4)/(-20) - 45/(-25). Let l(z) be the first derivative of 2/7*z - 4/7*z**r - 3 + 2/7*z**3. Let l(n) = 0. What is n?
1/3, 1
Let r = -10/13 + 33/26. Let -r*k**3 + 0*k**2 + 0 + 0*k = 0. What is k?
0
Let j(g) be the first derivative of -g + 1/4*g**4 + 1 - 1/2*g**2 + 1/3*g**3. Let j(n) = 0. What is n?
-1, 1
Suppose -4*v + 5*i + 2 = 0, -5*v + i = 3*i - 19. Factor 2*u**2 + u**2 + 3*u**v + 3*u - 4*u - 5*u.
3*u*(u - 1)*(u + 2)
Let p(i) = i**3 - 2*i**2 + 2. Let l be p(2). Suppose -z**2 + 3 + l - 5 = 0. Calculate z.
0
Let j(d) = -2*d**3 + 5*d**2 + 27*d - 3. Let o(w) = 3*w**3 - 5*w**2 - 28*w + 2. Let b(q) = -2*j(q) - 3*o(q). Factor b(f).
-5*f*(f - 3)*(f + 2)
Let h(m) = 7*m**4 + 8*m**3 - 7*m**2 - 8*m - 6. Let p(a) = a**4 + a**3 - a**2 - a - 1. Let i(n) = h(n) - 6*p(n). Solve i(d) = 0 for d.
-2, -1, 0, 1
Let -4/3*r**3 - 2/3*r**5 + 0*r + 0 + 2*r**4 + 0*r**2 = 0. What is r?
0, 1, 2
Let q be 14/(-4) + (-4 - -4 - -4). Find t such that 1/4 + 0*t + 0*t**3 - q*t**2 + 1/4*t**4 = 0.
-1, 1
Let d = 1048/5643 + -2/513. Solve d*c**3 + 0 + 2/11*c**2 - 2/11*c**4 - 2/11*c = 0.
-1, 0, 1
Let p(m) be the first derivative of m**3/24 - 3*m**2/8 + 9*m/8 + 16. Suppose p(b) = 0. Calculate b.
3
Let g = 8 + -6. Let h(i) be the first derivative of 1/16*i**4 + 2 + 1/12*i**3 - 1/20*i**5 + 0*i - 1/8*i**g. Find y, given that h(y) = 0.
-1, 0, 1
Let t(r) be the second derivative of -r**4/51 + 25*r**3/51 - 12*r**2/17 + 40*r. Determine g, given that t(g) = 0.
1/2, 12
Suppose 0*y - 5*y = -25. Let m(n) = -n**3 + 6*n**2 - 4*n - 5. Let r be m(y). Factor -6/7*q**5 + r*q**2 - 2/7*q**4 + 4/7*q**3 + 0*q + 0.
-2*q**3*(q + 1)*(3*q - 2)/7
Solve -80*b - 5*b**5 - 95*b**3 - 72*b**2 - 35*b**4 - 53*b**2 + 3 - 23 = 0.
-2, -1
Let l(v) = 4*v - 5. Let u be l(5). Suppose 3*c + 3*d - u = 0, -c + 5*c - d = -5. Determine b, given that c - 2/7*b**2 + 2/7*b = 0.
0, 1
Let j be (961/(-6))/((-2)/(-4)). Let p = j - -323. Determine c so that -1/3*c + p*c**2 - 2/3 - 5/3*c**3 = 0.
-2/5, 1
Let s(y) be the first derivative of 25*y**4/18 + 10*y**3/9 - y**2 + 2*y/9 - 3. Factor s(u).
2*(u + 1)*(5*u - 1)**2/9
Solve 0 - 2/3*g**4 + 8/3*g - 22/3*g**2 - 2/3*g**5 + 6*g**3 = 0 for g.
-4, 0, 1
Let u(j) = j**3 + 6*j**2 + 3. Let p be u(-6). Let r be p + 4/(-8)*0. Factor -8/11*h**2 - 8/11*h**4 + 0 - 2/11*h**5 - 2/11*h - 12/11*h**r.
-2*h*(h + 1)**4/11
Let n be ((-5)/(-5))/(2/6). Find p such that -20/7*p**n - 4*p - 4/7*p**4 - 36/7*p**2 - 8/7 = 0.
-2, -1
Let x(f) be the second derivative of f**6/2520 + f**5/210 + f**4/42 + 3*f**3/2 + 3*f. Let c(w) be the second derivative of x(w). What is r in c(r) = 0?
-2
Let w(u) be the second derivative of 1/35*u**7 + 0*u**2 - 3/50*u**5 + 0 - 1/15*u**4 + 0*u**3 + 2/75*u**6 - 4*u. Find p, given that w(p) = 0.
-1, -2/3, 0, 1
Suppose -2 = -3*g + 13. Let p = -13/3 + g. Determine q, given that 0 + 0*q + p*q**2 = 0.
0
Factor -4/5*i**2 - 1/5*i**4 + i**3 + 0 + 0*i.
-i**2*(i - 4)*(i - 1)/5
Let q = -62 + 66. Let j(h) be the third derivative of 1/110*h**5 + 1/220*h**6 - 2*h**2 + 0*h + 1/1155*h**7 + 0 + 0*h**3 + 1/132*h**q. Factor j(l).
2*l*(l + 1)**3/11
Solve 0*d**2 + 0*d + 4/3*d**3 + 40/3*d**5 + 0 - 26/3*d**4 = 0.
0, 1/4, 2/5
Suppose -8*j + 2*j = -84. Let b be ((-16)/(-20))/(j/5). Suppose -b + 2/7*p**5 + 4/7*p**3 + 6/7*p**4 - 6/7*p - 4/7*p**2 = 0. Calculate p.
-1, 1
Factor -72/5 - 2/5*u**2 + 24/5*u.
-2*(u - 6)**2/5
Suppose -26 = 5*n - 8*n + 5*z, -n + 18 = -4*z. Factor 0 - 3/4*h**3 - 27/4*h - 9/2*h**n.
-3*h*(h + 3)**2/4
Let a(z) be the second derivative of 3*z + 1/21*z**7 + 0*z**3 + 0 + 1/6*z**4 - 1/10*z**5 + 0*z**2 - 1/15*z**6. Factor a(m).
2*m**2*(m - 1)**2*(m + 1)
Let b(c) be the first derivative of c**3/3 - c**2/4 + 21. Let b(m) = 0. Calculate m.
0, 1/2
Let s(f) be the third derivative of f**9/20160 + f**8/5040 + f**7/5040 + f**5/60 + 4*f**2. Let w(p) be the third derivative of s(p). What is x in w(x) = 0?
-1, -1/3, 0
Find h such that -2*h + 3 + 1/3*h**2 = 0.
3
Let j be 2/8 - 280/(-32). Solve 8*t - j*t**3 - 5 + 6*t**2 - 1 + t = 0.
-1, 2/3, 1
Suppose -4*c + 4*m = -40, -2*m + 0 = 4*c - 28. Factor 2*u**4 - c*u**2 + 5*u**2 + 2 - u**2.
2*(u - 1)**2*(u + 1)**2
Let y(s) be the first derivative of -8*s**6/3 - 4*s**5/15 + s**4/3 + 8. Find d such that y(d) = 0.
-1/3, 0, 1/4
Factor -12/7*i - 6/7*i**2 - 8/7 - 1/7*i**3.
-(i + 2)**3/7
Let c = -1018 + 1018. Suppose -1/4*q**4 - 1/4*q**2 + c + 0*q - 1/2*q**3 = 0. What is q?
-1, 0
Let r(b) be the second derivative of -2*b**4/3 - b**3 + b**2 + 2*b. Let r(k) = 0. Calculate k.
-1, 1/4
Let n(m) be the third derivative of -m**7/840 - m**6/240 + m**5/240 + m**4/48 + 20*m**2. Factor n(y).
-y*(y - 1)*(y + 1)*(y + 2)/4
Let q = -6 - -8. Suppose -q*o + 1 = -3. What is p in 2 - 4*p + p**2 + 2*p**2 - p**o = 0?
1
Let l(q) = -2*q**2 - 7*q + 6. Let s(v) = -3*v**2 - 6*v + 5. Let r(a) = -4*l(a) + 3*s(a). Let c be r(9). Factor c*z**2 - 2/5*z + 2/5*z**3 + 0.
2*z*(z - 1)*(z + 1)/5
Suppose -162 = 4*s - 2*m, 3 = -5*m - 2. Let q = s + 62. Factor -72*f - 16 + 57*f**4 + 9*f**3 - 73*f**2 + q*f**2 - 7*f**4 + 81*f**3.
2*(f - 1)*(f + 2)*(5*f + 2)**2
Suppose 2*a = -c + 13, -4*c + 10 = 2*a - 0*c. Let b be 0 - (-1)/(a/2). Factor 2/7*t**2 + b*t + 0.
2*t*(t + 1)/7
Let n(u) be the first derivative of -5*u**6/2 - 7*u**5 - 5*u**4 - 60. Determine w, given that n(w) = 0.
-4/3, -1, 0
Solve 2*a**4 + a**4 + 15*a**2 + 12*a**3 + 6*a + 0*a**4 + 0*a = 0 for a.
-2, -1, 0
Let g = 25 - 19. Determine x so that x**4 + 6*x**3 - g*x**3 + x**3 = 0.
-1, 0
Suppose 3*s - 11 + 2 = 0. Factor -2*g - 14*g**3 + 6 - 8*g**5 - 16*g**s - g**5 - 30*g**4 + 17*g.
-3*(g + 1)**4*(3*g - 2)
Suppose 20*j = 11*j + 10*j. Let a(p) be the third derivative of 0*p + 1/1008*p**8 + 0*p**5 + 0*p**6 + 0*p**7 + 4*p**2 + 0*p**4 + 0 + j*p**3. Factor a(t).
t**5/3
Let d(b) be the third derivative of b**7/420 - b**6/40 + 13*b**5/120 - b**4/4 + b**3/3 - 28*b**2. Find z, given that d(z) = 0.
1, 2
Let t(k) be the second derivative of 3*k**7/56 + k**6/8 + 3*k**5/80 - k**4/16 + 3*k. Factor t(f).
3*f**2*(f + 1)**2*(3*f - 1)/4
Let a(d) be the first derivative of -4*d - 8/3*d**3 + 5*d**2 + 1/2*d**4 + 4. Solve a(n) = 0.
1, 2
Let f(x) = 14*x. Let z be f(1). Suppose -5*b + z = -d - d, -3*d = 3*b. Factor -t**2 + 2*t**2 - t + b*t.
t*(t + 1)
Factor 0 - 33*o**2 - 6 - 6765*o + 6726*o.
-3*(o + 1)*(11*o + 2)
Let o(i) = -2*i**3 - 2*i**2 + 3*i + 3. Let v be o(-2). Suppose 4*m = 4*c, 0 = -2*m + 4*m - v*c. Factor 1/2*s**5 + 0 - 1/2*s**3 - 1/2*s**2 + 1/2*s**4 + m*s.
s**2*(s - 1)*(s + 1)**2/2
Let c = 2003/10 + -395/2. Factor 8/5 + 32/5*n + c*n**2.
2*(n + 2)*(7*n + 2)/5
Suppose f - 5 + 2 = 0. Let 3*d**3 + 0*d**f + 2*d + 0*d + 3 - 3*d**2 - 5*d = 0. What is d?
-1, 1
Let o = 32 - 32. Let v(r) be the first derivative of 0*r**2 + 2/5*r**6 + o*r + 3/5*r**4 + 2 - 22/25*r**5 - 2/15*r**3. Find d such that v(d) = 0.
0, 1/3, 1/2, 1
Let x(d) = d**5 - 49*d**4 - 81*d**3 - 47*d**2 - 25*d - 9. Let q(h) = -12*h**4 - 20*h**3 - 12*h**2 - 6*h - 2. Let n(r) = -9*q(r) + 2*x(r). Factor n(a).
2*a*(a + 1)**3*(a + 2)
Let y(g) be the second derivative of -g**8/280 - g**7/75 - g**6/100 + g**5/50 + g**4/30 + g**2 + 2*g. Let p(t) be the first derivative of y(t). Factor p(d).
-2*d*(d + 1)**3*(3*d - 2)/5
Let p(z) = -12*z**4 - 9*z**3 + 3*z**2 - 15*z + 15. Let u(i) = 3*i**4 + 2*i**3 - i**2 + 4*i - 4. Let f(a) = -4*p(a) - 15*u(a). Factor f(s).
3*s**2*(s + 1)**2
Let l be 274/(-70) + 22/110 - -4. Factor l*r**2 + 8/7*r + 6/7.
2*(r + 1)*(r + 3)/7
Determine a, given that -17*a**2 + 15*a**2 - 3*a**3 - 2*a**5 + 4*a**3 + 2*a**4 + a**3 = 0.
-1, 0, 1
Suppose -t = -2*t + 15. Determine z, given that -2*z**2 + 17*z**4 + 32*z**5 - 8*z**3 + t*z**4 + 6*z**3 = 0.
-1, -1/4, 0, 1/4
Let t(j) be the second derivative of -j**5/20 + 3*j**4/4 - j**3 - 5*j**2 + 3*j. Let a be t(8). Factor a*y**3 - y**2 - y**2 - 8*y**3.
-2*y**2*(y + 1)
Factor 4/5*v**4 + 12/5*v**3 + 0 + 0*v**2 - 16/5*v.
4*v*(v - 1)*(v + 2)**2/5
Let u(w) be the first derivative of -21/4*w**4 - 3*w**2 + 9*w**3 - 2 + 0*w. Factor u(r).
-3*r*(r - 1)*(7*r - 2)
Let t(d) be the first derivative of d**8/840 + d**7/105 + d**6/30 + d**5/15 + d**4/12 - 2*d**3/3 + 5. Let q(y) be the third derivative of t(y). Factor q(m).
2*(m + 1)**4
Factor 2*j**3 + 5 - 2 - j + 5*j**2 + 8*j - j**3.
(j + 1)**2*(j + 3)
Let s(w) be the first derivative of 3 - 1/6*w**3 - 1/2*w**2 - 1/2*w. Determine n, given that s(n) =