. Determine a, given that -1/2*a**3 + 2 - 7/2*a**2 + y*a**4 + 1/2*a**5 + 0*a = 0.
-2, -1, 1
Suppose 4*n - 2*t + 2 = -4*t, -5*n - 5 = 3*t. Determine g so that 0*g**n + 4/3*g - 2/3*g**4 + 2/3 - 4/3*g**3 = 0.
-1, 1
Factor -70*x + 95*x**2 - 5/2*x**5 + 20 - 125/2*x**3 + 20*x**4.
-5*(x - 2)**3*(x - 1)**2/2
Let r(u) be the third derivative of -3*u**6/40 + u**5/4 - u**4/8 - u**3/2 - 4*u**2. Find i such that r(i) = 0.
-1/3, 1
Let f(l) be the first derivative of 5 - 1/5*l**3 + 3/5*l + 0*l**2. Factor f(s).
-3*(s - 1)*(s + 1)/5
Let s be 1 - -15*(-5)/165. Factor 0 - 2/11*h**2 - s*h.
-2*h*(h + 3)/11
Factor -2/7*h**3 + 0 + 0*h + 1/7*h**4 + 0*h**2.
h**3*(h - 2)/7
Let o(y) be the first derivative of -3/8*y**4 + 0*y - 1/4*y**2 + 1/10*y**5 + 4 + 1/2*y**3. Factor o(m).
m*(m - 1)**3/2
Let k(g) be the first derivative of 4/15*g**5 + 4/9*g**3 - 1/18*g**6 + 0*g - 1/2*g**4 - 1/6*g**2 - 8. Let k(w) = 0. What is w?
0, 1
Let i(v) = -v + 2. Let c be i(0). Let h be (-3)/12 - (-1)/4. Solve t**3 + 3*t - 1 + h*t**3 + 2*t**c - 5*t**2 = 0.
1
Let m(x) = -x - 1. Suppose -2*d - 3*d = k - 17, 2*k + 2 = -d. Let c be m(k). Factor 13*l**3 + 3 - 3 - 4*l**3 - 7*l**c - 2*l.
l*(l - 1)*(9*l + 2)
Let f(b) = -3*b + 6. Let s(a) be the third derivative of a**5/60 + 5*a**4/24 - 11*a**3/6 + 4*a**2. Let p(k) = -5*f(k) - 3*s(k). Factor p(r).
-3*(r - 1)*(r + 1)
Let j(z) be the third derivative of 0 - 1/280*z**7 + 1/24*z**3 + 0*z + z**2 + 1/240*z**6 - 1/32*z**4 + 1/120*z**5 + 1/1344*z**8. Factor j(n).
(n - 1)**4*(n + 1)/4
Let m(f) be the second derivative of -f**6/5 + f**5/10 + f**4/2 - f**3/3 - 11*f. Find b, given that m(b) = 0.
-1, 0, 1/3, 1
Suppose -3*g**2 + 2*g**2 + 2*g**2 - 3 - 1563*g + 1561*g = 0. What is g?
-1, 3
Suppose 4 = -2*a + 4*a. Factor 2*u**4 + 8*u**3 - 4*u**3 + 2*u**2 + u**2 - u**a.
2*u**2*(u + 1)**2
Let r be (6/(-4))/(18/48). Let z be (1/r)/(2/(-4)). Factor 0*n**2 + 1/4 - 1/4*n**4 + z*n**3 - 1/2*n.
-(n - 1)**3*(n + 1)/4
Suppose 4*n + w = -70, 40 = -2*n + 4*w - 2*w. Let z be (-32)/n + (-6)/(-27). Determine y so that 1/2*y**5 + 0*y**z - y**3 + 0 + 0*y**4 + 1/2*y = 0.
-1, 0, 1
Factor -6*n**2 - 758 + 132*n - 694 + 8*n**2 - 5*n**2.
-3*(n - 22)**2
Solve 1/2*p - 1/8*p**2 - 1/2 = 0 for p.
2
Suppose 0 = 2*j - j - 3. Factor f**5 + 6*f**5 - 4*f**j - 3*f**5.
4*f**3*(f - 1)*(f + 1)
Let g(h) = h**2 - h. Let c(b) = 5*b**2 - 6*b + 1. Let f(s) = c(s) - 4*g(s). Solve f(t) = 0.
1
Let c be (9/(-6))/(27/(-12)). Factor 0 - 2/3*g - c*g**2.
-2*g*(g + 1)/3
Let g = 4 - 1. Factor k**3 + 3*k**4 - 5*k**4 - g*k**3.
-2*k**3*(k + 1)
Factor 1/2*s - 3/4 + 1/4*s**2.
(s - 1)*(s + 3)/4
Let k(x) = -x**2 + 14*x + 6. Let s(d) = -2*d**2 + 43*d + 17. Let w(t) = -17*k(t) + 6*s(t). Factor w(o).
5*o*(o + 4)
Factor 3*p + 111*p**2 + 53*p - 196 - 115*p**2.
-4*(p - 7)**2
Let o be ((-6)/(-9))/((-2)/(-18)). Find t such that -3*t**3 + t**2 + o*t**2 - 2*t**2 - 2*t**2 + 3*t - 3 = 0.
-1, 1
Let z(n) be the second derivative of -n**7/126 + n**5/20 - n**4/18 + 7*n. Suppose z(y) = 0. Calculate y.
-2, 0, 1
Let d(l) = l**3 - 7*l**2 + 8*l - 9. Suppose -8 - 16 = -4*t. Let y be d(t). Solve 1/4*m**2 - 1/4 + 1/4*m**y - 1/4*m = 0 for m.
-1, 1
Let a(v) be the second derivative of -1/6*v**3 + 1/20*v**5 + 1/12*v**4 - 1/2*v**2 - 3*v + 0. Solve a(k) = 0 for k.
-1, 1
Find z such that 2/9*z**2 + 2/3 + 8/9*z = 0.
-3, -1
Let w = 3 + -1. Factor 1 - d**w + 1 + 6*d - 3*d - 2*d.
-(d - 2)*(d + 1)
Let v be 4/8 + (-9)/6 + 3. Let p(j) be the third derivative of 0 + 1/24*j**4 + 0*j + j**v + 1/3*j**3 - 1/60*j**5. Suppose p(a) = 0. What is a?
-1, 2
Let p = 112 - 2015/18. Let l(w) be the first derivative of p*w**4 - 2/27*w**3 + 1 + 0*w + 0*w**2. Let l(y) = 0. Calculate y.
0, 1
Let y be 66/88 - 26/56. Solve -y*q**2 + 6/7 - 4/7*q = 0 for q.
-3, 1
Let z(v) = 4*v**3 + 4*v**2 - 4*v - 9. Let t(s) = -2*s**3 - 2*s**2 + 2*s + 4. Let x = -2 + 2. Let h = x - -5. Let c(n) = h*t(n) + 2*z(n). Factor c(l).
-2*(l - 1)*(l + 1)**2
Let d(i) be the first derivative of 2/5*i**5 - 1/2*i**4 + 4 + 0*i**2 + 2/9*i**3 - 1/9*i**6 + 0*i. Let d(p) = 0. What is p?
0, 1
Let m(j) = -22*j**2 + 120*j - 180. Let r(v) = -7*v**2 + 40*v - 60. Let f(i) = -2*m(i) + 7*r(i). Factor f(a).
-5*(a - 6)*(a - 2)
Let w be (6/18)/((-51)/18 - -3). Factor 1/7*b**w + 1/7*b**3 - 1/7 - 1/7*b.
(b - 1)*(b + 1)**2/7
Let c(n) = 2*n**2 + 2*n - 1. Let b be c(-2). Suppose -6*k = -8*k - 2*k. Factor -b + 3*x**2 + 4*x**2 - 4*x**2 + k*x**2.
3*(x - 1)*(x + 1)
Suppose -152*u**3 - 4*u**4 + 140*u**3 + 8*u**2 + 8*u**2 = 0. Calculate u.
-4, 0, 1
Let p be -36 + 26 - 68/(-6). Factor 4*n - 4/3 + p*n**3 - 4*n**2.
4*(n - 1)**3/3
Let q(u) be the first derivative of 1/2*u**3 - 2 + 1/8*u**4 - 3/10*u**5 - 1/4*u**2 + 0*u. Factor q(k).
-k*(k - 1)*(k + 1)*(3*k - 1)/2
Find z, given that 0*z**4 + 1/4*z**3 + 0*z + 0*z**2 + 0 - 1/4*z**5 = 0.
-1, 0, 1
Let n(g) be the second derivative of -g**7/56 + 3*g**5/40 - g**3/8 - 9*g. Factor n(i).
-3*i*(i - 1)**2*(i + 1)**2/4
Suppose 3*m - 3*j = -6, -4*j + 10 = -2*m - 0*m. Let g be (m/9)/((-9)/(-54)). Suppose 2/3*x + 1/3 - 4/3*x**2 - g*x**3 + x**4 = 0. Calculate x.
-1, -1/3, 1
Let m be -3 + ((-35)/(-2))/5. What is x in m*x - 1/2*x**3 - 3/2*x**2 + 0 + 3/2*x**4 = 0?
-1, 0, 1/3, 1
Let q(t) be the second derivative of -2*t**7/21 - 4*t**6/15 + 2*t**4/3 + 2*t**3/3 + 9*t. Find u such that q(u) = 0.
-1, 0, 1
Let j be 1/3*4/(-56)*-7. Let i(l) be the second derivative of 2/3*l**3 - l**2 - l - j*l**4 + 0. Factor i(t).
-2*(t - 1)**2
Let l(y) be the second derivative of -1/3*y**4 + 0 + 7*y - 11/6*y**3 + 3/2*y**2. Factor l(w).
-(w + 3)*(4*w - 1)
Factor 2/15*i**3 - 2/15*i - 2/15*i**4 + 0 + 2/15*i**2.
-2*i*(i - 1)**2*(i + 1)/15
Suppose 0 = 5*u - 4*u - 2*q - 4, -4*u = -q - 16. Factor 24*d**4 + 2*d**3 - 5*d**4 - 6*d**u - 11*d**4.
2*d**3*(d + 1)
Factor 3/7*n**4 - 6/7 - 9/7*n**3 + 3/7*n**2 + 9/7*n.
3*(n - 2)*(n - 1)**2*(n + 1)/7
Let t(d) be the second derivative of 0*d**2 - 8*d - 1/8*d**4 - 3/40*d**5 + 0*d**3 + 0. Solve t(y) = 0.
-1, 0
Let f(d) = -27*d**2 - 27*d - 15. Let q(u) = -7*u**2 - 7*u - 4. Let x(n) = -4*f(n) + 15*q(n). Find c such that x(c) = 0.
-1, 0
Let a(w) be the first derivative of 0*w + 2/15*w**5 + 0*w**2 - 1/6*w**4 - 5 + 0*w**3. Factor a(d).
2*d**3*(d - 1)/3
Let c = -3/10 - -31/70. Let g(a) be the second derivative of 0 - c*a**7 + 7/15*a**6 + 0*a**3 - 1/2*a**5 + 2*a + 0*a**2 + 1/6*a**4. Factor g(j).
-2*j**2*(j - 1)**2*(3*j - 1)
Let l(m) be the first derivative of 1/26*m**4 + 0*m**3 + 1/39*m**6 + 0*m - 7 + 0*m**2 - 4/65*m**5. Solve l(v) = 0 for v.
0, 1
Let s(j) = -5*j**4 + 10*j**3 + 10*j**2 - 10*j + 5. Let n(l) = 5*l**4 - 10*l**3 - 9*l**2 + 10*l - 4. Let p(i) = 5*n(i) + 4*s(i). Determine f so that p(f) = 0.
-1, 0, 1, 2
Solve -5 - 10*k**2 + 49*k**3 - 57*k**3 - 2*k + 5 = 0.
-1, -1/4, 0
Let r = 0 + -3. Let q = r + 6. Factor j**3 + j - 2 - 5*j**q + 2*j + 1.
-(j + 1)*(2*j - 1)**2
Suppose -8 = -2*o + 2. Let -i**o + 10*i**2 - 5*i + 4 - 4*i**3 - 6*i**3 + 5*i**4 - 3 = 0. What is i?
1
Let b(k) be the third derivative of -2*k**7/105 - k**6/15 + k**4/3 + 2*k**3/3 - 16*k**2. Let b(t) = 0. Calculate t.
-1, 1
Let m(l) = 2*l**5 + 5*l**4 + l**2 + l + 3. Let k(r) = 4*r**5 + 2*r**4 + 2*r**4 - 3*r**5 + 2 + r. Let b(q) = 3*k(q) - 2*m(q). Find x such that b(x) = 0.
-1, 0, 1
Let i(r) be the first derivative of 0*r + 1/10*r**5 - 1/8*r**4 + 1/4*r**2 - 1 - 1/6*r**3. Factor i(w).
w*(w - 1)**2*(w + 1)/2
Let m be ((-726)/(-18))/11 + 3*-1. Factor 5/3*h - h**2 - m - 1/3*h**3 + 1/3*h**4.
(h - 1)**3*(h + 2)/3
Factor -7*p**2 + 0*p**4 + 22*p**3 + 3*p**2 - 2*p - 8*p**4 - 8*p**3.
-2*p*(p - 1)**2*(4*p + 1)
Suppose 3*s - 4*o = -o - 24, 0 = s - 2*o + 12. Let p be (-1)/2 - s/4. Factor -c**3 - 1/2*c**4 - p + 1/2*c**5 + 1/2*c + c**2.
(c - 1)**3*(c + 1)**2/2
Let g(q) be the first derivative of q**4/20 - 4*q**3/15 + q**2/2 - 2*q/5 + 6. Factor g(a).
(a - 2)*(a - 1)**2/5
Factor 1 + 16*p + 2*p**3 - 10 - p - 7*p**2 - p**3.
(p - 3)**2*(p - 1)
Let i(c) = c**2 - c. Let x(m) = 4*m**2 + 14*m + 12. Let g(j) = i(j) - x(j). Factor g(n).
-3*(n + 1)*(n + 4)
Let q(o) = 6 - 2*o + o**2 - o - 2*o**2. Let n be q(-4). Factor 2/7*r**n - 2/7*r + 0.
2*r*(r - 1)/7
Let g(f) be the second derivative of f**4/48 - f**3/12 + f**2/8 - 7*f. Suppose g(z) = 0. Calculate z.
1
Let f(d) be the third derivative of -d**9/7560 + d**7/700 + d**6/450 + 7*d**3/6 + 3*d**2. Let u(p) be the first derivative