0, 1
Let y(a) be the first derivative of -a**7/2520 + a**6/120 - 3*a**5/40 + 3*a**4/8 + 5*a**3/3 + 5. Let o(n) be the third derivative of y(n). Factor o(b).
-(b - 3)**3/3
Let p = -232 - -235. Factor 9/5*o**4 - 3/5 - 6/5*o**p + 9/5*o - 6/5*o**2 - 3/5*o**5.
-3*(o - 1)**4*(o + 1)/5
Let a(q) = q**4 - 3*q**3 + q**2 + 3*q - 7. Let g(o) = -1. Let l(f) = -a(f) + 5*g(f). Find x, given that l(x) = 0.
-1, 1, 2
Let f(k) be the third derivative of 0*k - 1/735*k**7 + 1/420*k**6 + 4*k**2 + 0*k**3 - 1/84*k**4 + 0 + 1/210*k**5. Suppose f(g) = 0. Calculate g.
-1, 0, 1
Let b = -147 + 1325/9. Let u be (-1)/(-2)*-1*-6. Let -2/3*l + b + 2/3*l**2 - 2/9*l**u = 0. What is l?
1
Let b = -10 - -12. Factor 2*u + 4*u**2 - 20*u**b + 14*u + 0*u + 4*u**3.
4*u*(u - 2)**2
Let u(o) = -o**3 - 4*o**2 - 3*o - 2. Let v be u(-3). Let z = v + 2. Factor -2/3*m**4 + 0 + 0*m**2 + z*m - 2/3*m**3.
-2*m**3*(m + 1)/3
Let v be 10/(-45) - (-76)/18. Factor 2*m - 4*m + m**2 - v + m**2.
2*(m - 2)*(m + 1)
Let b(f) be the second derivative of -f**7/21 - f**6/5 - f**5/5 - 3*f. Find p, given that b(p) = 0.
-2, -1, 0
Suppose v - 38 = -h, -4*v - 4*h = -3*h - 158. Let o = v - 35. Determine p so that 0 - 1/4*p**4 - 1/2*p**3 + 0*p + 0*p**2 + 1/4*p**o = 0.
-1, 0, 2
Let j(d) = d**3 - 6*d**2 + d - 3. Let p be j(6). Factor 2*l**2 + 2 + 3*l**2 - 2*l**3 + p*l**2 - 2*l**2 - 6*l.
-2*(l - 1)**3
Suppose 0*w + 5 = 5*w. Let p be (w/3)/(4/3). Suppose -1/4*k**2 + 0*k + 0 + p*k**3 = 0. Calculate k.
0, 1
Let u = 4/3 + -2/15. Solve 3/5*c**2 + 3/5 + u*c = 0 for c.
-1
Suppose -33*d = -27*d. Solve 0*j + d + 2/11*j**2 = 0.
0
Let s(h) = 4*h**3 - 5*h**2 - 4*h + 5. Let x(t) = t**2 - t**3 + 0*t**2 + 0*t**3 + t - 1 + 0*t**2. Let i(w) = -s(w) - 3*x(w). Factor i(p).
-(p - 2)*(p - 1)*(p + 1)
Factor -2/9*o**2 + 0 - 2/9*o.
-2*o*(o + 1)/9
Let g(a) be the third derivative of -2*a**7/245 + 4*a**6/105 - 2*a**5/35 + 2*a**3/21 + 3*a**2. Determine k, given that g(k) = 0.
-1/3, 1
Let 0 - 2*k**5 - 4/7*k**2 + 0*k + 24/7*k**4 - 6/7*k**3 = 0. Calculate k.
-2/7, 0, 1
Let i(c) = 6*c**2 - c. Let y(k) = 4*k**2. Let q(z) = -4*i(z) + 5*y(z). Factor q(n).
-4*n*(n - 1)
Let k(g) = 6*g**2 + 0*g + 11 + 7 + 23*g - 6. Let p(f) = -3*f**2 - 11*f - 6. Let o(q) = -2*k(q) - 5*p(q). Factor o(i).
3*(i + 1)*(i + 2)
Factor 2/11*m + 2/11*m**3 - 4/11*m**2 + 0.
2*m*(m - 1)**2/11
Let s(f) be the third derivative of 1/120*f**4 + 1/600*f**6 - 1/150*f**5 + 0 + 0*f**3 - 6*f**2 + 0*f. Let s(q) = 0. What is q?
0, 1
Let v(b) = -b**3 + 2*b**2 - 3*b. Let g be v(2). Let a = -3 - g. Find w, given that 2*w**2 + 2*w**4 - w**4 + 2*w - a*w**4 - 2*w**3 = 0.
-1, 0, 1
Let s(y) = 4*y**2 + 14*y + 24. Let x = 27 + -55. Let n be (12/(-4))/((-6)/x). Let h(o) = o**2 + 3*o + 5. Let q(v) = n*h(v) + 3*s(v). Factor q(c).
-2*(c - 1)*(c + 1)
Let u = 0 - -2. Suppose 4 - u = k. Determine f so that 2*f**4 - 4*f**2 + 2 - f**k + 0*f**4 + 2*f**5 - 4*f**3 + f**2 + 2*f = 0.
-1, 1
Let s(n) = n**2 + 9*n + 4. Let x be s(-9). Determine j, given that -2*j**3 + 1/2*j**x + 1/2 - 2*j + 3*j**2 = 0.
1
Let w = 901/12 - 75. Let s(z) be the third derivative of -1/35*z**7 - 1/30*z**5 + z**2 + 0*z**3 + 0 + w*z**6 - 1/12*z**4 + 0*z. Factor s(k).
-2*k*(k - 1)**2*(3*k + 1)
Let a(r) be the third derivative of r**5/120 + r**4/12 + r**3/3 - 16*r**2. Determine l, given that a(l) = 0.
-2
Let u(a) = -a + 4. Let j be u(0). Let r = j - 0. Factor 4*t**r - 3 - 3*t**3 + 3 - t**2.
t**2*(t - 1)*(4*t + 1)
Let b be -2 - ((-6)/3 - 0). Suppose 0*n - 3*n - 13 = o, 5*o - 3*n - 25 = b. Let r**2 - 3*r**2 + 1 + 2*r + 3*r**o = 0. Calculate r.
-1
Let s be 24 - 22 - 10/(-2) - 5. Determine p so that 0 - 1/5*p**3 - 4/5*p - 4/5*p**s = 0.
-2, 0
Let q(w) = w**2 + 9*w + 10. Let j be q(-8). Suppose -j*s = s. Factor 1/4*z + s - 1/4*z**2.
-z*(z - 1)/4
Determine f, given that 4/13*f**3 + 2/13*f**5 - 4/13*f**2 - 2/13 - 6/13*f + 6/13*f**4 = 0.
-1, 1
Let s(r) be the third derivative of -r**6/210 + r**4/42 + 11*r**2. Determine a, given that s(a) = 0.
-1, 0, 1
Let a(s) = 0 + 0 - 2 - s. Let h be a(-4). Factor 0*r - 2/7*r**3 + 0 - 2/7*r**h.
-2*r**2*(r + 1)/7
Let -2*l**5 + 254 - 2*l**2 + 2*l**4 + 2*l**3 - 254 = 0. Calculate l.
-1, 0, 1
Let q = 5 + -2. Let -8*c + 18*c**4 + 19*c**2 + 12*c**2 - 42*c**q - 12*c**2 + 13*c**2 = 0. What is c?
0, 2/3, 1
Let 2/17*g**2 + 0*g**3 - 2/17*g**4 + 0*g + 0 = 0. Calculate g.
-1, 0, 1
Let j(f) be the second derivative of -f**4/72 - f**3/36 + f**2/6 + f - 2. Solve j(w) = 0 for w.
-2, 1
Let y = -13 - -17. Let f(h) be the first derivative of 0*h**2 + 1/5*h**5 + 0*h**3 - 2 - 1/4*h**y + 0*h. Factor f(t).
t**3*(t - 1)
Factor 20 + 0*v**2 + 5*v**2 + 8*v - 22*v - 11*v.
5*(v - 4)*(v - 1)
Factor -4/3*o + 10/3*o**2 - 8/3*o**3 + 2/3*o**4 + 0.
2*o*(o - 2)*(o - 1)**2/3
Solve g + 3*g**2 + 3*g - 5*g - 4*g**2 = 0 for g.
-1, 0
Let s(u) = 2 + 3*u + 6*u**2 + u**2 - 8*u**2. Let z be s(2). Suppose -1/4*o**5 + 0*o**2 + 0*o**z + 1/2*o**3 + 0 - 1/4*o = 0. Calculate o.
-1, 0, 1
Let m = 3/8 - -9/8. Let z(g) be the first derivative of -1/4*g**4 - m*g**2 + g - 1 + g**3. Find r such that z(r) = 0.
1
Let z(x) = -x**5 - 2*x**3 - 5*x - 4. Let t(v) = -v**3 - v - 1. Let c(q) = -q**3 + 6*q**2 + 6*q + 8. Let j be c(7). Let y(k) = j*z(k) - 4*t(k). Factor y(l).
-l*(l - 1)**2*(l + 1)**2
Let o(f) = -3*f**2 - 7*f + 3. Let s(p) = p**2 + 4*p - 1. Let h(u) = 4*o(u) + 9*s(u). Let h(k) = 0. Calculate k.
-1/3, 3
Let r be (-4)/(-30) + (-24)/180. Factor r + 1/3*s**3 + 1/3*s - 2/3*s**2.
s*(s - 1)**2/3
Let h = 2 - -2. Let r be (-18)/144 - (-2)/16. Factor 0*y**2 + 4/3*y**5 + r + 0*y - 1/3*y**3 - y**h.
y**3*(y - 1)*(4*y + 1)/3
Let q(t) be the third derivative of 0 + 1/2*t**3 - 1/20*t**5 - 5*t**2 + 0*t + 0*t**4. Suppose q(z) = 0. What is z?
-1, 1
Let r(m) be the second derivative of m**7/210 + m**6/75 + m**5/100 - 3*m. Suppose r(l) = 0. What is l?
-1, 0
Let y(f) = 3*f + 2. Let r be y(-2). Let q(p) = -6*p**3 - 2*p + 4. Let u(w) = -5*w**3 - w + 3. Let l(o) = r*u(o) + 3*q(o). Factor l(s).
2*s*(s - 1)*(s + 1)
Suppose 12*m**3 - 5*m**2 + 18*m - m**3 - 20*m - 4*m**4 = 0. Calculate m.
-1/4, 0, 1, 2
Let v(u) be the second derivative of u**5/70 - u**4/21 - u**3/21 + 2*u**2/7 - 22*u. Factor v(l).
2*(l - 2)*(l - 1)*(l + 1)/7
Let v = 10 - 8. Determine u so that -v - u**3 + 4 - u**3 + 2 + 6*u = 0.
-1, 2
Let k(r) be the third derivative of 1/3*r**3 - r**2 + 1/210*r**7 + 1/480*r**6 - 1/24*r**4 + 0 + 1/1344*r**8 + 0*r - 1/24*r**5. Factor k(d).
(d - 1)**2*(d + 2)**3/4
Let a(v) be the first derivative of 3/5*v**2 + 7 + 2/5*v**3 + 2/5*v + 1/10*v**4. Factor a(p).
2*(p + 1)**3/5
Let t(l) = 5*l + 123. Let m be t(-24). Let g(a) be the first derivative of 0*a**m - 1/2*a**4 + 3*a**2 - 4*a - 1. Factor g(w).
-2*(w - 1)**2*(w + 2)
Suppose -4*n = 4*u - 20, -5*n = -u - u - 25. Factor u*l + 0*l**3 - 2*l**4 + 8/3*l**2 + 0 - 2/3*l**5.
-2*l**2*(l - 1)*(l + 2)**2/3
Let d = 5 - 5. Let f be 2 + (d - -1)/1. Factor 4*a + f*a**2 - a**2 - 2*a.
2*a*(a + 1)
Let k = 249345/57134 + -3/5194. Factor -k*n**2 + 8/11*n + 98/11*n**4 + 0 + 42/11*n**3.
2*n*(n + 1)*(7*n - 2)**2/11
Let r(o) be the first derivative of 1/6*o**2 + 2/3*o - 1/6*o**4 - 6 + 1/18*o**6 + 2/15*o**5 - 4/9*o**3. Find z, given that r(z) = 0.
-2, -1, 1
Let q(o) be the third derivative of -3*o**2 + 1/75*o**6 + 0*o**4 + 0*o + 0 - 1/280*o**8 + 0*o**5 + 4/525*o**7 + 0*o**3. What is j in q(j) = 0?
-2/3, 0, 2
Factor 1/2*f**2 + 4*f + 8.
(f + 4)**2/2
Let t(d) be the second derivative of d**6/10 + 3*d**5/5 + 5*d**4/4 + d**3 - 8*d. Factor t(b).
3*b*(b + 1)**2*(b + 2)
Let a(z) be the first derivative of -z**6/33 - 8*z**5/55 - 3*z**4/22 + 8*z**3/33 + 4*z**2/11 + 10. Find v such that a(v) = 0.
-2, -1, 0, 1
Let r(d) = 4*d - 24. Let b be r(6). Let v(n) be the second derivative of -1/36*n**4 + 0*n**3 + 1/30*n**5 - 1/90*n**6 + n + 0 + b*n**2. Factor v(o).
-o**2*(o - 1)**2/3
Factor -10/7*y**2 + 2/7*y - 2/7*y**3 + 10/7.
-2*(y - 1)*(y + 1)*(y + 5)/7
Suppose n - 4*g = 20, -g - 8 = -4*n - 3*g. Suppose b + 5 = -3*v + 4*v, -25 = 2*b - 5*v. Determine k, given that 7*k**2 + b - 3*k**n + 0 - 4*k**2 = 0.
-1, 0, 1
Let k(n) be the second derivative of 0*n**2 - 1/3*n**3 + 0 - 4*n - 3/20*n**5 + 2/15*n**6 - 3/4*n**4. Suppose k(m) = 0. Calculate m.
-1, -1/4, 0, 2
Let h = -63 - -63. Let o(j) be the second derivative of -3/8*j**4 - 7/12*j**3 - 1/60*j**6 - j + h - 1/8*j**5 - 1/2*j**2. Let o(m) = 0. Calculate m.