, 1/4, 1
Let p(l) = 6*l**2 + 3*l - 3. Let x be -3 + (1 - 1) + -2. Let a = x - -9. Let s(u) = -7*u**2 - 4*u + 4. Let d(m) = a*p(m) + 3*s(m). Factor d(w).
3*w**2
Let x(m) be the second derivative of -m**7/14 + 7*m**6/10 - 27*m**5/10 + 5*m**4 - 4*m**3 + 3*m. Solve x(v) = 0 for v.
0, 1, 2
Suppose -5*n = -n + 5*f - 18, 3*n = -4*f + 14. Let l be 6/(-9)*n/(-1). Factor 4/3 + 1/3*k**2 + l*k.
(k + 2)**2/3
Suppose 0*v - 4*v = 0, v + 2 = k. Factor -3 - 15/2*n + 21/2*n**k.
3*(n - 1)*(7*n + 2)/2
Let z(v) be the third derivative of v**6/540 - 2*v**5/135 + 5*v**4/108 - 2*v**3/27 + 3*v**2. Let z(p) = 0. What is p?
1, 2
Let q(i) be the third derivative of i**6/420 - i**5/70 + i**4/42 + 5*i**2. Factor q(j).
2*j*(j - 2)*(j - 1)/7
Let y(z) = 7*z**5 - 16*z**4 + 15*z**3 - 10*z**2. Let x(p) = p**5 - p**4 - p**2. Let a(n) = 4*x(n) - y(n). Let a(k) = 0. What is k?
0, 1, 2
Let p(s) be the third derivative of 17/60*s**5 + 0 - 1/60*s**6 + 1/6*s**3 + 0*s - 4/35*s**7 - s**2 + 1/3*s**4. Find n, given that p(n) = 0.
-1/2, -1/3, -1/4, 1
Let b(z) = -27*z**2 - 21*z. Let g(c) = -7*c**2 - 5*c. Let m(f) = 4*b(f) - 15*g(f). Factor m(y).
-3*y*(y + 3)
Let v(t) be the first derivative of -1 - 4/3*t**3 + t**2 + 0*t + 1/2*t**4. Factor v(n).
2*n*(n - 1)**2
Let n(r) = 18*r**3 + 19*r**2 - 4*r. Let c(g) = 9*g**3 + 10*g**2 - 2*g. Let v(x) = 10*c(x) - 6*n(x). Factor v(s).
-2*s*(s + 1)*(9*s - 2)
Let t(j) be the first derivative of j**6/18 - j**4/4 + 2*j**3/9 + 10. Solve t(u) = 0 for u.
-2, 0, 1
Factor -3/2*d + 2 - 1/2*d**2.
-(d - 1)*(d + 4)/2
Suppose 106*d**2 + 0*d + 2*d - 98*d**2 + 8*d**3 = 0. Calculate d.
-1/2, 0
Let k = -553 - -558. Find t, given that 50/3*t**k + 30*t**4 - 16*t - 8/3 - 2/3*t**3 - 82/3*t**2 = 0.
-1, -2/5, 1
Let f(y) be the first derivative of y**4/4 - 5*y**3/3 + 2*y - 2. Let n be f(5). Factor -2*s**2 + 0*s**2 - 2*s**4 - 4*s**3 + 4*s**n - 4*s**2.
-2*s**2*(s + 1)**2
Let m(d) = 10*d**2 + 11*d - 5. Let j(v) = 11*v**2 + 12*v - 6. Let n(c) = -6*j(c) + 7*m(c). Determine s, given that n(s) = 0.
-1, -1/4
Let a(l) be the first derivative of -48*l**5/35 + 30*l**4/7 - 17*l**3/7 + 3*l**2/7 - 10. Find p, given that a(p) = 0.
0, 1/4, 2
Let f be -64*3/(-234) - (-2)/(-13). Factor -38/3*h**3 - f*h**5 - 50/3*h**2 - 14/3*h**4 - 32/3*h - 8/3.
-2*(h + 1)**3*(h + 2)**2/3
Let w(b) = 2*b**2 + 5*b + 7. Let i be w(-2). Let d(m) be the second derivative of 0*m**2 + 1/30*m**i + 2*m + 0 - 1/9*m**3 + 0*m**4. Factor d(z).
2*z*(z - 1)*(z + 1)/3
Let z(d) be the third derivative of d**7/357 + d**6/85 + 3*d**5/170 + d**4/102 - 7*d**2. Factor z(m).
2*m*(m + 1)**2*(5*m + 2)/17
Let y(d) be the third derivative of d**11/1164240 - d**9/105840 + d**7/17640 - d**5/12 - 3*d**2. Let g(t) be the third derivative of y(t). Factor g(r).
2*r*(r - 1)**2*(r + 1)**2/7
Let c(y) be the first derivative of 2*y**3/3 + 3*y**2 + 4*y + 4. Solve c(l) = 0.
-2, -1
Let t be (-6)/(-15) - 5*1/25. Solve -t*a**4 + 1/5*a**3 - 1/5*a + 0 + 1/5*a**2 = 0.
-1, 0, 1
Factor 0 + 1/7*d**2 + 2/7*d.
d*(d + 2)/7
Let u be (-2)/1 - (-15)/1. Let t = u - 10. Determine z, given that z**4 + z**3 + z**2 + z**3 + 2*z**t - 2*z**3 = 0.
-1, 0
Suppose -31 = -7*q - 10. Let m(j) be the second derivative of 1/10*j**2 + 1/100*j**5 + 0 + 1/20*j**4 + j + 1/10*j**q. Factor m(o).
(o + 1)**3/5
Find j, given that -24*j + 14*j - 5*j**2 - 3*j**4 + 3*j**3 + 8*j**2 + 7*j = 0.
-1, 0, 1
Suppose 5*q - 5*l - 1595 = 0, -5*q + 3*l + 327 = -4*q. Let u be 125/q + (-2)/18. Suppose -4/7*a - 2/7 - u*a**2 = 0. What is a?
-1
Let b = 253 + -6829/27. Let g(c) be the second derivative of -1/90*c**5 + b*c**3 + 0*c**2 + c + 0 + 1/54*c**4. Factor g(p).
-2*p*(p - 2)*(p + 1)/9
Factor -3/7*f**2 - 9/7*f**4 + 0 - 3/7*f**5 - 9/7*f**3 + 0*f.
-3*f**2*(f + 1)**3/7
Let c(n) be the second derivative of n**6/720 - n**5/360 - n**4/144 + n**3/36 - 2*n**2 + 5*n. Let q(w) be the first derivative of c(w). Factor q(z).
(z - 1)**2*(z + 1)/6
Let g(c) = 2*c. Let k be g(2). Suppose -3 - 5 = -k*d. Factor -o**2 - 3*o**2 + 5*o**d.
o**2
Let t(h) = 131*h**3 - 475*h**2 + 314*h - 66. Let v(f) = -392*f**3 + 1425*f**2 - 943*f + 197. Let s(r) = -17*t(r) - 6*v(r). Factor s(d).
5*(d - 3)*(5*d - 2)**2
Let k = -155 - -157. Factor -k*u - 2*u**2 - 1/2.
-(2*u + 1)**2/2
Let f(c) be the second derivative of -c**5/4 + 25*c**4/12 - 20*c**3/3 + 10*c**2 - 10*c. Determine a, given that f(a) = 0.
1, 2
Let b(a) = -a**2 + 4*a - 3. Let j be b(1). Find k, given that -1/3*k**4 - 1/3 + 2/3*k**2 + j*k**3 + 0*k = 0.
-1, 1
Suppose -4*k + 6 = -3*l - 23, 10 = -k - 5*l. Factor 2/3*c**3 + 0 + 0*c + 0*c**2 - 2/3*c**k + 0*c**4.
-2*c**3*(c - 1)*(c + 1)/3
Factor 1/4*u + 0 - 1/4*u**5 + 0*u**3 - 1/2*u**2 + 1/2*u**4.
-u*(u - 1)**3*(u + 1)/4
Let m(g) be the third derivative of -g**6/720 - g**5/120 - g**4/48 - g**3/36 - 2*g**2. Let m(n) = 0. Calculate n.
-1
Let k(r) = 5*r**2 + 18*r + 27. Let u(m) = 11*m**2 + 36*m + 54. Let t(f) = 5*k(f) - 2*u(f). What is s in t(s) = 0?
-3
Suppose -j + 2*j = 5*l - 6, -l = 2*j - 10. Let f(d) be the first derivative of 0*d - 2/5*d**l + 1 - 2/15*d**3. Factor f(h).
-2*h*(h + 2)/5
Factor 2*i + 3*i**2 - 6*i + 0*i + 3*i - 2*i**3.
-i*(i - 1)*(2*i - 1)
Let a(v) be the second derivative of v**4/78 - 4*v**3/39 + 3*v**2/13 + 13*v. Solve a(x) = 0 for x.
1, 3
Suppose 23 = 3*d + 17. Let u(g) be the first derivative of -1/12*g**4 + 0*g - 1/9*g**3 + 0*g**d - 2 + 1/15*g**5 + 1/18*g**6. Let u(z) = 0. What is z?
-1, 0, 1
Let b(x) be the first derivative of -4 + 1/9*x**3 + 1/3*x - 1/3*x**2. Find d such that b(d) = 0.
1
Let y(g) be the third derivative of -g**5/300 + g**4/40 - g**2. Factor y(r).
-r*(r - 3)/5
Solve 1/4 - 1/4*u**3 - 3/4*u + 3/4*u**2 = 0 for u.
1
Let q(i) = -6*i**4 + 57*i**3 - 15*i**2 - 27*i + 6. Let k(h) = h**4 - 8*h**3 + 2*h**2 + 4*h - 1. Let y(p) = 15*k(p) + 2*q(p). What is a in y(a) = 0?
-1, 1
Let s(n) be the first derivative of -2*n**5/45 + n**4/18 + 2*n**3/27 - n**2/9 - 12. Suppose s(z) = 0. What is z?
-1, 0, 1
Let c(k) = -k**3 - 8*k**2 + 8*k - 1. Let j = 0 - 9. Let o be c(j). Solve -2*g**5 - 3*g**5 - 29*g**2 - 27*g**4 - o*g + 10*g**2 - 50*g**3 - 17*g**2 = 0.
-2, -1, -2/5, 0
Suppose -4*q - 20 = -q + 4*y, -3*y - 15 = 0. Suppose q*v + 12 = 3*v. Factor 0*p + 1/2*p**2 + 1/2*p**v - p**3 + 0.
p**2*(p - 1)**2/2
Let a(x) be the second derivative of -1/72*x**4 + 1/2*x**2 + 0*x**3 + 0 - 2*x + 1/360*x**5. Let r(l) be the first derivative of a(l). Factor r(q).
q*(q - 2)/6
Let u be (1/(-2))/((-1)/4). Let p be (4 + 0 - 5) + 4. Factor 2*b**3 + 7*b**p - 3*b**2 - 3*b**u.
3*b**2*(3*b - 2)
Solve -16/11*r + 2/11*r**2 + 32/11 = 0 for r.
4
Let c(k) be the third derivative of k**9/60480 - k**8/13440 + k**6/1440 - k**5/480 - k**4/8 - k**2. Let o(t) be the second derivative of c(t). Factor o(s).
(s - 1)**3*(s + 1)/4
Let r = -1124/115 + -301994/1035. Let n = 302 + r. Factor 2/9*v**5 + 0*v**4 + 2/9*v - n*v**3 + 0 + 0*v**2.
2*v*(v - 1)**2*(v + 1)**2/9
Determine n so that 9 + 3*n**2 - 1/3*n**3 - 9*n = 0.
3
Let c = 125/34 + -54/17. Factor -1/2*a**2 - c - a.
-(a + 1)**2/2
Let w(l) be the first derivative of -l**4/8 - 2*l**3/3 + 11*l**2/4 - 3*l + 48. Factor w(p).
-(p - 1)**2*(p + 6)/2
Determine f, given that -2/9*f**5 + 2/9*f**3 + 2/9*f**4 - 2/9*f**2 + 0*f + 0 = 0.
-1, 0, 1
Let w(c) be the third derivative of c**7/2940 - c**6/1260 - c**5/105 + c**4/21 - 7*c**3/6 - 7*c**2. Let i(g) be the first derivative of w(g). Factor i(l).
2*(l - 2)*(l - 1)*(l + 2)/7
Let f(s) be the second derivative of s**6/27 - s**5/5 + 17*s**4/54 - 4*s**2/9 + 7*s. Determine o so that f(o) = 0.
-2/5, 1, 2
Let i(k) be the second derivative of -k**5/10 - k**4/3 + k**3/3 + 2*k**2 + 6*k. Solve i(o) = 0 for o.
-2, -1, 1
Let n = -9959/30 - -332. Let c(d) be the second derivative of n*d**4 + 0 - 2*d + 0*d**3 - 1/5*d**2. Factor c(u).
2*(u - 1)*(u + 1)/5
Let y be 1 - 6/(-1220)*132. Let t = y - 3/61. Suppose 14/5*p**2 - 2/5 + t*p**3 + 4/5*p = 0. Calculate p.
-1, 1/4
Let x = 24 - 9. Suppose -5*f + 55 = x. Factor 2*k - 9*k**2 + 0*k**4 + f*k**3 + 2*k**3 - 3*k**4.
-k*(k - 2)*(k - 1)*(3*k - 1)
Let o be 32/14 - (-12)/(-42). Determine f, given that -3*f**2 + f**4 + 9*f**3 - 4 + o - 2*f**2 + 6*f**4 - 9*f = 0.
-1, -2/7, 1
Let s(b) be the third derivative of b**8/2856 + 2*b**7/1785 - b**6/255 - 4*b**5/255 - 20*b**2 - 1. Determine h, given that s(h) = 0.
-2, 0, 2
What is i in -2/3*i + 2/3*i**2 + 0 = 0?
0, 1
Supp