. Determine a so that -4*a - r*a**2 + 5*a**2 - 3*a**2 + 4*a**2 + 2 = 0.
1
Let v(c) be the first derivative of c**8/5040 - c**7/840 + c**6/360 - c**5/360 + c**3/3 + 2. Let b(w) be the third derivative of v(w). Factor b(k).
k*(k - 1)**3/3
Factor 0 - 4/3*k**3 + 2*k**2 + 0*k + 2/9*k**4.
2*k**2*(k - 3)**2/9
Let c(x) = -5*x**3 - 30*x**2 - 43*x - 18. Let z(f) = 35*f**3 + 210*f**2 + 300*f + 125. Let q(u) = 15*c(u) + 2*z(u). Suppose q(h) = 0. What is h?
-4, -1
Let t(y) be the third derivative of -y**6/240 - y**5/120 + 5*y**4/48 - y**3/4 + y**2. Let t(q) = 0. What is q?
-3, 1
Suppose 2*x = -3*r - 11, 4*x - 28 = 3*r - 5. Determine i, given that 0*i**4 - 3*i**4 - i**3 + i - i**x + 4*i**4 = 0.
-1, 0, 1
Let r(a) = -a**3 - 2*a**2 + 3*a + 2. Let j be r(-3). Let -3*s - 12*s**3 - 8*s**2 - 8*s**4 + s - 2*s**5 - 2*s + j*s = 0. Calculate s.
-1, 0
Let c = 119 + -117. Factor 2/3*t**4 - 4/3*t + 4/3*t**3 + 0*t**c - 2/3.
2*(t - 1)*(t + 1)**3/3
Let m(b) = -b**2 - 4*b + 5. Let n be m(-5). Factor -4/9*k**2 + n*k**3 + 4/9*k**4 - 2/9*k**5 + 0 + 2/9*k.
-2*k*(k - 1)**3*(k + 1)/9
Let u(q) be the third derivative of -q**8/10080 + q**7/4200 + q**6/900 + q**5/20 + 3*q**2. Let w(f) be the third derivative of u(f). Let w(a) = 0. Calculate a.
-2/5, 1
Let i(w) be the first derivative of -w**8/5880 - w**7/980 + w**5/105 - w**3 + 1. Let u(s) be the third derivative of i(s). Factor u(t).
-2*t*(t - 1)*(t + 2)**2/7
Suppose 6*d - d - 30 = 0. What is w in d*w**4 + 6*w**2 - 8*w**4 + 1 + 2*w**3 + 3 - 10*w = 0?
-2, 1
Let s(a) be the third derivative of -a**10/10080 - a**9/5040 + a**8/2240 + a**7/840 - a**4/24 - a**2. Let h(k) be the second derivative of s(k). Factor h(x).
-3*x**2*(x - 1)*(x + 1)**2
Let m(h) be the first derivative of -2/5*h**5 + 0*h**3 + 0*h**2 + 0*h**4 + 0*h - 1/3*h**6 - 10. Factor m(c).
-2*c**4*(c + 1)
Let p be ((-20)/(-25))/(4/10). Let 2/11*j**3 + 0*j - 2/11*j**5 - 6/11*j**4 + 14/11*j**p - 8/11 = 0. What is j?
-2, -1, 1
Let t(x) be the third derivative of -x**8/2184 - 2*x**7/1365 + 7*x**6/780 + 2*x**5/39 + x**4/13 + 47*x**2. Find d, given that t(d) = 0.
-2, -1, 0, 3
What is s in -2/3*s**3 + 1/3*s**4 + 0*s**2 + 2/3*s - 1/3 = 0?
-1, 1
Let t(u) = u**2 + u + 2 - 2 - 1. Let a(z) = -3*z**2 + 3*z - 1. Let w be 1*(2 + (-7 - -4)). Let c(f) = w*t(f) - a(f). Factor c(q).
2*(q - 1)**2
Find m such that -3*m**2 + 6*m + 9 - 18 + 2*m**2 = 0.
3
Let x = -4 - -8. Factor -21*d - 4*d**2 + 9*d - 4 - x.
-4*(d + 1)*(d + 2)
Let f(c) be the third derivative of c**7/2520 - c**6/480 + c**5/240 - c**4/288 + 35*c**2. Find j such that f(j) = 0.
0, 1
Let m(i) be the third derivative of i**7/840 - i**6/160 + i**4/24 + 22*i**2. Factor m(h).
h*(h - 2)**2*(h + 1)/4
Let l(b) = -b**3 + 28*b**2 - 25*b - 54. Let q be l(27). Let t be 1 + -2 - (0 - 3). Factor q*n**3 + 1/3*n**t - 1/3*n**4 + 0*n + 0.
-n**2*(n - 1)*(n + 1)/3
Let n(r) = r - 6. Let u = 19 + -11. Let j be n(u). Factor 0*l**j + 4*l + l**2 - 5*l - 2.
(l - 2)*(l + 1)
Let z(n) be the third derivative of n**8/1680 + n**7/1260 - n**6/360 + n**4/6 + 5*n**2. Let h(x) be the second derivative of z(x). Solve h(f) = 0.
-1, 0, 1/2
Let x = -3 - -5. Find s such that 0 + 14*s**2 - 12*s**x + 0 = 0.
0
Let j = -82 - -248/3. Let a(w) = -52*w - 50. Let l be a(-1). Determine x, given that -j*x**l - 2/3*x + 0 = 0.
-1, 0
Let c = -48/5 - -49/5. Factor -2/5 - 9/5*k**2 + 7/5*k + k**3 - c*k**4.
-(k - 2)*(k - 1)**3/5
Factor 3/2*n**4 + 0 + 63/2*n**2 + 12*n**3 + 27*n.
3*n*(n + 2)*(n + 3)**2/2
Let i(t) be the first derivative of 7*t**5/25 - t**4/10 - 7*t**3/15 + t**2/5 + 26. Factor i(x).
x*(x - 1)*(x + 1)*(7*x - 2)/5
Let r(f) = -5*f**4 + 8*f**3 + 2*f**2 - 8*f + 1. Let b(x) = x**4 - x**3 - x**2 + x + 1. Let t(s) = 2*b(s) + r(s). Factor t(q).
-3*(q - 1)**3*(q + 1)
Let r(i) be the first derivative of i**5/40 - 7*i**4/32 + 5*i**3/8 - 13*i**2/16 + i/2 - 13. Find p, given that r(p) = 0.
1, 4
Factor -8*j - 11*j + 3*j + j - 5*j**2.
-5*j*(j + 3)
Let g be (-2 + 3 + -3)*-1. Let p be (-6)/(-15)*1 + 0. Solve -6/5*u**g + 0*u + 4/5*u**3 + p = 0.
-1/2, 1
Factor -5*g**4 + 20*g + 18*g**2 - 6*g**2 - 12*g**2 - 15*g**3.
-5*g*(g - 1)*(g + 2)**2
Let d(i) be the first derivative of 121*i**5 - 385*i**4/4 - 200*i**3/3 - 10*i**2 - 12. Let d(m) = 0. What is m?
-2/11, 0, 1
Let r(k) be the third derivative of -k**6/300 + k**5/50 - k**4/20 + k**3/15 - 7*k**2. Find j such that r(j) = 0.
1
Let p = 3 - 9. Let l = -6 - p. Factor l*q**2 + 2/9*q**4 + 0*q + 0 + 2/9*q**3.
2*q**3*(q + 1)/9
Let d(y) = 9*y**3 + 18*y**2 + 3*y - 3. Let f(r) = -r**4 - r**3 + r**2 - r - 1. Let s(v) = -d(v) + 3*f(v). What is w in s(w) = 0?
-2, -1, 0
Suppose -750 = -3*f - 0*f. Let a be 2/3*f/20. Determine l, given that -8*l**2 - 4/3*l + 0 - 15*l**3 - a*l**4 = 0.
-1, -2/5, 0
Let g(q) be the third derivative of -q**8/6720 - q**7/840 + q**6/80 + q**5/60 + 6*q**2. Let i(o) be the third derivative of g(o). Factor i(b).
-3*(b - 1)*(b + 3)
Let x = 2 + 3. Find i such that -2*i**5 + 7*i**3 - 3*i**3 + 3*i**5 + 3*i**x + 8*i**4 = 0.
-1, 0
Let j(v) be the first derivative of 23/4*v**4 + v**5 + 2*v**2 + 1 - 8*v + 10*v**3. Factor j(i).
(i + 1)*(i + 2)**2*(5*i - 2)
Let s(y) = y**5 - y**4 + y**3 + y**2 + y - 1. Let h(c) = -c**5 + 7*c**4 - c**3 - 3*c**2 - 3*c + 3. Let f(x) = 2*h(x) + 6*s(x). Factor f(w).
4*w**3*(w + 1)**2
Let p(i) be the first derivative of 0*i + 2 + 0*i**2 + 1/3*i**3. Factor p(t).
t**2
Let p(b) = -b**3 + b**2 - b. Let t be (-9)/(-2)*4/(-3). Let x(i) = 4*i**3 - 4*i**2 + 10*i. Let w(k) = t*p(k) - x(k). Find l, given that w(l) = 0.
-1, 0, 2
Let k(u) = 12*u**2 + 33*u + 3. Let j(s) = -3*s**2 - 8*s - 1. Let a(r) = -9*j(r) - 2*k(r). Determine q, given that a(q) = 0.
-1
Let c(s) be the second derivative of 4/3*s**4 + 9*s + s**2 + 0 + 7/20*s**5 + 11/6*s**3. Factor c(n).
(n + 1)**2*(7*n + 2)
Let -6/5*k + 8/5*k**4 - 8/5*k**2 + 4/5*k**3 + 2/5*k**5 + 0 = 0. What is k?
-3, -1, 0, 1
Let -4/5*p**3 - p**2 + 0 - 2/5*p - 1/5*p**4 = 0. Calculate p.
-2, -1, 0
Let p(o) = o**4 - 4*o**3 - 9*o**2 + 4*o + 11. Let n(m) = 6*m**4 - 23*m**3 - 53*m**2 + 24*m + 65. Let k(u) = -6*n(u) + 34*p(u). Suppose k(f) = 0. Calculate f.
-2, -1, 2
Let s = 26 + -23. Solve 4*a**2 + a**2 - 5*a**2 + 3*a - 3*a**s = 0.
-1, 0, 1
Let z be (-16)/(-10) + (-10)/(-25). Find k, given that 3*k**5 - 2*k - 9*k**5 + 2*k**5 + 4*k**z - 4*k**4 + 6*k**5 = 0.
-1, 0, 1
Let c(z) = 2*z**2 - 4*z - 2. Suppose 0 = -3*q + m - 4*m - 3, 3*m = q + 9. Let x(u) = -2*u**2 + 4*u + 3. Let r(l) = q*c(l) - 2*x(l). Factor r(i).
-2*i*(i - 2)
Factor j**2 + 3*j**2 - 7*j**4 - 4*j**3 + j**4 + 1 + 1 - 2*j**5 + 6*j.
-2*(j - 1)*(j + 1)**4
Let w(q) = -11*q - 52. Let i be w(-5). Factor 0 + 0*o - 1/5*o**2 + 1/5*o**i.
o**2*(o - 1)/5
Let g(b) be the first derivative of -16*b**3/3 - 18*b**2 - 8*b + 4. Factor g(s).
-4*(s + 2)*(4*s + 1)
Let k(b) = -8*b**2 + b**2 + 5*b**2 + b**2 - b. Let v(h) be the first derivative of -h**3 - 2*h**2 + 1. Let l(i) = 4*k(i) - v(i). Factor l(z).
-z**2
Let m = 1 + 2. Let j(w) = 4*w**4 + 4*w**3 + 2. Let u(f) = 5*f**4 + 5*f**3 + f**2 + f + 3. Let x(i) = m*j(i) - 2*u(i). Determine s, given that x(s) = 0.
-1, 0, 1
Let k = -7067/95 - -373/5. Find i such that -2/19*i**2 + k*i + 6/19 = 0.
-1, 3
Let h(r) = r + 15. Let p be h(-10). Let y be 3/2 - p/(-10). Determine g so that 1/4 + 1/2*g**y - 3/4*g = 0.
1/2, 1
Let c(v) = -v**3 - 2*v**2 + v - 1. Let k be -7 + 3 + (1 - 1). Let l = k - -7. Let x(o) = -o**3 - 3*o**2 + o - 1. Let m(s) = l*x(s) - 4*c(s). Factor m(y).
(y - 1)**2*(y + 1)
Let o be 115/150 - (-10)/(-15). Let v(k) be the second derivative of 0*k**4 + 0*k**2 + 4/15*k**6 + 2*k + 0*k**3 + o*k**5 + 0. Factor v(s).
2*s**3*(4*s + 1)
Determine u so that -9/4*u + 1/2 - 5/4*u**2 = 0.
-2, 1/5
Let z(l) be the second derivative of l**4/6 - l**3/3 - l**2 + 2*l. Let r be z(2). Factor 2*y**2 + 0*y**2 + 2*y**2 - y**r - 3*y.
3*y*(y - 1)
Let p(r) be the second derivative of -r**4/4 - r**3/3 + r**2/2 - 10*r. Factor p(s).
-(s + 1)*(3*s - 1)
Let u(v) be the second derivative of -v**4/3 + 4*v**3/3 - 2*v**2 - 7*v. Factor u(p).
-4*(p - 1)**2
Let i(j) be the third derivative of 0*j**5 + 2*j**2 + 0*j + 0*j**3 + 0*j**4 + 0 + 0*j**7 + 0*j**6 - 1/336*j**8. Determine k, given that i(k) = 0.
0
Suppose -6*a = -11 - 7. Suppose 4/5*n**a + 6/5*n**2 + 1/5*n**4 + 4/5*n + 1/5 = 0. What is n?
-1
Let s = 185/497 + 4/71. Factor s*b**2 + 0*b - 3/7.
3*(b - 1)