c**5 + 2*c**3 + 674*c**2 - c**4.
-c**3*(c + 1)*(3*c - 2)
Factor 1/2*h**3 + 0 + 0*h - 1/2*h**5 + 1/2*h**4 - 1/2*h**2.
-h**2*(h - 1)**2*(h + 1)/2
Suppose -4/3*x**2 + 20/3*x - 4 - 4/3*x**3 = 0. What is x?
-3, 1
Suppose -19*f**3 + 67*f**5 - 28*f**4 - 80*f**4 + f - 202*f**5 + f**3 + 4*f**2 = 0. Calculate f.
-1/3, 0, 1/5
Let r(x) = x**2 - 21*x + 112. Let a be r(12). Suppose 0*n**2 + 2/3*n**3 - 1/3*n**5 + 0*n**a + 0 - 1/3*n = 0. What is n?
-1, 0, 1
Let s(u) = u + 7. Let d be s(-5). Suppose 31 = d*m + 5*y, -6*m = -m + 5*y - 40. Factor -3*b**3 - 3 + b**5 + 3*b + 2*b**5 + 2*b**3 - 5*b**3 + 6*b**2 - m*b**4.
3*(b - 1)**3*(b + 1)**2
Let f(z) = -z**2 - 8*z - 3. Let u be f(-7). Let b(o) be the first derivative of -2*o + 2/3*o**3 + 1/2*o**u - 2 - o**2. Solve b(j) = 0 for j.
-1, 1
Let l be (-13)/(-2) - 6/4. Let s = l - 3. Solve 6*q - q**2 - s*q - q**2 - 2*q = 0 for q.
0, 1
Let j(d) be the second derivative of -3*d**5/140 + 6*d. Find w, given that j(w) = 0.
0
Let w = 137/8 - 17. Let b(p) be the first derivative of 0*p - w*p**2 + 1/16*p**4 + 0*p**3 + 2. Factor b(a).
a*(a - 1)*(a + 1)/4
Let q(f) be the second derivative of f**9/3024 - f**8/840 - f**7/280 + f**6/90 + f**5/30 + f**3/3 - 6*f. Let l(v) be the second derivative of q(v). Factor l(n).
n*(n - 2)**2*(n + 1)**2
Suppose i - 4 = 0, -z + 0*i - i = -11. Determine o, given that z*o**2 - 14*o + 5*o**2 + 12*o**2 - 4 - 6*o**2 = 0.
-2/9, 1
Let v(u) be the second derivative of -u**5/15 + u**4/6 - u**3/9 + 3*u. Factor v(i).
-2*i*(i - 1)*(2*i - 1)/3
Suppose 0*v - 3*v - 9 = 0. Let g = v + 5. Suppose 5*c**2 - g*c**2 - 3*c**2 - 2*c**2 - 4*c - 2 = 0. What is c?
-1
Let v(s) be the second derivative of -s**4 + 1/10*s**5 - 8*s**2 + 4*s**3 - 6*s + 0. Factor v(n).
2*(n - 2)**3
Let o be (2*-1)/(12/(-18)). Factor 4*v - 4*v**4 - 2*v**o - 2*v**3 + 2*v**2 + 4*v**2 - 2*v**2.
-4*v*(v - 1)*(v + 1)**2
Let x(j) be the third derivative of 0*j + 7/48*j**4 + 3/40*j**5 - 1/6*j**3 + 0 + 3*j**2. Factor x(r).
(r + 1)*(9*r - 2)/2
Let k(x) be the third derivative of -x**7/210 - x**6/80 - x**5/120 - 4*x**2. Solve k(j) = 0 for j.
-1, -1/2, 0
Let p(w) be the second derivative of w**5/150 - w**4/45 - w**3/45 + 2*w**2/15 + 3*w. Solve p(b) = 0.
-1, 1, 2
Factor 5*w**3 + 10 + 2*w - 10*w**2 - 5*w - 2*w.
5*(w - 2)*(w - 1)*(w + 1)
Let i(t) be the third derivative of -t**5/180 + t**3/18 + 2*t**2. Factor i(x).
-(x - 1)*(x + 1)/3
Let w(m) be the second derivative of 2*m**7/21 - m**6/5 - 3*m**5/10 + m**4/3 + 16*m. Solve w(c) = 0.
-1, 0, 1/2, 2
Suppose -c = -6*c + 10. Suppose -4/3*f**c + 2/3*f**4 + 2/3 + 2*f**5 + 2*f - 4*f**3 = 0. Calculate f.
-1, -1/3, 1
Let s(g) be the second derivative of -1/4*g**3 - 3*g + 1/24*g**4 + 1/2*g**2 + 0. Factor s(v).
(v - 2)*(v - 1)/2
Let u(x) be the first derivative of -x**4/4 + x**3 - 4*x - 38. Factor u(q).
-(q - 2)**2*(q + 1)
Let s(w) = -w**3 + 3*w**2 + 4*w + 2. Let x be s(4). Factor o**x + 18 - 18 - o**4.
-o**2*(o - 1)*(o + 1)
Let -8/3 - 2/9*p**2 - 16/9*p = 0. Calculate p.
-6, -2
Let b(t) = 9*t**4 + 5*t**3 - 5*t**2 + 7*t + 8. Let n(v) = -9*v - 6*v + 10*v**2 - 11*v**3 - 2 - 19*v**4 - 15. Let g(p) = -13*b(p) - 6*n(p). Factor g(c).
-(c - 1)**2*(c + 1)*(3*c + 2)
Let q(o) be the first derivative of 1/9*o**6 + 5/6*o**4 - 3 + 0*o**2 + 4/9*o**3 + 8/15*o**5 + 0*o. Solve q(w) = 0.
-2, -1, 0
Suppose 0 = 4*f - 8*f. Let u(t) be the third derivative of 0 + f*t**4 + 0*t**5 + 0*t**3 + 1/300*t**6 + 0*t - 3*t**2. Solve u(s) = 0 for s.
0
Let g be 164/287 + 24/7. Determine z, given that 4/9*z - 14/9*z**g + 0 + 14/9*z**2 - 4/9*z**3 = 0.
-1, -2/7, 0, 1
Let i(q) be the first derivative of -q**6/30 - 3*q**5/25 - q**4/10 + 2*q**3/15 + 3*q**2/10 + q/5 + 6. Factor i(j).
-(j - 1)*(j + 1)**4/5
Suppose 0 = -3*h - 3 + 12. Find b, given that -39*b**h - 4*b + 10*b**4 + 25*b**2 + b**2 - 7*b**3 + 14*b**4 = 0.
0, 1/4, 2/3, 1
Factor -16/17*g + 10/17*g**2 - 2/17*g**3 + 8/17.
-2*(g - 2)**2*(g - 1)/17
Let c(t) be the third derivative of -1/672*t**8 + 0 - 1/105*t**7 + t**2 + 0*t - 1/48*t**4 + 0*t**3 - 1/30*t**5 - 1/40*t**6. Suppose c(f) = 0. Calculate f.
-1, 0
Let j(n) be the third derivative of -n**8/560 + 9*n**7/350 - 13*n**6/100 + 9*n**5/50 + 27*n**4/40 - 27*n**3/10 - 32*n**2. Suppose j(w) = 0. Calculate w.
-1, 1, 3
Let v(d) be the first derivative of -d**7/70 + d**6/20 - d**4/4 + d**3/2 + 5*d**2/2 - 4. Let k(g) be the second derivative of v(g). Let k(h) = 0. Calculate h.
-1, 1
Factor -1 + 4 + 3*b + 2*b**2 + 3 + 5*b.
2*(b + 1)*(b + 3)
Factor -6*s**4 - 16*s**2 - 21*s**4 + 32*s**3 + 7*s**4 + 14*s**5 - 10*s**5.
4*s**2*(s - 2)**2*(s - 1)
Let w be 1/5*(-1 - (-3 + 0)). Suppose -3/5*d - w - 1/5*d**2 = 0. What is d?
-2, -1
Suppose -3*y + 18 = 5*a, -3*a = -2*y + 4*y - 11. Suppose -9 + a = -u. Factor u*s**2 + 2*s + 3 + 0*s**2 - 7.
2*(s + 1)*(3*s - 2)
Suppose 3*i = 5*h + 19, 5*h + 25 = 5*i - 0*h. Let p(r) be the first derivative of 4/3*r + 2 - 1/3*r**2 - 2/9*r**i. Factor p(a).
-2*(a - 1)*(a + 2)/3
Let u(j) be the second derivative of 10*j + 0 - 2*j**2 - 1/3*j**3 - 1/48*j**4. Determine b so that u(b) = 0.
-4
Let v(y) = 3*y + 2. Let u be v(5). Suppose 5 + 1 = -4*c - 3*o, -3*c = -3*o - 6. Solve -2*x**3 + 10*x**2 + c + x + 8 - u*x = 0.
1, 2
Suppose 0*a - 4*a = 0. Solve -6*c**4 + 4*c**2 + 3*c**4 + a*c**4 - 5*c**3 + 0*c**4 + 4*c = 0.
-2, -2/3, 0, 1
Find i, given that -8 - 16*i**2 - i - i - 4*i**3 - 18*i = 0.
-2, -1
Let h = -114 + 1028/9. Solve 4/9*a + h*a**2 + 0 = 0 for a.
-2, 0
Let c(j) be the third derivative of 0*j + 1/18*j**3 - 1/90*j**6 - 1/36*j**4 + 0 - 7/180*j**5 - 3*j**2. Factor c(f).
-(f + 1)**2*(4*f - 1)/3
Let z = -7 + 9. Let y(k) be the first derivative of -z - 4/3*k**3 - k + 7/4*k**2 + 3/8*k**4. Factor y(i).
(i - 1)**2*(3*i - 2)/2
Let w(x) be the first derivative of -x**6/6 + x**5/10 - x - 1. Let u(l) be the first derivative of w(l). Factor u(z).
-z**3*(5*z - 2)
Factor 2*x**2 - 22*x**2 - 35 - 25*x + 30.
-5*(x + 1)*(4*x + 1)
Let r be (-9)/(405/(-42)) + (-18)/30. Determine b so that 0 + 1/3*b**2 - r*b = 0.
0, 1
Let l(h) be the third derivative of h**7/245 - 13*h**6/280 + 3*h**5/28 + h**4/56 - 5*h**3/14 + 29*h**2 + h. Let l(i) = 0. Calculate i.
-1/2, 1, 5
Let j(s) = -s + 9. Let c be j(16). Let h(x) = -6*x**2 + 2*x - 4. Let v(b) = 12*b**2 - 3*b + 7. Let l(d) = c*h(d) - 4*v(d). Find r such that l(r) = 0.
-1/3, 0
Let z(q) be the third derivative of -q**8/23520 + q**7/4410 - q**6/2520 - q**4/12 + 4*q**2. Let l(j) be the second derivative of z(j). Factor l(w).
-2*w*(w - 1)**2/7
Let o(x) be the second derivative of -x**5/40 - 5*x**4/24 - 7*x**3/12 - 3*x**2/4 - 14*x. Factor o(q).
-(q + 1)**2*(q + 3)/2
Let v = -737 + 737. Factor v - 8/3*s + 2*s**3 - 2/3*s**4 + 0*s**2.
-2*s*(s - 2)**2*(s + 1)/3
Let h(g) = -g**2 - 6*g - 8. Let m be h(-4). Let i(d) be the second derivative of 0*d**4 + 1/6*d**3 - 1/20*d**5 + m*d**2 + d + 0. Factor i(j).
-j*(j - 1)*(j + 1)
Let d(g) be the first derivative of -g**6/9 + 5. Factor d(q).
-2*q**5/3
What is g in 6*g - 4 + g**2 + 2*g**2 - 3*g**2 - 2*g**2 = 0?
1, 2
Suppose d + 3*d = -8. Let n be (0 + d + -1)*-1. Solve -5*c**n - 4*c + 10*c**2 + 9*c**3 - 2*c**3 + 12*c**3 = 0 for c.
-1, 0, 2/7
Suppose 2*q + 14 = -12. Let l = -10 - q. Determine z, given that 0*z + 0 + 2/3*z**4 + 0*z**l - 2/3*z**2 = 0.
-1, 0, 1
Let b(k) be the third derivative of 2*k**7/735 - k**5/105 - 14*k**2. Suppose b(u) = 0. Calculate u.
-1, 0, 1
Factor -1/4 + c**3 - c + 1/4*c**2.
(c - 1)*(c + 1)*(4*c + 1)/4
Suppose -2 = x + x, 42 = 5*i + 3*x. Let c be -2 + 1 + i/6. Determine w, given that 0 + 0*w + c*w**2 + 1/2*w**3 = 0.
-1, 0
Let d(w) be the third derivative of 0*w**4 + 3*w**2 + 0*w - 1/40*w**6 - 1/60*w**5 + 0*w**3 + 0 - 1/105*w**7. Determine k so that d(k) = 0.
-1, -1/2, 0
Suppose 5*p + 4*k = 1 - 9, -3*p - 4 = 2*k. Factor h**2 + p - 1/2*h**3 - 1/2*h.
-h*(h - 1)**2/2
Let s = -82 + 493/6. Let z(u) be the first derivative of 0*u - 2 + 1/9*u**3 - s*u**2. Factor z(d).
d*(d - 1)/3
Let q(a) = 3*a**2 + 61*a + 20. Let b be q(-20). Factor b*l**3 - 2/5*l**2 + 0*l + 1/5*l**4 + 1/5.
(l - 1)**2*(l + 1)**2/5
Let u(b) be the third derivative of b**6/60 - b**5/15 + b**4/12 + 2*b**2. Factor u(q).
2*q*(q - 1)**2
Let u be -3*4/48 - 12/(-24). Determine g so that 0*g**2 + 0 - u*g**4 + 3/4*g**3 + 0*g = 0.
0, 3
Suppose 3*m = -4 + 19. Let s(w) = w. Let n(g) be the third derivative of -g**5/20 + g**4/12 + g**2