2*r**3 + 0 - 1/160*r**6 + 3/80*r**5. Determine a, given that o(a) = 0.
-1, 2
Factor 0*r**2 - 210*r + 245*r + 5*r**2 + 30.
5*(r + 1)*(r + 6)
Suppose -42*k - 4 = -44*k. Solve -1/5*v - 2/5*v**4 + 2/5*v**k + 1/5*v**5 + 0*v**3 + 0 = 0 for v.
-1, 0, 1
Let u(h) = -h**2 + h + 5. Let m be u(0). Suppose s - 15 = m. Solve 0*t**3 + 9*t**2 + t**3 + 27*t + 7 + s = 0.
-3
Let q(g) be the third derivative of 1/105*g**7 + 1/60*g**4 - 1/100*g**6 - 1/150*g**5 + 0*g + 0*g**3 - 1/420*g**8 - 2*g**2 + 0. Factor q(a).
-2*a*(a - 1)**3*(2*a + 1)/5
Suppose -6*t + 10 = 2*s - 3*t, -5*s + 16 = 3*t. Suppose -s = l - 6. Determine f, given that -6/7*f**3 + 2/7*f**l + 6/7*f**2 + 0 - 2/7*f = 0.
0, 1
Let u(c) be the second derivative of -c**5/10 - 19*c**4/18 - 11*c**3/3 - 3*c**2 + 13*c. Factor u(v).
-2*(v + 3)**2*(3*v + 1)/3
Let z(p) = 3*p**2 - 2*p + 2. Let i be z(1). Let f(s) be the second derivative of 0 + 1/6*s**i + 2*s + 0*s**2 - 1/12*s**4. Factor f(c).
-c*(c - 1)
Let f(r) be the third derivative of r**7/245 - r**5/70 + 33*r**2. Factor f(x).
6*x**2*(x - 1)*(x + 1)/7
Let p be 1 + 4 + 4*-1 + 1. Factor 1/3*x**3 + x**p + x + 1/3.
(x + 1)**3/3
Let u(g) = g**5 + g**4 + g**3 - g**2 - g - 1. Let q(j) = 4*j**5 - j**4 - 6*j**3 + j**2 + j + 1. Let i(h) = -q(h) - u(h). Determine b so that i(b) = 0.
-1, 0, 1
Let c be (-5 + 66/12)/((-6)/(-20)). Factor -4/3*y**2 - c*y - 1/3.
-(y + 1)*(4*y + 1)/3
Suppose -2*q + 30 = q. Let r(f) = -f**3 + 3*f**2 - 2*f + 3. Let k(j) = 4*j**3 - 10*j**2 + 6*j - 10. Let s = 2 - -1. Let l(t) = q*r(t) + s*k(t). Factor l(a).
2*a*(a - 1)*(a + 1)
Suppose 5*b - 18 = 12. Let z be 122/b*(1 - -5). Factor 22*m**4 - 27*m**5 - 171*m**3 - 12*m**2 - 8 - 74*m**4 - z*m**2 - 56*m**4 - 52*m.
-(m + 1)**2*(3*m + 2)**3
Let z(x) = x + 1. Let d be ((-22)/8 - -3)*4. Let i be z(d). Factor 1/3*y**3 - 1/3*y - 1/3*y**4 + 0 + 1/3*y**i.
-y*(y - 1)**2*(y + 1)/3
Suppose 1 = n + 4. Let m = n - -5. Suppose 0*l - 3*l + 1 + 0*l + 3*l**m - l**3 = 0. Calculate l.
1
Suppose 4*n - 3*n = 2. Determine i, given that 0*i**3 + 0*i + 6*i**4 + 3*i**3 - 3*i - 3*i**4 - 9*i**n + 6 = 0.
-2, -1, 1
Let u = -140/9 - -148/9. Let y(p) be the first derivative of -1/3*p**2 - u*p**3 - p**4 - 1/9*p**6 + 1 - 8/15*p**5 + 0*p. Factor y(c).
-2*c*(c + 1)**4/3
Let 4/11*r + 0 + 2/11*r**2 = 0. Calculate r.
-2, 0
Let l(i) be the first derivative of 2*i**5/35 - i**4/14 - 10*i**3/21 - 3*i**2/7 - 2. Solve l(a) = 0.
-1, 0, 3
Let d(v) be the second derivative of -v**6/360 - v**2 + v. Let r(z) be the first derivative of d(z). Let r(m) = 0. Calculate m.
0
Let o(u) be the first derivative of -4*u**3/15 + 2*u**2/5 + 6. Determine n, given that o(n) = 0.
0, 1
Let u(k) be the third derivative of -k**9/30240 - k**8/2520 - k**7/504 - k**6/180 + k**5/60 + 3*k**2. Let x(t) be the third derivative of u(t). Factor x(o).
-2*(o + 1)**2*(o + 2)
Let v(c) be the first derivative of c**6/15 + 2*c**5/25 - c**4/5 + 14. Let v(h) = 0. What is h?
-2, 0, 1
Let f(a) = -a**4 + a**2 - a. Let l(b) = 2*b**4 + 21*b**3 - 59*b**2 + 65*b - 24. Let o(h) = 5*f(h) + l(h). Factor o(c).
-3*(c - 2)**3*(c - 1)
Factor -5/4 + 1/4*z**2 - z.
(z - 5)*(z + 1)/4
Suppose -2*c - 2*x + x = -11, -5*c = -3*x - 33. Let y be ((-4)/c)/((-4)/12). Factor -b**3 + 3*b + b + 4 - 3*b**y + 0*b - b**3 + b**4.
(b - 2)**2*(b + 1)**2
Find n such that 6/5*n**2 + 4/5 + 1/5*n**3 + 9/5*n = 0.
-4, -1
Let o = 24 + -17. Suppose -3*t + o = 1. Factor 1/3*k**4 + 0 + 1/3*k**3 + 0*k**t + 0*k.
k**3*(k + 1)/3
Let g = -3 - -4. Let z = g - -3. Let 3*n**2 + n + n**3 + n**z + n**3 + n**3 = 0. What is n?
-1, 0
Let i(u) be the second derivative of -2*u + 0 + 1/10*u**4 + 2/15*u**3 + 1/150*u**6 + 1/25*u**5 + 1/10*u**2. Factor i(o).
(o + 1)**4/5
Let g(y) be the third derivative of y**5/20 - 4*y**4 + 128*y**3 + 24*y**2. Factor g(v).
3*(v - 16)**2
Let l = -275/2 - -138. Let 1/2*s**2 + 0 + l*s = 0. Calculate s.
-1, 0
Let k(o) = 11*o**2 + 21*o + 1. Let m(n) = -3*n**2 - 5*n. Let f(v) = -v. Let s be f(7). Let r be 0/(-1) - (s - 2). Let z(h) = r*m(h) + 2*k(h). Factor z(c).
-(c + 1)*(5*c - 2)
Suppose 2*d = -2*d - 2*a + 16, -5*d + 20 = -4*a. Suppose -2*b + i - 2 + 4 = 0, 0 = b - 3*i + 4. What is u in -1 + b*u - 4 + 3*u**2 - d*u**2 + 4 = 0?
1
Suppose -4*k + 7*k = 0. Suppose -3*n - n + 2*j + 20 = 0, -5*j - 20 = k. Factor -5*u**4 + 2*u**4 + 2*u**2 - 4*u**5 + 3*u**5 + 3*u - 2*u**n + 0*u**5 + 1.
-(u - 1)*(u + 1)**4
Suppose 2*q = 4 + 4. Suppose 4 = -3*x + q*x. Solve 0*w**x - w**5 + 2 + 2*w**4 + 2*w**3 - 3*w**2 - w**2 - 3*w + 2*w = 0.
-1, 1, 2
Let u be (-14)/(-11) - 0/3. Factor 16/11*i**3 - u*i**4 - 4/11*i - 4/11*i**2 + 4/11*i**5 + 2/11.
2*(i - 1)**4*(2*i + 1)/11
Let a(l) = l**2. Let n(i) = -3*i**3 - 18*i**2 + 3*i + 6. Let z(f) = -12*a(f) - n(f). Factor z(b).
3*(b - 1)*(b + 1)*(b + 2)
Let s = -210/31 + 3489/62. Find m such that s*m**3 - 75/4*m**5 + 15/4*m**4 + 0 + 33*m**2 + 6*m = 0.
-1, -2/5, 0, 2
Let v = 22 + -16. Let k(h) = 7*h**2 + 5. Let t(d) = -4 + 1 - 3*d**2 - d**2. Let u(q) = v*k(q) + 10*t(q). Determine i so that u(i) = 0.
0
Let i(l) be the first derivative of -l**6/120 - l**5/20 - l**4/12 + l**2 - 2. Let q(c) be the second derivative of i(c). Suppose q(n) = 0. What is n?
-2, -1, 0
Let k(z) be the first derivative of z**4/28 + 5*z**3/21 - z**2/14 - 5*z/7 - 55. Suppose k(x) = 0. Calculate x.
-5, -1, 1
Let q = -482/3 + 162. Let h(p) be the first derivative of -4/5*p**5 + 0*p + q*p**3 + p**2 + 0*p**4 - 1/3*p**6 - 1. Find b such that h(b) = 0.
-1, 0, 1
Let l(p) be the third derivative of -5*p**8/336 + p**6/24 - p**2. Factor l(g).
-5*g**3*(g - 1)*(g + 1)
Let t(p) = -3*p + 1. Let w be t(-1). Factor 2*j**3 - 2*j**w + 2*j**3 - 2*j**2 + 0*j**2.
-2*j**2*(j - 1)**2
Let t be -2*((-21)/(-6) - 3). Let s be 1 + 2 + 2 + t. Factor m**2 + m**2 - 2*m**5 + m**3 + 3*m**5 - 2*m**s - 2*m**3.
m**2*(m - 2)*(m - 1)*(m + 1)
Let f(m) be the second derivative of -11/2*m**4 - 4*m**2 + 0 - 2*m + 9/5*m**5 + 20/3*m**3. Find z, given that f(z) = 0.
1/2, 2/3
Let k(l) be the second derivative of -l**6/900 + l**5/75 - l**4/15 - 5*l**3/3 - 3*l. Let a(u) be the second derivative of k(u). What is f in a(f) = 0?
2
Suppose 2*s + 9 = 5*s. Let q(g) = g + 1. Let l be q(s). Factor -o**5 - 4*o**4 - o**4 + 3*o**l + o**4.
-o**4*(o + 1)
Let c(f) = -8*f**3 + 64*f**2 - 119*f + 9. Let q(u) = -2*u**3 + 16*u**2 - 30*u + 2. Let k(p) = 4*c(p) - 18*q(p). Factor k(y).
4*y*(y - 4)**2
Find p, given that 9*p**3 - 3*p - 40*p**4 + 13*p**4 - 9*p - 8*p**2 + 32*p**2 = 0.
-1, 0, 2/3
Suppose 4*y = 5*y - 3. Determine o so that y*o - 4*o**2 + 7 - 2 - 10*o**3 - 1 + 7*o = 0.
-1, -2/5, 1
Let z(h) be the second derivative of h**5/210 - h**3/21 - 3*h**2/2 + 8*h. Let d(a) be the first derivative of z(a). What is u in d(u) = 0?
-1, 1
Suppose -15 = 19*j - 53. Solve 24/7*h**5 + 8/7 + 264/7*h**3 + 218/7*h**j + 134/7*h**4 + 72/7*h = 0 for h.
-2, -1, -1/3, -1/4
Let h(a) be the first derivative of -2*a**3/27 - 2*a**2/3 - 16*a/9 - 28. Factor h(g).
-2*(g + 2)*(g + 4)/9
Let m(z) be the first derivative of -3 + 1/2*z**2 + 0*z - 1/30*z**4 + 1/150*z**5 + 0*z**3. Let t(y) be the second derivative of m(y). Solve t(f) = 0 for f.
0, 2
Let t be 3*((-14)/6 + -1). Let g = t + 12. Factor -l - 1/2*l**g - 1/2.
-(l + 1)**2/2
Let x = -1 + 5. Factor 4*s**3 - x*s**2 - 2*s**3 - 5*s**2 - 5*s**3.
-3*s**2*(s + 3)
Suppose 0 = -t + 5*t - 12. Let w = 4 - -2. Determine x so that t*x**2 - 4*x**3 - 4*x**2 - w*x**4 + 3*x**2 = 0.
-1, 0, 1/3
Let w(c) be the third derivative of -c**7/315 - c**6/54 + 5*c**4/54 + c**3/9 - 4*c**2. Determine t, given that w(t) = 0.
-3, -1, -1/3, 1
Let z = -6 - -13. Suppose 4*a + 29 = 5*j, 2*j = z*j + 5*a - 20. Factor -2*i**3 + 2*i**4 - 3*i**4 + 3*i**5 + i**2 - i**j.
i**2*(i - 1)*(i + 1)*(2*i - 1)
Let o = 20 + -11. Let m(z) = z**3 - 5*z**2 - 6*z + 2. Let t(g) = -3*g**3 + 21*g**2 + 24*g - 9. Let f(k) = o*m(k) + 2*t(k). Determine x so that f(x) = 0.
-1, 0, 2
Let d(h) be the third derivative of 0*h + 3/40*h**5 + 3*h**2 + 3/448*h**8 - 1/3*h**3 - 23/480*h**6 - 1/70*h**7 + 0 + 1/8*h**4. Suppose d(n) = 0. What is n?
-1, 2/3, 2
Solve 66*t**3 - 14*t**3 + 210*t**2 - 705*t**4 + 3*t**3 + 710*t**4 + 200 + 340*t = 0 for t.
-5, -2
Let o(x) = x**3 - 4*x**2 + 3*x + 2. Let y be o(3). Let 0 + 0*z - 2/3*z**y - 2/3*z**3 = 0. What is z?
-1, 0
Let z be 9/18 - (-10 - 3). Determine o so that 27/2*o + 9/2*o**2 + 1/2*o**3 + z = 0.
-3
Let h(r