et v be 9/(-18)*8/(-20). Factor 0*c + 1/5*c**5 + 1/5*c**4 + 0 - 1/5*c**3 - v*c**2.
c**2*(c - 1)*(c + 1)**2/5
Let c(i) be the third derivative of 6*i**2 + 0 + 0*i + 4/3*i**3 + 23/30*i**5 - 13/6*i**4 - 11/120*i**6. Factor c(l).
-(l - 2)**2*(11*l - 2)
Let g(i) = 3*i**2 + 5*i + 6. Let b = 5 + 6. Let k(w) = -6*w**2 - 11*w - 12. Let l(q) = b*g(q) + 6*k(q). Determine o, given that l(o) = 0.
-3, -2/3
Let -1/8*p**4 - 1/8 - 3/4*p**2 + 1/2*p + 1/2*p**3 = 0. Calculate p.
1
Let a = 0 + 0. Factor a*c**3 + 3*c**2 - 2*c**3 + c**2 + 0*c**3.
-2*c**2*(c - 2)
Let s(j) be the second derivative of -j**7/7 - 2*j**6/15 + 2*j**5/5 + j**4/3 - j**3/3 + 8*j. Suppose s(y) = 0. What is y?
-1, 0, 1/3, 1
Suppose 3*o - o = 0. Suppose u = -v + 12, 3*u + 4*v + o*v - 36 = 0. Let -11 + 2*k**3 - 4 + 24*k - 1 - u*k**2 = 0. Calculate k.
2
Let x be (-4)/10 - 4/(-10). Suppose -6*t**3 + x*t**2 - 29*t + 6*t**2 + 27*t + 2*t**4 = 0. What is t?
0, 1
Let g(s) be the first derivative of -3*s**5/5 + 3*s**4/4 + 12*s**3 + 6*s**2 - 48*s + 38. Factor g(j).
-3*(j - 4)*(j - 1)*(j + 2)**2
Factor -3*n**2 - 9*n - 9 - 1/3*n**3.
-(n + 3)**3/3
Let x be 2/(-2) + -3 - -6. Let m(f) be the third derivative of 1/72*f**4 + 0*f**3 + 0*f + 2*f**x + 0 + 7/180*f**5 + 1/24*f**6 + 1/70*f**7. Factor m(v).
v*(v + 1)*(3*v + 1)**2/3
Let i(m) be the third derivative of 0 - 1/210*m**7 + 0*m + 1/60*m**5 + 2*m**2 - 1/24*m**4 + 1/120*m**6 + 0*m**3. Factor i(q).
-q*(q - 1)**2*(q + 1)
Let m(h) = -h**2 - 3*h - 2. Let f(y) = 3*y**2 + 8*y + 5. Suppose 0 = 2*a - 1 - 15. Let k(t) = a*m(t) + 3*f(t). Solve k(j) = 0.
-1, 1
Let r = -8 - -10. Let n be ((-15)/(-9))/(r/18). Let f(t) = -3*t**2 + 4*t. Let k(a) = a**2 - 2*a. Let q(m) = n*k(m) + 6*f(m). Find g, given that q(g) = 0.
-2, 0
Solve -3*i**3 - 8*i + 9*i**2 + 8*i - 12 = 0.
-1, 2
Let w(v) be the third derivative of -v**6/210 + v**5/35 - v**4/14 + 2*v**3/21 - 5*v**2. Suppose w(p) = 0. What is p?
1
Let d = -241/4 + 62. Let o(b) be the first derivative of -3 + 1/5*b**5 - d*b**2 + 1/8*b**4 - b - b**3. Find v, given that o(v) = 0.
-1, -1/2, 2
Let r = 6 + -4. Let j(s) = s**3 - s**2 - 1. Let v be j(2). What is l in -4*l + 4*l**v + 4*l**2 - 2 - l**r + 2*l**2 - 3*l**2 = 0?
-1, -1/2, 1
Let v = 555 - 2205/4. Suppose 4*b - 11 + 1 = -2*y, 3*b + 5 = y. Suppose -3/2*s**4 - 15/4*s - 3/2 + 15/2*s**3 + 3*s**2 - v*s**y = 0. What is s?
-1, -2/5, 1
What is j in 2/7 - 1/7*j**3 + 4/7*j**2 - 5/7*j = 0?
1, 2
Let x(u) be the first derivative of 9*u**4/4 + 4*u**3 + 9*u**2/2 + 6*u + 8. Let d(r) = r**3 - r. Let f(h) = 6*d(h) - x(h). Determine c, given that f(c) = 0.
-2, -1
Let d(g) = 15*g**5 - 12*g**4 + 6*g**3 + 24*g**2 - 21*g + 12. Let j(x) = -x**5 - x**2 + x - 1. Let m(n) = -d(n) - 12*j(n). What is i in m(i) = 0?
-1, 0, 1, 3
Let g(x) be the second derivative of -x**6/360 + x**5/90 - 2*x**2 - x. Let y(j) be the first derivative of g(j). Factor y(u).
-u**2*(u - 2)/3
Suppose -3*k + 3 + 3 = 0. Let 8*i + k*i**2 - 4 + 5 + 5 + 0 = 0. What is i?
-3, -1
Let p = -30 - -30. Let b(s) be the third derivative of p*s + 0 - 1/6*s**4 + 1/3*s**3 - 2*s**2 + 1/30*s**5. Factor b(i).
2*(i - 1)**2
Determine t so that 2/3*t**4 + 0 - 8/3*t + 2/3*t**3 - 8/3*t**2 = 0.
-2, -1, 0, 2
Let o(p) = -4*p**3 + p**2 - p - 1. Let f be o(-1). Suppose 0 = -k - 3*y - 16 + 1, -f*k - 4*y = 20. Factor 2/5*r**3 + 0 + 2/5*r**5 + k*r**2 + 0*r - 4/5*r**4.
2*r**3*(r - 1)**2/5
Factor 6*t**3 - 138 + 138 + 4*t**2 - 2*t**3.
4*t**2*(t + 1)
Suppose 5*z = -0*z. Let m(l) be the second derivative of 1/10*l**5 + 0 + z*l**2 + 0*l**3 - 1/12*l**4 - 2*l - 1/30*l**6. Determine w, given that m(w) = 0.
0, 1
Factor 18/11*a**2 - 10/11*a - 14/11*a**3 + 4/11*a**4 + 2/11.
2*(a - 1)**3*(2*a - 1)/11
Factor -10*o - 70*o**2 + 1 + 45*o**5 - 10*o**5 - 5*o + 60*o**4 - 20*o**3 + 9.
5*(o - 1)*(o + 1)**3*(7*o - 2)
Let d(m) = 114*m**3 + 225*m**2 + 109*m + 9. Let p(h) = 23*h**3 + 45*h**2 + 22*h + 2. Let w(z) = -2*d(z) + 11*p(z). Let w(f) = 0. What is f?
-1, -2/5
Suppose 4*q - 4*c + 2*c = 12, 2*q - 5*c = 14. Factor 1 - 1 - q*m + 4*m + 2*m**2.
2*m*(m + 1)
Let o = 30/7 + -113/28. Factor 1/2*v**2 + 0 - 1/2*v**4 - o*v + 1/4*v**5 + 0*v**3.
v*(v - 1)**3*(v + 1)/4
Let t(r) = r**2 + r + 1. Let i(u) = 7*u**3 + 4*u**2 - 3*u - 5. Let x(p) = 2*i(p) + 10*t(p). Suppose x(n) = 0. Calculate n.
-1, -2/7, 0
Let s(p) = -15*p**2 - 21*p - 6. Let b(y) = 6 + 2*y**2 + 11*y + 11*y + 14*y**2. Let h(r) = -6*b(r) - 5*s(r). Let h(m) = 0. What is m?
-1, -2/7
Let n(c) be the second derivative of c**4/48 - c**3/8 + c**2/4 - 4*c. Suppose n(a) = 0. What is a?
1, 2
Let m(w) be the second derivative of w**8/4200 - w**7/1050 + w**6/900 - w**3/6 - 3*w. Let g(l) be the second derivative of m(l). Let g(h) = 0. Calculate h.
0, 1
Let d(y) be the third derivative of -7/360*y**6 - 1/630*y**7 + 0*y - 1/10*y**5 - 5/18*y**4 + 0 - 4/9*y**3 - 4*y**2. Factor d(a).
-(a + 1)*(a + 2)**3/3
Let t be ((-12)/(-14))/(6/(-84)). Let n = 15 + t. Find p such that 0*p - 5/4*p**4 + 1/2*p**5 + p**n - 1/4*p**2 + 0 = 0.
0, 1/2, 1
Let o = -298031/336 + 887. Let g(d) be the third derivative of 1/105*d**7 + 0*d**3 + d**2 + 0*d**4 + 0 + 0*d**5 + 1/120*d**6 + 0*d + o*d**8. Factor g(m).
m**3*(m + 1)**2
Let n(d) = d**2 + 3*d + 2. Let k be n(-3). Let f be 1 - k - (-17 + 14). Factor -2/3*q**f - 2/3*q**3 + 0 - 2/9*q**4 - 2/9*q.
-2*q*(q + 1)**3/9
Let x(k) = -k**3 + 2*k**2 + 3*k - 8. Let a(u) = u**3 - u**2 - 2*u + 5. Let v(g) = -8*a(g) - 5*x(g). Factor v(f).
-f*(f + 1)*(3*f - 1)
Let u(b) = -6*b**3 + 37*b**2 - 35*b + 25. Let r(j) = -2*j**3 + 12*j**2 - 12*j + 8. Let d(m) = 7*r(m) - 2*u(m). Factor d(h).
-2*(h - 3)*(h - 1)**2
Let q(p) be the third derivative of -p**8/420 - p**7/525 + p**6/300 - 8*p**2. Factor q(i).
-2*i**3*(i + 1)*(2*i - 1)/5
Suppose 6/11*d**2 - 2/11*d**3 + 18/11*d + 10/11 = 0. Calculate d.
-1, 5
Suppose -3*f = -3*g + 2*g + 18, -2*g = -4*f - 28. Let h be g*(-4 + 28/6). Factor -6/5*v**2 + 0 - 2/5*v - 6/5*v**3 - 2/5*v**h.
-2*v*(v + 1)**3/5
Let m be 2/6 - (7/(-6) - -1). Factor 3/2*j**3 + m*j + 0 - 3/2*j**2 - 1/2*j**4.
-j*(j - 1)**3/2
Suppose 3*p = 9, 4*p - 18 = 2*b - 5*b. Factor -2/7*s + 0 - 2/7*s**b.
-2*s*(s + 1)/7
Let o(m) = -m**3 + m**2 + 4. Let h be o(0). Suppose -b + 2*s + 2 = -5, 2*b + s = h. Factor 4*z**2 + 2*z**b - 3*z + z - 4*z**3.
-2*z*(z - 1)**2
Factor -12*y + 3/2*y**4 + 3*y**2 + 15/2*y**3 + 0.
3*y*(y - 1)*(y + 2)*(y + 4)/2
Factor -4/7*q**3 + 0 - 16/7*q - 16/7*q**2.
-4*q*(q + 2)**2/7
Let x(b) be the first derivative of b**5/90 + b**4/36 - b**2/2 + 1. Let j(n) be the second derivative of x(n). Factor j(g).
2*g*(g + 1)/3
Suppose 2*z - 12 = -2*z. Let h(m) be the second derivative of -1/4*m**z + 3*m + 1/2*m**2 + 0 + 0*m**4 + 1/40*m**5. Factor h(d).
(d - 1)**2*(d + 2)/2
Let y(r) be the second derivative of r**5/40 + 3*r**4/4 + 9*r**3 + 54*r**2 + r + 8. Factor y(x).
(x + 6)**3/2
Let i(g) = -g**2 + 6*g - 5. Let b be i(4). Let k be (b/6)/((-2)/(-8)). What is x in -6*x + 3 + 2 + 3*x**k - 2 = 0?
1
Let g(c) be the second derivative of c**6/50 + 3*c**5/50 + c**4/20 - 27*c. What is q in g(q) = 0?
-1, 0
Let c(b) = 4*b**3 + b**2 - 1. Let s be c(1). Factor -3*o**3 + 5*o**s + o**4 - o**3.
2*o**3*(3*o - 2)
Determine y, given that 3*y**4 + 3*y**4 - 4*y - 8*y**2 - 3*y**5 + 2*y**4 + 7*y**5 = 0.
-1, 0, 1
Let i be (-12)/16*(0 - 16). Let c = 17 - i. What is p in -5*p**2 + p**3 + 6*p**2 - p**c - p**4 + 3 - 3 = 0?
-1, 0, 1
What is k in 8/13*k + 8/13 - 2/13*k**2 - 2/13*k**3 = 0?
-2, -1, 2
Let n = 8 - 5. Let w(i) be the first derivative of 0*i**5 + 1 + 1/9*i**6 - 1/3*i**4 + 0*i**n + 1/3*i**2 + 0*i. Factor w(o).
2*o*(o - 1)**2*(o + 1)**2/3
Let c(d) = -d**3 - 6*d**2 + 8*d + 9. Let v be c(-7). Factor -6 + 3*r**v - 10*r**2 - 14*r**2 - 27*r.
-3*(r + 1)*(7*r + 2)
Let v be 0/8*-2*(-2)/(-8). Factor v*g + 2/5*g**3 + 0*g**2 + 2/5*g**5 + 0 - 4/5*g**4.
2*g**3*(g - 1)**2/5
Let g = -9 + 15. Factor 8*r**3 - 8*r**5 + 28*r**5 + 3*r**4 - g*r**3 - 17*r**4.
2*r**3*(2*r - 1)*(5*r - 1)
Suppose 5*x = -0*x + 10. Let 3*i**x - i**2 + 4*i**4 - 4*i**2 - 3*i**4 + 1 = 0. Calculate i.
-1, 1
Let h be 2/(-10) - (-3)/15. Let q = 758/9 - 84. Factor 2/9*c + h + 0*c**2 - q*c**3.
-2*c*(c - 1)*(c + 1)/9
Let i(x) = -x**3 + x**2 + 4*x. Let m(v) = v**3 - v**2 - 5*v. Let s(f) = 3*i(f) + 2*m(f). Factor s(q).
-q*(q - 2)*(q + 1)
Let a(p) be the third derivative of p**5/15 + p**4/3 + 2*p**3/3 - 5*p**2. Find y such that