t -2/3*u**2 - 8/3*u + 10/3 = 0.
-5, 1
Let p(c) = c**2 - 5*c - 6. Let r(b) = b**2 + 4*b - 6. Let j be r(-6). Let w be p(j). Factor 2/7*q**4 + 0*q**2 + 0 + 2/7*q**3 + w*q.
2*q**3*(q + 1)/7
Suppose 14*p**3 - 9*p**3 - 4*p**3 + p**2 = 0. Calculate p.
-1, 0
Let a(w) be the first derivative of w**7/105 - w**6/75 - w**5/50 + w**4/30 + 3*w + 1. Let m(s) be the first derivative of a(s). Find l such that m(l) = 0.
-1, 0, 1
Let l(s) = -s**3 + s**2 + s - 1. Let h(b) = -2*b**4 - 28*b**3 + 18*b**2 + 22*b - 22. Let q(g) = -2*h(g) + 44*l(g). Find a such that q(a) = 0.
-2, -1, 0
Let o(k) = -125*k**3 - 152*k**2 + 178*k - 42. Let g(h) = -500*h**3 - 609*h**2 + 711*h - 169. Let z(d) = 2*g(d) - 9*o(d). Factor z(y).
5*(y + 2)*(5*y - 2)**2
Solve 0*v + 1/2*v**5 + 5/2*v**4 + 3/2*v**2 + 7/2*v**3 + 0 = 0 for v.
-3, -1, 0
Let w(s) be the first derivative of -s**6/39 + 8*s**5/65 - 5*s**4/26 + 4*s**3/39 + 8. Find a, given that w(a) = 0.
0, 1, 2
Let p = 29 - 29. Factor 0*z - 1/2*z**4 + p*z**2 + 0 + 0*z**3.
-z**4/2
Let x(y) be the second derivative of 2*y**6/15 - 2*y**5/5 + y**4/3 - 4*y. Determine k, given that x(k) = 0.
0, 1
Let x(l) = l + 10. Let s be x(-12). Let v(u) = 2*u**2 - u. Let j(g) = g**3 + g**2 - g. Let h(a) = s*v(a) + 2*j(a). Factor h(b).
2*b**2*(b - 1)
Let u be (-3 - (-2 - 0)) + 22/14. Factor u*s + 2/7 + 2/7*s**2.
2*(s + 1)**2/7
Let q(a) be the second derivative of -a**6/15 + a**5 - 4*a**4 - 10*a**3/3 + 25*a**2 + 9*a. Factor q(c).
-2*(c - 5)**2*(c - 1)*(c + 1)
Let i be 1 + 2 + 4/(-2). Suppose -b + 4 = -i. Factor 5 + 8*y + 2*y**3 - b + 8*y**2.
2*y*(y + 2)**2
Let b(j) = 5*j**4 - 33*j**3 - 27*j**2 - 16*j - 9. Let g(r) = -r**4 + 8*r**3 + 7*r**2 + 4*r + 2. Let k(n) = 2*b(n) + 9*g(n). Find d such that k(d) = 0.
-4, -1, 0
Let a(w) be the third derivative of -w**5/60 + w**4/4 - w**3/6 - 4*w**2. Let v be a(5). Suppose 2/5*b**v + 0*b**2 + 4/5*b**3 - 4/5*b - 2/5 = 0. What is b?
-1, 1
Let n be (-10)/(-8) + 3/4. Factor -2*k - 4 - k**2 + 2*k**2 - 4*k**n + 5*k**2.
2*(k - 2)*(k + 1)
Let p(f) be the second derivative of -f**5/30 + f**4/9 + f**3/3 + 2*f. What is r in p(r) = 0?
-1, 0, 3
Suppose n = 3*v + 15, -27 = n + 5*v - 2. Let l(t) be the second derivative of n*t**2 + 0*t**3 + 0*t**5 - t + 0 + 1/30*t**6 - 1/12*t**4. Factor l(o).
o**2*(o - 1)*(o + 1)
Factor -3*u**3 + 54/5 + 96/5*u**2 - 171/5*u.
-3*(u - 3)**2*(5*u - 2)/5
Let x be (6/4)/((-15)/80). Let k = x - -8. Let 0*z + 2/7*z**3 - 4/7*z**2 + k - 6/7*z**5 + 8/7*z**4 = 0. Calculate z.
-2/3, 0, 1
Let d(t) be the first derivative of 1/16*t**4 - 1/4*t**3 + 4 - 1/4*t + 3/8*t**2. Let d(c) = 0. What is c?
1
Let v(t) be the third derivative of -t**7/2520 + t**5/120 + t**4/4 - 3*t**2. Let o(x) be the second derivative of v(x). Factor o(q).
-(q - 1)*(q + 1)
Let v(b) = 10*b + 2*b**2 + 0*b**2 + b**3 - 3*b**3 + 2. Let o be 0 + (4 - 6)/(-2). Let r(t) = t**3 + t**2 - t. Let u(h) = o*v(h) + 4*r(h). Factor u(k).
2*(k + 1)**3
Let q(v) be the second derivative of -8*v**6/45 + 2*v**5/15 - v**4/36 + 23*v. Factor q(g).
-g**2*(4*g - 1)**2/3
Suppose 10*k = 5*k + 3*k. Solve 5/2*r**3 + 0 + 1/2*r**5 + 2*r**4 + k*r + r**2 = 0 for r.
-2, -1, 0
Let k(f) be the third derivative of f**6/180 - f**5/45 - 8*f**2. Let k(y) = 0. Calculate y.
0, 2
Let q(i) = i + 7. Let k be q(-5). Let a(b) be the second derivative of 0 - 2*b + 1/12*b**4 - 1/3*b**3 + 1/2*b**k. Let a(f) = 0. Calculate f.
1
Let w(q) be the third derivative of q**7/490 - q**6/840 - q**5/84 + q**4/168 + q**3/21 + 10*q**2. Suppose w(o) = 0. Calculate o.
-1, -2/3, 1
Let n = -5 + -3. Let v be n/(-2) + 3/(-3). Factor x - 3*x - v*x**2 + x**2.
-2*x*(x + 1)
Let a(j) be the second derivative of j**5/100 - 13*j**4/60 + 7*j**3/6 + 49*j**2/10 - j. Factor a(s).
(s - 7)**2*(s + 1)/5
Suppose i = 4*u - 3233, -6*i + 3*i = -u + 800. Let d = -4019/5 + u. Factor 14/5*o - 6*o**2 + d*o**3 - 8/5*o**4 - 2/5.
-2*(o - 1)**3*(4*o - 1)/5
Let f be (-41)/(-5) + -3 - 5/1. Factor f*o**2 + 1/5*o + 0.
o*(o + 1)/5
Let m = -4/229 + -2021/2290. Let h = -1/2 - m. Factor -h*n**2 + 2/5*n + 0.
-2*n*(n - 1)/5
Let l(b) be the third derivative of -b**6/360 - b**5/60 - b**4/24 - b**3/2 - 2*b**2. Let a(n) be the first derivative of l(n). Factor a(d).
-(d + 1)**2
Let m(b) = -7*b - 31. Let l be m(-5). Factor 2/3*a**2 - 1/3 - 1/3*a**l + 0*a**3 + 0*a.
-(a - 1)**2*(a + 1)**2/3
Let c(o) be the third derivative of o**9/3024 + o**8/1680 - o**3/3 + 2*o**2. Let z(u) be the first derivative of c(u). Factor z(r).
r**4*(r + 1)
Factor -16*i - 8 + 6*i**3 - 12*i**3 + 4*i**3 - 10*i**2.
-2*(i + 1)*(i + 2)**2
Let f(g) = -g**2 - 2*g - 1. Let i be f(-3). Let n be (-2)/i*(-4)/(-8). Factor n*m**2 + 1/4*m + 0.
m*(m + 1)/4
Let y = 750/217 + -54/31. Let l = -53/35 + y. Suppose l - 2/5*w**3 + 2/5*w + 0*w**2 - 1/5*w**4 = 0. Calculate w.
-1, 1
Let m(u) be the second derivative of 3*u + 1/2*u**4 + 1/10*u**5 + 0*u**2 + 2/3*u**3 + 0. Factor m(d).
2*d*(d + 1)*(d + 2)
Factor 8/5*b**3 + 2/5 + 2/5*b**4 + 12/5*b**2 + 8/5*b.
2*(b + 1)**4/5
Suppose -4/5*g**3 + 14/5*g**2 - 2/5*g**4 + 8*g + 24/5 = 0. Calculate g.
-2, -1, 3
Determine t so that 16/3*t**3 + 2/3*t**4 + 32/3 + 16*t**2 + 64/3*t = 0.
-2
Suppose 0 = -0*p - 5*p. Suppose 2*k + 5*t - 11 = p, 4*t - 14 = -3*k - t. Determine g so that -g**4 + 0*g - 1/3*g**2 + 1/3*g**5 + g**k + 0 = 0.
0, 1
Let h(o) = o**3 - 7*o**2 + 8*o - 8. Let q be h(6). Let m = -4 + q. Determine c so that 2*c + m*c + 0*c - 2*c**3 = 0.
-1, 0, 1
Let j be (-18)/5*((-26)/3)/13. Factor -j*g + 3/5*g**2 + 12/5.
3*(g - 2)**2/5
Let v(p) be the first derivative of 2*p**5/35 - p**4/14 - 2*p**3/21 + p**2/7 - 4. Suppose v(u) = 0. Calculate u.
-1, 0, 1
Let j(t) be the third derivative of t**10/15120 + t**9/3780 - t**7/630 - t**6/360 + t**4/8 + t**2. Let c(b) be the second derivative of j(b). Factor c(w).
2*w*(w - 1)*(w + 1)**3
Let q(p) be the first derivative of -p**6/120 + p**5/20 - p**4/8 + 2*p**3/3 - 2. Let z(y) be the third derivative of q(y). Solve z(u) = 0.
1
Let g(q) be the third derivative of 0*q - 1/300*q**6 + 0*q**3 + 0 + 4*q**2 + 0*q**4 - 1/75*q**5. Factor g(u).
-2*u**2*(u + 2)/5
Suppose 4*i = -i + 25, 2*f - 3*i = 15. Suppose f = -3*k, k = -5*m - 3*k - 10. Determine y so that 1/2*y**m + 2 - 2*y = 0.
2
Let q = 8 + -4. Suppose o - 21 = -q*u - 10, -o = -3*u + 17. Factor -2/3*h**3 + 0 + 2/3*h**2 + 2/3*h - 2/3*h**u.
-2*h*(h - 1)*(h + 1)**2/3
Let c(y) = 5*y**2 - 45*y + 40. Let j(k) = 2*k**2 - 23*k + 20. Let i(f) = -3*c(f) + 5*j(f). Factor i(t).
-5*(t - 2)**2
Let c(o) be the second derivative of 0*o**2 + 3/20*o**5 + 0 + 2*o + 0*o**4 - 1/2*o**3. Solve c(q) = 0.
-1, 0, 1
Let v = 2601/7 + -371. Factor -4/7*n**4 - 8/7*n + 8/7*n**3 + v + 0*n**2.
-4*(n - 1)**3*(n + 1)/7
Factor -9*f**2 + 10*f**4 + 6 - 7*f**2 + 4*f**3 + 0*f - 4*f.
2*(f - 1)*(f + 1)**2*(5*f - 3)
Factor 2/7*q**3 - 4/7 - 2/7*q + 4/7*q**2.
2*(q - 1)*(q + 1)*(q + 2)/7
Let p(s) = 12*s**5 - 9*s**4 - s**3 - 2*s**2 + 2*s - 2. Let z(j) = 48*j**5 - 36*j**4 - 3*j**3 - 9*j**2 + 9*j - 9. Let n(t) = 9*p(t) - 2*z(t). Factor n(x).
3*x**3*(x - 1)*(4*x + 1)
Let p(f) = -f**3 + 5*f**2 - 3*f - 2. Let m be p(4). Factor -2*s**2 + 4*s**m + 0*s + 2*s.
2*s*(s + 1)
Let u be 139/(-15) + (-5)/(-25). Let d = -26/3 - u. Suppose 0 - 2/5*b**2 + 2/5*b**3 - 2/5*b + d*b**4 = 0. Calculate b.
-1, 0, 1
Let k(b) be the second derivative of 0*b**3 + 0*b**2 + 0 + 1/6*b**4 + 2*b. Find f, given that k(f) = 0.
0
Solve 13*r**3 - 6 + 8*r**2 - 15*r**2 + 8*r**3 + 43*r**2 + 9*r = 0.
-1, 2/7
Let i(h) be the third derivative of -1/35*h**7 + h**2 + 3/40*h**6 + 1/20*h**5 + 0 - 3/8*h**4 + 0*h + 1/2*h**3. Suppose i(c) = 0. What is c?
-1, 1/2, 1
Let d = -54 - -219/4. Let a be (-2)/6 + (-62)/(-24). Determine o, given that -3/4*o**4 - 9/4*o**2 + a*o**3 + 0 + d*o = 0.
0, 1
Let g(n) = n**3 + 5*n**2 + 4*n. Let f = -7 + 3. Let p be g(f). Factor 3/2*t**4 + p*t + 1/2*t**2 + 0 + 1/2*t**5 + 3/2*t**3.
t**2*(t + 1)**3/2
Let h(o) be the first derivative of -o**4/18 - 8*o**3/27 - 5*o**2/9 - 4*o/9 + 3. Factor h(x).
-2*(x + 1)**2*(x + 2)/9
Let t = -139 - -139. Suppose 2/5 + t*l**2 - 2/5*l**4 + 4/5*l**3 - 4/5*l = 0. Calculate l.
-1, 1
Solve 1/4 - 1/2*b - 1/4*b**4 + 0*b**2 + 1/2*b**3 = 0 for b.
-1, 1
Let -2/3*f**3 + 0*f**2 + 0*f**4 + 0 + 2/3*f**5 + 0*f = 0. Calculate f.
-1, 0, 1
Let v = -5 + 10. Factor 3*x + 5*x**2 - 3*x**2 - 6 + v*x**2 - 4*x**2.
3*(x - 1)*(x + 2)
Solve 0 - 2/5*a + 2/5*