 y(o) be the first derivative of 1/4*o**4 + 3/20*o**5 + 0*o**2 + 30 - o**3 + 34*o. Let l(u) be the first derivative of y(u). Factor l(j).
3*j*(j - 1)*(j + 2)
Let y(f) be the second derivative of -1/20*f**4 + 13/10*f**3 - 18/5*f**2 + 0 + 101*f. Find m such that y(m) = 0.
1, 12
Let n(g) be the third derivative of g**6/600 + 79*g**5/150 - 3025*g**2. Factor n(y).
y**2*(y + 158)/5
Let n = -99413 + 99415. Determine o so that -13/2*o**3 - 3/4*o**4 + 0 - 8*o - 16*o**n = 0.
-4, -2/3, 0
What is f in 3/4*f**3 + 135/4*f + 18*f**2 + 33/2 = 0?
-22, -1
Let q = 10729/6 - 52997/30. Factor -14/5*b**4 - 2/5*b**5 + 0 + 54/5*b**2 + q*b - 18/5*b**3.
-2*b*(b - 2)*(b + 3)**3/5
Let g(y) be the first derivative of y**7/3360 - y**6/360 + y**5/160 - 12*y**3 + y**2 - 2. Let o(z) be the third derivative of g(z). Factor o(w).
w*(w - 3)*(w - 1)/4
Solve 0 - 4/5*w**3 + 744/5*w - 148*w**2 = 0.
-186, 0, 1
Let w(r) be the first derivative of -r**3/3 + 36*r**2 + 148*r - 1062. Factor w(t).
-(t - 74)*(t + 2)
Let u(a) be the first derivative of a**7/1890 + 11*a**6/1080 - 13*a**5/270 + 35*a**2 - 2*a - 65. Let c(q) be the second derivative of u(q). Factor c(x).
x**2*(x - 2)*(x + 13)/9
Suppose -15 = -3*m - 27. Let g be 1 - ((-2)/1 + m + 4). Factor -g*d**4 + 3*d**3 + 2*d**3 - 2*d**2 + 10*d**4.
d**2*(d + 1)*(7*d - 2)
Let w(u) = -80*u + 84. Let z be w(-7). Factor 69*i**2 - z*i**3 + 645*i**3 - 141*i + 34 + 37.
(i - 1)**2*(i + 71)
Let d(q) = 3*q**3 + 31*q**2 - 25*q - 48. Let g(k) = -2*k**2 - k. Let w(n) = d(n) + 5*g(n). Factor w(f).
3*(f - 2)*(f + 1)*(f + 8)
Let d(p) be the third derivative of -p**7/385 + 67*p**6/132 - 5704*p**5/165 + 8896*p**4/11 + 12288*p**3/11 - 5534*p**2. Solve d(c) = 0.
-1/3, 16, 48
Let r(u) be the third derivative of u**7/504 + u**6/48 - 7*u**5/6 - 35*u**4/24 - u**3/3 - 122*u**2. Let f(g) be the second derivative of r(g). Factor f(s).
5*(s - 4)*(s + 7)
Let q(r) = -7*r**5 - 23*r**4 + 140*r**3 - 89*r**2 - 133*r + 157. Let b(z) = -z**5 + z**4 - z**2 + z + 5. Let h(j) = 18*b(j) - 2*q(j). Solve h(v) = 0 for v.
-1, 1, 7, 8
Let n = -3/19757 + 19763/39514. Factor -n*a**3 - 1/4*a**4 - 1 + a + 3/4*a**2.
-(a - 1)**2*(a + 2)**2/4
Suppose 0 = -6*v + 2*v. Suppose -5*n - 4*m + 146 = 0, 163 = 4*n - 5*m + 38. Factor -30*h + v*h - 5*h**2 + n + 5.
-5*(h - 1)*(h + 7)
Let n = -60/191 - -431/764. Let h(w) be the first derivative of -n*w**4 + 10 - w + 1/3*w**3 + 1/2*w**2. Factor h(o).
-(o - 1)**2*(o + 1)
Let k(s) be the second derivative of 5 + 0*s**2 - 1/12*s**3 - 1/80*s**5 + 1/16*s**4 - 18*s. Factor k(v).
-v*(v - 2)*(v - 1)/4
Suppose -5*n = -3*j - 51, 5*n + 3*j + 1 = -20. Factor -3/7*z**2 + n*z + 0.
-3*z*(z - 7)/7
Let t be (-84)/(-22) + (-120)/(-55) + -2. Let s(r) = r - 7. Let j be s(9). Find n, given that n**3 + 2*n**2 + 17*n - j*n**t - 19*n + n**3 = 0.
-1, 0, 1
Suppose 956*g + 2/7*g**2 + 799694 = 0. Calculate g.
-1673
Solve 312*d**2 - 637 + 171*d - 161*d**2 + 293 - 154*d**2 + 2126 = 0.
-9, 66
Let v(u) be the first derivative of 5*u**2 - 15*u - 48 + 5/3*u**3. Determine s so that v(s) = 0.
-3, 1
Let f be 20/(24/468*-3). Let z be (f/(-260))/(2/8). Factor -27/8*a + 3/8 - 15/4*a**z.
-3*(a + 1)*(10*a - 1)/8
Let c be (6 - 8)/1 + 10. Let a be ((-38)/(-228))/(2/c). Factor 0 + 22/3*j - a*j**2.
-2*j*(j - 11)/3
Suppose -10*o = -54*o - 12936. Let s be (-6)/28*343/o. Let s*w**2 + 3/4*w + 1/2 = 0. Calculate w.
-2, -1
Let a(z) be the third derivative of -2*z**2 + 3/19*z**3 + 5/114*z**4 - 1/114*z**6 - 1/1995*z**7 + 13 + 0*z - 4/285*z**5. Find r such that a(r) = 0.
-9, -1, 1
Let o(m) = -594*m - 1185. Let i be o(-2). Determine t, given that -i*t + 0 - 2/3*t**3 - 3*t**2 = 0.
-3, -3/2, 0
Let r(f) be the third derivative of 0*f - 7/240*f**6 + 1/140*f**7 - 95*f**2 - 1/1344*f**8 + 1/15*f**5 + 1/12*f**3 + 0 - 3/32*f**4. Factor r(y).
-(y - 2)*(y - 1)**4/4
Let b(x) be the second derivative of -x**7/6300 + x**6/60 - 3*x**5/4 + 15*x**4/2 - 79*x. Let v(h) be the third derivative of b(h). Factor v(k).
-2*(k - 15)**2/5
Let y(z) = -42*z - 11 + 2*z**2 + 4 + 43*z. Let d(t) = t**2 + 2*t - 1. Let u(a) = -3*d(a) + y(a). Factor u(b).
-(b + 1)*(b + 4)
Let b(s) be the third derivative of s**7/1260 + s**6/180 - s**5/12 - 17*s**4/36 - 35*s**3/36 - 198*s**2 + 1. Factor b(k).
(k - 5)*(k + 1)**2*(k + 7)/6
Let p = 34500 + -34492. Let f(j) be the first derivative of 1/2*j**4 + p*j + 13/3*j**3 - 42 + 11*j**2. Factor f(z).
(z + 2)*(z + 4)*(2*z + 1)
Let a(v) be the third derivative of v**6/480 + 33*v**5/20 - 2998*v**2. Suppose a(t) = 0. Calculate t.
-396, 0
Let w be (-65)/(-6) + -9 - 3/6. Let d be (-1375)/(-225) - (1 + 4). Factor d*b - w - 2/9*b**2.
-2*(b - 3)*(b - 2)/9
Let c(p) be the second derivative of -p**5/120 + 7*p**4/12 - 15*p**3 + 162*p**2 + 9*p + 47. Factor c(t).
-(t - 18)**2*(t - 6)/6
Suppose -18 = -5*c + 37. Suppose 3*n - c + 5 = 0. Factor z**2 + 0*z**n - 13 + 12.
(z - 1)*(z + 1)
Let o be (-5)/((-25)/(-5)) - -7. Let c(q) = -q**3 + 6*q**2 + 2. Let v be c(o). Factor -4*f**4 - 12*f + 4*f - 11*f**3 + 3*f**2 - 5*f**3 - 23*f**v.
-4*f*(f + 1)**2*(f + 2)
Let t(f) = f**2 - 1901*f + 246774. Let i be t(140). Suppose -12*n + i + 2/13*n**2 = 0. Calculate n.
39
Let o(f) = -3*f + 59. Let n be o(19). Suppose -98 - 12*r + 98 + 3*r**5 - 35*r**n + 6*r**4 - 9*r**3 + 11*r**2 = 0. Calculate r.
-2, -1, 0, 2
Let w be 14/35 + 208/30. Let p(c) = 49*c + 49. Let t be p(-1). Factor w*d**3 + t - 14/3*d**2 - 10/3*d**4 + 2/3*d.
-2*d*(d - 1)**2*(5*d - 1)/3
Let n(q) be the second derivative of -3*q**5/20 + 7*q**4/2 + 2*q**3 - 84*q**2 - 292*q. Factor n(b).
-3*(b - 14)*(b - 2)*(b + 2)
Let g be (-2)/(-12) - (-3)/(-18). Suppose 0 = -49*i + 60*i. Find y such that i*y**3 - 1/2*y**2 + 1/4 + g*y + 1/4*y**4 = 0.
-1, 1
Suppose -7*q = -21*q. Suppose q = 7*v - 10*v. Find n such that 8/19*n**2 + v - 2/19*n**3 + 0*n = 0.
0, 4
Let c = 50188/4677 - 100/1559. Factor 20/3*v**3 + 88/3*v**2 + 112/3*v + c.
4*(v + 2)**2*(5*v + 2)/3
Factor -6200/7*y - 30000/7 - 212/7*y**2 - 2/7*y**3.
-2*(y + 6)*(y + 50)**2/7
Let f(n) = -9*n**3 + 32*n**2 - 73*n + 40. Let a(p) = 28*p**3 - 96*p**2 + 220*p - 120. Suppose 16*t + 2*t + 90 = 0. Let y(b) = t*a(b) - 16*f(b). Factor y(v).
4*(v - 5)*(v - 2)*(v - 1)
Let v(a) = -21*a**3 - 2*a**2 + 23*a - 8. Let n(h) = 45*h**3 + 3*h**2 - 48*h + 18. Let s(r) = -4*n(r) - 9*v(r). Factor s(g).
3*g*(g - 1)*(3*g + 5)
Suppose -1429*l = -1426*l - 6. Let m(b) be the second derivative of 0*b**l + 0 - 1/2*b**3 + 3/20*b**5 - 8*b + 1/10*b**6 - 1/4*b**4. Find y such that m(y) = 0.
-1, 0, 1
Let m = 104699 + -104695. Suppose -38/15*n**3 - 8/15 - 16/15*n + 18/5*n**2 + 8/15*n**m = 0. What is n?
-1/4, 1, 2
Factor -170*r**2 - 84*r + 167*r**2 - 41*r - 996 - 203*r + 67*r.
-3*(r + 4)*(r + 83)
Suppose -56 + 14 = 13*t - 34*t. Let a(m) be the third derivative of 6*m**3 + 1/15*m**5 + 0*m + 24*m**t + m**4 + 0. Factor a(p).
4*(p + 3)**2
Factor -424/13*n**2 + 144/13*n + 0 + 300/13*n**3 + 18/13*n**4.
2*n*(n + 18)*(3*n - 2)**2/13
Let l(m) = -m**2 + 2*m. Let x(g) = 51*g**2 + 20*g + 8. Let q(n) = -5*l(n) + x(n). Let z(h) = -3*h**2. Let c(y) = -2*q(y) - 36*z(y). Factor c(d).
-4*(d + 1)*(d + 4)
Let q(s) be the first derivative of -5*s + 144*s**5 - 75*s**4 - 340/3*s**3 + 30 - 75/2*s**2. Suppose q(g) = 0. Calculate g.
-1/4, -1/6, 1
Factor 942*b - 173*b**2 - 249*b**2 + 242*b**2 - 57*b**2 + 24.
-3*(b - 4)*(79*b + 2)
Let g(z) be the first derivative of -z**5/20 - 11*z**4/16 - 19*z**3/6 - 13*z**2/2 - 6*z - 1215. Solve g(t) = 0.
-6, -2, -1
Suppose 3412 + 1994 = 2879*w + 2900 - 3252. Solve -8/3*x**3 - 2/3*x**4 + 2/9*x**5 + 40/9*x**w + 32/3*x + 0 = 0.
-2, 0, 3, 4
Determine u, given that 1688/5 - 3372/5*u + 4/5*u**3 + 336*u**2 = 0.
-422, 1
Determine d so that -285/2*d - 375/2*d**2 + 285/2*d**3 + 207 - 39/2*d**4 = 0.
-1, 1, 2, 69/13
Factor 304*p**2 + 339*p**2 + 416 + 414*p - 645*p**2.
-2*(p - 208)*(p + 1)
Factor 477613*b**2 + 407 + 297*b - 477610*b**2 + 8 + 449.
3*(b + 3)*(b + 96)
Let q = 156868 + -313733/2. Solve -3/2*m - 3/2 + q*m**2 + 3/2*m**3 = 0.
-1, 1
Factor -2135*p - 7231 - 405*p**2 + 839*p**2 + 781 - 429*p**2.
5*(p - 430)*(p + 3)
Let i = -243 - -207. Let p(r) = -r**3 + 3*r**2 + 18*r - 27. Let m(x) = 1 + x + 1 - 2. Let y(w) = i*m(w) + 4*p(w). Factor y(f).
-4*(f - 3)**2*(f + 3)
Let r be (((-88)/66)/((-4)/6))/(-2). Let n be 8/18 + 96/(-270)*r. Factor -4/5 - 1/5*k**2 + n*k.
-(k - 2)**2/5
Let a(f) be