0*g - 1. Let b(r) = 15*r**2 - 51*r - 6. Let j(y) = -4*b(y) + 21*n(y). Let j(k) = 0. Calculate k.
1
Let q(l) be the second derivative of -l**6/10 - 3*l**5/5 - 3*l**4/4 + 2*l**3 + 6*l**2 - 6*l. Factor q(s).
-3*(s - 1)*(s + 1)*(s + 2)**2
Suppose -8/3*n**2 + 2/3 + 0*n = 0. Calculate n.
-1/2, 1/2
Suppose 6*v = -0*v. Let l(p) be the third derivative of 0*p**4 + 0*p**5 - p**2 + 0*p + 0*p**3 - 1/945*p**7 - 1/270*p**6 + v. Find s, given that l(s) = 0.
-2, 0
Let g(w) be the second derivative of -w**4/3 + 4*w**3 - 18*w**2 + 9*w. Factor g(n).
-4*(n - 3)**2
Let g be (3/(-18))/(4/(-84)) + -3. Let o(s) be the second derivative of 1/24*s**4 + 0 + g*s**2 + s - 1/4*s**3. Factor o(j).
(j - 2)*(j - 1)/2
Factor -k**2 + 1/3*k**4 - 1/3*k + 2/3 + 1/3*k**3.
(k - 1)**2*(k + 1)*(k + 2)/3
Let m(k) = 12*k**2 + 5 + 2*k**4 + 8*k**3 - 3 - 4*k + 3*k + 18*k. Let t(w) = w**4 + 4*w**3 + 6*w**2 + 8*w + 1. Let j(h) = -4*m(h) + 9*t(h). Factor j(d).
(d + 1)**4
Let k(b) be the third derivative of b**9/120960 - b**8/40320 - b**5/60 - 2*b**2. Let n(s) be the third derivative of k(s). Solve n(z) = 0 for z.
0, 1
Let p(j) be the first derivative of -j**5/90 + j**3/27 - 3*j - 2. Let d(a) be the first derivative of p(a). Factor d(w).
-2*w*(w - 1)*(w + 1)/9
Determine c, given that 1/6*c**4 - 2*c - c**3 + 2/3 + 13/6*c**2 = 0.
1, 2
Determine f so that 2/15*f**3 + 2/5*f + 0 + 2/15*f**4 - 2/3*f**2 = 0.
-3, 0, 1
Let s(l) = -l + 5. Let b be s(3). Let v be 2/3*3 + -2. Determine p, given that -1/2*p + 1/2*p**3 + 0 + v*p**b = 0.
-1, 0, 1
Let b(h) be the second derivative of h**5/4 - 5*h**4/12 - 5*h**3/3 - h + 17. Factor b(q).
5*q*(q - 2)*(q + 1)
Let v(i) = i**3 - 16*i**2 + 16*i - 13. Let x be v(15). Let p = 7/2 + -2. Find b such that p*b**x + b + 0 = 0.
-2/3, 0
Let g(p) = -4*p - 2. Let n be g(-1). Let i(f) be the first derivative of n - 1/5*f**2 - 1/15*f**3 - 1/5*f. Determine z so that i(z) = 0.
-1
Let y(g) be the third derivative of g**5/20 - g**4/8 - g**3 - 4*g**2. Factor y(k).
3*(k - 2)*(k + 1)
Let p(y) = -y**3 - 10*y**2 + 10*y - 13. Let s be p(-11). Let d be (-4)/(-3)*(-1)/s. Suppose -1/3*j**3 + 0*j + d*j**2 + 0 = 0. Calculate j.
0, 2
Suppose 3*h - 40 = 3*f + 2*f, 5*h = f + 30. Factor -33/4*w**3 + 0 - 29/4*w**4 - 15/4*w**2 - 9/4*w**h - 1/2*w.
-w*(w + 1)**3*(9*w + 2)/4
Let t be (-33)/(-6) + -5 + 0. Let j(a) be the first derivative of 0*a - 1/3*a**3 + t*a**2 + 1. Factor j(n).
-n*(n - 1)
Let b(h) be the third derivative of -h**9/20160 + h**7/1680 - h**5/60 + 3*h**2. Let g(i) be the third derivative of b(i). Factor g(w).
-3*w*(w - 1)*(w + 1)
Let w(l) be the second derivative of -l**7/14 + 3*l**6/10 - 3*l**5/20 - 3*l**4/4 + l**3 - 10*l. Suppose w(r) = 0. What is r?
-1, 0, 1, 2
Suppose 24*n - 84*n**2 - 16/7 + 98*n**3 = 0. What is n?
2/7
Let m be -1*(3/(-6) + 0) - 0. Determine n so that 1/2*n - m*n**2 + 0 = 0.
0, 1
Let t be (-24)/9 + (-3)/(-1). Factor -2/3 + p - t*p**2.
-(p - 2)*(p - 1)/3
Let k be (2 - 10/6) + (-299)/(-345). Factor -k*j + 1/5*j**2 + 9/5.
(j - 3)**2/5
Suppose -4*n - 20 = 0, 0*z + 3*z + 3*n = -3. Let k(g) be the second derivative of 1/12*g**z - g - 1/2*g**2 + 1/6*g**3 - 1/20*g**5 + 0. Factor k(l).
-(l - 1)**2*(l + 1)
Let v(b) = -7*b**5 + 7*b**4 - 7*b**3 + b**2 - 2*b + 4. Let y(g) = 13*g**5 - 14*g**4 + 13*g**3 - g**2 + 3*g - 7. Let c(q) = -7*v(q) - 4*y(q). Factor c(w).
-w*(w - 1)**3*(3*w + 2)
Let g be 3 + 0 - (1 - 7 - -5). Let o(q) be the second derivative of 1/12*q**3 + 0 + 3*q - 1/12*q**g + 1/40*q**5 + 0*q**2. Factor o(m).
m*(m - 1)**2/2
Factor 0*m**2 + 3/5 - 3/5*m**4 + 6/5*m - 6/5*m**3.
-3*(m - 1)*(m + 1)**3/5
Let o(l) be the second derivative of -l**4/4 + 6*l**2 + 10*l. Factor o(n).
-3*(n - 2)*(n + 2)
Let 1/5*z**4 + 0*z**2 - 1/5 + 2/5*z**3 - 2/5*z = 0. What is z?
-1, 1
Let z(p) be the first derivative of -2*p**4 + 2*p**3 + 3*p**2/2 - p - 8. Factor z(f).
-(f - 1)*(2*f + 1)*(4*f - 1)
Let c = 7 - 33. Let i be c/(-10) - 6/(-15). Find y, given that -70*y**4 - y**i - 41*y**5 + 20*y**2 - 4*y + 4*y**3 - 8*y**5 = 0.
-1, 0, 2/7
Suppose -2*b = -4*y - 8, 0*y - 4*y - 44 = -5*b. Let q be (-63)/(-14)*b/45. Factor q*i**3 + 0*i - 4/5*i**2 - 2/5*i**4 + 0.
-2*i**2*(i - 2)*(i - 1)/5
Find j such that 3*j + 3*j + 4 - 9*j - j**2 = 0.
-4, 1
Let m be 150/(-20)*2/(-24). Let i = m + 13/56. Suppose -4/7*d**3 - 2/7*d**5 + i*d - 2/7 + 6/7*d**4 - 4/7*d**2 = 0. What is d?
-1, 1
Suppose -2*q + 0*h - 4*h = 0, -3*q = 4*h. Suppose -i + 2*d - d = 0, -i = -2*d. Factor q*t - 2/5*t**2 + i.
-2*t**2/5
Suppose 3/2*k**2 + 3/2 + 3*k = 0. Calculate k.
-1
Suppose -1 + 21 = 5*v. Let x(l) be the first derivative of l**2 - l**v - 4/9*l**3 + 2/3*l + 2/15*l**5 + 1/3*l**6 - 1. What is h in x(h) = 0?
-1, -1/3, 1
Factor 0*d + 0 + 2/9*d**2 + 2/9*d**3.
2*d**2*(d + 1)/9
Factor 6/5*h - 2/5*h**3 + 0 + 4/5*h**2.
-2*h*(h - 3)*(h + 1)/5
Factor -2/5*a**4 + 0*a + 0*a**2 + 0 + 2/5*a**3.
-2*a**3*(a - 1)/5
Let h(y) be the second derivative of -50*y**7/7 - 76*y**6/3 + 88*y**5/5 + 80*y**4 - 352*y**3/3 + 64*y**2 + 6*y. Find m, given that h(m) = 0.
-2, 2/5, 2/3
Suppose 3*h = -5*i - 16, -5*h + 0*h - 18 = 4*i. Let l be h - 2*5/(-2). Factor j**4 + 8*j**2 + j + 3*j + 2*j**l + 3*j**3.
j*(j + 1)*(j + 2)**2
Suppose s + 2*s = 12. Solve 3/4*x**s + 3*x + 3/4 + 3*x**3 + 9/2*x**2 = 0 for x.
-1
Suppose 0 = 3*o - 0*o - 7*o. Factor o*p + 1/4*p**3 + 0 - 1/2*p**2.
p**2*(p - 2)/4
Let n(i) be the first derivative of -i**6/3 + i**4 - i**2 + 8. Let n(p) = 0. What is p?
-1, 0, 1
Let b(n) be the first derivative of 0*n**3 + 1/22*n**4 - 3/11*n**2 + 2 + 4/11*n. Solve b(g) = 0 for g.
-2, 1
Let c(x) = 5*x**2 + 5*x + 8. Let h(i) = -6*i**2 - 4*i - 8. Let m(q) = 4*c(q) + 3*h(q). Factor m(t).
2*(t + 2)**2
Let z(l) be the first derivative of l**7/70 + l**6/40 - l**5/20 - l**4/8 + 5*l**2/2 - 1. Let s(p) be the second derivative of z(p). Factor s(x).
3*x*(x - 1)*(x + 1)**2
Let h(x) be the first derivative of x**6/21 - x**4/14 - 5. Solve h(a) = 0 for a.
-1, 0, 1
Let n(p) be the second derivative of -p**6/900 + p**3/2 - 3*p. Let v(t) be the second derivative of n(t). Factor v(s).
-2*s**2/5
Suppose -9 = -5*v - 0*f - f, 0 = 5*v + 3*f - 7. Find x such that -7/5*x - 2/5*x**v + 7/5*x**3 + 2/5 = 0.
-1, 2/7, 1
Let p(v) be the third derivative of v**7/105 - v**6/12 + 3*v**5/10 - 7*v**4/12 + 2*v**3/3 - 62*v**2. Factor p(o).
2*(o - 2)*(o - 1)**3
Let o = -157 + 473/3. Factor -2/3 + 2/3*j**2 - o*j + 2/3*j**3.
2*(j - 1)*(j + 1)**2/3
Let p be (-130)/180 - -2*3/8. Let l(i) be the third derivative of -2*i**2 - p*i**4 + 0*i**5 + 0 + 0*i**3 + 1/180*i**6 + 0*i. What is y in l(y) = 0?
-1, 0, 1
Let o be (-8)/(-225)*1251/66. Let p = o - 2/275. Factor 0 + 1/3*r + 1/3*r**3 + p*r**2.
r*(r + 1)**2/3
Let i(v) be the second derivative of -v**5/70 + 2*v**4/21 - 4*v**3/21 - 17*v. Factor i(c).
-2*c*(c - 2)**2/7
Let t(a) = -2 - 35*a**2 - 2*a**3 + 3*a**3 + 5*a + 0*a + 30*a**2. Let y be t(4). Factor -34/11*r**4 - y*r**2 - 42/11*r**3 + 0 - 10/11*r**5 - 4/11*r.
-2*r*(r + 1)**3*(5*r + 2)/11
Let a(p) = p**2 - p + 1. Let i(s) = -3*s**2 - 7*s - 2. Let k(x) = x. Let d(o) = -3*i(o) - 21*k(o). Let l(u) = 6*a(u) - d(u). Solve l(c) = 0.
-2, 0
Let m be 34/5 + (-2)/(-10). Let h(r) = r**2 - 8*r + 9. Let s be h(m). Factor -s*f + 0*f + 2*f**3 + 0*f**3.
2*f*(f - 1)*(f + 1)
Let c(d) be the second derivative of d**4/12 + d**3/6 - d**2 - 25*d. Determine f, given that c(f) = 0.
-2, 1
Let i(x) = -8*x**3 + 7*x**2 - 6*x + 7. Let a(y) = -7*y**3 + 6*y**2 - 5*y + 6. Let f(v) = 7*a(v) - 6*i(v). What is b in f(b) = 0?
-1, 0, 1
Let q = 1/241 - -959/1205. Let j be (-4)/3*(-6)/20. Factor 0 + 0*r + 0*r**2 + q*r**3 - 6/5*r**5 - j*r**4.
-2*r**3*(r + 1)*(3*r - 2)/5
Suppose -30 = -f - 4*f. Find d, given that -7*d**5 - 2*d**3 + 5*d**5 - f*d**4 + 2*d**4 = 0.
-1, 0
Suppose -2 = -4*l + 14. Let x = 49/2 + -24. Factor -1/2*o + 1/2*o**3 - x*o**2 + 0 + 1/2*o**l.
o*(o - 1)*(o + 1)**2/2
Let v(s) be the second derivative of 8*s**6/15 + 3*s**5/5 - 3*s**4 + 4*s**3/3 + 2*s. Factor v(q).
4*q*(q - 1)*(q + 2)*(4*q - 1)
Let n be (-3 - 2) + 2/4. Let t = 5 + n. Suppose g**2 + 0 - t*g - 1/2*g**3 = 0. Calculate g.
0, 1
Factor 4/3*w + 0*w**3 - 2/3*w**4 + 2*w**2 + 0.
-2*w*(w - 2)*(w + 1)**2/3
Let d(c) = -3*c**3 - c**2 - 2*c - 1. Let x be d(-1). Suppose x*z + z = 0. Solve -4*a**5 - 10/3*a**2 + 10/3*a**3 + 10/3*a**4 + 2/3*a + z = 0 for a.
-1, 0, 1/3, 1/2, 1
Let w(l) be the first de