/(3/15). Suppose 0*a**4 + 0*a + 1/4*a**m + 0*a**f - 1/4*a**5 + 0 = 0. What is a?
-1, 0, 1
Let j(d) be the third derivative of -d**7/945 - d**6/270 - d**5/270 + 28*d**2. Find v such that j(v) = 0.
-1, 0
Let v(j) = j + 1. Let m be v(7). Let r be m/5 - (-6)/15. Suppose 2 - z**2 - 2*z**4 - 4 + 5*z**r = 0. What is z?
-1, 1
Let c(n) be the third derivative of n**6/240 + 2*n**3/3 + 7*n**2. Let j(b) be the first derivative of c(b). Factor j(g).
3*g**2/2
Let a = -7 - -14. Let o = -5 + a. Factor 5/3*z + 4/3*z**o + 1/3*z**3 + 2/3.
(z + 1)**2*(z + 2)/3
Let q be -17 + 10 - (-3 - 4). Determine p so that q + 1/3*p**2 + 0*p = 0.
0
Let o be 9/(2/((-64)/(-12))). Let w be (o/132)/((-1)/(-2)). Factor 10/11*p + w + 8/11*p**2 + 2/11*p**3.
2*(p + 1)**2*(p + 2)/11
Suppose -n + 6 = n. Suppose 6*h - 2*h - 48 = -n*y, -y - 2*h + 18 = 0. Factor -2*u - 11*u**5 - y*u**3 + 8*u**2 + 9*u**5 - 4*u**4 + 12*u**4.
-2*u*(u - 1)**4
Suppose -5*l - 83 = -2*t, 2*l - 65 = -2*t + l. Solve 21*n**2 + 10*n - 15*n**3 - t*n + 4 + 43*n**3 + 21*n**3 = 0 for n.
-1, 2/7
Factor -u**2 - 36*u**3 + 0*u + 21*u**3 + 5*u + 11*u**2.
-5*u*(u - 1)*(3*u + 1)
Determine s, given that 1/3*s**3 + 0*s + 1/3*s**4 + 0 - 1/3*s**2 - 1/3*s**5 = 0.
-1, 0, 1
Let y be ((-10)/(-8)*(-3 - 1))/(-1). Find g such that 26/7*g**2 - 22/7*g**4 + 20/7*g**y + 2/7*g - 4/7 - 22/7*g**3 = 0.
-1, -2/5, 1/2, 1
Let v(y) be the first derivative of 3*y**4/8 + y**3/3 - 3*y**2/4 - y - 26. Factor v(m).
(m - 1)*(m + 1)*(3*m + 2)/2
Let o(c) be the first derivative of c**5/5 - 11*c**4/6 + 5*c**3/9 + 7*c**2/3 - 48. Suppose o(w) = 0. What is w?
-2/3, 0, 1, 7
Suppose 0 = -3*v - t + 10, -15 - 5 = -v + 3*t. Suppose -v*x + 3 + 2 = 0. Factor x + 0*b - b - 6*b**2 + 4*b**2.
-(b + 1)*(2*b - 1)
Let a = 67 - 67. Let p(l) be the third derivative of 0*l**4 - 3/40*l**5 + 0*l**3 + a + 0*l + 1/80*l**6 - 3*l**2. Factor p(c).
3*c**2*(c - 3)/2
Factor -3/2*x**2 + 5/2*x + 6.
-(x - 3)*(3*x + 4)/2
Let p(h) = -6*h**3 + 17*h**2 - 25*h + 7. Let w(a) = -2*a**3 + 6*a**2 - 8*a + 2. Let t(f) = -2*p(f) + 7*w(f). Factor t(z).
-2*z*(z - 3)*(z - 1)
Suppose 3*x - 6 = 3*i, 8*i + x - 14 = 3*i. Let c = 4 - 2. Solve -4*y - 6*y**2 - 3*y**3 + c*y - i*y**4 - 3*y**3 = 0 for y.
-1, 0
Suppose -p - n = 2*n + 5, -5*p + 5*n + 55 = 0. Let c = p - 3. Solve 1/4*w - 1/4*w**c - 1/4*w**3 + 0 + 1/4*w**2 = 0.
-1, 0, 1
Let z = 3 - 1. Let m be -4*(-2)/(-84)*-3. Find y, given that -6/7*y - m*y**z - 4/7 = 0.
-2, -1
Suppose -4/7 - 6/7*s - 2/7*s**2 = 0. Calculate s.
-2, -1
Find w such that 3/5*w**4 - 1/5*w**3 - 1/5*w**5 - 3/5*w**2 + 0 + 2/5*w = 0.
-1, 0, 1, 2
Let v(g) = 10*g**4 - 45*g**3 - 80*g**2 + 45*g - 35. Let p(t) = t**4 - 5*t**3 - 9*t**2 + 5*t - 4. Let q(l) = -35*p(l) + 4*v(l). Factor q(s).
5*s*(s - 1)**2*(s + 1)
Let j = 72 - 214/3. Factor 0 + 0*z - 2/3*z**5 + 2/3*z**2 - 2/3*z**4 + j*z**3.
-2*z**2*(z - 1)*(z + 1)**2/3
Factor 24*q**2 + 3/2 - 12*q.
3*(4*q - 1)**2/2
Let h(z) = -z**3 + 12*z**2 + z - 8. Let b be h(12). Suppose -3*w + 3 = b*v - 4*w, 3*v + 3 = -w. Factor v*y + 1/2*y**4 + 0*y**2 + 1/2*y**3 + 0.
y**3*(y + 1)/2
Let u(i) be the third derivative of 0*i**3 - i**2 + 0 + 1/210*i**7 + 1/45*i**6 + 7/180*i**5 + 0*i + 1/36*i**4. Factor u(l).
l*(l + 1)**2*(3*l + 2)/3
Solve 1/7*z**3 - 1/7 - 1/7*z + 1/7*z**2 = 0.
-1, 1
Let i(l) = l**2 - l - 3. Let r(w) = 2. Suppose -9*g + 6*g = -18. Let q(s) = g*r(s) + 4*i(s). Factor q(x).
4*x*(x - 1)
Suppose -2 = 4*w - 2*w - 2*o, 35 = 5*w + 5*o. Suppose 7*p - 2*p = 8*p. Factor -2*c + 50*c**4 - 2*c**2 + p + 55/2*c**w.
c*(4*c - 1)*(5*c + 2)**2/2
Let g(b) be the second derivative of b**6/75 - b**4/15 + b**2/5 + 12*b. Factor g(t).
2*(t - 1)**2*(t + 1)**2/5
Suppose -3*j + 7 = 1. Suppose 4*x = a + j, -5*a + 1 = -2*a - 5*x. Factor 2/7*y**a - 2/7*y + 0.
2*y*(y - 1)/7
Let k(p) = 3*p**2 + 3*p - 9. Let q(a) = 1 - 3 + 0 + 1. Let m(v) = -k(v) + 9*q(v). Factor m(x).
-3*x*(x + 1)
Suppose 0*b = 3*b. Suppose b = -3*q - q. Factor -3/5*r**2 - 3/5*r + q.
-3*r*(r + 1)/5
Let z(o) be the second derivative of -o**8/672 - o**7/105 - o**6/40 - o**5/30 - o**4/48 + o**2 - 4*o. Let t(x) be the first derivative of z(x). Factor t(a).
-a*(a + 1)**4/2
Let s(v) be the second derivative of -9*v**5/10 - v**4/4 + v**3 - 22*v. Determine f, given that s(f) = 0.
-2/3, 0, 1/2
Let n be 21/5 - (-2)/(-10). Solve -y**5 + y**n + y**4 - 2*y**2 + 0*y**2 - 3*y + 4*y = 0 for y.
-1, 0, 1
Let c(u) be the first derivative of u**5/30 - u**4/12 + u**2/6 - u/6 - 8. Determine w so that c(w) = 0.
-1, 1
Let o(s) = -4*s - 1. Let h be o(-4). Suppose -3*r = 15, 5*j - 20 - h = 5*r. Let 4*d**4 - 4 - 4*d**2 + 2*d + 4 - j*d**5 = 0. What is d?
-1, 0, 1
Let h be 28/(-6)*86/(-301). Solve -2/3*k**2 + 0 - h*k = 0 for k.
-2, 0
What is j in 16/7 + 12/7*j**2 + 2/7*j**3 + 24/7*j = 0?
-2
Let g(i) be the second derivative of -i**4/6 + i**2 - 26*i. Factor g(n).
-2*(n - 1)*(n + 1)
Let c(p) be the first derivative of -3*p**5/10 - p**4/6 - 2*p - 3. Let h(j) be the first derivative of c(j). Factor h(y).
-2*y**2*(3*y + 1)
Let z(t) be the first derivative of t**7/840 - t**6/160 + t**5/80 - t**4/96 - t**2 - 1. Let v(j) be the second derivative of z(j). Factor v(g).
g*(g - 1)**3/4
Let b(t) = t**2 - 10*t + 2. Let i(m) = -m. Let f(p) = -3*b(p) + 21*i(p). Find c such that f(c) = 0.
1, 2
Let p(g) be the second derivative of -g**6/60 - g**5/20 + g**3/6 + g**2/4 + 5*g. Factor p(o).
-(o - 1)*(o + 1)**3/2
Let d(l) be the second derivative of l**4/12 + l**3/6 + 2*l. Let j be d(1). Let 2*s + j*s**2 + 2/3*s**3 + 2/3 = 0. Calculate s.
-1
Let r(h) be the second derivative of 2*h**6/15 + 13*h**5/20 + 11*h**4/12 + h**3/3 + 2*h. Factor r(d).
d*(d + 1)*(d + 2)*(4*d + 1)
Let j(g) be the first derivative of -3*g**4/16 + 4*g**3/3 - 3*g**2/2 - 4*g + 12. Let j(a) = 0. Calculate a.
-2/3, 2, 4
Find o, given that 3/5*o + 0 - 3/5*o**3 + 0*o**2 = 0.
-1, 0, 1
Let v(g) be the first derivative of -2*g**4 + 6*g**3 - 6*g**2 + 2*g - 1. Solve v(h) = 0 for h.
1/4, 1
Let p = 2 - 0. Factor -z**2 - 2*z - z**2 + z**p.
-z*(z + 2)
Let y(z) = -z**3 + 4*z**2 - 2*z - 1. Let x(n) = -n**3 - 5*n**2 + 2*n + 7. Let o be x(-5). Let c(i) = i**3 - 1. Let j(d) = o*c(d) - y(d). Factor j(m).
-2*(m - 1)*(m + 1)*(m + 2)
Let r(w) be the first derivative of -3*w**4/2 - 10*w**3/3 - 2*w**2 - w - 1. Let q(j) = -5*j**3 - 9*j**2 - 3*j - 1. Let t(b) = 7*q(b) - 6*r(b). Factor t(m).
(m - 1)**3
Let s(o) = -o - 2. Let r be s(-4). Suppose -f + 2*c = -11, -4*f + 4*c = -6*f - 2. Find v, given that 4*v**5 - f*v**5 + r*v**2 - v**4 - v**2 + v**3 = 0.
-1, 0, 1
Let c be 1/(-2) + (-10)/(-4). Factor 10*j**3 - 2*j**c + 0*j**2 + 8*j**5 + j**4 - 17*j**4.
2*j**2*(j - 1)*(2*j - 1)**2
Suppose 5*i - 2*i = 0. Suppose -3*o + 6 = -4*t, -o + 5*t = -i*t - 2. Solve -1 - 2*j**3 + 3 + 2*j - 3*j**2 + j**o = 0.
-1, 1
Let l(a) be the first derivative of a**6/45 - a**4/30 - 3. Let l(v) = 0. What is v?
-1, 0, 1
Factor 2*o**2 - 8 - 2*o + 3*o - o.
2*(o - 2)*(o + 2)
Let g(f) = -f**4 + 5*f**3 - f**2 + f - 2. Let q = 19 - 16. Let v(a) = a**3 + a**2 - 1. Let s(h) = q*g(h) - 6*v(h). What is c in s(c) = 0?
0, 1
Let s(o) be the third derivative of -o**6/300 - o**5/100 + o**3/30 - 9*o**2. Factor s(x).
-(x + 1)**2*(2*x - 1)/5
Let g(w) = -8*w - 32. Let b be g(-4). Factor -p**2 - 2/5*p + b + 3/5*p**3.
p*(p - 2)*(3*p + 1)/5
Suppose 75*i - 8 = 73*i. Factor 0 - 2*d**2 - 2/5*d + 18/5*d**i - 6/5*d**3.
2*d*(d - 1)*(3*d + 1)**2/5
Let i = 6435/4 - 1672. Let y = -63 - i. Factor 0*j + 1/4*j**3 + 0 - y*j**2 - 1/4*j**5 + 1/4*j**4.
-j**2*(j - 1)**2*(j + 1)/4
Let c = 4 + -1. Suppose -p = 3, 4*j - c - 2 = -p. Suppose -y**2 - 5 + 5 + 2*y + 8*y**3 - 9*y**j = 0. What is y?
0, 1/4, 1
Let s(i) be the third derivative of i**8/672 - i**7/105 + i**6/80 + i**5/30 - i**4/12 + 5*i**2. Solve s(k) = 0 for k.
-1, 0, 1, 2
Let s = -14 - -4. Let r be s/(-4) - (-1)/2. Determine t, given that t**4 - 6*t**r + 5*t**3 + 0*t**4 = 0.
0, 1
Suppose 0 = -m - u + 1, 4*m - 5*u + 5 = 18. Solve 2/9*a - 1/9 + 1/3*a**m = 0 for a.
-1, 1/3
Solve 4/7*y**2 - 2/7*y**3 - 2/7*y + 0 = 0.
0, 1
Suppose 4*s - 5*p = -7, s = -s + 4*p - 2. Let x be (s/(-6) + -1)/(-2). Find z such that x*z**2 + 1/4*z - 1/2 = 0.
-2, 1
Suppose -5*z**4 + 110*z**3 + 2560*z - 535*z**2 + 10*z**3 - 425*z**2 + 0*z**4 = 0. Calculate z.
0, 8
Factor 3/4*o**2 + 0 + 3/2*o.
3*o*(o + 2)/4
Let a = -123 + 125. Let d(t) be the first derivative of -2/9*t**3 +