-6, -1, 3
Let h(u) be the third derivative of u**6/40 - 41*u**5/25 + 127*u**4/40 + 16*u**3/5 + u**2 - 820*u. Factor h(p).
3*(p - 32)*(p - 1)*(5*p + 1)/5
Suppose -405 = -d + 6*d + 5*q, 137 = -2*d + 3*q. Let z = -72 - d. Find n such that -2*n**3 + 2*n**z - 53*n**2 + 27*n**2 + 22*n**2 = 0.
-1, 0, 2
Let i = 295659 + -2365269/8. What is s in 29/4*s + 5/8*s**2 - i*s**3 - 5 = 0?
-4, 2/3, 5
Suppose 13/3*n**2 + 128/3*n + 68 = 0. Calculate n.
-102/13, -2
Let r be ((6 + -5)*-4)/((-3534)/1116 - (-4)/6). What is l in -2/15*l**3 - r*l - 4/5*l**2 - 16/15 = 0?
-2
Let w(l) be the third derivative of -2*l**7/21 + 55*l**6/24 - 41*l**5/6 - 5*l**4 + 3814*l**2. Let w(u) = 0. What is u?
-1/4, 0, 2, 12
Suppose -4*i + 147 + 14 = n, -132 = -3*i - 3*n. Let k = i - 31. Factor 7*h**5 - 194*h**2 - k*h**4 - 3*h**5 + 194*h**2.
4*h**4*(h - 2)
Factor 1/3*l**3 + 53*l - 124/3 - 12*l**2.
(l - 31)*(l - 4)*(l - 1)/3
Let i(x) be the first derivative of 5*x**3/3 - 130*x**2 - 1425*x - 671. Factor i(t).
5*(t - 57)*(t + 5)
Let b(l) be the second derivative of 3*l**6/20 + 1767*l**5/20 + 344557*l**4/24 - 116033*l**3/3 + 38809*l**2 - 1542*l + 1. Factor b(c).
(c + 197)**2*(3*c - 2)**2/2
Let b = -164564 - -493693/3. Factor 2*f**2 + 3*f - 14/3 - b*f**3.
-(f - 7)*(f - 1)*(f + 2)/3
Let n(g) = -g + 14. Let b be n(10). Suppose 8*i = b*i + 12. Find w, given that 8*w + 1 - 18*w**3 + 10*w**i - 5 + w**4 + 3*w**4 = 0.
-1, 1
Suppose 903*r - 47 - 806 = 953. Solve -7/5*a + 1/5*a**3 - 2/5*a**r - 4/5 = 0.
-1, 4
Let o(n) be the second derivative of -16/9*n**3 + 64/3*n**2 + 1/18*n**4 + 128*n + 0. Suppose o(u) = 0. Calculate u.
8
Let b be (((-456)/16)/(-19))/((-6)/(-16)). Let w(v) be the third derivative of -5/6*v**b + 0*v**3 + 0 + 0*v - 8*v**2 + 1/15*v**5. Let w(k) = 0. What is k?
0, 5
Suppose -4*d = 5*c - 79, -2*c - 5*d - 20 + 55 = 0. Suppose -7*t - 15 + c = 0. Factor 0*w + t + 2/3*w**2.
2*w**2/3
Let f(n) be the second derivative of n**7/84 - 23*n**6/4 + 341*n**5/40 + 1037*n**4/24 - 287*n**3/2 + 172*n**2 - 8467*n. Factor f(p).
(p - 344)*(p - 1)**3*(p + 2)/2
Let d(u) be the first derivative of 0*u - 1/14*u**6 - 3/4*u**4 + 3/7*u**3 + 3/7*u**5 + 52 + 0*u**2. Find t, given that d(t) = 0.
0, 1, 3
Suppose -65/2*a + 0 - 127/2*a**3 + a**4 - 97*a**2 = 0. What is a?
-1, -1/2, 0, 65
Let 1/8*t**2 + 1045/8 - 107/4*t = 0. What is t?
5, 209
Let n(m) = 5*m**2 - 8*m + 20. Let g(b) = 38*b**2 - 61*b + 160. Let w(v) = 6*g(v) - 46*n(v). Let w(r) = 0. Calculate r.
-4, 5
Let w(a) = 205*a**2 + 10454*a - 48. Let d be w(-51). Suppose -40*t**4 - 385/3*t**d + 45*t**5 - 100*t + 40/3 + 210*t**2 = 0. What is t?
-2, 2/9, 2/3, 1
Let k(x) be the first derivative of -704/5*x**5 + 79 - 24*x**3 + 0*x + 105*x**4 + 0*x**2 + 128/3*x**6. Solve k(a) = 0.
0, 3/8, 2
What is w in 30*w**4 - 63*w**2 + 169/2*w**3 - 228 - 346*w + 1/2*w**5 = 0?
-57, -2, -1, 2
Factor 53*k + 60*k**3 + 305*k**2 - 17*k**4 - k + 89*k + 12*k**4 + 99*k.
-5*k*(k - 16)*(k + 1)*(k + 3)
Let k(b) = -b**2. Suppose 3*x - 9 = -3. Let q(g) = -3*g + 3*g**x + 0*g - 2*g + 2 + 4*g. Let f(u) = -4*k(u) - q(u). Factor f(s).
(s - 1)*(s + 2)
Solve 7762*g**2 - 7729*g**2 + 108 + 108*g + 2*g**3 + g**3 = 0 for g.
-6, -3, -2
Let g(v) = 100*v**2 + 1924*v - 272. Let x(y) = 33*y**2 + 641*y - 93. Let q(t) = 3*g(t) - 8*x(t). Factor q(d).
4*(d + 18)*(9*d - 1)
Let 3/4*w**4 - 6291/4*w - 2673/2 - 9/4*w**3 - 957/4*w**2 = 0. Calculate w.
-9, -1, 22
Let p be ((-6)/15)/((-6)/2040). Let u be 4/(-14) + p/84. Let u*n**2 - 2/3*n**4 + 2/3*n - 4/3*n**3 - 2/3 + 2/3*n**5 = 0. Calculate n.
-1, 1
Suppose -3*w + 50 = -4*t, 0 = 4*w - 6*w + t + 25. Factor 30*d**3 + 319*d**4 + 22*d**5 - 243*d**4 + 14*d**5 + w*d**3.
4*d**3*(d + 1)*(9*d + 10)
Let j(i) be the second derivative of 21*i - 3/4*i**3 + 0*i**2 - 3/20*i**5 + 2 - 11/16*i**4 + 1/40*i**6. Factor j(h).
3*h*(h - 6)*(h + 1)**2/4
Let c(s) be the first derivative of -s**6/720 - s**5/8 - 75*s**4/16 - 73*s**3/3 - 1. Let b(h) be the third derivative of c(h). Find a, given that b(a) = 0.
-15
Factor -140*k**2 - 137*k**2 + 408*k**2 - 2464900 + 7282*k - 1002*k - 135*k**2.
-4*(k - 785)**2
Let f(r) be the first derivative of 0*r - 2/5*r**5 + 171 - 24*r**3 - 32*r**2 - 6*r**4. Solve f(t) = 0.
-8, -2, 0
Let r(v) be the third derivative of -11*v**7/840 - 41*v**6/160 - 77*v**5/60 - 19*v**4/8 - 4*v**3/3 - 1473*v**2. Solve r(x) = 0 for x.
-8, -2, -1, -2/11
Let x(h) = h**2 + 177*h + 1356. Let q be x(-8). Let g(o) be the third derivative of 0*o + 0 - 1/4*o**5 + 1/24*o**6 + 0*o**3 + 5/12*o**q - 21*o**2. Factor g(p).
5*p*(p - 2)*(p - 1)
Suppose 5*c = 3*c. Suppose c = 5*n - 5*p - 2 - 13, -3*p = -5*n + 15. Solve 3*k**n + 3*k**4 + 3*k**3 - 3*k**5 + 0*k**3 + 0*k**4 = 0 for k.
-1, 0, 2
Let x(b) = -465*b**4 - 1529*b**3 - 445*b**2 + 36*b + 11. Let g(t) = -155*t**4 - 509*t**3 - 148*t**2 + 12*t + 4. Let z(w) = 11*g(w) - 4*x(w). Factor z(c).
c*(c + 3)*(5*c + 2)*(31*c - 2)
Let l be 5/(6*(-10)/(-36)). What is x in -10*x - 3*x**4 + 9*x - 5*x - 15*x**2 - 12*x**l = 0?
-2, -1, 0
Suppose -7*c = -20 - 190. Let p be (-30)/(c/6) - -9. Find a such that 2/7*a + 0 - 2/7*a**p + 2/7*a**4 - 2/7*a**2 = 0.
-1, 0, 1
Let m(n) = 40*n**2 - 3292*n + 678980. Let l(s) = -31*s**2 + 3293*s - 678979. Let w(o) = 4*l(o) + 3*m(o). Factor w(r).
-4*(r - 412)**2
Let o(q) = 2*q**2 - 2*q - 7. Let m(y) = -5*y**2 + 5*y + 18. Let j = -555 - -552. Let i(s) = j*m(s) - 8*o(s). Factor i(f).
-(f - 2)*(f + 1)
Let c(p) be the second derivative of p**6/780 - p**5/78 + p**4/39 + 15*p**2 + 40*p + 2. Let n(z) be the first derivative of c(z). Suppose n(o) = 0. Calculate o.
0, 1, 4
Let s(i) be the third derivative of -i**5/120 + 337*i**4/48 - 28*i**3 - 2*i**2 - 1761. Factor s(k).
-(k - 336)*(k - 1)/2
Suppose 624*y - 1710*y = -1 + 1. What is p in -69/7*p**2 - 3/7*p**3 + y + 72/7*p = 0?
-24, 0, 1
Let p(r) be the second derivative of -10*r**7/21 - 8*r**6/15 + r**5/5 - 599*r - 2. Find a, given that p(a) = 0.
-1, 0, 1/5
Suppose -4 = -2*x + r, -x - 2*r + 51 - 59 = 0. Suppose x = -k - 93*k. Factor k + 36/5*c**3 - 44/5*c**2 + 8/5*c.
4*c*(c - 1)*(9*c - 2)/5
Let -2100/17 + 12/17*p**2 - 2/17*p**3 + 2090/17*p = 0. Calculate p.
-30, 1, 35
Let l(h) = 8*h - 126. Let n be l(14). Let t be ((-114)/133)/(6/n). What is q in -3/2*q - 3/2*q**3 + 3*q**t + 0 = 0?
0, 1
Let b(w) = -w**2 + w - 2. Let l(p) be the first derivative of p**3/3 - p**2/2 + 5*p - 101. Let y(u) = 7*b(u) + 4*l(u). What is o in y(o) = 0?
-1, 2
Let n(m) be the second derivative of m**4/36 + 2198*m**3/9 + 2415602*m**2/3 - 9965*m. Factor n(z).
(z + 2198)**2/3
Let p(q) = q**3 - 2*q**2 - q - 1. Let b(c) = 12*c**3 - 20*c**2 - 18*c - 13. Let z(k) = -b(k) + 13*p(k). Factor z(w).
w*(w - 5)*(w - 1)
Find f, given that 20/3*f**3 + 4/9*f**4 - 964/9*f**2 + 0 + 100*f = 0.
-25, 0, 1, 9
Suppose 4794*f = 3683*f + 2222. Factor f*l**2 + 0 - 1/3*l**3 - 5/3*l.
-l*(l - 5)*(l - 1)/3
Determine k, given that -4*k**4 - 51*k**3 + 50*k**2 + 155*k**3 + 104*k**2 + 74*k**2 - 104*k - 224 = 0.
-2, -1, 1, 28
Find p, given that 0 + 0*p**2 + 0*p**3 - 8/3*p**4 + 0*p + 1/3*p**5 = 0.
0, 8
Let z(g) be the third derivative of -g**6/45 + 73*g**5/180 - 121*g**4/72 + 7*g**3/9 + 2*g**2 + 449*g. Factor z(l).
-(l - 7)*(l - 2)*(8*l - 1)/3
Find b such that 876/7*b - 2/7*b**2 - 95922/7 = 0.
219
Let o(h) be the second derivative of 5*h**4/12 + 295*h**3/2 + 440*h**2 - 1028*h. Solve o(t) = 0 for t.
-176, -1
Let g = -5753/3 - -28801/15. Factor 24/5 - g*i - 18/5*i**2 - 3/5*i**4 + 3*i**3.
-3*(i - 2)**3*(i + 1)/5
Suppose 177*z - 24*z = -154*z + 1228. Let f(a) be the third derivative of 1/480*a**6 - 8*a**2 + 1/60*a**5 + 5/96*a**z + 1/12*a**3 + 0 + 0*a. Factor f(t).
(t + 1)**2*(t + 2)/4
Factor 76418*w**5 - 30*w**3 - 4*w + 29*w**4 + 4*w - 76417*w**5.
w**3*(w - 1)*(w + 30)
Factor -1/5*k**2 - 2/5 + 3/5*k.
-(k - 2)*(k - 1)/5
Suppose 106*f = 102*f + 8. Factor -4 + 50*o + o + o - 169*o**f.
-(13*o - 2)**2
Let b(r) = r**3 + 25*r**2 - 53*r + 41. Let m be b(-27). Factor 798*t - t**2 - 5 + m - 790*t.
-(t - 9)*(t + 1)
Factor 70 + 213251*q + 62 - 213210*q - q**2.
-(q - 44)*(q + 3)
Let y be 130 - 118 - (-8819)/(-735). Let i(k) be the third derivative of -4*k**2 + 0 + 0*k**3 + 0*k - 1/105*k**5 + 1/420*k**6 + y*k**7 + 0*k**4. Factor i(u).
2*u**2*(u - 1)*(u + 2)/7
Let b(g) = -6*g**4 + 11*g**4 + 2 + 1 - 3*g**3 - 2*g**2. Let a(f) = -4*f**4 + 2*f**3 + 2*f**2 - 2. Let m(z) = 3*a(z) + 2*b(