
Let x be (8/(-35630))/((-16)/(-81160)). Let i = 2/509 - x. Factor i - 6/7*a**2 + 0*a - 2/7*a**3.
-2*(a - 1)*(a + 2)**2/7
Let l be 8/6*108/(-24). Let n be l/(-4) + (-3)/2. Determine q, given that -2/9*q**2 + n*q + 2/9 = 0.
-1, 1
Let a be -32 - -25 - 102/(-14). Determine p, given that 6/7*p**3 + 2/7*p + 0 - 6/7*p**2 - a*p**4 = 0.
0, 1
Factor -2/3*p**2 - 2/3*p + 2/3 + 2/3*p**3.
2*(p - 1)**2*(p + 1)/3
Let l = -124 - -499/4. Suppose l*n**2 - 3/4*n + 1/4 - 1/4*n**3 = 0. Calculate n.
1
Let w(g) be the second derivative of 0*g**2 + 0*g**4 - 1/20*g**5 + 1/42*g**7 + 0*g**6 - 2*g + 0 + 0*g**3. Factor w(r).
r**3*(r - 1)*(r + 1)
Suppose 38*u = 36*u. Find w, given that -2/9*w - 4/9*w**2 + u - 2/9*w**3 = 0.
-1, 0
Let g be -1*(5/2)/(-5). Let o be (-48)/(-30) - (-4)/10. Factor -1/2 - g*m**o + m.
-(m - 1)**2/2
Let l(s) be the first derivative of -7*s**6/48 - 23*s**5/40 - 27*s**4/32 - 13*s**3/24 - s**2/8 - 18. Factor l(h).
-h*(h + 1)**3*(7*h + 2)/8
Let v(n) = 4*n. Let p be v(8). What is y in 20*y**4 - 16 + 2*y**5 - y**5 - 3*y**2 + 3*y**5 - y**2 - p*y + 28*y**3 = 0?
-2, -1, 1
Let u = 2/117 - -113/234. Factor 1/2*z**2 - 3/4*z + 1/4*z**5 + u*z**3 + 1/4 - 3/4*z**4.
(z - 1)**4*(z + 1)/4
Let -2/5*u**3 + 6/5*u**2 - 2/5*u**5 + 4/5*u - 6/5*u**4 + 0 = 0. What is u?
-2, -1, 0, 1
Let a(j) be the first derivative of -j**4/10 + 4*j**3/15 - j**2/5 - 4. Factor a(n).
-2*n*(n - 1)**2/5
Let l(k) be the first derivative of k**9/1512 - k**8/280 + k**6/45 + 2*k**3/3 + 6. Let s(y) be the third derivative of l(y). Suppose s(v) = 0. What is v?
-1, 0, 2
Factor -18*a**4 - 36*a**2 + 109*a**3 + 3*a - 283*a**5 - 108*a**4 + 332*a**5 + a.
a*(a - 1)**2*(7*a - 2)**2
Suppose 3/2*w**4 + 7/6*w**2 - 8/3 + 1/6*w**5 + 23/6*w**3 - 4*w = 0. Calculate w.
-4, -1, 1
Let h(j) = j**4 - j**3 + j**2 - j. Let s(y) = -y**4 + 18*y**3 + 3*y**2 + 8*y. Let p(a) = 6*h(a) + s(a). Determine d so that p(d) = 0.
-1, -2/5, 0
Let c(h) be the third derivative of h**7/1470 + h**6/840 - h**5/420 - h**4/168 - 19*h**2. Factor c(i).
i*(i - 1)*(i + 1)**2/7
Let m(a) be the first derivative of 10*a**3/3 + 5*a**2/2 - 5*a + 17. Find k, given that m(k) = 0.
-1, 1/2
Let y(u) = 2 + 3*u**2 + u**3 - 5 + 4*u + 3*u**2. Let j be y(-5). Factor -3*h + 7*h + 4 - 2 + 2*h**j.
2*(h + 1)**2
Let d(x) = 7 + 2 - 8*x**3 + x - 5*x - 2*x**2 - 7. Let w(a) = a**3 + a. Suppose 0 = -2*k - 12 - 0. Let n(b) = k*w(b) - d(b). Find i such that n(i) = 0.
-1, 1
Let n(j) be the third derivative of -4/3*j**3 - 2*j**2 + 0*j + 0 - 1/2*j**4 - 1/15*j**5. Solve n(h) = 0.
-2, -1
Suppose -j - 5*a - 23 = 0, 28 = 4*j - 7*a + 3*a. Factor h**j + h**2 - 5*h + 2*h**2 + 1.
(h - 1)*(4*h - 1)
Let n = -9 + 11. Let 2*j**3 + j**n - 2*j**2 + 0*j**3 + 3*j**2 = 0. What is j?
-1, 0
Let c(j) be the first derivative of j**7/70 - 3*j**5/100 + 3*j + 3. Let i(a) be the first derivative of c(a). Determine q so that i(q) = 0.
-1, 0, 1
Let v(x) = -x + 2*x + 6 - 3*x**2 + 3. Let f(b) = -2*b**2 + 5. Let p(c) = -5*f(c) + 3*v(c). Factor p(d).
(d + 1)*(d + 2)
Let y = 9 + -6. Let -4/3*o**4 + 0 + 1/3*o**y + 4/3*o**2 - 1/3*o = 0. What is o?
-1, 0, 1/4, 1
Let l(h) = -2*h**3 - 6*h**2 - 3*h + 4. Let t(k) = -k + 8. Let u be t(5). Let v(x) = 3 - 5*x**2 + 6 - x**u - 5 - 2*x. Let r(p) = 2*l(p) - 3*v(p). Factor r(q).
-(q - 2)**2*(q + 1)
Let l(u) be the first derivative of 2 + 1/9*u**2 - 1/18*u**4 + 2/27*u**3 - 2/9*u. Factor l(t).
-2*(t - 1)**2*(t + 1)/9
Let m be (-4 - -1)/(21/(-14)). Factor -g**5 + 6*g**m + g**3 + g**4 - 7*g**2 + 0*g**2.
-g**2*(g - 1)**2*(g + 1)
Let r(i) be the first derivative of -i**7/315 + i**6/90 - i**5/90 + i**2/2 + 2. Let o(h) be the second derivative of r(h). Let o(s) = 0. What is s?
0, 1
Let h = 5 + -10. Let y = h + 5. Determine d, given that 2*d**4 + 14*d**3 - 6*d**2 - 4*d + y*d**5 - 7*d**5 - 3*d + 2*d**2 + 2 = 0.
-1, 2/7, 1
Let t(i) = i**3 - 5*i**2 + 3*i. Let f be t(4). Let a be 100/36 + f/(-18). Suppose 3*k**3 + 4*k**4 - 2*k**3 + 2*k**5 - 3*k**3 + 4*k**a = 0. What is k?
-1, 0
Let w be 28/6 + 4/12. Determine h so that 3*h**3 - h**5 - 3*h**5 + h**w = 0.
-1, 0, 1
Let r be (3 - 0)/((-24)/64). Let o = r + 8. Suppose 0 + 4/5*f**2 - 4/5*f**4 + 2/5*f**5 + o*f**3 - 2/5*f = 0. Calculate f.
-1, 0, 1
Let v(b) be the first derivative of -2*b**6/3 + 12*b**5/5 - b**4 - 4*b**3 + 4*b**2 + 5. Determine p, given that v(p) = 0.
-1, 0, 1, 2
Let g(s) be the third derivative of 0*s**3 - 1/40*s**4 + 1/300*s**5 + 0 + 0*s - 4*s**2. What is v in g(v) = 0?
0, 3
Let d be (-1)/(-3)*(-12 + 14). What is a in -1/3*a - 1/3*a**2 + d = 0?
-2, 1
Let g(c) = -5*c**2. Let m(j) = -2*j**2. Let b(x) = 4*g(x) - 9*m(x). Find t such that b(t) = 0.
0
Let f(s) be the first derivative of 44*s**3/3 + 26*s**2 + 8*s - 6. Factor f(b).
4*(b + 1)*(11*b + 2)
Let v = 1/5 - -3/10. Let 1/4*t**2 - v - 1/4*t = 0. What is t?
-1, 2
Let r(n) be the second derivative of -1/2*n**2 + 0 - 2*n + 1/16*n**4 - 1/12*n**3 + 1/30*n**5. Let u(x) be the first derivative of r(x). What is a in u(a) = 0?
-1, 1/4
Let s be (28 - 34)*2/(-10). Suppose 9/5*n + s + 3/5*n**2 = 0. Calculate n.
-2, -1
Let a(v) be the second derivative of -4/3*v**2 - 2*v + 0*v**3 + 0 + 1/18*v**4. Suppose a(c) = 0. What is c?
-2, 2
Factor 0*a + 0 + 1/2*a**4 - 1/2*a**3 - a**2.
a**2*(a - 2)*(a + 1)/2
Suppose 2*q = -3*q + 15. Suppose -5*j - q + 13 = -5*a, -4*j - 4*a = -8. Factor 1/2 - 1/2*b**3 - 1/2*b**j + 1/2*b.
-(b - 1)*(b + 1)**2/2
Suppose y = 2*y. Let b(g) be the third derivative of 1/3*g**5 + y + 1/20*g**6 + 2/3*g**3 - g**2 + 0*g + 3/4*g**4. Determine p, given that b(p) = 0.
-2, -1, -1/3
Let d(r) be the third derivative of r**5/90 + r**4/12 + 2*r**3/9 + 7*r**2. Let d(h) = 0. What is h?
-2, -1
Let c(j) be the third derivative of -j**6/165 + 7*j**5/330 + j**4/66 + 14*j**2. Factor c(h).
-2*h*(h - 2)*(4*h + 1)/11
Let o = 68 - 68. Let c(v) be the third derivative of 1/12*v**4 + 0*v**3 + o - 3*v**2 + 0*v + 1/60*v**6 + 1/15*v**5. Suppose c(r) = 0. What is r?
-1, 0
Let r(t) be the first derivative of t**6/160 - 3*t**5/40 + 3*t**4/8 - t**3 - t**2/2 + 2. Let n(f) be the second derivative of r(f). Solve n(w) = 0.
2
Let c = -167/15 + 37/3. Factor -3*n**2 + 3/5*n + c + 6/5*n**3.
3*(n - 2)*(n - 1)*(2*n + 1)/5
Factor 0 + 1 + q - 3*q + q**2.
(q - 1)**2
Let q(n) = -3 + 7*n - n + 8*n**2 + n**3 - 1. Let y be q(-7). Suppose -5*b**4 - 2*b + b**2 + b**4 + 2*b - 3*b**y = 0. What is b?
-1, 0, 1/4
Let z be ((-7)/1 - -1)*518/(-2331). Suppose z*f + 2 + 2/9*f**2 = 0. What is f?
-3
Let y(a) be the third derivative of -a**7/945 + a**6/540 + a**5/135 - a**2. Determine h, given that y(h) = 0.
-1, 0, 2
Let a(q) be the first derivative of 5 - 1/3*q**3 - q**2 - q. Factor a(m).
-(m + 1)**2
Let w(l) be the third derivative of l**8/840 + l**7/105 + l**6/45 - l**3/6 - 2*l**2. Let c(j) be the first derivative of w(j). Suppose c(m) = 0. Calculate m.
-2, 0
Let p(c) be the first derivative of -3*c**5/5 - 3*c**4/2 + 3*c**2 + 3*c - 4. Let p(o) = 0. Calculate o.
-1, 1
Let a(z) be the second derivative of -z**6/15 + z**4/6 - 4*z. Find w, given that a(w) = 0.
-1, 0, 1
Suppose -10 = -2*g + 3*i, 4*i = -4*g - 0*g. Suppose 3*m - 2*m**g - 4 - 5*m**3 + 14*m - 5*m - m**2 = 0. Calculate m.
-2, 2/5, 1
Suppose -c + 0*c = 5*o - 7, 5*c = -o - 13. Suppose 2/5*z + 4/5 - 2/5*z**o = 0. Calculate z.
-1, 2
Factor 0 - 1/2*a + a**3 + 0*a**4 + 0*a**2 - 1/2*a**5.
-a*(a - 1)**2*(a + 1)**2/2
Let w(q) be the third derivative of q**9/60480 - q**8/13440 - q**7/10080 + q**6/1440 - q**4/8 + 3*q**2. Let i(s) be the second derivative of w(s). Factor i(n).
n*(n - 2)*(n - 1)*(n + 1)/4
Factor 3/4*v**2 + 0*v - 3/2*v**3 + 3/4*v**4 + 0.
3*v**2*(v - 1)**2/4
Let r(n) be the second derivative of -n**4/15 + 2*n**3/15 - 16*n. Factor r(j).
-4*j*(j - 1)/5
Let z(n) = 2*n**2 - 9*n + 5. Let v be z(4). Let w be (-1)/(v + 0) - -1. What is t in -1/4*t**2 + 1/4*t**4 + 0*t - t**3 + t**5 + w = 0?
-1, -1/4, 0, 1
Factor o**2 - 118*o**4 - 7*o**2 + 98*o**4 + o**2 + 25*o**3.
-5*o**2*(o - 1)*(4*o - 1)
Let x(z) be the third derivative of z**6/1800 + z**5/600 - z**3/6 - z**2. Let t(v) be the first derivative of x(v). Factor t(k).
k*(k + 1)/5
Let i be (-15)/(-18) + (8 - 930/108). Suppose 2*p - 6 + 2 = 0. Factor -2/9*j**p + 0 - i*j.
-2*j*(j + 1)/9
Let o(n) = -12*n - 250. Let r be o(-21). Factor -16/7*l - 2/7*l**r - 32/7.
-2*(l + 4)**2/7
Let z = -32 + 24. Let q = z - -10. Factor -6/5*u - 3/5 - 