0 + 0*p + 1/3*p**2 + 1/3*p**4 + s*p**3 = 0.
-1, 0
Let c be 1 + 15 + 0 + 0. Let w(v) = v**2 + v. Let a(l) = -4*l**3 - 24*l**2 - 20*l. Let d(p) = c*w(p) + a(p). Factor d(j).
-4*j*(j + 1)**2
Let f(j) be the third derivative of j**7/1050 + j**6/300 - j**5/300 - j**4/60 + 2*j**2. Factor f(y).
y*(y - 1)*(y + 1)*(y + 2)/5
Let s = 2149/11 - 195. Find g, given that -2/11*g**3 - s*g**2 + 0*g + 0 = 0.
-2, 0
Suppose 0 = -4*j + 3*h - 29, 0*j - 5*h = 2*j + 21. Let b = 8 + j. Determine u, given that -2/7*u**2 + 4/7*u**3 - 2/7*u**4 + b + 0*u = 0.
0, 1
Suppose -7*v = -2*v - 10. Suppose 5 = v*y + 1. Determine x, given that 2*x**3 + 1/2*x**4 - 2*x - 2 + 3/2*x**y = 0.
-2, -1, 1
Factor -10 - 6*c + c - 525*c**2 + 535*c**2 + 5*c**3.
5*(c - 1)*(c + 1)*(c + 2)
Let k(p) be the second derivative of p**5/5 - p**4 + 8*p**2 - 5*p. Factor k(w).
4*(w - 2)**2*(w + 1)
Let g(p) = 6*p - 2. Let i be g(1). Let k = 0 + i. Find q such that 0*q + 1/5*q**2 + 1/5*q**3 - 1/5*q**5 + 0 - 1/5*q**k = 0.
-1, 0, 1
Let y = -749279/240 + 3122. Let f(d) be the third derivative of 0 + 0*d**3 + y*d**5 + 3*d**2 + 0*d + 0*d**4. Factor f(s).
s**2/4
Let u be 7/((-14)/8) + 3. Let l be (-5)/(u + 0) - 2. Determine i, given that i**3 - 33*i + 63*i**2 + 9*i**4 + 1 + 5 - 49*i**l + 3*i**4 = 0.
1/2, 1, 2
Find u such that 6/5*u + 2/5*u**2 + 0 = 0.
-3, 0
Let k(d) be the third derivative of d**10/604800 - d**8/80640 + 7*d**5/60 - 6*d**2. Let l(i) be the third derivative of k(i). Suppose l(u) = 0. Calculate u.
-1, 0, 1
Suppose 0 = -b - b + f + 23, b - 9 = -2*f. Let d = b - 7. What is n in 2 - 2*n**2 + d*n**2 + 10*n**2 + 8*n**3 + 2*n**4 + 8*n = 0?
-1
Let i(a) = -3*a**3 - 2*a**2 - 2*a - 1. Let u be i(-1). Suppose 0 = -3*h + 2*q + 6, h + u*q = -0*h + 10. Solve -7*r**3 - 4 + 12*r**2 + h + 4*r = 0 for r.
-2/7, 0, 2
Let z(b) be the third derivative of -b**8/140 + 2*b**7/105 - 7*b**6/360 + b**5/120 - 2*b**3/3 + b**2. Let y(c) be the first derivative of z(c). Factor y(w).
-w*(2*w - 1)**2*(3*w - 1)
Suppose 5*n - 3 = 4*n, n = 2*o - 3. Let 2*h + 7*h**2 - 3*h**3 - 2*h**2 + 3*h**3 + h**4 + 4*h**o = 0. What is h?
-2, -1, 0
Let d be 108/238 + (-5)/((-85)/2). Determine r, given that 2/7*r - d + 2/7*r**2 = 0.
-2, 1
Let u(w) be the second derivative of -w**6/10 + 9*w**5/20 - w**4/4 - 3*w**3/2 + 3*w**2 - 5*w. Factor u(f).
-3*(f - 2)*(f - 1)**2*(f + 1)
Let d be 5*-4*4/(-40). Let b(g) be the second derivative of -1/6*g**4 + 0 + g + 2/3*g**3 - g**d. Let b(a) = 0. What is a?
1
Let x(q) = 4*q**3 - 2*q**2 - 16*q - 4. Let o(z) = 7*z**3 - 5*z**2 - 31*z - 8. Let k(n) = 6*o(n) - 11*x(n). Let k(a) = 0. Calculate a.
-2, -1
Let t(a) be the third derivative of 1/6*a**4 + 0 + a**2 - 1/30*a**5 - 1/3*a**3 + 0*a. Factor t(n).
-2*(n - 1)**2
Let y(m) = -m**2 - 2*m. Let g be y(-3). Let l be (0/g - 0)/(-2). What is u in 1/4*u**2 + 0*u + l = 0?
0
Factor 0*k**4 + 1/5*k**5 + 0 + 0*k**2 + 1/5*k - 2/5*k**3.
k*(k - 1)**2*(k + 1)**2/5
Let m(f) be the second derivative of 0 - 5/6*f**4 + 3/2*f**3 - 1/5*f**5 + 2/5*f**6 - 5/42*f**7 - 4*f - f**2. Factor m(s).
-(s - 1)**3*(s + 1)*(5*s - 2)
Let q = 16 + -14. Let i be (-32)/(-14) + q/(-7). Suppose 18/5*p - 4/5 - 2*p**i + 14/5*p**4 - 18/5*p**3 = 0. What is p?
-1, 2/7, 1
Let d be 141/45 + (-14)/105. Let p(m) be the first derivative of -2 - 4/3*m - 2/9*m**d - m**2. What is x in p(x) = 0?
-2, -1
Let v(k) be the third derivative of -k**6/96 - k**5/24 + 5*k**4/24 + 5*k**3/3 - 11*k**2. Determine d, given that v(d) = 0.
-2, 2
Let r be (-2)/(3*4/24). Let l be (4 + r/(-8))/1. Factor -3/4*h**5 - l*h**3 + 0 - 3*h**2 - 3/4*h - 3*h**4.
-3*h*(h + 1)**4/4
Let k(h) be the second derivative of 3*h**5/80 - h**4/4 - h**3/8 + 3*h**2/2 + 13*h. Suppose k(y) = 0. Calculate y.
-1, 1, 4
Factor -3*i + 145*i**2 + 0 - 10 - 2*i - 140*i**2.
5*(i - 2)*(i + 1)
Let n be (8/(-4)*-1)/1. Factor 3 - 4*t**4 - 5*t**3 + 4*t + 12*t**n + t**3 - 11 + 0*t**4.
-4*(t - 1)**2*(t + 1)*(t + 2)
Let w be -1*(-3)/(21/2). Let q = 438 + -3060/7. Let 0 + 2/7*m**4 - 6/7*m**3 - w*m + q*m**2 = 0. What is m?
0, 1
Factor -3*f**3 - 3/5*f + 6/5 - 24/5*f**2.
-3*(f + 1)**2*(5*f - 2)/5
Find j, given that 16/5 - 2/5*j**3 + 8/5*j - 4/5*j**2 = 0.
-2, 2
Let d(b) be the third derivative of -b**6/24 - b**5/4 + 10*b**3/3 - 3*b**2. Find r, given that d(r) = 0.
-2, 1
Let w(p) be the second derivative of -1/40*p**6 + 0*p**3 - p + 0 + 0*p**2 - 3/40*p**5 - 1/16*p**4. Find i such that w(i) = 0.
-1, 0
Suppose 0 = -5*c + 6*c. Let o be (c/(3/(-1)))/1. Solve -1/5*x + 2/5*x**2 + o - 1/5*x**3 = 0.
0, 1
Let u(p) be the second derivative of 0*p**3 + p + 1/12*p**4 + 0 + 0*p**2 - 1/40*p**5. Factor u(s).
-s**2*(s - 2)/2
Suppose 3*v - 3/4*v**3 - 6 + 3/2*v**2 = 0. What is v?
-2, 2
Let d(y) be the third derivative of -y**7/70 - y**6/18 + y**5/15 - 4*y**3/3 + 9*y**2. Let n(w) be the first derivative of d(w). Solve n(m) = 0 for m.
-2, 0, 1/3
Let x(a) be the first derivative of -4*a**5/5 + a**4 + 16*a**3/3 - 8*a**2 + 1. Determine d so that x(d) = 0.
-2, 0, 1, 2
Let h = 18 - 13. Suppose 0 = -s - 3*s - h*v + 35, -3*s = v - 18. Factor n**4 + n**s + 1 - 1.
n**4*(n + 1)
Let m = 247/9 + -27. Let s(i) be the first derivative of 1/2*i**4 + 0*i**5 + 1 - 1/9*i**6 - m*i**3 + 0*i + 0*i**2. Let s(d) = 0. What is d?
-2, 0, 1
Let x(y) be the third derivative of y**11/498960 - y**9/45360 + y**7/7560 + y**5/60 - 2*y**2. Let q(c) be the third derivative of x(c). Solve q(b) = 0 for b.
-1, 0, 1
Let x be (0 - (1 - 0)) + 212/20. Let a be (-4)/6 - (-92)/30. Determine f, given that 2/5 + 32/5*f**4 + x*f**3 - a*f + 2/5*f**2 = 0.
-1, 1/4
Let g(c) = -14*c**3 + 6*c**2 - 8*c - 17. Let o(q) = 5*q**3 - 2*q**2 + 3*q + 6. Let r(p) = 4*g(p) + 11*o(p). Factor r(z).
-(z - 2)*(z - 1)*(z + 1)
Let c(y) = -y**2 + 5*y. Let v be c(4). Let a(u) be the first derivative of u**2 + 8/3*u**3 + 1/2*u**v - u + 2 - 2/3*u**6 - 7/5*u**5. Factor a(i).
-(i - 1)*(i + 1)**3*(4*i - 1)
Let u(b) = b + 27. Let t be u(-27). Find p, given that 0*p**2 + 0*p - 2/3*p**3 + 0 + 2/3*p**5 + t*p**4 = 0.
-1, 0, 1
Let d(i) = -9*i**2 + 9*i + 6. Let n(h) be the second derivative of 2*h**4/3 - 4*h**3/3 - 5*h**2/2 - h. Let b(z) = -5*d(z) - 6*n(z). Find y such that b(y) = 0.
0, 1
Let c(w) be the first derivative of -2/7*w**2 - 2/7*w - 2/21*w**3 - 1. Let c(x) = 0. Calculate x.
-1
Let u(m) be the second derivative of -3*m**5/20 - 11*m**4/24 - m**3/2 - m**2/4 + 6*m. Factor u(v).
-(v + 1)*(2*v + 1)*(3*v + 1)/2
Let g(d) = -23*d**4 - 43*d**3 - 13*d**2 + 53*d. Let b(l) = 11*l**4 + 21*l**3 + 6*l**2 - 26*l. Let t(x) = 13*b(x) + 6*g(x). Factor t(y).
5*y*(y - 1)*(y + 2)**2
Let y be 0 + 0 + 4/2. Suppose 6 = -2*z, -y*s - 16 = -4*s + 4*z. Factor 2*o + 2 - s - 2*o**3.
-2*o*(o - 1)*(o + 1)
Let m = 25 - -5. Let g be (16/10)/(12/m). Factor 0*i**2 + 1/2*i**3 + 1/4 - 1/2*i - 1/4*i**g.
-(i - 1)**3*(i + 1)/4
Let v(z) be the third derivative of 7*z**5/270 - z**4/18 + z**2 - 2. Factor v(j).
2*j*(7*j - 6)/9
Let l(o) be the first derivative of 2/9*o**3 + 1 - 2*o**2 + 6*o. Suppose l(d) = 0. Calculate d.
3
Let m(r) be the third derivative of r**8/672 + r**7/420 - r**6/120 - r**5/60 + r**4/48 + r**3/12 + 5*r**2. Let m(t) = 0. What is t?
-1, 1
Let n(g) be the first derivative of 3*g**5/5 - 9*g**4/2 + g**3 + 36*g**2 + 48*g - 17. Factor n(i).
3*(i - 4)**2*(i + 1)**2
Let x(v) be the third derivative of -1/480*v**6 - 1/96*v**4 + 3*v**2 + 0 - 1/120*v**5 + 0*v**3 + 0*v. Factor x(m).
-m*(m + 1)**2/4
Let h = 0 + 4. Find m such that 1 + 2*m + 2*m**2 - 3 + 2*m + h = 0.
-1
Let t(b) = 14*b - 263. Let c be t(19). Factor 0*p**c + 0*p + 6/5*p**4 + 0 + 2/5*p**5 - 8/5*p**2.
2*p**2*(p - 1)*(p + 2)**2/5
Let f(p) = 3*p**2 - 5*p - 32. Let n(j) = -4*j**2 + 8*j + 48. Let r(x) = -8*f(x) - 5*n(x). Find y, given that r(y) = 0.
-2, 2
Let v(b) = -4*b**3 - 1. Let f be v(1). Let a = f - -7. Factor -1/3*z**a + 1/3*z**3 + 0 + 0*z.
z**2*(z - 1)/3
Let s(h) be the first derivative of 5*h**3/3 + 10*h**2 - 21. What is f in s(f) = 0?
-4, 0
Let i = -38 - -9. Let p = i - -32. Find b such that 3*b**2 - 3*b - 3/4*b**p + 0 = 0.
0, 2
Let a(h) be the first derivative of -1/3*h**3 + 1/2*h**2 + h + 1/12*h**4 + 1. Let n(t) be the first derivative of a(t). Factor n(v).
(v - 1)**2
Factor -26*z**4 + z**3 + 17*z**3 + 10*z**5 + 2*z**2 - 2*z - 2*z.
2*z*(z - 1)**3*(5*z + 2)
Let a be 2 - (-200)/(-105) - (-8)/14. Factor a*w**2 + 4/3*w + 2/3.
2*(w + 1)**2/3
Let y(k) be 