).
2*j*(4*j - 1)/5
Determine t so that 0 + 2/3*t**2 - 4/3*t = 0.
0, 2
Let z(u) = -u**3 + 7*u**2 + 5. Let c be z(7). Find h such that -4*h**c + 2*h - 4*h**3 + 0*h + 6*h**5 = 0.
-1, 0, 1
Suppose 0 = -y - y + 20. Let v(c) = -7 + 2*c - 6*c + y*c**3 - 2*c**4 + 2*c + c**4. Let t(w) = -w**4 + w**3 + w - 1. Let o(p) = 4*t(p) - v(p). Factor o(j).
-3*(j - 1)*(j + 1)**3
Let b(w) be the first derivative of w**5/30 - w**4/4 + 2*w**3/3 + w**2 + 1. Let s(q) be the second derivative of b(q). Solve s(f) = 0 for f.
1, 2
Suppose -8 = 26*n - 28*n. Factor 0*d**2 + 0*d**3 + 0*d + 1/4*d**5 + 0 - 1/2*d**n.
d**4*(d - 2)/4
Let j(c) be the third derivative of 0*c - 4*c**2 + 0*c**3 - 1/360*c**6 + 0*c**4 + 0 + 0*c**5. Factor j(p).
-p**3/3
Factor 5*u**3 - 3*u**3 + 3*u**2 - 3*u**4 - 5*u**3 - 6*u**3 + 6*u + 3*u**5.
3*u*(u - 2)*(u - 1)*(u + 1)**2
Let p be (-480)/(-448) + 8/(-14). Factor 0 + f**3 + p*f**2 + 1/2*f**4 + 0*f.
f**2*(f + 1)**2/2
Let p(y) be the second derivative of -y**9/5040 - 3*y**8/1120 - 3*y**7/280 + y**4/6 - 4*y. Let h(m) be the third derivative of p(m). What is z in h(z) = 0?
-3, 0
Factor -120*k**2 + 45*k + 35*k**3 + 24*k**3 + 7*k**3 + 10 - k**3.
5*(k - 1)**2*(13*k + 2)
Let d be 0*-1*1*(-2 + 1). Let x(l) be the third derivative of d*l**4 + 1/30*l**5 - 1/105*l**7 + 0*l**3 + 0*l**6 + 0 + 2*l**2 + 0*l. Find t such that x(t) = 0.
-1, 0, 1
Let k(a) be the first derivative of 1 - 2/27*a**3 + 0*a + 0*a**2. Factor k(s).
-2*s**2/9
Suppose -c + 3*r + 10 = 0, -5 = -c + 4*r + 7. Suppose b**2 - c*b**3 + b**4 + 6*b**5 - 2*b**5 + 0*b**3 - 2*b**4 = 0. What is b?
-1, 0, 1/4, 1
Let z = -140 - -143. Determine g, given that 6/5*g**z + 0 - 12/5*g**5 + g**4 + 1/5*g**2 + 0*g = 0.
-1/3, -1/4, 0, 1
Let t = -5/32 - -117/32. Suppose 0 + t*u**3 + 5/2*u**2 - u = 0. What is u?
-1, 0, 2/7
Let u(p) be the second derivative of -p**4/24 + p**3 - 9*p**2 - 13*p. Determine b, given that u(b) = 0.
6
Let q be 5*(-6)/(-10) - 2/2. Let 0*f**q + 0 - 2/3*f**3 + 0*f = 0. What is f?
0
Suppose 1 - 13 = -3*c. Factor 9 - 2*k**4 - 1 + 4*k**c + 4*k**3 + k**2 - 8*k - 7*k**2.
2*(k - 1)**2*(k + 2)**2
Let k(f) = f**3 + f**2 - f - 1. Let z(g) = 2*g**3 + 3*g**2 - 2*g - 3. Let v = 11 + -8. Let m(s) = v*k(s) - z(s). Let m(r) = 0. Calculate r.
-1, 0, 1
Let h(g) be the third derivative of -g**5/60 + g**2. Determine a so that h(a) = 0.
0
Factor -3*l**3 - l**5 + 2*l**2 + 6*l**3 + 7*l**2 - 7*l**2.
-l**2*(l - 2)*(l + 1)**2
Let u(c) = -c**3 - 40*c**2 + 43*c + 84. Let w be u(-41). Suppose 0 + 1/4*j**3 + 0*j**4 + 0*j**w - 1/8*j - 1/8*j**5 = 0. What is j?
-1, 0, 1
Factor 51*g + 2*g**5 - 24*g**3 + 2*g**4 - 83*g - 5*g**2 - 51*g**2.
2*g*(g - 4)*(g + 1)*(g + 2)**2
Let z(g) = -g**5 + g**3 + g**2 - g. Let p(j) = 24*j**5 + 32*j**4 + 4*j**3 - 36*j**2 - 16*j - 8. Let u(o) = -p(o) - 12*z(o). Let u(a) = 