
-5*(o + 3)**2/4
Let d be 5 - 4 - (-3)/(-2 + -1). Solve d - 1/5*j - 1/5*j**2 = 0 for j.
-1, 0
Let i(p) be the second derivative of 3*p + 0*p**3 + 1/15*p**6 - 1/5*p**5 + 1/6*p**4 + 0*p**2 + 0. Factor i(u).
2*u**2*(u - 1)**2
Let k(g) be the second derivative of g**4/4 - g**3/3 + g**2/2 + 6*g. Let n(x) = -4*x**2 + 3*x - 2. Let m(b) = 3*k(b) + 2*n(b). Determine j, given that m(j) = 0.
-1, 1
Let k(v) be the third derivative of -v**7/1995 - v**6/228 - 2*v**5/285 - 13*v**2 + v. Factor k(z).
-2*z**2*(z + 1)*(z + 4)/19
Let r be (-106)/(-36) - 4/18. Let u(d) be the first derivative of 4/9*d**2 + 0*d + 56/27*d**3 + r*d**4 + 2. Factor u(j).
2*j*(7*j + 2)**2/9
Suppose -o + z = -6, 0 + 12 = o - 4*z. Let q be (0 - -8)/(1 - 0). Factor 2 - 2*u**5 + 9*u + 2 + 4*u**2 + u - 8*u**o - q*u**3.
-2*(u - 1)*(u + 1)**3*(u + 2)
Let m = 6 + -8. Let i(s) = -s**3 - 3*s**2 - 3*s - 2. Let y be i(m). Factor y*q + 1/2*q**2 - 1/2.
(q - 1)*(q + 1)/2
Solve 34/15*w**3 + 8/15 - 16/15*w + 2/5*w**5 - 2/5*w**2 - 26/15*w**4 = 0.
-2/3, 1, 2
Let l(p) be the third derivative of -p**6/780 + p**5/78 + p**4/12 + 7*p**3/39 + 7*p**2. Suppose l(i) = 0. Calculate i.
-1, 7
Let u(j) = -j**2 - 6*j - 5. Let r be u(-3). Find s such that -5/3*s**2 - 2/3*s**5 + 0 - 1/3*s - 7/3*s**r - 3*s**3 = 0.
-1, -1/2, 0
Let m(n) = n**2 - n - 2. Let l be m(-1). Let j(v) be the second derivative of 1/15*v**3 + 0*v**2 - 3*v + 1/30*v**4 + l. Factor j(s).
2*s*(s + 1)/5
Let y be (0 + -3)/(3/2). Let u = y - -5. Factor 2*c**2 + 2*c**4 + 4*c - 4*c - 4*c**2 - c**5 + c**u.
-c**2*(c - 2)*(c - 1)*(c + 1)
Let g = -1 + 3. Determine s, given that 2*s**2 + 4*s**g + 4*s - 4*s**2 = 0.
-2, 0
Let h = 1/2 + -4/9. Let o(g) be the first derivative of 2 + h*g**4 + 2/45*g**5 - 1/9*g**2 - 2/27*g**3 + 0*g. Factor o(v).
2*v*(v - 1)*(v + 1)**2/9
Let p(g) be the third derivative of 0*g + 0*g**3 + 1/210*g**5 + 0*g**4 + 0 + 1/420*g**6 - 2*g**2. Factor p(a).
2*a**2*(a + 1)/7
Let j = 16 - 14. Let w(x) be the first derivative of -2/3*x**3 + 4*x - x**j - 2. Find f, given that w(f) = 0.
-2, 1
Let p(k) be the first derivative of 3/7*k**3 + 2/7*k - 2 - 11/14*k**2. Let p(t) = 0. What is t?
2/9, 1
Solve 0 - 2/5*m**2 + 4/5*m = 0 for m.
0, 2
Let a(q) be the first derivative of -4*q**3/3 + 10*q**2 - 16*q + 33. Solve a(m) = 0 for m.
1, 4
Let b(t) be the second derivative of t**8/4200 + t**7/700 + t**6/900 - t**5/100 - t**4/30 - t**3/3 - t. Let r(n) be the second derivative of b(n). Factor r(q).
2*(q - 1)*(q + 1)**2*(q + 2)/5
Let q(b) be the second derivative of b**7/252 - b**5/40 - b**4/36 - 15*b. Factor q(u).
u**2*(u - 2)*(u + 1)**2/6
Let n = -1/15 + 19/60. Factor n*l**5 - 3/4*l - 1/2*l**2 + 3/4*l**4 - 1/4 + 1/2*l**3.
(l - 1)*(l + 1)**4/4
Let l be ((-2)/2)/1 - -3. Let j(i) be the third derivative of 0*i + l*i**2 + 0 + 0*i**3 + 1/120*i**5 - 1/24*i**4. Factor j(p).
p*(p - 2)/2
Let x(h) be the third derivative of -h**8/1512 + h**6/540 - 15*h**2. Factor x(y).
-2*y**3*(y - 1)*(y + 1)/9
Let n(s) be the first derivative of 2*s**3/33 - 5*s**2/11 + 12*s/11 - 18. Factor n(t).
2*(t - 3)*(t - 2)/11
Let w(a) be the first derivative of 13/22*a**4 - 8/11*a**3 + 1/33*a**6 + 0*a + 4/11*a**2 - 12/55*a**5 + 1. Solve w(r) = 0.
0, 1, 2
Let a(b) = b**3 + 12*b**2 - b - 12. Let l be a(-12). Factor 6/5*o - 3*o**2 + 3/5*o**4 + l + 9/5*o**3 - 3/5*o**5.
-3*o*(o - 1)**3*(o + 2)/5
Suppose -3*z + 8*z - 3*v = -2, -3*z + 14 = 2*v. Factor 3*k**5 - 2*k**4 + 4*k**2 + k**5 - z*k**5 - 2*k**3 - 2*k**2.
2*k**2*(k - 1)**2*(k + 1)
Let s(f) = 5*f**3 - 4*f**2 - 5*f + 4. Let k(h) = -h**3 + 9*h**2 - h**2 + h - 8*h**2. Let z(m) = 6*k(m) + 2*s(m). Suppose z(x) = 0. Calculate x.
-1, 1, 2
Suppose 18 = -16*q + 19*q. Factor -q*h**2 - 9*h - 9*h**2 + 18*h**2.
3*h*(h - 3)
Suppose -44*f = -40*f - 20. Suppose -2 = 3*r - 8. Factor 0*d**5 + 0*d**f + d**r - d**5 + d**3 - d**4.
-d**2*(d - 1)*(d + 1)**2
Suppose 4 + 0 = 4*z. Let s(j) be the first derivative of 1/2*j**2 + 2/3*j**3 + z + 1/4*j**4 + 0*j. Factor s(y).
y*(y + 1)**2
Let i(v) = -49*v**2 - 3*v. Let j(h) = -25*h**2 - h. Let l(w) = 3*i(w) - 5*j(w). Let l(x) = 0. What is x?
-2/11, 0
Let j(q) be the third derivative of -q**8/16 - 17*q**7/140 + 27*q**6/80 + q**5/5 - q**4/4 - 2*q**2. Suppose j(i) = 0. Calculate i.
-2, -1/2, 0, 2/7, 1
Let s(k) = 5*k - 5*k + 2*k + k**2 + k**5 - 3*k. Let p(j) = -12*j**5 + 10*j**4 - 20*j**3 + 10*j**2 + 2. Let v(w) = -p(w) - 10*s(w). Let v(x) = 0. What is x?
1
Suppose 80 = 20*j + 20*j. Factor 2/3*n + 0 - 2/3*n**3 - 1/3*n**j + 1/3*n**4.
n*(n - 2)*(n - 1)*(n + 1)/3
Solve -6/11*x**4 + 4/11*x**3 + 6/11*x**2 + 0 - 4/11*x = 0 for x.
-1, 0, 2/3, 1
Suppose 6*q**2 + 21*q**4 + 93/2*q**3 - 6*q + 0 = 0. What is q?
-2, -1/2, 0, 2/7
Let c = 183 + -1279/7. Solve -2/7*i**2 - 4/7*i + c*i**4 + 0 + 4/7*i**3 = 0.
-2, -1, 0, 1
Let t(w) = 16*w**4 - 12*w**3 + 24*w**2 - 8*w - 20. Let v(r) = -r**4 + r**3 - r**2 + 1. Let j(m) = -t(m) - 20*v(m). Factor j(k).
4*k*(k - 2)*(k - 1)*(k + 1)
Suppose 9*z - 9/2*z**3 + 0 - 21/2*z**2 = 0. What is z?
-3, 0, 2/3
Suppose -17 = -2*v - 0*y - 3*y, -3*v + 4*y = 0. Determine t, given that 6/7*t**3 + 0*t + 0 - 4/7*t**2 - 2/7*t**v = 0.
0, 1, 2
Suppose 2*j - 3*l - 20 = 0, 4*j - 32 = -l + 5*l. Factor 4*y**j + 3*y**2 + y**3 + 10*y**3 + 5*y**2 + y**3.
4*y**2*(y + 1)*(y + 2)
Suppose 0 = -f + 3*q + 20, 4*f + 0*q = 4*q + 48. Let x be (4/f)/(2/12). Factor -z**3 + 3*z + z**4 - x*z.
z**3*(z - 1)
Let g be 2/7 + 406/(-49). Let a be (g/(-10))/((-11)/(-55)). Let 0*q**2 + 0 + 0*q**a - 4/3*q**3 + 2/3*q + 2/3*q**5 = 0. What is q?
-1, 0, 1
Let o = 5 - 5. Let m(g) be the third derivative of -1/3*g**3 - 2*g**2 + 0 + 1/4*g**4 - 1/10*g**5 + 1/60*g**6 + o*g. Factor m(c).
2*(c - 1)**3
Solve -1/2 - 1/2*v**2 - v = 0 for v.
-1
Let t(i) be the first derivative of i**6/135 + i**5/45 - i - 6. Let u(v) be the first derivative of t(v). Factor u(y).
2*y**3*(y + 2)/9
Suppose -3*h**3 - 6*h**2 - h**4 - 2*h**3 + h**3 - 44 + 43 - 4*h = 0. What is h?
-1
Let c(a) be the third derivative of 0 - 1/120*a**6 + 0*a + 1/24*a**4 + 0*a**3 + 1/210*a**7 - 1/60*a**5 - 3*a**2. Factor c(l).
l*(l - 1)**2*(l + 1)
Let q(t) = -3*t**2 + 24*t + 2. Let w be q(8). Suppose -1/2*j**2 - 2*j - w = 0. What is j?
-2
Let d be (6/(-4))/((-3)/4). Let 5*p**3 - p**4 + 0*p**3 - p**2 - 3*p**5 - 2*p + 2*p**d = 0. What is p?
-1, 0, 2/3, 1
Let o be (1 + 1 - 1 - 1)/(-3). Solve 0*a + 0 + 1/2*a**3 + o*a**2 = 0.
0
Suppose 14*n - 10 = 9*n. Let f(p) be the first derivative of 1/2*p**4 + n*p**2 + 13/9*p**3 + 4/3*p - 2 + 1/15*p**5. Factor f(x).
(x + 1)**2*(x + 2)**2/3
Factor -4*g**2 - 7 + 6*g + g**2 + 4.
-3*(g - 1)**2
Let i(c) be the first derivative of -2*c**5/45 - c**4/9 - c**3/9 - 9*c**2/2 - 3. Let g(m) be the second derivative of i(m). Factor g(f).
-2*(2*f + 1)**2/3
Let m(l) = -3*l**3 - 4*l**2 + 2*l - 5. Let y(g) = -8*g**3 - 12*g**2 + 6*g - 14. Let n(h) = 14*m(h) - 5*y(h). Factor n(u).
-2*u*(u - 1)**2
Let h(a) = a**2 - 6*a - 2. Let j(n) = 3*n**2 - 13*n - 3. Let s(f) = -5*h(f) + 2*j(f). Find k such that s(k) = 0.
-2
Suppose -15 = -3*x - 4*p + p, -3*x + 5*p = -47. Suppose -5*u = 2*s - 50, 2*u + 3*s = -0*u + x. Let z**3 - 15*z**4 + u*z**4 + 0*z**3 + 2*z**3 = 0. Calculate z.
0, 1
Let k(c) = -3*c**5 - 4*c**4 - 5*c**3 - 4*c**2. Let t(h) = 4*h**5 + 5*h**4 + 6*h**3 + 5*h**2. Suppose 5*j + 21 = 1. Let x(v) = j*t(v) - 5*k(v). Factor x(u).
-u**3*(u - 1)*(u + 1)
Let w(m) be the first derivative of 3*m**5/10 + 3*m**4/4 - 2*m**3 - 3*m**2/2 + 9*m/2 + 19. Suppose w(k) = 0. Calculate k.
-3, -1, 1
Factor 4/3*r**3 + 0*r**4 - 2/3*r**5 - 2/3*r + 0*r**2 + 0.
-2*r*(r - 1)**2*(r + 1)**2/3
Let j(z) be the third derivative of 0*z - 5/72*z**4 - 1/36*z**6 - 1/126*z**7 - 4*z**2 - 1/18*z**5 - 1/1008*z**8 - 1/18*z**3 + 0. Suppose j(i) = 0. Calculate i.
-1
Let b be (-500)/6875*(-11)/2. Suppose 5*n = 2*n + 6. Suppose 0*a - b + 2/5*a**n = 0. What is a?
-1, 1
Let m(l) be the third derivative of 3*l**2 + 0*l - 1/36*l**4 + 0 + 1/180*l**5 + 1/18*l**3. Find a, given that m(a) = 0.
1
Let q(g) be the first derivative of g**4/20 - 3*g**2/10 + 2*g/5 + 7. Factor q(o).
(o - 1)**2*(o + 2)/5
Find l, given that -l**4 - 3*l**3 - 20*l + 2*l**2 - l**3 + 24*l - l**4 = 0.
-2, -1, 0, 1
Let r(l) = 3*l**2 + 19*l - 11. Let f be r(-7). Suppose 2*d = 5*d - 6. Factor -4/11*a**f + 2/11*a**4 + 0*a + 0 + 2/11*a**d.
2*a**2*(a - 1)**2/11
Let v(j) = -4*j**5 + 4*j**4 + j**3 - 