4.
3*(k - 1)**2*(k + 1)*(k + 176)
Let p(d) be the third derivative of d**5/240 - 5*d**4/32 - 9*d**3/4 - 1696*d**2. Suppose p(h) = 0. Calculate h.
-3, 18
Let p(c) = 4*c**3 + c**2 - 5. Let x be p(2). Let m = x - 27. Find v such that -m + 4*v**2 + 303*v - 303*v = 0.
-1, 1
Suppose 0 = 3*l + 3*k - 4221, 0 = -34*l + 39*l - 5*k - 7055. Let c = l - 1406. Factor 0 + 1/3*a**5 + 0*a + 0*a**2 + 2/3*a**c - a**4.
a**3*(a - 2)*(a - 1)/3
Let g(o) = o**3 + 24*o**2 + 40*o - 85. Let h = -725 - -703. Let c be g(h). Factor 6/7 + 30/7*d**2 + 27/7*d + 9/7*d**c.
3*(d + 1)*(d + 2)*(3*d + 1)/7
Suppose x = 4*b + 56, -5*b - 208 = -5*x - 9*b. Let n = x - 39. Factor 2*w**n - 11*w**3 - 17*w**5 + 2*w**3 - 3*w**2 + 27*w**4.
-3*w**2*(w - 1)**2*(5*w + 1)
Factor 12*j**2 - 39*j**2 + 20*j**2 - 245*j - 1332 + 9*j**2 + 683*j.
2*(j - 3)*(j + 222)
Let p(m) be the second derivative of -m**6/15 + 17*m**5/10 - 13*m**4 + 140*m**3/3 - 88*m**2 + 4*m - 24. Factor p(s).
-2*(s - 11)*(s - 2)**3
Solve 75*b - 370*b**4 + 4*b**2 - 59*b**2 - 100*b**3 + 25*b**5 + 286*b**2 + 139*b**2 = 0.
-1, -1/5, 0, 1, 15
Let t(w) = -4*w**3 + 309*w**2 + 574*w - 6. Let f(y) = -7*y**3 + 610*y**2 + 1148*y - 10. Let h(u) = -3*f(u) + 5*t(u). Factor h(g).
g*(g - 287)*(g + 2)
Let j(l) be the first derivative of -l**5/5 - 3*l**4/4 + l**3/6 + 3*l**2 + 223*l + 8. Let b(m) be the first derivative of j(m). Let b(k) = 0. Calculate k.
-2, -1, 3/4
Let j = 42216 - 42214. Let t(n) be the third derivative of -14*n**j + 1/280*n**6 + 0*n**3 + 0*n**5 + 0*n + 0 - 1/56*n**4. Determine y, given that t(y) = 0.
-1, 0, 1
Suppose -140*w = -141*w + 5. Let p(o) be the first derivative of 4/25*o**w + 0*o + 16 + 1/5*o**6 + 0*o**3 + 0*o**2 + 0*o**4. Let p(y) = 0. Calculate y.
-2/3, 0
Let y(t) be the second derivative of -3*t**5/100 - 23*t**4/20 - 31*t**3/5 - 12*t**2 + 799*t. Factor y(s).
-3*(s + 1)*(s + 2)*(s + 20)/5
Suppose -39*u = -46*u - 56. Let i be (-1)/u + (4 - 810/336). Determine l so that 12/7 + 3/7*l**2 - i*l = 0.
2
Let d(u) be the first derivative of u**8/84 + 2*u**7/35 + u**6/30 - u**5/5 - u**4/3 + 29*u**2/2 - 33. Let y(q) be the second derivative of d(q). Factor y(x).
4*x*(x - 1)*(x + 1)**2*(x + 2)
Let q(b) = 23*b**2 - 568*b + 1380. Let l(u) = -9*u**2 + 226*u - 552. Let c(a) = -13*l(a) - 5*q(a). Determine n, given that c(n) = 0.
3, 46
Let i = 137 + -93. Determine q, given that 249 + i*q - 14*q - q**2 - 249 - 4*q**2 = 0.
0, 6
Let w be (10/(-6))/(45/(-81)). Let n(q) be the first derivative of 21 + 0*q + 3*q**2 + 15/2*q**4 - 9/5*q**5 - 9*q**w. Suppose n(i) = 0. Calculate i.
0, 1/3, 1, 2
Let n = -558746 + 558749. Solve -13/6*o**2 + 0 - 2*o - 1/6*o**n = 0 for o.
-12, -1, 0
Let m(x) = -x**3 + 7*x**2 + 19*x + 9. Let y be m(9). Let o be (-2*y/30)/(-3). Factor 0 - 2/5*n**4 - o*n**2 + 0*n + 4/5*n**3.
-2*n**2*(n - 1)**2/5
Let z(g) be the first derivative of 18 - 2/5*g**5 - 3/2*g**4 - 8*g + 3*g**2 + 10/3*g**3. Factor z(r).
-2*(r - 1)**2*(r + 1)*(r + 4)
Suppose 13*w - 2538 = 1544. Let g = -312 + w. Factor 2/15*v**5 + 10/3*v**3 - 32/3*v - 8/3*v**g + 128/15 + 4/3*v**4.
2*(v - 1)**2*(v + 4)**3/15
Let m = 818 + -814. Let c be m/18 + (-150)/(-540). Factor c*l + 0 + 1/6*l**2.
l*(l + 3)/6
Let h = -487 - -491. Solve -48*r + 52*r**2 - 24*r**3 - 3*r**h - 7 + 12 + 7*r**4 + 11 = 0 for r.
1, 2
Let n be -157 - (43 + -197) - (-5 - (1 + 0)). Suppose 0*i**2 + 0 + 6/7*i**n + 0*i + 99/7*i**4 + 39*i**5 = 0. Calculate i.
-2/7, -1/13, 0
Suppose 9*b + 1 = 37. Find w, given that 4*w**3 + 5*w - 2*w**2 - 11*w - 2*w**3 - 2*w - b*w = 0.
-2, 0, 3
Let g(l) = 6*l + 233. Let f be g(-38). Let m be (f - 4 - 6) + 57/6. Factor -3/2*s**2 - 3 + m*s.
-3*(s - 2)*(s - 1)/2
Let p(g) be the third derivative of g**8/16128 + g**7/10080 + 13*g**5/30 + g**4/12 - 28*g**2 + 4. Let w(i) be the third derivative of p(i). Factor w(z).
z*(5*z + 2)/4
Let w(s) be the second derivative of 5/42*s**7 - 2 + 0*s**3 + 11*s + 1/6*s**6 + 0*s**4 + 0*s**2 - 3/2*s**5. Factor w(c).
5*c**3*(c - 2)*(c + 3)
Let u(o) be the first derivative of -3*o**6/40 + 3*o**5/10 - o**4/2 - 176*o**3/3 + 5. Let g(a) be the third derivative of u(a). Solve g(q) = 0.
2/3
Suppose 0 = -9*u - 67 + 283. Let v be (-96)/u + (-92)/(-22). Factor v*s**2 + 0*s - 2/11*s**3 + 0.
-2*s**2*(s - 1)/11
Let q(n) be the second derivative of n**6/90 - 7*n**5/30 + n**4 + n**3/3 - 9*n**2/2 + 125*n. Let a(m) be the second derivative of q(m). Factor a(u).
4*(u - 6)*(u - 1)
Solve 1568/13*g + 2/13*g**2 + 307328/13 = 0 for g.
-392
Suppose -5*n - t - 142 = -3*n, 381 = -5*n + 4*t. Let z = -48 - n. Factor -4*l**2 - 13*l + 12*l**3 + l + 21*l**4 - z*l**4 + 8.
-4*(l - 2)*(l - 1)**2*(l + 1)
Suppose -f - 15 = -6*f. Suppose -3*u + 4*u - 27 = -5*t, -t - 1 = -f*u. Factor 4*y - 3*y**2 - 9*y**2 + 14*y**u.
2*y*(y + 2)
Factor 6/5*v**3 + 14/5*v**4 - 46/5*v**2 + 2/5*v**5 - 64/5*v - 24/5.
2*(v - 2)*(v + 1)**3*(v + 6)/5
Factor 440*o**2 - 828*o**2 - 1568 - 252*o + 384*o**2.
-4*(o + 7)*(o + 56)
Suppose 39 + 117 = 6*s. Factor s - 2 - 3*r**2 - 64477*r + 64456*r.
-3*(r - 1)*(r + 8)
Let i be 468/(-81) + 6 - 32/(-18). Factor -9 + 94*t**i + 61 - 9*t**3 + 35*t**2 - 160*t.
-(t - 13)*(3*t - 2)**2
Let s(t) be the third derivative of 1/4*t**6 - 5/6*t**4 - 1/42*t**7 - 3/4*t**5 + 10*t**3 + 0 + 0*t + 3*t**2. Factor s(r).
-5*(r - 3)*(r - 2)**2*(r + 1)
Suppose 2*d + 8 = 4*d - 4*t, t = d - 1. Let m be d/(3/(66/(-4))). Factor -10 + m*h**4 + 12*h**2 + 10 - 3*h**5 - 24*h**3 + 4*h**4.
-3*h**2*(h - 2)**2*(h - 1)
Let o = 1437 - 1433. Suppose n - 1 = -2*t, -3*n - 1 = -4*t - o. Find g such that -5/3*g**5 + 10*g + 5*g**4 + t - 55/3*g**2 + 5*g**3 = 0.
-2, 0, 1, 3
Let l(g) be the third derivative of -g**5/60 + 379*g**4/24 + 11*g**2 + 7*g. Factor l(j).
-j*(j - 379)
Suppose -210825 + 210888 = 21*o. Find c such that 0 - 3/5*c**o - 3*c**2 - 12/5*c = 0.
-4, -1, 0
Let b be ((-603)/(-162) + -4)/(20/(-54)). Determine t, given that 3/2*t**3 + 2*t**2 + b*t + 0 + 0*t**4 - 1/4*t**5 = 0.
-1, 0, 3
Let n(g) be the first derivative of -9/25*g**5 - 27/5*g**2 + 0*g + 3*g**3 + 21/20*g**4 - 1/10*g**6 + 61. Find a, given that n(a) = 0.
-3, 0, 1, 2
Suppose 0 = 158*b - 154*b - 8860. Let p = -38 + 41. Solve 18 + 18*i**2 + 2182*i - 3*i**p + 0*i**3 - b*i = 0.
1, 2, 3
Let j = 151/4 + -1357/36. Let s(c) be the first derivative of 14/27*c**3 + j*c**4 - 1/27*c**6 - 19 - 8/9*c + 0*c**2 - 2/15*c**5. Suppose s(z) = 0. What is z?
-2, -1, 1
Let v(s) be the third derivative of -2*s**7/105 + 196*s**6/15 + 394*s**5/15 - 196*s**4/3 - 262*s**3 - 8400*s**2. Determine t so that v(t) = 0.
-1, 1, 393
Find q such that -1/5*q**4 + 18/5*q**3 + 12/5*q**2 - 288/5 - 40*q = 0.
-2, 4, 18
Let l be (8/(-20))/(16/(-20))*6. Solve -50*f + f**3 - 26 + 6*f**l - 5*f**3 - 22*f**2 + 0*f**3 = 0.
-1, 13
Let t = -1465 - -1468. Let s(f) be the second derivative of 0 - 1/33*f**4 + 9/110*f**5 + 0*f**2 + 0*f**t - 9*f. What is l in s(l) = 0?
0, 2/9
Let r(n) = 7*n**4 + 3*n**3 - 4*n**2 - 3*n. Let p(a) = 4*a**2 - 8*a**4 + 0*a + 8*a**3 - 6*a**3 + 4*a - 6*a**3. Let v(z) = -3*p(z) - 4*r(z). Factor v(f).
-4*f**2*(f - 1)*(f + 1)
Let g be 3/((386/(-4825))/(4/(-30))). Let b(h) be the first derivative of -14/5*h**g - 37 + 19/2*h**4 + 0*h**2 + 4*h**3 + 0*h. Find a, given that b(a) = 0.
-2/7, 0, 3
Let k = 190 + -235. Let o be (-3)/k*(6 + 3). Solve 2/5*i**2 + 1/5 + o*i = 0 for i.
-1, -1/2
Factor -p**4 - 75306*p - 60*p**2 + 75378*p + 5*p**4 - 16*p**3.
4*p*(p - 6)*(p - 1)*(p + 3)
Suppose 104*q - 98*q = 54. Factor 50*p - 22*p**3 + 5 + p**3 + 45*p**2 - q*p**3 + 10*p**3 - 20.
-5*(p - 3)*(p + 1)*(4*p - 1)
Suppose -32*b + 576 - 512 = 0. Let f(t) be the first derivative of -5 + t**b - 2/3*t - 4/9*t**3. Let f(v) = 0. What is v?
1/2, 1
Suppose -706 = -677*h + 215*h + 218. Factor -22/17*s**h - 50/17 - 70/17*s - 2/17*s**3.
-2*(s + 1)*(s + 5)**2/17
Solve 18/19*m**2 + 20/19*m - 2/19*m**3 + 0 = 0 for m.
-1, 0, 10
Let j(v) = 19*v**3 + 24*v**2 + 61*v + 21. Let z(g) = -8*g**3 - 12*g**2 - 30*g - 11. Let m(q) = -3*j(q) - 7*z(q). Factor m(x).
-(x - 14)*(x + 1)**2
Let p(i) be the first derivative of 22/15*i**3 + 6/5*i + 2/5*i**4 + 49 + 2*i**2. Factor p(v).
2*(v + 1)**2*(4*v + 3)/5
Let l(j) be the third derivative of -201243*j**5/100 - 259*j**4/10 - 2*j**3/15 - 2321*j**2. Factor l(t).
-(777*t + 2)**2/5
Let f(s) = -9*s**4 + 2*s**3 + 202*s**2 - 1087*s + 857. Let o(t) = 4*t**4 - t**3 - 102*t**2 + 543*t - 429. Let x