Let v(g) = 0. Calculate g.
-1, 0, 1
Let w be ((-1)/(-2))/(10/45). Find j, given that 3/4*j**2 + w - 15/4*j + 3/4*j**3 = 0.
-3, 1
Let q(i) = i**3 + i**2 + i - 1. Let o(r) = -5*r**3 + 55*r**2 + 230*r + 190. Let y(d) = -o(d) - 10*q(d). Factor y(x).
-5*(x + 1)*(x + 6)**2
Let i(c) be the first derivative of c**8/840 + c**7/420 + 2*c**3 - 7. Let f(d) be the third derivative of i(d). Find q, given that f(q) = 0.
-1, 0
Let l(t) be the second derivative of 5*t**7/21 + 2*t**6/15 - 4*t**5/5 - t**4/3 + t**3 + 8*t. Determine a so that l(a) = 0.
-1, 0, 3/5, 1
Solve s**4 + 8*s**2 - 36*s - 7*s**3 + 32*s + 2*s**3 = 0 for s.
0, 1, 2
Let h(g) = -g**3 + g**2 - g - 1. Let d = 31 + -34. Let f = -2 + 1. Let w(q) = 4*q**3 - 2*q**2 + 3*q + 3. Let s(c) = d*h(c) + f*w(c). Find u such that s(u) = 0.
-1, 0
Factor -6*s**5 + 16*s**3 - 36*s**3 - 12*s**4 + 4 + 10*s - 8*s**4.
-2*(s + 1)**4*(3*s - 2)
Let h(n) be the third derivative of -4*n**2 + 0*n + 1/18*n**3 - 1/180*n**5 + 1/360*n**6 - 1/72*n**4 + 0. Factor h(r).
(r - 1)**2*(r + 1)/3
Let y(t) be the first derivative of 0*t - 1 - 2*t**2 + 1/2*t**4 + 2/3*t**3. Factor y(f).
2*f*(f - 1)*(f + 2)
Factor -4 + 10*p**4 + 0 - 60*p**2 + 14 - 5*p + 15*p**5 - 67*p**3 + 17*p**3.
5*(p - 2)*(p + 1)**3*(3*p - 1)
Let j be 6/4 + 1/2. Let a = 7 + -2. Factor 16*g**2 - a + j + 4*g + 1.
2*(2*g + 1)*(4*g - 1)
Suppose 3*w = -2*p - 15, -7*p - w - 5 = -8*p. Factor -g**4 + 0 + p*g**2 + 0*g**3 + 0*g - 1/2*g**5.
-g**4*(g + 2)/2
Let c(h) be the third derivative of 0 + 0*h - 1/240*h**5 - 1/48*h**4 - 3*h**2 - 1/24*h**3. Factor c(f).
-(f + 1)**2/4
Suppose -2 = -2*i + i. Factor -2*g**i - 2*g**3 + 8*g**2 - 2*g**4 - 6*g**2.
-2*g**3*(g + 1)
Let z(p) be the second derivative of -1/15*p**4 - 1/2*p**2 + 4/15*p**3 + 0 + 3*p + 1/150*p**5. Let c(g) be the first derivative of z(g). Factor c(t).
2*(t - 2)**2/5
Suppose 5*r + 15 = -5, -16 = -2*k + 3*r. Suppose -28 = k*g - 9*g. Suppose 0*o + 0 + 2/7*o**g + 8/7*o**2 - 8/7*o**3 = 0. What is o?
0, 2
What is s in 0*s**2 + 3*s**4 - 43*s**5 + 31*s**5 + 12*s**3 - 3*s**2 = 0?
-1, 0, 1/4, 1
Let n = -91 + 95. Factor 0 - 1/3*u**5 + 0*u - 1/3*u**3 + 2/3*u**n + 0*u**2.
-u**3*(u - 1)**2/3
Let j(a) = -a**2 - 11*a - 10. Let c(z) = -2*z - 2. Let t(d) = 22*c(d) - 4*j(d). Factor t(q).
4*(q - 1)*(q + 1)
Let x(y) = -20*y + 11. Let c(f) = -7*f + 4. Let w(z) = 17*c(z) - 6*x(z). Let b be w(0). Factor -4*i + i**b + 4*i.
i**2
Let k(w) be the third derivative of -w**7/35 + 3*w**6/40 + w**2. Let f(m) = 4*m**3 - 3*m**4 + 3*m - 3*m. Let z(x) = -5*f(x) + 2*k(x). Factor z(a).
a**3*(3*a - 2)
Let d = -4 - -8. Let l(t) be the second derivative of 0*t**3 - t + 0 + 0*t**2 + 1/12*t**d. Factor l(j).
j**2
Let s = 101/462 - 4/77. Let a(w) be the first derivative of 0*w - 2/15*w**5 - 1/9*w**6 - 3 + 0*w**2 + 2/9*w**3 + s*w**4. Factor a(i).
-2*i**2*(i - 1)*(i + 1)**2/3
Determine u, given that 0*u**3 - 5*u**2 + 47*u - 17*u - 6*u**3 + u**3 = 0.
-3, 0, 2
Suppose -t + 12 = 3*k - 16, 2*t + 24 = 4*k. Let n = 10 - k. Solve 11/4*g**n - 1/2*g + 0 - 9/4*g**3 = 0 for g.
0, 2/9, 1
Factor 87*d**4 - 88*d**4 - 2*d + 2*d**3 - 1 + 2.
-(d - 1)**3*(d + 1)
Let f(s) be the first derivative of s**3/12 + 3*s**2/8 + s/2 - 6. Factor f(m).
(m + 1)*(m + 2)/4
Suppose 2*i = 5*i. Suppose 4*c + 0*c = i. Determine n so that c + 6/5*n**2 + 1/5*n = 0.
-1/6, 0
Let p(a) be the second derivative of 0*a**3 + 1/21*a**7 + 2/15*a**6 + 2*a + 0*a**4 + 0*a**2 + 0 + 1/10*a**5. Factor p(m).
2*m**3*(m + 1)**2
Factor -15/4*w + 3/4*w**2 + 3/4*w**3 + 9/4.
3*(w - 1)**2*(w + 3)/4
Factor -18/5 - 2/5*a**2 + 12/5*a.
-2*(a - 3)**2/5
Let m(b) be the first derivative of b**6/240 + b**5/60 + b**4/48 + 2*b**2 - 2. Let s(n) be the second derivative of m(n). Factor s(q).
q*(q + 1)**2/2
Let h(y) = -1. Let v(n) = 2*n**2 + 2*n**2 + n**2 - 8 - 7*n**2 - 4*n. Let f(g) = -6*h(g) + v(g). Let f(p) = 0. What is p?
-1
Let s = -8 - -13. Suppose s*n = 9 + 6. Solve 0*c**4 + 0*c**3 + c**2 + 3*c**n + c**5 + 3*c**4 = 0 for c.
-1, 0
Let h be (16/(-10))/((-1)/10). Solve 3*c**2 + 18*c - 4 - c**2 - h*c = 0 for c.
-2, 1
Let j(z) = -z - 5. Let w be j(-7). Let l be -2 + -2 + 12/2. What is c in -w*c - 3*c**2 - 3*c**l + 4*c**2 = 0?
-1, 0
Let k(f) be the first derivative of -3*f**4/2 - 5*f**3/3 + f**2 + 4*f + 2. Let p(z) = z**3 - z + 1. Let c(i) = -k(i) - 5*p(i). Factor c(s).
(s - 1)*(s + 3)**2
Let m(k) be the second derivative of 2/5*k**2 - 1/50*k**5 + 0 - 1/3*k**3 - k + 2/15*k**4. Factor m(a).
-2*(a - 2)*(a - 1)**2/5
Let s = 12 + 3. Let g be (-3)/s + 1/5. Let -2/3*a**5 - 5/3*a**4 + g + 0*a - 1/3*a**2 - 4/3*a**3 = 0. Calculate a.
-1, -1/2, 0
Let h be 16*1*(-5)/2. Let t be 48/h*(-10)/4. Factor 1/4*a**t + 1/2 + 5/4*a + a**2.
(a + 1)**2*(a + 2)/4
Let v(x) be the third derivative of -x**9/12096 + x**8/2240 - x**7/1120 + x**6/1440 - x**3/3 + 7*x**2. Let i(t) be the first derivative of v(t). Factor i(a).
-a**2*(a - 1)**3/4
Suppose -2*u = -5*u + 132. Let m = -3 - -7. Solve -61*o**3 - 4*o + 12*o**2 - 2*o**4 + 16*o**2 - o**5 - 8*o**5 + u*o**m = 0 for o.
0, 1/3, 2
Let 3/2*c**2 + 0 + 3*c = 0. Calculate c.
-2, 0
Factor 2/11*c**4 - 2/11*c**5 + 0*c**2 + 0*c**3 + 0*c + 0.
-2*c**4*(c - 1)/11
Suppose -51*u + 45*u + 18 = 0. Determine r, given that -4/9*r**2 + 2/9*r**4 - 2/9*r**u + 0*r + 0 = 0.
-1, 0, 2
Let a be 28/(-35) + (-66)/(-80). Let f(w) be the third derivative of a*w**5 + 3*w**2 + 1/12*w**3 - 1/16*w**4 - 1/240*w**6 + 0 + 0*w. Factor f(q).
-(q - 1)**3/2
Let s(g) = -7*g**4 + 12*g**2 - 11*g. Let p(m) = 6*m**4 - 12*m**2 + 10*m. Let i(x) = 3*p(x) + 2*s(x). Solve i(y) = 0 for y.
-2, 0, 1
Suppose -3*n = -2*y - 63, -3*y - 5*n - 20 = 27. Let b be 3*(y/(-45) - 0). Suppose 8/5*s**3 + 6/5*s**4 - 14/5*s**2 + b - 8/5*s = 0. What is s?
-2, -1, 2/3, 1
Determine u, given that -2/3*u - 1/3*u**2 + 0 = 0.
-2, 0
Suppose 3*r + 22 = 5*r. Let n = r - 7. Factor 0*j + 0*j**3 + 1/2*j**n + 0 + 0*j**2.
j**4/2
Let f(i) be the first derivative of -5*i**4 + 28*i**3/3 - 4*i**2 + 3. Suppose f(m) = 0. Calculate m.
0, 2/5, 1
Let z(j) be the second derivative of j**6/10 - j**4/2 + 3*j**2/2 - 4*j. Let z(d) = 0. Calculate d.
-1, 1
Let y(z) be the second derivative of z**4/60 - z**3/30 - z**2/5 - 16*z. Factor y(a).
(a - 2)*(a + 1)/5
Suppose 0 = -2*t + 29 + 7. Suppose 22*p = t*p. Factor 0*x + p + 9/4*x**4 + 3/4*x**2 + 9/4*x**3 + 3/4*x**5.
3*x**2*(x + 1)**3/4
Suppose 0 = -4*y + 5*y - 15. Let u be ((-4)/y)/((-5)/100). Let u*v + 64/3*v**3 - 16*v**2 - 32/3*v**4 - 2/3 = 0. What is v?
1/2
Let u(i) = i**2 + 1. Let b(r) = 15*r**2 - 12*r - 13. Let y(d) = -b(d) - 5*u(d). Factor y(h).
-4*(h - 1)*(5*h + 2)
Let z(l) = -l**2 - 6*l - 7. Let n be z(-5). Let b = 1 - n. Factor 3*y**5 + 2*y**3 + b*y**4 - 7*y**4 - y**3.
y**3*(y - 1)*(3*y - 1)
Let p(x) be the second derivative of x**6/20 + 3*x**5/8 + x**4 + x**3 - 3*x. Suppose p(j) = 0. Calculate j.
-2, -1, 0
Let f(v) be the third derivative of v**5/330 - v**3/33 - 12*v**2. Factor f(w).
2*(w - 1)*(w + 1)/11
Let m(w) be the second derivative of -w**6/160 - 9*w**5/80 - 27*w**4/32 - 27*w**3/8 - 3*w**2/2 + w. Let y(j) be the first derivative of m(j). Factor y(f).
-3*(f + 3)**3/4
Factor 3 - 10*h**2 - 2*h**4 + 5*h**2 - 2*h**3 - 11*h + h**3 + 16*h**2.
-(h - 1)**2*(h + 3)*(2*h - 1)
Let v(p) be the first derivative of p**3/3 + 3*p**2 - 3. Factor v(x).
x*(x + 6)
Let f(s) = s**3 + s**2 + s - 1. Let k(n) = -3*n + 0*n - 2*n**3 - 3*n**2 - 2*n**3 + 2*n**3 + 3. Let v(x) = 3*f(x) + k(x). Factor v(y).
y**3
Let j(r) be the first derivative of r**4/66 - 2*r**3/33 + r**2/11 + 5*r + 5. Let o(y) be the first derivative of j(y). Factor o(z).
2*(z - 1)**2/11
Let o(a) = 533*a**2 + 495*a - 22. Let p(b) = -178*b**2 - 165*b + 7. Let r(k) = -3*o(k) - 8*p(k). Factor r(j).
-5*(j + 1)*(35*j - 2)
Let k(c) = 4*c**2 + 5*c**4 - c**4 + 3*c + 5*c**3 + 10*c. Let z(f) = f**4 + f**3 + f**2 + 3*f. Let a(w) = -6*k(w) + 26*z(w). Factor a(h).
2*h**2*(h - 1)**2
Let f(t) be the third derivative of -t**8/56 - t**7/15 + t**6/10 + 2*t**5/5 - 2*t**4/3 + 2*t**2. Find z, given that f(z) = 0.
-2, 0, 2/3, 1
Let d(q) be the first derivative of 1 + 4/3*q**3 + 3/2*q**4 - q**2 + 0*q. Factor d(f).
2*f*(f + 1)*(3*f - 1)
Let o be 6/24 - (-5)/4. Determine z so that -o*z**2 + z + 1/2*z**4 + 0 + 0*z**3 = 0.
-2, 0, 1
Suppose -14*s + 100 = 11*s. Suppose 2*n**2 + s*n**3 - 4/3*n - 1 + 5/3*n**4 = 0. What is n?
-1, 3/5
Let p(z) be the seco