*5/270 - m**3/3 - 3*m. Let i(u) be the second derivative of q(u). Factor i(x).
-2*x*(x - 2)*(x + 1)**2/9
Let x be -1 + 0 - 216/(-168). Factor -10/7*p**2 + 16/7*p - 8/7 + x*p**3.
2*(p - 2)**2*(p - 1)/7
Let r(q) be the second derivative of -q**4/24 - q**3 - 9*q**2 - 17*q. Suppose r(l) = 0. What is l?
-6
Let q(r) be the second derivative of -r**4/3 - 4*r**3/3 - 2*r**2 + 6*r. Factor q(u).
-4*(u + 1)**2
Let m(d) be the first derivative of -2*d**5/45 - d**4/9 + 2*d**3/27 + 2*d**2/9 + 1. Let m(w) = 0. Calculate w.
-2, -1, 0, 1
Suppose -4*y + 13 = 5*p - 5, 2*p = -2*y + 8. Suppose 0 = -5*t - 2*q + 18, -q - p*q + 18 = 3*t. Factor 0*f - t*f + 2*f**2 + 0*f.
2*f*(f - 1)
Let d(f) be the third derivative of -f**8/3024 + f**7/1890 + f**6/1080 - f**5/540 + 15*f**2. Suppose d(q) = 0. What is q?
-1, 0, 1
Let b = 11 - 4. Suppose d + 2*k - 2 = 0, 4*d - 8 = -0*k + 2*k. Factor -b*z**3 + 0*z**4 + 3*z**3 - 4*z - z**4 - 6*z**d - 1.
-(z + 1)**4
Let h(p) be the third derivative of -p**5/180 - p**4/36 - p**3/18 + p**2. Factor h(s).
-(s + 1)**2/3
Let n = -8 - -6. Let s be -1 + (-1)/n - -1. Let 1/4*m**2 - s - 1/4*m = 0. What is m?
-1, 2
Let i(c) be the third derivative of -c**6/60 - c**5/30 + 5*c**4/6 - 8*c**3/3 - 5*c**2 - c. Find j such that i(j) = 0.
-4, 1, 2
Let o(g) = -g - 14. Let d be o(-13). Let t be (3 - 4)*(-6 - d). What is l in 10/7*l**3 + 0*l - 8/7*l**4 - 4/7*l**2 + 0 + 2/7*l**t = 0?
0, 1, 2
Let m(o) = 3*o - 7. Let i be m(3). Suppose l**3 - 2*l**5 + 8*l**5 + l**i - 7*l**5 - l**4 = 0. What is l?
-1, 0, 1
Let 3/8 - 3/8*r**2 + 0*r = 0. Calculate r.
-1, 1
Suppose -5 = -o - 2. Let t = 3 - o. Factor 6*n**3 - 2*n**5 - 4*n**3 - 3*n**4 + 4*n**2 + t*n**3 - 1.
-(n - 1)*(n + 1)**3*(2*n - 1)
Let w(k) be the second derivative of 2*k**7/315 - k**6/75 + k**4/90 - 17*k. Determine h, given that w(h) = 0.
-1/2, 0, 1
Let v(w) be the first derivative of w**3 - 3*w**2/2 - 6*w + 4. Let v(d) = 0. Calculate d.
-1, 2
Let y = 131/2 - 391/6. Let -1/3*g**4 + 0*g + 1/3*g**2 + 0 + 1/3*g**5 - y*g**3 = 0. What is g?
-1, 0, 1
Suppose 0 = 5*z - 7*z + 4. Let -2*m**z - 3*m**4 + 2*m + 11*m**3 - 13*m**3 + 5*m**4 = 0. Calculate m.
-1, 0, 1
Suppose -22 = -4*g + 18. Let c = g + -10. Factor -2/7*x**3 + 0*x + 2/7*x**4 + c + 2/7*x**5 - 2/7*x**2.
2*x**2*(x - 1)*(x + 1)**2/7
Let w(m) be the second derivative of -m**4/30 - 22*m. Suppose w(c) = 0. What is c?
0
Let h(v) be the first derivative of 2 + 2/3*v - 4/3*v**2 + 10/9*v**3 - 1/3*v**4. Factor h(c).
-2*(c - 1)**2*(2*c - 1)/3
Let v(y) be the second derivative of y**6/480 + y**5/240 - y**4/96 - y**3/6 + 2*y. Let t(i) be the second derivative of v(i). Factor t(k).
(k + 1)*(3*k - 1)/4
Let x(j) be the second derivative of j**6/135 - j**4/18 + 2*j**3/27 - 34*j. Suppose x(o) = 0. Calculate o.
-2, 0, 1
Let y(m) = -m**3 + 8*m**2 + 9*m - 2. Let j be y(9). Let d be 2 - (j/(-1) - 2). Factor -4*b + 2*b**d - 7 - 4*b**2 - 2*b + 3.
-2*(b + 1)*(b + 2)
Let g(f) be the third derivative of -3*f**8/784 + f**7/49 - f**6/280 - 9*f**5/70 + f**4/14 + 4*f**3/7 - 7*f**2. Suppose g(l) = 0. What is l?
-1, -2/3, 1, 2
Factor -36*l**2 + 27/2*l + 0 - 12*l**4 + 3/2*l**5 + 33*l**3.
3*l*(l - 3)**2*(l - 1)**2/2
Let k(y) = y**2 - 12*y + 23. Let f = -15 + 25. Let o be k(f). Find c such that 0 - 1/3*c**o + 0*c + 1/3*c**2 = 0.
0, 1
Let u(h) = -17*h + 22. Let d be u(1). Factor 0*i**2 + 1/4*i**3 + 1/4*i**d + 0*i + 0 + 1/2*i**4.
i**3*(i + 1)**2/4
Let t(p) be the first derivative of -1/3*p**3 + 4*p + 2 - 4/5*p**5 + 0*p**2 + 11/12*p**4 + 7/30*p**6. Let s(m) be the first derivative of t(m). Factor s(g).
g*(g - 1)**2*(7*g - 2)
Let a(u) = 3*u**2 - 66*u + 294. Let t(z) = -z - 1. Let o(p) = -a(p) + 6*t(p). Factor o(b).
-3*(b - 10)**2
Let p(v) be the third derivative of -v**8/1680 - v**7/210 - v**6/90 - v**3/3 + 2*v**2. Let a(l) be the first derivative of p(l). Factor a(h).
-h**2*(h + 2)**2
Let j(h) = h**2 + h - 1. Let y(m) be the second derivative of 7*m**4/12 + 7*m**3/6 - 4*m**2 - 2*m. Let s(c) = -6*j(c) + y(c). Find q, given that s(q) = 0.
-2, 1
Let y(f) be the third derivative of -f**8/120960 - f**7/7560 - f**6/1080 + f**5/60 + 7*f**2. Let d(c) be the third derivative of y(c). Factor d(s).
-(s + 2)**2/6
Suppose 0*v + 0*v = -4*v. Determine g, given that 2/3*g - 2/3*g**2 + v = 0.
0, 1
Suppose -2 = -o - 0. Let b be (-9)/6*o*-1. Suppose 0 + 0*k**b + 0*k - 1/2*k**2 + 1/2*k**4 = 0. What is k?
-1, 0, 1
Let w(k) = 4*k + 4*k**2 - 5*k**2 + 3*k**2. Suppose -3*o + o = 6. Let s(c) = c**2 + 3*c. Let n(t) = o*s(t) + 2*w(t). Factor n(y).
y*(y - 1)
Let b(d) be the second derivative of d**8/1008 - d**6/180 + d**4/72 - 5*d**2/2 - 5*d. Let f(x) be the first derivative of b(x). Factor f(s).
s*(s - 1)**2*(s + 1)**2/3
Let x(c) be the third derivative of 0 + 0*c - 1/2*c**3 + c**2 + 1/20*c**5 - 1/40*c**6 + 1/8*c**4. Factor x(d).
-3*(d - 1)**2*(d + 1)
Let f = -232 + 4874/21. Let k(l) be the first derivative of 0*l - f*l**3 - 4 + 0*l**2. Determine h so that k(h) = 0.
0
Let u(h) = -4*h**2 + 9*h. Let v be u(8). Let d = 1292/7 + v. Factor -d*k**2 + 0 + 2/7*k**3 + 2/7*k.
2*k*(k - 1)**2/7
Suppose -2 = -v + 1. Factor 11*t - v + 8*t**2 - t**3 - 5*t**3 - 1 - 9*t.
-2*(t - 1)**2*(3*t + 2)
Let v(f) be the third derivative of 0*f + 4*f**2 + 2/21*f**3 + 1/28*f**4 - 1/105*f**5 + 0. Determine g, given that v(g) = 0.
-1/2, 2
Let p(w) be the second derivative of -w**7/168 - 5*w**6/24 - 21*w**5/10 - 3*w**4 + 3*w - 12. Let p(a) = 0. Calculate a.
-12, -1, 0
Suppose 3 + 1 = f. Let a = f + -2. Factor -2/7*p**4 + 0 + 0*p + 2/7*p**a + 0*p**3.
-2*p**2*(p - 1)*(p + 1)/7
Let k(p) = -p**2 + 1. Let y(w) = -3*w**2 + 6*w + 6. Let a(f) = -6*k(f) + y(f). Factor a(c).
3*c*(c + 2)
Let n be 8/12 - 2/3. Let s(o) be the third derivative of -1/12*o**4 - 2*o**2 + n + 0*o**3 + 0*o + 0*o**5 + 1/60*o**6. What is l in s(l) = 0?
-1, 0, 1
Let b(l) be the third derivative of -l**6/120 - l**5/15 - l**4/6 - l**2. Find y such that b(y) = 0.
-2, 0
Let z = 49 + -29. Factor -20 + 3*y**2 + z - 6*y**2.
-3*y**2
Suppose 4 + 2 = 2*s. Factor 2 + 3*k**2 + s - 8 + 0*k**2.
3*(k - 1)*(k + 1)
Let x be 2 + 5/15*0. Factor -1/5*i - 1/5*i**x + 0.
-i*(i + 1)/5
Let v(k) be the third derivative of k**6/1620 - k**5/270 + k**4/108 - 2*k**3/3 - 3*k**2. Let f(w) be the first derivative of v(w). Suppose f(a) = 0. What is a?
1
Let q(z) be the second derivative of -z**4/36 - z**3/18 + z**2 + 39*z. Determine s so that q(s) = 0.
-3, 2
Let n(d) be the second derivative of d**5/30 - 2*d**4/9 - 22*d. Factor n(g).
2*g**2*(g - 4)/3
Let n(i) = i**2 + 8*i - 2. Let b be n(-9). Let k(m) = -m**3 + 2 - b + 8*m**3 + 2*m**4. Let f(d) = -d**4 - 3*d**3 + 2. Let y(t) = 5*f(t) + 2*k(t). Factor y(s).
-s**3*(s + 1)
Let l(k) be the third derivative of 81*k**8/448 + 27*k**7/40 + 171*k**6/160 + 15*k**5/16 + k**4/2 + k**3/6 - 11*k**2. Determine z, given that l(z) = 0.
-2/3, -1/3
Let a be (-27)/(-6)*6/9. Factor -4*w + 2*w**4 - 4*w**4 + 0*w**5 + w**5 + 2*w**2 + a*w.
w*(w - 1)**3*(w + 1)
Let m(h) be the first derivative of -9/2*h - 1/2*h**3 - 2 - 3*h**2. What is y in m(y) = 0?
-3, -1
Suppose 18 = -5*z + 2*z. Let x be (-5 + 1)*z/8. Determine l so that -5/4*l**3 - x*l - 9/2*l**2 + 2 = 0.
-2, 2/5
Let q = -1585/24 - -11/8. Let s = -64 - q. Factor 1/3*k**2 - 2/3*k**3 + s*k - 1/3.
-(k - 1)*(k + 1)*(2*k - 1)/3
Let r = 2/15 + 11/30. Factor l**3 - 1/2*l**5 + 0 + 0*l**2 - r*l + 0*l**4.
-l*(l - 1)**2*(l + 1)**2/2
Factor -1/6*a**3 - 1/2*a - 1/2*a**2 - 1/6.
-(a + 1)**3/6
Solve -42*g**3 + 4/3 + 27*g**4 + 28/3*g + 13/3*g**2 = 0 for g.
-2/9, 1
Let g = -37 - -39. Solve 0 - 1/2*s**2 - g*s**4 + 3/4*s**5 + 0*s + 7/4*s**3 = 0.
0, 2/3, 1
Let y(n) = -n**2 + 6*n - 1. Let u(l) = 2*l**2 - 12*l + 1. Let c(p) = -6*u(p) - 13*y(p). Let q be c(5). Find g, given that -q*g + 0*g - 4*g + 2*g - 2*g**2 = 0.
-2, 0
Let j(l) = 24*l. Let k be j(1). Let u = -71/3 + k. Solve u*n**2 + 0*n + 1/3*n**3 + 0 = 0 for n.
-1, 0
Factor 18*w**2 - 18*w - 7*w - 3*w**2 + 5*w**3 - 5*w**4 + 10.
-5*(w - 1)**3*(w + 2)
Let k = -5/19 - -29/38. Let d = -2 - -4. Factor 0*q - 1/2*q**d + k.
-(q - 1)*(q + 1)/2
Suppose 0 = -5*p + 2*f + 15, 8 = 3*p - f - 1. Factor -6/5*t**4 + 0 + 0*t - 2/5*t**2 - 6/5*t**p - 2/5*t**5.
-2*t**2*(t + 1)**3/5
Let t be -5 - (-14)/((-1232)/(-456)). Factor t*r**2 + 18/11 + 12/11*r.
2*(r + 3)**2/11
Let a be -37 + (2 - (-2 - -2)). Let z be 6/(-21) + (-24)/a. Suppose -4/5*v**2