2*v + 4 = 5*p, 0 = -4*p - 3*v + 14. Solve 0*n**5 + 0*n**5 + 4*n**5 - 2*n**4 - p*n**3 + 2*n**2 - 2*n**5 = 0 for n.
-1, 0, 1
Let f(u) be the third derivative of 7/15*u**4 + 0 - 4/45*u**3 + 0*u + 3*u**2 - 49/50*u**5. Determine j, given that f(j) = 0.
2/21
Let i(p) = p**2 - 17*p - 108. Let r be i(22). Solve 0*q**r - 2/7*q**4 + 0 - 4/7*q**3 + 0*q = 0 for q.
-2, 0
Suppose 2*n - 3*u = -4, n = -u + 3*u - 4. Suppose -4*c**n - 12*c**2 - 4*c**5 + 20*c**2 - 8*c**4 + 8*c**2 = 0. Calculate c.
-2, 0, 1
Let y(l) = l + 2. Let d be y(0). Let h = 45 - 45. Solve -7*c**2 - 5*c + 5*c**2 + 3*c + h*c**d = 0.
-1, 0
Let z = -1632 - -1632. Factor 4/3*x**2 + 1/3*x + z.
x*(4*x + 1)/3
Let x = -1092 + 1095. Factor 0 + 2/17*f**x + 0*f - 2/17*f**2.
2*f**2*(f - 1)/17
Solve -1/2*j**2 - 43/2*j + 22 = 0.
-44, 1
Let k(s) = -s - 7. Let z be k(-11). Factor -8*m**2 - 5 - 7*m**2 + 7*m - z - 31*m.
-3*(m + 1)*(5*m + 3)
Let b(o) be the third derivative of -13*o**2 + 0*o**3 - 8/105*o**7 + 0 - 1/5*o**6 - 1/84*o**8 - 4/15*o**5 - 1/6*o**4 + 0*o. Let b(j) = 0. What is j?
-1, 0
Let t(j) be the second derivative of -5/2*j**2 + 10*j - 1/270*j**5 + 1/18*j**4 - 1/3*j**3 + 0. Let i(z) be the first derivative of t(z). Factor i(p).
-2*(p - 3)**2/9
Solve -26/3*s**2 - 32*s - 2/3*s**3 - 24 = 0 for s.
-6, -1
Let b(n) be the second derivative of -n**9/21168 - 17*n**8/47040 + n**7/1260 + n**6/630 - 3*n**4 + n. Let v(k) be the third derivative of b(k). Factor v(f).
-f*(f - 1)*(f + 4)*(5*f + 2)/7
Suppose 2*a - 1111 = 7*a - 2*l, 5*a + 2*l = -1099. Let u = a + 665/3. Factor -2/3*d**2 + 0 + u*d**4 + 2/3*d - 2/3*d**3.
2*d*(d - 1)**2*(d + 1)/3
Let z(f) be the first derivative of -f**6/6 - 3*f**5/5 + f**4/4 + f**3 - 13. Suppose z(n) = 0. What is n?
-3, -1, 0, 1
Suppose 26*z - 18 = 23*z. Let i(t) be the third derivative of 0*t + 0*t**3 + 1/60*t**6 - 1/10*t**5 + 0 - z*t**2 + 1/6*t**4. Factor i(p).
2*p*(p - 2)*(p - 1)
Let f be 96/48*(-4 - 33/(-8)). Determine u, given that -3/4*u + f*u**2 + 0 = 0.
0, 3
Let j be 3/(-4 - -1) + 3. Find c such that 6*c**4 + 13*c**4 + 2*c + j - 6*c**2 - 15*c**4 - 2*c**3 = 0.
-1, -1/2, 1
Let i(z) be the third derivative of 0 + 1/60*z**5 + 11*z**2 + 0*z + 1/6*z**4 + 1/2*z**3. Factor i(w).
(w + 1)*(w + 3)
Let h be (-3381)/(-6072) - (-2)/(-11). Let q(u) be the first derivative of 1/24*u**3 - 2 - 1/4*u**2 + h*u. Factor q(m).
(m - 3)*(m - 1)/8
Let r(w) = -w**2 - 39*w - 84. Let l be r(-17). Let h = l - 286. Solve -2/11*n**5 + 4/11*n**3 - 2/11*n + 4/11*n**2 - 2/11 - 2/11*n**h = 0 for n.
-1, 1
Let 12 + 8 - 15*u + 49915*u**2 - 49920*u**2 = 0. What is u?
-4, 1
Suppose 5*v - 40 = -5*x, -5*x - 7*v = -5*v - 25. Factor -15/4*a**2 - 125/4 - 1/4*a**x - 75/4*a.
-(a + 5)**3/4
Suppose -2*q + 84*q - 246 = 0. Let d(o) be the third derivative of -1/120*o**6 + 1/8*o**4 + 0 + 0*o - 1/3*o**q + 12*o**2 + 0*o**5. Factor d(t).
-(t - 1)**2*(t + 2)
Let m(v) be the first derivative of -20*v**2 - v**5 + 0*v - 24 + 5/2*v**4 + 20/3*v**3. Factor m(k).
-5*k*(k - 2)**2*(k + 2)
Let f(i) be the first derivative of i**4/6 + 58*i**3/3 - 59*i**2 + 178*i/3 + 420. What is x in f(x) = 0?
-89, 1
Let p(n) be the first derivative of n**3/9 + 61*n**2/6 + 118*n/3 - 635. Determine v, given that p(v) = 0.
-59, -2
Let p(v) be the third derivative of v**6/60 - 7*v**5/10 + 6*v**4 - 68*v**3/3 - 6*v**2 - 2*v. Suppose p(r) = 0. What is r?
2, 17
Let l(u) = -u**3 + 2*u**2 + 10*u + 7. Let g be l(-1). Let 1/5*b**3 + 0*b + 2/5*b**4 + 1/5*b**5 + g + 0*b**2 = 0. Calculate b.
-1, 0
Factor 4/5*p**3 - 8/5*p**4 + 3/5*p**5 - 7/5*p + 2/5 + 6/5*p**2.
(p - 1)**3*(p + 1)*(3*p - 2)/5
Let -31*s**2 + 26*s**2 - 623 + 128 + 120*s - 620*s = 0. Calculate s.
-99, -1
Let g(s) be the third derivative of s**4/24 - s**3/2 - 5*s**2. Let w be g(4). Solve u**3 - 2*u**3 - w + u**5 - 3*u**4 - 3 + 7*u**2 = 0 for u.
-1, 1, 2
Let a(h) be the third derivative of h**6/80 + 21*h**5/20 + 41*h**4/16 - 15*h**2 + 10*h. Determine p, given that a(p) = 0.
-41, -1, 0
Factor -51744*y**2 + 44 + 51650*y**2 + 14*y**3 + 4 + 140*y.
2*(y - 4)*(y - 3)*(7*y + 2)
Suppose 5*s - 2 - 8 = 0, -3*s = -5*i + 2299. Factor i - 461 - 30*y - 5*y**2.
-5*y*(y + 6)
Determine b, given that 67/4*b - 33/2 - 1/4*b**2 = 0.
1, 66
Let l = 24543 + -24540. What is v in 1/3*v**3 + 5*v - l*v**2 + 25/3 = 0?
-1, 5
Suppose 5*k = -20*a + 23*a + 22, 0 = 3*k + 3*a + 6. Determine i so that 0 - 3/2*i**k + 1/2*i**3 + 0*i = 0.
0, 3
Suppose -5*k = -11 + 1. Determine s so that 68*s**4 - 71*s**4 + 4 - s**5 - s**3 - 12*s + 2*s**5 + 11*s**k = 0.
-2, 1, 2
Let g = 523 - 523. Let n(b) be the second derivative of 3*b + 1/15*b**6 + 0*b**3 + 0*b**2 + 0*b**4 - 1/10*b**5 + g. Factor n(z).
2*z**3*(z - 1)
Let i(m) = 2*m + 17. Let z be i(-6). Let y(q) be the first derivative of 0*q**2 - 1/6*q**6 + 0*q**3 - 3 + 0*q + 0*q**z + 1/4*q**4. Factor y(c).
-c**3*(c - 1)*(c + 1)
Let z(a) be the third derivative of -a**7/420 - 19*a**6/240 - 17*a**5/40 - 49*a**4/48 - 4*a**3/3 + 3*a**2 + 14*a. Factor z(p).
-(p + 1)**3*(p + 16)/2
Suppose -5*n - 2*k + 20 = -3*n, 4*n - 33 = 3*k. Factor -14*f**4 + n*f**5 + 15*f**2 - 21*f**4 - 45*f**3 + 50*f**3 - 34*f**5.
-5*f**2*(f + 1)**2*(5*f - 3)
Let x(s) = 6*s**2 - 5*s + 11. Let b be x(-6). Factor -b*q**3 + 1176*q**2 + 128 + 88*q**3 - 672*q - 517*q**3.
-2*(7*q - 4)**3
Suppose 4*y + 2*u = 10, 0 = -6*y + 4*y + u + 7. Factor -266*n + 294*n + 4 + 52*n**4 + 88*n**y - 2*n**5 + 72*n**2 + 14*n**5.
4*(n + 1)**4*(3*n + 1)
Suppose -3*t = -3*n + 3, -5*n + 5 = -0*n + 4*t. Let k be ((-3)/(-3))/(n/2). Suppose 4*q**2 + 2*q - 2*q**4 - 2*q**3 - 4 + 0*q**4 + 2*q**k = 0. What is q?
-2, -1, 1
Let z(m) be the third derivative of 0 + 0*m**3 - 1/40*m**6 + 0*m + 1/20*m**5 - m**2 + 0*m**4. Factor z(r).
-3*r**2*(r - 1)
Let h = 355 + -355. Let j(g) be the third derivative of 0*g - 1/525*g**7 + 1/150*g**6 - g**2 + 1/15*g**3 + h*g**5 + 0 - 1/30*g**4. Factor j(r).
-2*(r - 1)**3*(r + 1)/5
Let q(n) be the first derivative of -n**6/3 + 22*n**5/15 + 7*n**4/2 - 2*n**3/3 - 10*n**2/3 + 47. Suppose q(y) = 0. What is y?
-1, 0, 2/3, 5
Let j(y) be the first derivative of 2*y**3/27 - 13*y**2/3 + 59. Determine b so that j(b) = 0.
0, 39
Factor -1362*w**2 - 458*w**2 + 420*w**2 + 12*w**3 - 245*w - 223*w.
4*w*(w - 117)*(3*w + 1)
Let w(y) be the first derivative of -6 + 0*y**2 + 0*y**4 + 1/12*y**3 - 1/40*y**5 - 2*y. Let s(f) be the first derivative of w(f). Find b such that s(b) = 0.
-1, 0, 1
Let v(f) be the second derivative of f**5/240 + f**4/16 - 4*f**2 - 17*f. Let m(g) be the first derivative of v(g). Let m(h) = 0. What is h?
-6, 0
Suppose -82*w = 207*w - 480 - 387. Factor -3/7*k**w + 3/7*k - 2/7 + 2/7*k**2.
-(k - 1)*(k + 1)*(3*k - 2)/7
Suppose -17 = -64*d + 175. Solve -35/8*r**d + 1/4 + 9/2*r**2 - 15/8*r + 3/2*r**4 = 0.
1/4, 2/3, 1
Let g(o) be the third derivative of 0*o**4 - 1/120*o**6 + 0 + 0*o + 20*o**2 + 1/420*o**7 + 0*o**5 + 0*o**3 + 1/672*o**8. Let g(d) = 0. What is d?
-2, 0, 1
Let p(x) = x**2 + 11*x + 14. Let o be p(-11). Suppose 2*c + 8 = o. Factor z**5 + 4*z**4 + 3*z**2 + 12*z**c + 2*z**4 + 0*z**5 + 5*z**2.
z**2*(z + 2)**3
Let a(v) be the second derivative of -2/39*v**3 + 0*v**2 + 7*v - 1/195*v**6 + 1/26*v**4 + 0 + 0*v**5. Factor a(d).
-2*d*(d - 1)**2*(d + 2)/13
Let m(w) = 3*w**4 + 6*w**3 - 2*w + 1. Let l(h) = -4*h**4 - 8*h**3 + 3*h - 1. Let b(o) = -4*l(o) - 5*m(o). Factor b(a).
(a - 1)*(a + 1)**3
Let m(w) be the second derivative of 3*w**4/4 + 23*w**3 + 45*w**2/2 - 99*w. Determine a so that m(a) = 0.
-15, -1/3
Let q(r) = -2*r**2. Let o(v) = 9*v**2 - 9*v. Let y(x) = -o(x) - 5*q(x). Factor y(a).
a*(a + 9)
Factor 1/6*v**2 + 1 + 5/6*v.
(v + 2)*(v + 3)/6
Suppose -9*u = -316 + 118. Suppose -31*w = -20*w - u. Factor 2/7*f**5 + 32/7*f - 16/7*f**4 + 0 - 64/7*f**w + 48/7*f**3.
2*f*(f - 2)**4/7
Let a = 576 - 24191/42. Let m(g) be the second derivative of a*g**4 - 5*g + 0 + 9/7*g**2 + 2/7*g**3. Factor m(h).
2*(h + 3)**2/7
Let o(c) be the first derivative of -4*c**2 - 7 - 1/120*c**5 + 1/12*c**3 + 0*c + 0*c**4. Let b(y) be the second derivative of o(y). Find d, given that b(d) = 0.
-1, 1
Let v(l) = 6*l**2 + 27*l + 16. Let x(j) = -5*j**2 - 7*j. Let r(m) = 6*m**2 + 8*m. Let n(b) = -6*r(b) - 7*x(b). Let i(k) = -6*n(k) + 2*v(k). Factor i(s).
2*(3*s + 4)**2
Suppose -2*y + 3 = -1. Let t(n) be the second derivative of 7/2*n**3 - 9/4*n**4 + 0 + 3*n**y + 3*n. Factor t(g).
-3*(g - 1)*