 + 20)
Let h(m) be the second derivative of -5*m**8/1344 - m**7/42 + 5*m**6/96 + 19*m**2/2 + 106*m. Let i(q) be the first derivative of h(q). Solve i(n) = 0.
-5, 0, 1
Suppose 104 = 3*i + 2*c, -3*i - 2*c = 2*c - 100. Suppose i*w - 7*w = 0. Determine u, given that w + 1/6*u**2 - 1/6*u = 0.
0, 1
Factor -88/5*q + 1/5*q**2 + 87/5.
(q - 87)*(q - 1)/5
Let s(d) be the first derivative of 66*d**2 - 1452*d - 26 - 33*d**4 + 3/5*d**5 + 483*d**3. Factor s(w).
3*(w - 22)**2*(w - 1)*(w + 1)
Let s(k) be the second derivative of 16*k + 0*k**3 - 1/10*k**5 + 0*k**2 + 1/3*k**4 + 1/21*k**7 - 2/15*k**6 + 0. What is w in s(w) = 0?
-1, 0, 1, 2
Let k be (663/21 - 32)/((-4)/14). Let h(y) be the second derivative of 9/20*y**5 - 2*y**4 + 0 + k*y**3 + 1/5*y**6 + 7*y + 0*y**2. Factor h(s).
3*s*(s - 1)*(s + 3)*(2*s - 1)
Let q(w) be the second derivative of -5*w**4/12 + 10*w**3 - 90*w**2 - 1536*w. Solve q(y) = 0.
6
Let i(x) = 16*x**3 - 1704*x**2 + 727605*x - 1448392. Let c(u) = 19*u**3 - 1704*u**2 + 727605*u - 1448390. Let l(w) = 5*c(w) - 6*i(w). Solve l(a) = 0.
2, 851
Factor 27360*o**3 - 27075*o**2 + 0 + 3/4*o**5 + 0*o - 1143/4*o**4.
3*o**2*(o - 190)**2*(o - 1)/4
Let b(u) be the second derivative of u**5/110 - 4*u**4/3 + 2021*u**3/33 - 3698*u**2/11 - 1344*u - 1. Factor b(r).
2*(r - 43)**2*(r - 2)/11
Let y be 4/30 - (5460/(-675))/91. Factor 0 - y*k**3 + 2/9*k + 0*k**2.
-2*k*(k - 1)*(k + 1)/9
Suppose 18*n - 2642 = -2552. Let d(l) be the first derivative of 15/2*l**2 + 5/3*l**3 + l**n - 15/4*l**4 - 10*l - 14. Factor d(u).
5*(u - 2)*(u - 1)**2*(u + 1)
Let y(v) be the third derivative of -100*v**2 + 0*v + 1/270*v**5 + 3481/27*v**3 + 0 + 59/54*v**4. Solve y(k) = 0.
-59
Let k(u) be the first derivative of 1/30*u**4 - 74 + 0*u**2 + 0*u + 0*u**3 + 1/3*u**6 + 16/75*u**5. Determine s, given that k(s) = 0.
-1/3, -1/5, 0
Let j(m) = 97*m - 385. Let y be j(4). Let n(x) be the first derivative of -1/9*x**y - 20 - 5/6*x**2 - 4/3*x. Solve n(f) = 0 for f.
-4, -1
What is f in 715953 - f**2 - 715953 + 1038*f = 0?
0, 1038
Let d be 2/10 + (-56)/(-20). Suppose d*z + 0 = 5*b + 13, -b = -3*z + 29. Suppose 1 - 9*w + w**3 - 2*w + 3*w**2 - z*w + 25*w = 0. Calculate w.
-1
Let l(a) = 108*a - 751. Let u be l(7). Suppose c = -u*y - 0*c - 1, y + 2*c + 2 = 0. Factor -1/3*g**5 - 1/3*g**3 + 0*g + 0*g**2 + y - 2/3*g**4.
-g**3*(g + 1)**2/3
Let r(w) = 94*w + 940. Let c be r(-10). Let g(m) be the second derivative of c*m**3 + 0 - 1/60*m**5 - 2/3*m**2 + 1/12*m**4 + 20*m. Factor g(i).
-(i - 2)**2*(i + 1)/3
Suppose -2*y + 8 = -2*v, 4 = 3*y + v - 16. Suppose -3*t = -y*t + 6. Factor 4 + 24*i**t - 356*i + 12 - 4*i**3 + 320*i.
-4*(i - 4)*(i - 1)**2
Factor -4*r**5 - 11029*r**3 - 440640*r + 2677*r**3 + 777600 + 261282*r**2 + 312*r**4 - 169698*r**2.
-4*(r - 30)**2*(r - 6)**3
Suppose -4*f = 4*u - 12, -1 + 9 = 4*f + 5*u. Factor -4*g - 15*g**4 + 3*g**3 + 10*g**4 + g**5 + f*g**2 - 2*g**2 + 0*g**5.
g*(g - 4)*(g - 1)**2*(g + 1)
Factor y + 5/3*y**3 + 7/3*y**2 + 0 + 1/3*y**4.
y*(y + 1)**2*(y + 3)/3
Let v be ((-6)/60)/((-166)/830). Determine t, given that -31/4*t**2 + 31/4*t**4 + 0 + 29/4*t**5 - v*t - 27/4*t**3 = 0.
-1, -2/29, 0, 1
Factor 425*q**2 - 33*q + 3*q - 5422*q**4 - 460*q**3 + 5487*q**4.
5*q*(q - 6)*(q - 1)*(13*q - 1)
Suppose 0 = 2*d - 3*h - 10, 0 = -3*d - 2*d - 4*h + 2. Let a = -257131/5 - -51427. Factor 8/5 - a*n**3 + 16/5*n**d - 4*n.
-4*(n - 2)*(n - 1)**2/5
Let w be 6/14 + (-45)/105*1. Suppose -5*c = -3*k + 20, -3*k + 18*c - 20*c = 8. Factor k + w*u - 14/3*u**2 + 2/3*u**3.
2*u**2*(u - 7)/3
Let v be ((-165)/(-605))/(12*1/88). Factor -8/7*z**v + 2/7*z**5 + 0*z + 0 + 6/7*z**4 + 0*z**3.
2*z**2*(z - 1)*(z + 2)**2/7
Let o be 108/(-162) + (4/(-12) - -1). Let g(m) be the third derivative of 5*m**2 - 5/8*m**4 + o + 5/3*m**3 + 0*m + 1/12*m**5. Suppose g(y) = 0. Calculate y.
1, 2
Let i = 16/41 + 91/82. Let l = -147/2 + 75. Determine k, given that i - 15*k**3 - 15/2*k + 15/2*k**4 - l*k**5 + 15*k**2 = 0.
1
Let n be ((-1053)/12 - -2)*2/34. Let b = 90/17 + n. Factor 1/4*t**3 - 1/4*t + b*t**4 + 1/2 - 3/4*t**2.
(t - 1)**2*(t + 1)*(t + 2)/4
Suppose 38*v = 44*v - 12. Solve 527*f**2 - 23*f - 37*f - 20 - 492*f**v = 0.
-2/7, 2
Factor 9*k - 1/3*k**2 + 66.
-(k - 33)*(k + 6)/3
Let h(l) be the first derivative of l**5/20 + 7*l**4/16 + 11*l**3/12 - 7*l**2/8 - 3*l - 831. Suppose h(d) = 0. What is d?
-4, -3, -1, 1
Suppose -66*j + 40 = -3524. Let g be j/(-7 + (-17)/(-2)). Factor -g*m**2 + 96/5*m - 16/5 + 20*m**3.
4*(m - 1)*(5*m - 2)**2/5
Suppose 440 = 23*p - 12*p. Suppose 27*z - p - 68 = 0. Find f such that 0 + 0*f**2 + 3/4*f**z + 0*f + 3/8*f**5 + 3/8*f**3 = 0.
-1, 0
Let n = -248 + 252. Let u be (-3488)/(-66) + n/(-22). Determine g, given that -131/3*g**3 - 4/3*g + u*g**4 + 0 + 40/3*g**2 - 21*g**5 = 0.
0, 2/9, 2/7, 1
Let s = 16214 + -16204. Let y(c) be the second derivative of -s*c**2 + 0*c**6 - 25/3*c**4 + 5/42*c**7 + 0 - 25/2*c**3 - 5/2*c**5 - 8*c. Factor y(b).
5*(b - 4)*(b + 1)**4
Suppose -15*l = -21*l + 48. Let t be (-4)/(-3 - (8 - l)). Factor 4/3 + t*x + 1/3*x**2.
(x + 2)**2/3
Suppose -130 = -177*m + 151*m. Suppose -4*u + 15 = n - 4, 2*n = m*u - 14. Suppose -3/4*b**u + 0 + 3/4*b**2 - 3/4*b**3 + 3/4*b = 0. Calculate b.
-1, 0, 1
Let k = 139 + -152. Let r be (-53)/159 - k/3. Factor -2/3 - 4*u**2 + 8/3*u - 2/3*u**r + 8/3*u**3.
-2*(u - 1)**4/3
Let v be -26 - -1179*9/324. Factor -6*b**3 + 3/4*b**4 - 18*b + 33/2*b**2 + v.
3*(b - 3)**2*(b - 1)**2/4
Find s such that -4*s**3 - 7*s**2 - 3*s**4 + 36*s + 18 + 23*s**2 + s**4 = 0.
-3, -1, 3
Let 38/15*j**2 - 22/3*j - 2/15*j**3 - 10 = 0. Calculate j.
-1, 5, 15
Factor -269*w**3 + w**4 + 0*w - 3*w**2 + 12071 - 12609 + 809*w.
(w - 269)*(w - 1)**2*(w + 2)
Let p be 28/6 - (464/48 + -8). Let m(w) be the first derivative of 0*w - 26 + 4/9*w**p + 8/3*w**2. Factor m(o).
4*o*(o + 4)/3
Find l such that -2/5*l**2 + 108/5 + 106/5*l = 0.
-1, 54
Let z(n) be the third derivative of -146*n**2 + 0 + 1/780*n**6 + 0*n + 0*n**3 + 1/130*n**5 - 1/39*n**4. Factor z(u).
2*u*(u - 1)*(u + 4)/13
Suppose 568*g + 487*g = 1145*g. Let j = 94/5 + -22/15. Factor 0 + 16/3*q**2 + 16*q**4 - j*q**3 - 3*q**5 + g*q.
-q**2*(q - 4)*(3*q - 2)**2/3
Let f(i) be the second derivative of -1/10*i**5 + 2/3*i**4 + 32*i**2 - 2*i - 14 + 28/3*i**3. Factor f(g).
-2*(g - 8)*(g + 2)**2
Let u be 2/((-2)/(16/36))*18/(-20). Solve 12/5 - 2/5*d - u*d**2 = 0.
-3, 2
Let t(a) be the first derivative of -a**4/4 - 77*a**3 - 17787*a**2/2 - 56*a - 33. Let n(y) be the first derivative of t(y). Factor n(b).
-3*(b + 77)**2
Let d(s) be the first derivative of 165*s**4/32 + 217*s**3/4 + 156*s**2 - 36*s - 3373. Determine j, given that d(j) = 0.
-4, 6/55
Determine u, given that -3 + u**2 - 28/5*u + 2/5*u**3 = 0.
-5, -1/2, 3
Suppose -13*h + 9*h + 12 = 0. Determine p, given that 36 - 6*p**h + 30*p - 3465*p**2 + 3*p**4 + 3451*p**2 - p**4 = 0.
-2, -1, 3
Let f(h) be the second derivative of -h**5/240 - 3*h**4/32 - h**3/3 + 21*h**2/2 - 9*h + 5. Let t(c) be the first derivative of f(c). Let t(v) = 0. What is v?
-8, -1
Let z(d) be the second derivative of d**5/10 + 163*d**4/3 + 649*d**3/3 + 324*d**2 + 4137*d. Suppose z(a) = 0. What is a?
-324, -1
Let a(x) be the second derivative of 0*x**3 + 0 - 94*x + 5/12*x**4 + 0*x**2. Factor a(k).
5*k**2
Let r = -11002 - -11004. Find z such that -8/19*z**r - 2/19*z + 0 = 0.
-1/4, 0
Let h(v) be the third derivative of -v**6/420 - 9*v**5/14 - 1541*v**4/28 - 4489*v**3/21 - 305*v**2. Factor h(p).
-2*(p + 1)*(p + 67)**2/7
Let b(s) be the first derivative of 6/7*s**3 - 1/14*s**4 + 36 + 0*s + 0*s**2. Determine k so that b(k) = 0.
0, 9
Let b(f) be the third derivative of f**6/40 + 11*f**5/20 - f**4/2 - 22*f**3 + 7*f**2 - 11*f. Let b(i) = 0. Calculate i.
-11, -2, 2
Factor -20 + 12*y + 1245*y**2 - 1212*y**2 - 16 - 15*y**3.
-3*(y - 2)*(y + 1)*(5*y - 6)
Let i be 0 + -3 + (-4 - -8). Let b be 3/(-72)*3 + i/8. Solve 3/5*j**2 + 3/5*j + b = 0 for j.
-1, 0
Let o(p) be the first derivative of -p**4 - 168*p**3 + 1584*p**2 + 1718. Factor o(y).
-4*y*(y - 6)*(y + 132)
Let o(m) be the third derivative of -1/5*m**5 + 0*m - 1/60*m**6 + 1/24*m**4 - 109*m**2 + 1/336*m**8 + 0 + m**3 + 1/35*m**7. Factor o(b).
(b - 1)**2*(b + 1)**2*(b + 6)
Suppose 4*g + 2*n + 15 = 113, -5*g + 3*n + 139 = 0. Let -40*a - 5*a**2 - 4*a**4 + 28*a**2 - 79*a**2 - g*a**3 = 0. What is a?
-5/2, -2, 0
Factor 1