 + 3. Let a(i) = 1. Let z(t) = 3*a(t) - n(t). Factor z(d).
2*d**2
Suppose 0 = -3*o - 3 + 21. Let f(m) be the third derivative of 0*m - 11/21*m**4 + 0 + 9/245*m**7 + 3/7*m**5 - 27/140*m**o + 3*m**2 + 8/21*m**3. Factor f(d).
2*(d - 1)*(3*d - 2)**3/7
Let 72*p - 1/2*p**4 - 23*p**2 - 81/2 - 8*p**3 = 0. What is p?
-9, 1
Let 5/2*d - 2 - 1/2*d**2 = 0. Calculate d.
1, 4
Suppose 13*h - 3*h = 5*h. Let 2/3*z**2 + 0 - 2/3*z**4 + h*z**3 + 0*z = 0. What is z?
-1, 0, 1
Let -1/3*x**2 + 1/3*x**4 + 1/3*x + 0 - 1/3*x**3 = 0. What is x?
-1, 0, 1
Suppose 0 = -5*f - 15, 0*x = -x - 2*f. Let a(y) be the first derivative of 0*y**5 + 0*y + 1/9*y**2 + 1/27*y**x + 0*y**3 + 1 - 1/9*y**4. Factor a(k).
2*k*(k - 1)**2*(k + 1)**2/9
Let u(g) = 7*g**5 - 3*g**4 - 7*g**3 - 7*g**2 - 5. Let l(p) = -3*p**5 + p**4 + 3*p**3 + 3*p**2 + 2. Let z(n) = -15*l(n) - 6*u(n). What is h in z(h) = 0?
-1, 0, 1
Factor 10*a**2 + 64*a**3 - 5*a - 59*a**3 + 10*a.
5*a*(a + 1)**2
Let d(x) = -x + 8. Let z(o) = -2*o - 2. Let f be z(-4). Let j be d(f). Factor 14/11*u**4 - 2/11*u + 30/11*u**j - 38/11*u**3 - 4/11.
2*(u - 1)**3*(7*u + 2)/11
Let z(k) be the second derivative of -2/15*k**5 + 1/63*k**7 - 1/9*k**4 + 0 + 2*k + 1/3*k**3 + 0*k**6 + 2/3*k**2. Determine i, given that z(i) = 0.
-1, 1, 2
Let s(k) = -7*k**3 + 13*k**3 - 7*k**3 - k. Let n(x) = 4*x**3 - 6*x**2 + 6*x. Let l(p) = n(p) + 2*s(p). Determine o so that l(o) = 0.
0, 1, 2
Let p(l) = 3*l**5 - 12*l**4 - 5*l**3 - 4*l**2 + 7*l - 7. Let x(d) = -2*d**5 + 12*d**4 + 6*d**3 + 4*d**2 - 6*d + 6. Let y(z) = 6*p(z) + 7*x(z). Factor y(f).
4*f**2*(f + 1)**3
Let l(f) = 7*f**5 + 4*f**4 + 2*f**2 - 7*f - 6. Let t(q) = q**5 + q**4 - q - 1. Let u(m) = l(m) - 6*t(m). Let u(r) = 0. What is r?
-1, 0, 1
Let x be (-8)/20 + 41/90. Let b(c) be the second derivative of 2*c - 1/60*c**5 + 0*c**2 + x*c**3 + 1/90*c**6 + 0 - 1/36*c**4. Factor b(d).
d*(d - 1)**2*(d + 1)/3
Let b(q) be the first derivative of -q**3/3 - 4*q**2 - 16*q + 2. Determine k, given that b(k) = 0.
-4
Let f(m) = 2*m**3 - 9*m**2 - 11*m. Let x be 3/(6/(-14)) - -1. Let y = 0 + x. Let a(d) = d**3 - 4*d**2 - 5*d. Let c(k) = y*f(k) + 13*a(k). Factor c(g).
g*(g + 1)**2
Let b(r) = -5*r**3 + 75*r**2 - 381*r + 631. Let i(p) = 45*p**3 - 675*p**2 + 3430*p - 5680. Let z(u) = 55*b(u) + 6*i(u). Factor z(f).
-5*(f - 5)**3
Let m(u) be the third derivative of u**7/105 - u**6/60 + 7*u**2. Factor m(j).
2*j**3*(j - 1)
Suppose 3*m - 3*s + 2 = -1, m - 2*s = -4. Factor -7*c**m + c**3 + 12*c**2 - 6*c**2.
c**2*(c - 1)
Let x = 14 - 14. Factor x - 2/5*z**2 - 2/5*z.
-2*z*(z + 1)/5
Let z = 4 + -4. Suppose z*i + 2*i**2 - 5*i + 3*i = 0. What is i?
0, 1
Suppose 3*j + 2*j = 0. Let l(a) be the second derivative of 0*a**3 + 0*a**2 + j + 1/18*a**4 + a. Find s such that l(s) = 0.
0
Let t(z) be the third derivative of -z**6/540 - z**5/45 - 11*z**4/108 - 2*z**3/9 + 33*z**2. Factor t(v).
-2*(v + 1)*(v + 2)*(v + 3)/9
Suppose 9*a - 21 = -21. Factor -1/6*j**2 + a*j**4 + 0 - 2/3*j**5 + 0*j + 1/2*j**3.
-j**2*(j + 1)*(2*j - 1)**2/6
Let v(o) = -3*o**5 - 8*o**4 + 10*o**2 + 5*o - 2. Let f(h) = -5*h**5 - 15*h**4 + 20*h**2 + 10*h - 5. Let d(u) = -2*f(u) + 5*v(u). Solve d(b) = 0 for b.
-1, 0, 1
Let j(g) = 3 + g**2 - 2 + 2 - 5*g - 1. Let s be j(5). Factor 6 - 6 - 6*a**3 - 2*a**s - 6*a**4 - 2*a**5.
-2*a**2*(a + 1)**3
Let r(p) be the third derivative of p**6/120 + p**5/30 - p**4/24 - p**3/3 - p**2. Let r(t) = 0. Calculate t.
-2, -1, 1
Let x(d) be the first derivative of 0*d + 1/9*d**3 - 1/15*d**5 + 3 + 1/6*d**2 - 1/12*d**4. Determine a so that x(a) = 0.
-1, 0, 1
Find j such that -3/4*j**3 + 3/2*j - 3/4*j**2 + 0 = 0.
-2, 0, 1
Factor -2*n**2 - n - 18 - 7 - n + 29.
-2*(n - 1)*(n + 2)
Let i = -2031 + 54845/27. Let y(x) be the first derivative of i*x**3 + 1/9*x**2 + 1 + 0*x. Factor y(n).
2*n*(4*n + 1)/9
Let n(b) = b**2 - 2*b - b + 7*b + 3. Let l be (-20)/(-12) + (-1)/(-3). Let r(z) = z**2 + 3*z + 2. Let q(g) = l*n(g) - 3*r(g). Factor q(i).
-i*(i + 1)
Let i(h) be the first derivative of h**5/18 + h**4/3 + 4*h**3/9 - 5*h**2/2 + 4. Let f(o) be the second derivative of i(o). Find s, given that f(s) = 0.
-2, -2/5
Let t = 47 - 44. Let w(p) be the first derivative of 3 - p**3 + t*p - 3/2*p**2 + 3/4*p**4. Factor w(f).
3*(f - 1)**2*(f + 1)
Let m = 75 + -13. Let o = -37 + m. Solve -o*k**3 - k**5 - 1 - 19*k**2 - 2*k**5 - k**5 - 7*k - 16*k**4 = 0 for k.
-1, -1/2
Let u(r) = -4*r**4 - 8*r**3 - 6*r**2 - 2. Suppose v = 6*v - 45. Let f(k) = -17*k**4 - 33*k**3 - 24*k**2 + k - 9. Let s(h) = v*u(h) - 2*f(h). Factor s(m).
-2*m*(m + 1)**3
Let n(m) be the first derivative of -1/2*m**4 + 1/2*m**2 + 0*m + 1/6*m**6 + 0*m**3 - 3 + 0*m**5. Factor n(k).
k*(k - 1)**2*(k + 1)**2
Let o(f) = 4*f + 3. Let v be o(-2). Let p = -5 - v. Let -2/7*q**3 + p*q**2 + 2/7*q + 0 = 0. Calculate q.
-1, 0, 1
Let p be (-13)/5 - (-5 + 1). Let v(o) be the second derivative of 0 + 2*o**2 - 3/7*o**7 + p*o**5 - 4/3*o**4 - 5/3*o**3 - o + 2/5*o**6. Solve v(u) = 0 for u.
-1, -2/3, 1/3, 1
Suppose 23*u - 24*u + 2 = 0. Determine g, given that 2/9*g**u + 2/9*g - 2/9*g**3 - 2/9 = 0.
-1, 1
Let w(k) = -2*k + 0*k + 3*k**3 - 2*k**2 + 3*k. Let v be w(1). Factor -3*o + 2 + 0 + o**v + 0.
(o - 2)*(o - 1)
Let h(q) = 2 - q + 2 + q**2 - 1 - q**3. Let r be h(0). Factor -r + 2*w - 5*w**2 + 4*w**2 + 2.
-(w - 1)**2
Let c be (-5)/9*(-6)/15. Factor 2/9*w**3 + 0*w - c*w**2 + 0.
2*w**2*(w - 1)/9
Let w(s) = 6*s**4 - 12*s**3 + 14*s**2 - 8*s - 4. Let j(c) = -25*c**3 - 17*c - 7 + 13*c**4 - 2 + 10*c**2 + 19*c**2. Let i(l) = 4*j(l) - 9*w(l). Factor i(m).
-2*m*(m - 2)*(m - 1)**2
Suppose 2*v - 12 = -2. Let y = v + 0. Factor -2*r**3 + 0*r**3 - y*r**2 + r**2.
-2*r**2*(r + 2)
Let s(z) = -3*z**5 + 4*z**4 - 4*z**2 - 3*z + 4. Let f(m) = -10*m**5 + 13*m**4 - m**3 - 12*m**2 - 10*m + 13. Let y(j) = 2*f(j) - 7*s(j). Factor y(u).
(u - 2)*(u - 1)**2*(u + 1)**2
Suppose 0 = -h - 4*y + 4, -4*h - y - 1 + 2 = 0. Find i such that 0*i + 1/2*i**4 + i**5 + h - i**3 - 1/2*i**2 = 0.
-1, -1/2, 0, 1
Let o(z) be the third derivative of -z**5/480 + z**4/192 - 23*z**2. Factor o(n).
-n*(n - 1)/8
Let z(v) be the first derivative of -v**7/210 + v**6/60 - v**5/60 - 2*v**2 + 3. Let b(u) be the second derivative of z(u). Factor b(h).
-h**2*(h - 1)**2
Suppose 0 = 4*u + 4*l - 4, -2*u - 4*l + 0 = 4. Factor 0*w + 0 + 2/5*w**3 - 1/5*w**u - 1/5*w**2.
-w**2*(w - 1)**2/5
Let h be (1 - 65/25)*-3. Find v, given that 0 + 8/5*v**2 + h*v**3 + 2*v**4 + 0*v = 0.
-2, -2/5, 0
Let d(r) = -r**2 - r + 2. Let l be d(-2). Let q be 2 + (l - -1)*1. Determine x, given that x + 0*x - 1 + 5*x**2 - 4*x**q + 3*x**3 - 4*x**2 = 0.
-1, 1
Let l(i) = 28*i**4 - 60*i**3 - 32*i**2 + 80*i + 40. Let k(p) = -p**4 + p**3 + p**2 - 1. Let q(s) = 8*k(s) + l(s). Find j such that q(j) = 0.
-1, -2/5, 2
Let j(z) = 31*z + 29*z - 22*z - 18*z**2 - 5 - 15. Let w(d) = -6*d**2 + 13*d - 7. Let c(l) = -3*j(l) + 8*w(l). Find p, given that c(p) = 0.
2/3, 1
Suppose -21 = -a + 5*w, a - 4*a - w = 1. Let t be a/(-2) - (-3)/6. Suppose t*r**3 + 5*r - 3*r - 2*r**3 = 0. Calculate r.
-1, 0, 1
Determine j, given that 28/3*j**3 - 28/3*j + 8/3 - 8/3*j**2 = 0.
-1, 2/7, 1
Let i = 13 + -8. Suppose -1 = d - i. Find k such that 5*k**2 - 6*k**3 + k + k - 5*k**d - 4*k**4 = 0.
-1, -1/3, 0, 2/3
Let a = 7 - 6. Let n(c) = 3*c**2 - 1. Let v be n(a). Determine s, given that s - 3*s - s**v + 2*s**2 = 0.
0, 2
Suppose 0 = 3*f - 2*w - 8, -3*f = -4*w - 11 - 5. Suppose 2*b = 4*b - 4. Factor f - 2/7*r**b - 2/7*r.
-2*r*(r + 1)/7
Suppose 2*z - 20 = -3*z. Factor 5 + a**2 - z*a**2 + 3*a - 6*a**2 + 1.
-3*(a - 1)*(3*a + 2)
Suppose -5*d + 12 = 2. Let y = d - -2. Determine a, given that 4/3*a**2 + 0*a + 19*a**y + 12*a**5 + 28/3*a**3 + 0 = 0.
-2/3, -1/4, 0
Let q be (-2)/6*18/(-12). Factor 1/4*p**5 - 1/4 + q*p**3 - 1/2*p**2 + 3/4*p**4 - 3/4*p.
(p - 1)*(p + 1)**4/4
Let f(j) be the second derivative of j**4/20 + 2*j**3/5 + 9*j**2/10 - 7*j. Factor f(q).
3*(q + 1)*(q + 3)/5
Factor -4*k**4 - 2*k - k**2 + k**4 + 4*k**4 - 4*k**3 + 6*k.
k*(k - 4)*(k - 1)*(k + 1)
Let v(a) be the third derivative of -2/3*a**3 - 1/20*a**6 + 1/4*a**4 + 0*a + 0 + 1/105*a**7 - 5*a**2 + 1/30*a**5. Factor v(l).
2*(l - 2)*(l - 1)**2*(l + 1)
Let h(d) = -51*d**3 - 27*d**2 - 6*d. Let t(l) = -152*l**3 - 80*l**2 - 17*l. Let a(j) = -8*h(j) + 3*t(j). Suppose a(v) = 0. Calculate v.
-1/4, 0
Let p(u) be the second derivative of -u*