2
Let s(t) be the first derivative of t**4/48 - t**3/4 + 9*t**2/8 - t + 2. Let f(w) be the first derivative of s(w). Suppose f(p) = 0. Calculate p.
3
What is u in -9*u - 2 - 4*u**2 + 0 + u**2 - 4 = 0?
-2, -1
Let l(x) be the first derivative of 1/6*x**4 - 2/45*x**5 + 0*x - 1 - 4/27*x**3 + 0*x**2. Find h, given that l(h) = 0.
0, 1, 2
Let o be -2*(12/20 + 36/(-20)). Suppose 12/5*m + 3/5*m**4 + 18/5*m**2 + o*m**3 + 3/5 = 0. What is m?
-1
Let c(r) = -r**2 - r. Let h(s) = -14*s**2 - 6*s. Let i(v) = -8*c(v) + h(v). Factor i(n).
-2*n*(3*n - 1)
Suppose -u - 183 = -185. Solve -1/3 + z + 2/3*z**4 - 1/3*z**u - z**3 = 0 for z.
-1, 1/2, 1
Let b(a) be the second derivative of a**8/26880 + a**7/10080 - a**6/2880 - a**5/480 + a**4/3 + 2*a. Let p(x) be the third derivative of b(x). Factor p(f).
(f - 1)*(f + 1)**2/4
Let n(s) be the second derivative of s + s**2 + 1/24*s**3 + 0 - 1/60*s**5 - 1/32*s**4. Let r(m) be the first derivative of n(m). Suppose r(y) = 0. Calculate y.
-1, 1/4
Let q(a) = a**3 - 6*a**2 + 4. Let l be q(6). Suppose 0 = i + 4, 5*f + i = -l*i - 10. Factor 0*z**5 - f*z**5 - 2*z**2 + 2*z**4 + 4*z**5 - 2*z**3.
2*z**2*(z - 1)*(z + 1)**2
Suppose -2*o + 0 = 4. Let s = o + 4. Factor d**4 - s*d**3 - 2*d**2 - 2*d + 4*d**3 + d**4.
2*d*(d - 1)*(d + 1)**2
Let x(f) = -f**3 - 5*f**2 - 5*f + 1. Let y be x(-4). Let c(k) = k + 2. Let l be c(2). Solve -6*r**3 + r - 3*r**y - 8*r**l + 3*r**2 - 3*r**2 = 0.
-1, 0, 1/3
Let q = -34 - -36. Factor -2/7*p**q + 2/7*p**3 - 2/7*p + 2/7.
2*(p - 1)**2*(p + 1)/7
Factor -3*x**2 - 11*x + 5*x**2 + 13*x.
2*x*(x + 1)
Let 2 + 0*u**2 + 3 - 2*u - 2 - u**2 = 0. Calculate u.
-3, 1
Factor -y + 212*y**2 + 4*y - 211*y**2.
y*(y + 3)
Let b = 44 - 44. Factor b*j**2 + 2/9*j**3 - 4/9 - 2/3*j.
2*(j - 2)*(j + 1)**2/9
Suppose 11 - 3 = 4*a. Let j(s) = s**3 - 2*s**2 + 1. Let d be j(1). Solve 0 + 2/7*f**4 + 0*f**a + 2/7*f**3 + d*f = 0.
-1, 0
Factor 2/3*b**2 - 4/9*b + 0 + 10/9*b**3.
2*b*(b + 1)*(5*b - 2)/9
Let a = 1 + -4. Let d be 17/6 - a/(-2). Let d*n + 0 + 2/3*n**2 = 0. Calculate n.
-2, 0
Let x be -1 + (3 - -5)*2. Let w be 2/x - (-44)/165. Factor 6/5*m**2 - 6/5*m + 2/5 - w*m**3.
-2*(m - 1)**3/5
Let c(q) = q**2 + 2*q - 4. Let i(a) = a**2 - 6*a - 4. Let t be i(6). Let o be c(t). Determine f, given that 3*f**4 - 2*f**2 - f**o + 0*f**2 = 0.
-1, 0, 1
Factor -148*x**4 - 2560 + 18*x**4 - 5082*x - 998*x - 4600*x**2 - 5*x**5 - 1205*x**3.
-5*(x + 1)**2*(x + 8)**3
Let l(x) be the second derivative of -x**6/45 - x**5/18 + 23*x**4/54 - 19*x**3/27 + 4*x**2/9 + x + 46. Find q, given that l(q) = 0.
-4, 1/3, 1
Let s = -4/91 - -139/1092. Let h(l) be the second derivative of s*l**3 + 1/60*l**6 - 1/40*l**5 - 1/8*l**4 + 0 + 1/2*l**2 + 2*l. Determine a so that h(a) = 0.
-1, 1, 2
Let m(j) be the second derivative of j**6/15 - j**5/20 - j**4/2 + 7*j**3/6 - j**2 - 19*j. Factor m(q).
(q - 1)**2*(q + 2)*(2*q - 1)
Let u(o) be the third derivative of o**6/150 - o**5/75 - 3*o**2. Factor u(p).
4*p**2*(p - 1)/5
Let b = -782 - -784. Factor -2*o**3 - 1/5*o**5 + 1/5 + 2*o**b - o + o**4.
-(o - 1)**5/5
Let p be ((-20)/5)/(80/(-8)). Factor 0 + 0*t - 2/5*t**3 - 2/5*t**4 + p*t**2 + 2/5*t**5.
2*t**2*(t - 1)**2*(t + 1)/5
Let n be 142/24 + 145/174. Factor n*x + 21/4*x**2 + 3/2.
3*(x + 1)*(7*x + 2)/4
What is m in -20/3*m**4 - 86/9*m**3 + 14/9*m - 16/9*m**2 + 4/9 = 0?
-1, -1/2, -1/3, 2/5
Factor -4/7 + 0*c + 1/7*c**2.
(c - 2)*(c + 2)/7
Let g = 47 - 45. What is s in 0*s - 1/4*s**3 + 0 + 1/4*s**g = 0?
0, 1
Suppose -3*m - m - 4 = 0, 3*m = -5*t + 7. Let f(n) be the second derivative of 2*n + 2/11*n**t + 0 + 1/22*n**4 - 5/33*n**3. Suppose f(s) = 0. Calculate s.
2/3, 1
Let d(s) = 4*s**4 + 32*s**3 - 76*s**2 + 28*s + 12. Let n(k) = k**3 - 2*k**2 + 1. Let w(v) = -d(v) + 12*n(v). Factor w(m).
-4*m*(m - 1)**2*(m + 7)
Let u(x) = x**2 + 5*x + 3. Let p be u(-5). Suppose 0 = -3*d + h, d - 6*d = 4*h. Factor 6/7*o**2 + 2/7*o + 6/7*o**p + 2/7*o**4 + d.
2*o*(o + 1)**3/7
Let j = -9 - 0. Let b = j + 13. Factor -2/3*o**2 + 0 + o**3 + 5/3*o**b + 0*o.
o**2*(o + 1)*(5*o - 2)/3
Let o(q) be the first derivative of -q**4/16 + q**3/12 - 6. Suppose o(h) = 0. What is h?
0, 1
Find m such that -2*m + 3/4 + 5/4*m**2 = 0.
3/5, 1
Suppose 3*q = 2*q + 3, 2*m - 11 = -q. Suppose 3*s - 10 = -0*s + 2*v, -3*s = -m*v - 14. Factor -1/3*x + 1/3*x**s + 0.
x*(x - 1)/3
Let i = -1/12 - -3/4. Factor 2/3*f**2 + 2/3*f - i - 2/3*f**3.
-2*(f - 1)**2*(f + 1)/3
Let p = -359/3 - -121. Determine s, given that p*s**3 + 0*s - 2/3*s**4 - 2/3*s**2 + 0 = 0.
0, 1
Let q be (-8)/40 - 1/(-5). Let o(b) be the second derivative of q*b**3 - 2/15*b**6 + 2*b + 0 + 0*b**2 - 3/10*b**5 - 1/6*b**4. Factor o(j).
-2*j**2*(j + 1)*(2*j + 1)
Let u be 12/20 - 14/90. Factor 0 + 0*c - 2/9*c**5 - 2/9*c**3 + 0*c**2 + u*c**4.
-2*c**3*(c - 1)**2/9
Let 12*d - 27*d + 3*d**2 + 9*d = 0. Calculate d.
0, 2
Suppose -2*q - t = -q - 6, t + 3 = 0. Factor 0*x + 2*x**5 + 12*x**3 + x**2 + 2*x - 2*x**4 - 6*x**4 - q*x**2.
2*x*(x - 1)**4
Let k(a) = 3*a - 1. Let c be k(1). Let -6*q**4 + 3*q**4 - 2*q**3 - q**4 - c*q**3 - q**5 = 0. Calculate q.
-2, 0
Let p(r) be the third derivative of -3/40*r**6 + 0 - 1/70*r**7 + 5*r**2 + 0*r + 0*r**3 - 1/8*r**4 - 3/20*r**5. Factor p(o).
-3*o*(o + 1)**3
Let b be 15/6*9 + 2. Let j = b + -24. Let 0*a**3 + 0 + a**2 - a**4 - 1/2*a**5 + j*a = 0. Calculate a.
-1, 0, 1
Let r(y) = y**2 + 5*y - 1. Let z be r(-6). Factor -4*v + 18*v**2 + v - z*v**3 - 10*v**3.
-3*v*(v - 1)*(5*v - 1)
Let o(n) be the first derivative of 2*n**3/21 - 2*n**2/7 - 16*n/7 + 15. Determine q, given that o(q) = 0.
-2, 4
Let w(i) be the first derivative of -i**3/12 - i**2/2 - 3*i/4 + 1. Suppose w(g) = 0. What is g?
-3, -1
Let -3/8*v**2 + 3/4 + 3/8*v = 0. What is v?
-1, 2
Suppose -1/3*d**3 - 1/3*d + 0 + 2/3*d**2 = 0. Calculate d.
0, 1
Let a(b) be the first derivative of -b**5/20 + b**4/8 + 5*b**2/2 + 2. Let x(d) be the second derivative of a(d). Factor x(g).
-3*g*(g - 1)
Let w(s) = -s. Let n(q) = -q**2 + 5*q. Let u(r) = -n(r) - 2*w(r). Factor u(d).
d*(d - 3)
Let q = -9 + 9. Let x(c) = c**2 + c - 3. Let w be x(-3). Find s, given that -12/5*s**4 + 0*s**2 + q*s - 18/5*s**5 - 2/5*s**w + 0 = 0.
-1/3, 0
Let x(v) be the second derivative of -v**8/30240 + v**6/1080 + v**5/270 - v**4/6 - 3*v. Let z(d) be the third derivative of x(d). Suppose z(b) = 0. What is b?
-1, 2
Let s be 21/54 - (-1)/9. Determine g, given that -s*g**2 + 1/2*g**4 + 1/4*g + 0*g**3 - 1/4*g**5 + 0 = 0.
-1, 0, 1
Suppose 2 + 6 = 2*h. Suppose 4*x = h*o + 6 + 2, -2*o - 2*x + 4 = 0. Factor -1/3*q + o - 1/3*q**2.
-q*(q + 1)/3
Let i(f) be the second derivative of -f**4/6 + 2*f**3/3 + 18*f. Factor i(g).
-2*g*(g - 2)
Let z(r) be the first derivative of -3*r**2 - 52/3*r**3 + 3 + 4*r + 63/2*r**4 - 72/5*r**5. Let z(n) = 0. What is n?
-1/4, 1/3, 2/3, 1
Let o(i) be the second derivative of -i**4/6 - 7*i**3/4 - 5*i**2/4 - 5*i. Determine y so that o(y) = 0.
-5, -1/4
Let o be 0 - (-8 - (-3)/1). Factor l**5 - 20*l**4 + 17*l**4 - 4*l**o.
-3*l**4*(l + 1)
Factor h**4 + 4*h**5 - h**3 - 3*h**5 - 2*h**2 + 5*h**4 - 4*h**4.
h**2*(h - 1)*(h + 1)*(h + 2)
Let u = 102 - 304/3. Find c such that 0 + 4/9*c + 2/9*c**3 - u*c**2 = 0.
0, 1, 2
Suppose 0 = -q - 0*q + 5. Let 2/3*m**2 + 0 + 0*m**3 - 2/3*m**4 + 1/3*m - 1/3*m**q = 0. What is m?
-1, 0, 1
Let z(h) be the third derivative of -h**7/630 - h**6/180 + h**5/60 + h**4/18 - 2*h**3/9 - 3*h**2. Factor z(g).
-(g - 1)**2*(g + 2)**2/3
Let z = -1159/9 + 129. Solve z*i**2 + 0*i - 2/9 = 0.
-1, 1
Suppose 8 = 4*k - 2*w, 4 - 3 = -k - w. Suppose 0 = 3*g + 5*z - 21, k = g - 5*z + 14. Determine d, given that 0*d + 2*d + d**g - 4*d = 0.
0, 2
Let i(v) = -v**4 - v. Let l(m) = 13*m**4 - 2*m**3 - 2*m**2 + 13*m. Suppose -4*b - 66 = -b. Let q(z) = b*i(z) - 2*l(z). Find y such that q(y) = 0.
-1, 0, 1
Let c(f) be the second derivative of -f**4/6 - f**3 - 14*f. Determine h so that c(h) = 0.
-3, 0
Let l(o) = -o**2 - 1. Let h(u) = 2*u**3 + 4*u**2 + 6*u + 8. Let v be (-6)/(-9) - 2/(-6). Let j(s) = v*h(s) + 10*l(s). Factor j(b).
2*(b - 1)**3
Let p(i) be the first derivative of 0*i**2 + 0*i**3 + 1/12*i**4 - 2 - i. Let v(r) be the first derivative of p(r). Factor v(g).
g**2
Let i(j) = j**3 - 3*j**2 - 4*j - 4. Let t(u) = 6*u**3 - 15*u**2 - 21*u - 21. Let g(k) = -21*i(k) + 4*t(k). Factor g(l).
3*l**2*(l + 1)
Let j(w) be the third derivative of w**6/20 - w**5/