- 3*n = 5*w - 12, -2*n + 8 = -3*w. Let k(c) be the second derivative of 1/3*c**3 + 1/18*c**4 + 2/3*c**2 + w + 2*c. Let k(q) = 0. What is q?
-2, -1
Suppose -76 = 4*h + 3*s - 1, 4*s + 22 = -h. Let j be 4/h + (-10)/(-45). What is y in 1/4*y - 1/4*y**5 - 1/2*y**2 + 0*y**3 + 1/2*y**4 + j = 0?
-1, 0, 1
Let g(w) be the second derivative of w**6/1260 - w**5/420 + w**3/2 + 2*w. Let l(r) be the second derivative of g(r). Find y such that l(y) = 0.
0, 1
Factor -8/5 - 4/5*b**3 - 4*b - 16/5*b**2.
-4*(b + 1)**2*(b + 2)/5
Let u(s) be the second derivative of s**5 + 17*s**4/3 + 32*s**3/3 + 8*s**2 - 3*s. Factor u(i).
4*(i + 1)*(i + 2)*(5*i + 2)
Suppose 9 = k - 2*w, -w = -4*k - 2*w + 9. Factor -3*t + 0 + k + t**3 - 5.
(t - 2)*(t + 1)**2
Let a(j) = -2*j - 5. Let p be a(-5). Suppose -p*f + 21 = 1. Factor 0 + 4/5*d**f - 2/5*d**5 - 4/5*d**2 + 0*d**3 + 2/5*d.
-2*d*(d - 1)**3*(d + 1)/5
Suppose 0 = -3*y + 5*l + 11, -7*l = 2*y - 3*l. Let c(r) be the first derivative of -1/3*r**3 + 1/2*r + 0*r**4 + 1/10*r**5 + 0*r**2 - y. Factor c(z).
(z - 1)**2*(z + 1)**2/2
Suppose 3*s + 10 = 8*s. Let q be 1/(-1)*-2 + 0. Factor -3*p**s - 24*p**3 - 5*p**q - 22*p**4 + 4*p**4.
-2*p**2*(3*p + 2)**2
Factor -55*u**2 + u**3 - 3 - 21*u**3 - 15*u - 10*u + 13.
-5*(u + 1)*(u + 2)*(4*u - 1)
Factor 4*m**2 + 0*m + 2*m - m - 5*m.
4*m*(m - 1)
Let s(f) = f**3 + f**2. Let z(i) = 2*i**3 + 2*i**2. Let m(u) = -5*s(u) + 2*z(u). Let j be m(-1). Determine b so that 1 + j*b**2 + 1 - 2*b**2 = 0.
-1, 1
Let a(k) be the second derivative of -k**7/399 + 8*k**6/285 - 5*k**5/38 + k**4/3 - 28*k**3/57 + 8*k**2/19 - 6*k. What is m in a(m) = 0?
1, 2
Let q = -22/9 - -47/18. Let o = 2 + 0. Suppose q*s**o + 1/3*s + 0 = 0. Calculate s.
-2, 0
Let p(d) = -d**2 + 3*d + 3. Let y(a) = a + 1. Let v(o) = -p(o) + 2*y(o). Let j(l) = 5*l + 5. Let i(f) = 2*j(f) + 2*v(f). Let i(k) = 0. Calculate k.
-2
Let n(z) = z - 2. Let h(g) = g**2 - 6*g - 5. Let l be h(7). Let r be n(l). Suppose -6/11*d + 4/11 + r*d**2 + 2/11*d**3 = 0. What is d?
-2, 1
Let k(g) be the first derivative of 5*g**4/4 + 10*g**3 + 30*g**2 + 40*g + 21. Factor k(u).
5*(u + 2)**3
Let k be ((-14)/35)/(1/(-5))*1. Factor 2/3*u - 2/3*u**3 + 2/3*u**4 + 0 - 2/3*u**k.
2*u*(u - 1)**2*(u + 1)/3
Let k(s) be the first derivative of -s**4/4 - s**3/3 + 9. Let k(c) = 0. Calculate c.
-1, 0
Suppose 2/17*g**2 + 648/17 - 72/17*g = 0. What is g?
18
Let -9 + 10 + 2*q**2 - 13 - 2*q = 0. Calculate q.
-2, 3
Let a(w) be the first derivative of 2*w**3/15 - 26*w**2/5 + 338*w/5 + 28. Factor a(f).
2*(f - 13)**2/5
Let w(r) be the third derivative of -r**6/60 + r**5/10 - r**4/4 + r**3/3 + 2*r**2. Let w(c) = 0. What is c?
1
Let -5*p**2 + 9*p + 7*p + 2*p**2 - 32 + p**2 = 0. What is p?
4
Suppose 5*j - 1 = -4*t + 7, 6 = 3*t. Let u(m) be the third derivative of j + 1/270*m**5 + 0*m + 0*m**4 + 0*m**3 - 3*m**2. Find n such that u(n) = 0.
0
Let k(i) be the first derivative of -32*i - 2/5*i**5 - 16*i**3 - 4*i**4 - 32*i**2 - 2. Factor k(y).
-2*(y + 2)**4
Let d = -88 - -88. Let j(i) be the third derivative of 0 + d*i**3 + 0*i + 0*i**4 - 1/300*i**6 - i**2 + 0*i**5. Factor j(b).
-2*b**3/5
Factor 1/6*r - 1/3*r**2 + 1/6.
-(r - 1)*(2*r + 1)/6
Let u(d) be the first derivative of 1/10*d**5 + 1/4*d**2 + 1/2*d**3 - 2 + 0*d + 3/8*d**4. Solve u(f) = 0.
-1, 0
Let i be (-12)/(9/3)*-1. Let -7*b + 0 + i*b**2 - 4 + b - 2*b**5 + 8*b**3 = 0. What is b?
-1, 1, 2
Let c be (1 + (-22)/4)/(210/(-40)). Factor -18/7*a**3 + 10/7*a + 2/7 + c*a**2.
-2*(a - 1)*(3*a + 1)**2/7
Let x(r) be the first derivative of r**6/3 - 4*r**5/5 + 4*r**3/3 - r**2 + 1. Suppose x(q) = 0. What is q?
-1, 0, 1
Let j(x) be the second derivative of -2*x**6/15 + 6*x**5/5 - 13*x**4/3 + 8*x**3 - 8*x**2 + 11*x. Let j(p) = 0. What is p?
1, 2
Let y(b) = -b + 6. Let m be y(4). Let s(l) be the first derivative of -10/9*l**3 + 2/3*l**2 + m - 7/6*l**4 + 0*l. Solve s(x) = 0.
-1, 0, 2/7
Let s be -1 + 1 - (-2)/100. Let j(w) be the second derivative of -2*w - 8/5*w**2 - 4/5*w**3 - 1/5*w**4 + 0 - s*w**5. What is a in j(a) = 0?
-2
Let j(p) be the second derivative of -2*p**6/15 + p**4 - 4*p**3/3 - 43*p. What is k in j(k) = 0?
-2, 0, 1
Let l = -240 - -3126/13. Factor 0 - 2/13*v**2 + l*v.
-2*v*(v - 3)/13
Let c**4 + 20*c**2 - 15*c**3 - 8*c**4 + 4*c**4 - 2*c**4 = 0. Calculate c.
-4, 0, 1
Let s(j) be the first derivative of -2*j**3/19 - j**2/19 + 16. Factor s(m).
-2*m*(3*m + 1)/19
Let s(n) be the first derivative of 15*n**4/4 + 65*n**3/6 + 10*n**2 + 5*n/2 - 4. Find v, given that s(v) = 0.
-1, -1/6
Find f such that 9/5*f - 9/5*f**3 + 0 + 3/5*f**4 - 3/5*f**2 = 0.
-1, 0, 1, 3
Find j such that 0 + 3/8*j**2 + 0*j + 1/8*j**3 = 0.
-3, 0
Let s be -2*(16/(-7) - 34/(-119)). Solve -4/13*h + 4/13*h**3 + 0 + 2/13*h**2 - 2/13*h**s = 0.
-1, 0, 1, 2
Let a = 18 + -4. Factor 2*i**2 - a*i - 11*i + 21*i.
2*i*(i - 2)
Let l = 19 + -17. Suppose k = 3*d - 9, -4*k + 20 = -0*d + l*d. Factor -4/5*i**2 + 0*i + 0 - 2/5*i**k.
-2*i**2*(i + 2)/5
Let f(p) = -2*p**5 - 10*p**4 - 4*p**3 + 4*p**2. Let v(z) = z**4 - z**2. Let i(l) = -f(l) - 4*v(l). Factor i(o).
2*o**3*(o + 1)*(o + 2)
Let a(f) be the first derivative of -f**3/2 - 3*f**2/2 - 4. Solve a(h) = 0 for h.
-2, 0
Find y such that 4/3*y**2 - 1/3 + y = 0.
-1, 1/4
Let t(u) be the first derivative of 1/3*u**3 - 6 - 1/5*u**5 + 1/4*u**4 - 1/2*u**2 + 0*u. Factor t(z).
-z*(z - 1)**2*(z + 1)
Let t = -2 + 7. Let y = t - 5. Factor y - 2 - 4*v - v + v**2 + 6*v.
(v - 1)*(v + 2)
Let -1/3*a**4 + 4/3*a - 2/3*a**2 + 1 - 4/3*a**3 = 0. Calculate a.
-3, -1, 1
Let n(b) = b**2 - 4*b - 3. Let c(q) = -q**2 - 11*q - 13. Let y be c(-9). Let z be n(y). Find u, given that u**2 + 2*u**2 + u**3 - 2*u**z = 0.
-1, 0
Let p(v) be the first derivative of 1 - 8/15*v**3 - 4/5*v**2 - 2/5*v. Let p(c) = 0. Calculate c.
-1/2
Let l(o) = 2*o**2 + 11*o + 4. Let c(d) = -d. Let m(b) = 5*c(b) + l(b). What is s in m(s) = 0?
-2, -1
Suppose -5*r - 6 = -8*r. Let g be 4 - 16/(-20)*-4. Factor 2/5*a**r - g*a + 2/5.
2*(a - 1)**2/5
Suppose -10 = -n - 4*n. Suppose 0 = -n*y - 3*y + 15. Factor -2*j**y + j - 16*j**4 + j**5 + 16*j**4.
j*(j - 1)**2*(j + 1)**2
Let c = -107 - -109. Let v(y) be the third derivative of 0*y + 0 + 0*y**4 - 1/240*y**5 + 1/24*y**3 - 4*y**c. What is o in v(o) = 0?
-1, 1
Let b(m) = 2*m**2 + 8*m + 4. Let w be b(-4). Factor 2/3*z**w + 0*z**2 + 0*z**3 - 2/3*z**5 + 0 + 0*z.
-2*z**4*(z - 1)/3
Let d = 24 - 20. Let r(x) be the second derivative of 0*x**2 - 1/42*x**7 - 1/6*x**3 + 1/10*x**5 + 0 + 0*x**6 + 0*x**d - x. Factor r(w).
-w*(w - 1)**2*(w + 1)**2
Let d(z) = -z**2 - 11*z - 9. Let c be d(-9). Suppose 6*s - 3*s - c = 0. Factor -s - k**2 - 3*k + 0 + 1.
-(k + 1)*(k + 2)
Let l(v) = -v**3 - 7*v**2 + 8*v + 5. Let i be l(-8). Let g = i - 3. Factor -2/5*p**g + 4/5*p - 2/5.
-2*(p - 1)**2/5
Let l be -3 - 11/(1/(-1)). Let 18*u**2 + 111*u**2 + l + 95*u**3 - 49*u**5 + 48*u**3 + 53*u**2 + 68*u - 28*u**4 = 0. What is u?
-1, -2/7, 2
Let s(a) = -a**2 + 8*a + 51. Let n be s(12). Factor 0*x**2 + 0 + 0*x - 2/7*x**n.
-2*x**3/7
Let m(d) be the first derivative of 2*d**3/3 + 2*d**2 + 2*d + 2. Let a be m(-2). Factor a*o + 0*o**3 + 2*o**2 - 2*o**3 + 2*o - 2*o - 2*o**4.
-2*o*(o - 1)*(o + 1)**2
Let h(z) be the second derivative of -z**7/6 + 3*z**6/5 - 109*z**5/140 + 3*z**4/7 - 2*z**3/21 + 15*z. Solve h(j) = 0 for j.
0, 2/7, 1
Solve 27/4 + 9/2*s + 3/4*s**2 = 0 for s.
-3
Let -2*a**2 + 103*a - a**3 - 103*a = 0. What is a?
-2, 0
Let 3*b**5 - 5*b**3 - 3*b**4 + 2*b**3 + 3*b**4 = 0. What is b?
-1, 0, 1
Let r(v) be the third derivative of v**9/90720 + v**8/30240 - v**7/7560 - v**6/1080 - v**5/30 + 3*v**2. Let q(z) be the third derivative of r(z). Factor q(m).
2*(m - 1)*(m + 1)**2/3
Let j be (-6)/(-9)*(-12)/(-10). Suppose j + 2/5*x**2 + 6/5*x = 0. What is x?
-2, -1
Let t be ((-2)/(-1))/(3/(-12)). Let r = 10 + t. Solve -2/7*o + 4/7*o**r + 0 + 6/7*o**3 = 0.
-1, 0, 1/3
Let z(k) = -k - 1. Let y be z(-4). Suppose y*x = 4*x. Solve 1/2*m**2 + x + 0*m + 1/2*m**4 + m**3 = 0.
-1, 0
Suppose -2*t + 29 = -5*h, 2*t + h = 6*t - 13. Let d(l) be the first derivative of 0*l**3 + 0*l + l**t + 3 - 1/2*l**4. Factor d(c).
-2*c*(c - 1)*(c + 1)
Suppose 4*c = -3*a + 15, c + 20 = -3*c + 4*a. Factor 1/2*w**3 + 0*w - 1/2*w**4 + 0 + c*w**2.
-w**3*(w - 1)/2
Let j(h) be the second derivative of 0*h**2 + 2*h - 1/75*h**6 - 1/50*h**5 + 0 + 1/30*h**4 + 1/15*h**3. Determine 