-1/113. Find x such that -k - 14/3*x - 4*x**2 + 2*x**5 + 16/3*x**4 + 8/3*x**3 = 0.
-1, -2/3, 1
Let r(d) be the third derivative of 7*d**6/24 + 23*d**5/12 + 5*d**4/4 + 18*d**2. Factor r(u).
5*u*(u + 3)*(7*u + 2)
Let q(a) be the third derivative of a**4/24 - a**3/2 - 2*a**2. Let u be q(6). Factor p**2 + 3*p**2 - 14*p**3 + 0*p**u.
-2*p**2*(7*p - 2)
Let i(t) = 4*t + 15. Let w(c) = -2*c - 7. Let g(x) = -3*i(x) - 5*w(x). Let o be g(-5). Let o - 4/3*q + 2/3*q**3 + 2/3*q**2 = 0. What is q?
-2, 0, 1
Let s(j) be the first derivative of -5 + 4/13*j - 2/13*j**3 + 5/13*j**2. Determine a, given that s(a) = 0.
-1/3, 2
Let m be 3/5*10/15. Factor -1/5 + m*h + 4/5*h**3 + 7/5*h**2.
(h + 1)**2*(4*h - 1)/5
Let y(r) = -r**3 - 5*r**2 + 5*r - 4. Let f be y(-6). Solve -3 - 2*p**2 + 0*p**f + 2 + 3 = 0 for p.
-1, 1
Let y(a) be the third derivative of a**5/450 + a**4/180 - 12*a**2. Factor y(m).
2*m*(m + 1)/15
Factor 7/2*z + 0 - 1/2*z**2.
-z*(z - 7)/2
Let h(b) be the first derivative of -b**5 - 15*b**4/4 - 5*b**3/3 + 15*b**2/2 + 10*b - 9. Find g, given that h(g) = 0.
-2, -1, 1
Suppose 3*x - 4*x = -1. Suppose 4*q - 22 = 2*q + 3*p, -p + x = q. Factor -13/3*w**3 - 7/3*w - 1/3 - q*w**2 - 4/3*w**4.
-(w + 1)**3*(4*w + 1)/3
Let v(z) be the first derivative of -z**4/32 + z**3/8 - 3*z**2/16 + z/8 - 8. Factor v(h).
-(h - 1)**3/8
Let i(l) = -l**5 + l**3 - l. Let j = 2 - 3. Let s(a) = -6*a**4 + 3*a**3 + 6*a**2 - 6*a. Let z(q) = j*s(q) + 3*i(q). Solve z(v) = 0 for v.
-1, 0, 1
Suppose 6 - 24 = -9*u. Factor 0 - 1/2*y**3 + 0*y - 1/2*y**u.
-y**2*(y + 1)/2
Let x(u) be the first derivative of -u**3/7 + 3*u**2/7 + 9*u/7 + 8. Factor x(c).
-3*(c - 3)*(c + 1)/7
Suppose -3*t + t - 32 = -4*i, 3*i - 6 = -3*t. Let x(v) = -2*v - 9. Let a be x(-6). Suppose 2 + 0 - z**a - z**3 - 6*z + i*z**2 = 0. Calculate z.
1
Let s(d) be the third derivative of -d**10/378000 + d**8/50400 - d**5/60 + d**2. Let m(u) be the third derivative of s(u). Let m(z) = 0. What is z?
-1, 0, 1
Let x be 18/27 + 55/(-84). Let l(y) be the third derivative of 0 + 0*y + 2*y**2 + 1/120*y**5 + 0*y**3 - 1/30*y**6 + x*y**7 + 1/24*y**4. Solve l(g) = 0.
-2/5, 0, 1
Let r be (0 + (-1)/(-3))/((-5)/(-6)). Factor r*q + 0*q**2 + 0 - 2/5*q**3.
-2*q*(q - 1)*(q + 1)/5
Let f(y) be the third derivative of y**6/200 + y**5/20 + 3*y**4/20 + 23*y**2. Determine l, given that f(l) = 0.
-3, -2, 0
Let i(h) = -4*h**3 + 2*h**2. Let z(n) = -n**4 + 13*n**3 - 6*n**2 + n. Let u(b) = -7*i(b) - 2*z(b). Factor u(g).
2*g*(g - 1)*(g + 1)**2
Let r be 3 + 0 + 2 + -3. Let c(o) be the first derivative of 1 + 1/3*o**3 + 1/4*o**4 + 0*o**r - 1/5*o**5 - 1/6*o**6 + 0*o. Factor c(n).
-n**2*(n - 1)*(n + 1)**2
Let z(c) be the first derivative of -1/12*c**4 + 1/15*c**5 - 1/9*c**3 - 3 + 0*c + 1/6*c**2. Factor z(s).
s*(s - 1)**2*(s + 1)/3
Let b = -11 + 11. Suppose -4*v + v = b. Factor -3/2*w**2 + v + 3/4*w - 9/4*w**3.
-3*w*(w + 1)*(3*w - 1)/4
Let a = 131 - 392/3. Factor -8/3 - 2*b**2 - 4*b - a*b**3.
-(b + 2)**3/3
Factor 1/3*z**3 - 2/3 + 2/3*z**2 - 1/3*z.
(z - 1)*(z + 1)*(z + 2)/3
Let v(n) be the first derivative of -2*n**5/25 - n**4/5 + 2*n**2/5 + 2*n/5 - 6. Factor v(b).
-2*(b - 1)*(b + 1)**3/5
Let i = -2 - -5. Let s be ((-2)/i)/((-10)/6). Determine p so that 8/5*p**3 - 6/5*p**5 + 0 - s*p + 4/5*p**4 - 4/5*p**2 = 0.
-1, -1/3, 0, 1
Let h(c) = -5*c - 2 + 6*c - 3 + 2. Let s be h(5). Find d such that -3/4*d**s + 0 - 3/4*d = 0.
-1, 0
Let p(m) be the second derivative of 0 - 2*m**3 + m**4 + 0*m**2 - 3/20*m**5 + 8*m. Suppose p(o) = 0. Calculate o.
0, 2
Suppose -23*d - 10 = -56. Let p be -1 + 46/4 + 0. Find q such that -d - 3/4*q**4 - p*q**2 - 19/4*q**3 - 9*q = 0.
-2, -1/3
Let c = -61 - -65. Let g(u) be the second derivative of 1/21*u**3 - 1/105*u**6 - 1/70*u**5 + 4*u + 0*u**2 + 0 + 1/42*u**c. Solve g(w) = 0 for w.
-1, 0, 1
Suppose p + 4*p + 3*p = 0. Let y(r) be the first derivative of -1/3*r**2 - 1 + p*r + 2/9*r**3. Factor y(v).
2*v*(v - 1)/3
Let f(x) = -6*x**2 - 5*x + 11. Let s(t) be the second derivative of -t**4/12 - t**3/6 + t**2 + 3*t. Let l(o) = -2*f(o) + 11*s(o). What is p in l(p) = 0?
0, 1
Let c(j) = -32*j**3 + 117*j**2 - 120*j + 31. Let x(l) = 33*l**3 - 117*l**2 + 120*l - 30. Let t(z) = -6*c(z) - 5*x(z). Solve t(n) = 0 for n.
2/3, 3
Suppose -s - 15 = -4*s + 4*o, 3*s + 5*o + 12 = 0. Let b(t) be the first derivative of 2/15*t**3 + s - 3/5*t**2 + 4/5*t. Factor b(c).
2*(c - 2)*(c - 1)/5
Let z(o) be the first derivative of 0*o**2 - 1/5*o**4 + 0*o + 2/25*o**5 + 1/15*o**6 + 2 + 0*o**3. Factor z(b).
2*b**3*(b - 1)*(b + 2)/5
Let b be (6/(-40))/(4*3/(-12)). Let t(r) be the second derivative of 0*r**3 + 0 + 1/4*r**4 + 2*r + 0*r**2 + b*r**5. Factor t(u).
3*u**2*(u + 1)
Let l(o) be the third derivative of -2*o**7/105 - o**6/6 - 7*o**5/15 - o**4/2 + 7*o**2. Factor l(f).
-4*f*(f + 1)**2*(f + 3)
Let z(j) = -j**3 - 7*j**2 + 9*j + 12. Let i be z(-8). What is s in 4*s - 6*s + s - 5*s + 2*s**2 + i = 0?
1, 2
Let m(n) = n**2 - 2*n + 3. Let l be m(2). Let k(j) = -j**3 + j + 5. Let z be k(0). Factor -z + 1 + 2*o**2 + l - o.
(o - 1)*(2*o + 1)
Let s be ((-8)/(-126))/((-9)/(-63)). Find o such that 2/3 - s*o - 2/9*o**2 = 0.
-3, 1
Let v(s) = -s**3 + 5*s**2 - 6*s + 8. Let y be v(4). Factor -1/6*m**2 + y - 1/3*m.
-m*(m + 2)/6
Let u(z) = 2*z**2 + 4*z - 5. Let n(c) = 2*c - 3*c + 3*c + c**2 - 3. Let p(y) = -7*n(y) + 4*u(y). Solve p(t) = 0.
-1
Let y(r) be the second derivative of -r**4/132 + r**3/66 + r**2/11 - 18*r. Factor y(g).
-(g - 2)*(g + 1)/11
Let s = 8 - 6. Let w(k) be the first derivative of 0 + 3*k**3 - 4*k**3 - 3 + 0*k**s + 6*k**2 - 12*k. Find i such that w(i) = 0.
2
Let g(m) be the third derivative of -23*m**7/630 - m**6/180 + 23*m**5/60 + 13*m**4/18 + 2*m**3/9 + 11*m**2 + 1. Determine s, given that g(s) = 0.
-1, -2/23, 2
Let p(q) be the first derivative of q**4/4 + 14*q**3/3 + 6*q**2 - 10*q - 4. Let z be p(-13). Factor 1/3*m**z - 1/3*m + 1/3*m**2 - 1/3.
(m - 1)*(m + 1)**2/3
Let b be 1*4/12*(-2 + 2). Factor 2/3*f + 2*f**3 + 2*f**2 + b + 2/3*f**4.
2*f*(f + 1)**3/3
Let a = -1 + 6. Factor x**2 - 2*x**3 - a + x + x**3 + 4.
-(x - 1)**2*(x + 1)
Let w(g) be the second derivative of 1/48*g**4 + 3*g - 1/8*g**2 + 0*g**3 + 0. Find q such that w(q) = 0.
-1, 1
Solve 5/4*q**5 - 35/4*q**4 + 65/4*q + 45/2*q**3 - 15/4 - 55/2*q**2 = 0.
1, 3
Let u(g) be the first derivative of 5*g**4/4 + 5*g**3 + 15*g**2/2 + 5*g + 3. Factor u(m).
5*(m + 1)**3
Suppose -5*k + 18 + 12 = 0. Let r(b) = -3*b**2 - 6*b - 3. Let q(o) = -3*o**2 - 5*o - 2. Let a(j) = k*q(j) - 5*r(j). Factor a(l).
-3*(l - 1)*(l + 1)
Let w = -1 - 4. Let z be (4/30)/(w/(-30)). Factor -2*b**3 + 18/5*b**2 - 14/5*b + z + 2/5*b**4.
2*(b - 2)*(b - 1)**3/5
Suppose -4*k + d - 1 = 0, -k + 10*d - 24 = 5*d. Let z(b) be the first derivative of k + 0*b + 2/9*b**3 - 1/12*b**4 + 0*b**2. Factor z(j).
-j**2*(j - 2)/3
Let b(j) be the third derivative of -j**7/630 + 2*j**5/45 - 8*j**3/9 + 4*j**2. Factor b(g).
-(g - 2)**2*(g + 2)**2/3
Find m, given that -13/5*m**2 - 1 - 2/5*m**3 - 16/5*m = 0.
-5, -1, -1/2
Let h = -84 + 256/3. Factor -h*x - 2/3*x**4 + 2/3 + 0*x**2 + 4/3*x**3.
-2*(x - 1)**3*(x + 1)/3
Factor 0 - 2/3*o**2 - 2/3*o.
-2*o*(o + 1)/3
Suppose -25/6*f**4 - 35/6*f**5 - 40/3*f + 10/3 + 115/6*f**3 + 5/6*f**2 = 0. What is f?
-2, -1, 2/7, 1
Let x be (-21)/18*2 + 3. Let z = -6 - -9. Factor -2/3*i + x*i**z + 1/3 - 1/3*i**2.
(i - 1)*(i + 1)*(2*i - 1)/3
Let x(b) = -8*b**2 + 4*b + 4. Let p(l) = 23*l**2 - 12*l - 13. Let q(d) = -4*p(d) - 11*x(d). Factor q(g).
-4*(g - 2)*(g + 1)
Solve -2/7 + 9/7*y + 11/7*y**2 = 0 for y.
-1, 2/11
Let r = 3439/1744 + -31/109. Let g = 209/48 - r. Factor -g*z - 4/3 - z**2.
-(z + 2)*(3*z + 2)/3
Factor 0 + 9/4*n + 3/4*n**2.
3*n*(n + 3)/4
Let c(q) be the third derivative of 0*q - 1/70*q**7 + 0 - 1/12*q**4 - 1/504*q**8 - 2/45*q**6 - 1/18*q**3 - 4*q**2 - 7/90*q**5. Factor c(z).
-(z + 1)**4*(2*z + 1)/3
Let p be 2/(0 + 4 + -3). Suppose 2/5*a**3 - 2/5*a**4 + 2/5*a**p - 2/5*a + 0 = 0. What is a?
-1, 0, 1
Let b(f) = 4*f**2 + 4*f + 7. Let l(k) = 0*k + k**2 - 15 - 6*k**2 - 4*k**2 - 8*k. Let i(n) = 7*b(n) + 3*l(n). Suppose i(o) = 0. Calculate o.
-2
Suppose b - 3 = -y + 3, -4*b + 5*y = -60. Let v be (10/(-25))/((-2)/b). Factor 3*p**2 - 4 + 2*p**2 - 2*p + p**v.
2*(p - 1)*(3*p + 2)
Let m be 0/((-2)/((-2)/3)). Let c be m - (-5)/(10/4). Factor x**4 + 0*x**5 - x**4 + c*x**5 - 2*x**3