**3 + 2*w**2 + 3*w.
(w + 1)**2*(w + 4)/3
Let k(o) = o**3 - 26*o**2 + 51*o - 37. Let i be k(24). Let b be (37 - i)/((-2)/(-4)). Determine m, given that 4/7*m**b + 8/7 + 36/7*m**2 - 4*m - 20/7*m**3 = 0.
1, 2
Let o = -11156 - -11161. Let u(n) be the second derivative of 3/4*n**3 + 3/8*n**4 + 6*n + 3/40*n**o + 0 + 3/4*n**2. Factor u(p).
3*(p + 1)**3/2
Factor 114/11 - 32/11*j - 2/11*j**2.
-2*(j - 3)*(j + 19)/11
Let j(o) be the second derivative of -o**7/210 + 3*o**6/25 - 6*o**5/5 + 92*o**4/15 - 88*o**3/5 + 144*o**2/5 + 3436*o + 2. Suppose j(r) = 0. What is r?
2, 6
Let s be 0/(-21)*(-1)/6*-3*-1. Let f be 16/72 + (-124)/(-90). Suppose s + f*j + 8/5*j**2 + 2/5*j**3 = 0. What is j?
-2, 0
Let u(t) = -201*t**3 + 1236*t**2 - 1620*t - 60. Let r(v) = 203*v**3 - 1236*v**2 + 1620*v + 56. Let a(q) = 3*r(q) + 2*u(q). Factor a(w).
3*(w - 4)*(w - 2)*(69*w + 2)
Determine x so that 1340*x**2 - x**3 - 297675*x + 23020471 - 15487618 + 23723022 - 395*x**2 = 0.
315
Let m(b) = -b**2 + 11*b + 1. Let j(z) = -11*z**2 - 59*z - 564. Let f(q) = -j(q) + 6*m(q). Factor f(x).
5*(x + 6)*(x + 19)
Let n(v) be the second derivative of v**3 - 1/6*v**4 + 0*v**2 - 1 + 19*v. Suppose n(a) = 0. What is a?
0, 3
Let i = 46 + -44. Solve -16*p - 12*p**2 - 16*p**2 + 4*p**4 + 2*p**i + 0*p**3 + 10*p**2 + 4*p**3 = 0 for p.
-2, -1, 0, 2
Solve -642*x - 192 - 16807*x**4 - 18228*x**2 + 1912*x + 29841*x**3 + 2402*x + 472*x = 0 for x.
3/49, 4/7
Let d(c) = 8 - 5693*c - 4*c**2 + 5693*c. Let h(i) = -3*i**2 + 2 - i**2 - i + 6. Let s(p) = -3*d(p) + 4*h(p). Factor s(r).
-4*(r - 1)*(r + 2)
Suppose -12*j - 24 = -d - 10*j, 4*d + j - 132 = 0. Let c be (-7)/49*d + (4 - -1). Factor 0*m - c + 3/7*m**2.
3*(m - 1)*(m + 1)/7
Let i(b) be the first derivative of -3*b**5/20 - b**4/2 - b**3/2 + 129*b + 52. Let w(n) be the first derivative of i(n). What is u in w(u) = 0?
-1, 0
Determine f, given that 8*f**4 + 12*f**4 - 5*f**5 - 320*f + 109*f**3 - 49*f**3 - 160*f**2 - 126 + 126 = 0.
-2, 0, 4
Solve 77/2*o + 1/2*o**3 - 49 - 8*o**2 = 0 for o.
2, 7
Let t(a) be the third derivative of a**6/420 + 2*a**5/105 + a**4/28 + 1047*a**2 + 2. Find m, given that t(m) = 0.
-3, -1, 0
Let u(a) = a**4 + a**3 + 2*a - 4. Let g(s) = 4*s**5 + 690*s**4 + 682*s**3 - 688*s**2 - 680*s - 8. Let h(x) = -g(x) + 2*u(x). Suppose h(b) = 0. Calculate b.
-171, -1, 0, 1
Let c(x) be the first derivative of -28/3*x**2 + 40/3*x + 98/45*x**3 + 122. Solve c(z) = 0.
10/7
Let r = -301623/5 + 60325. Factor 12/5 - 26/5*p + r*p**2 + 4/5*p**3.
2*(p - 2)*(p + 3)*(2*p - 1)/5
Let k(w) be the second derivative of -2/15*w**6 + 0*w**2 - 3*w**4 + 8/3*w**3 + w + 2 + 6/5*w**5. Factor k(p).
-4*p*(p - 4)*(p - 1)**2
Let h be ((-36)/3 - -15) + 33/(-14). Let a = h - -13/154. Factor 6/11*k**3 + 0 - a*k + 0*k**2 - 2/11*k**4.
-2*k*(k - 2)**2*(k + 1)/11
Let p = -2290 + 2306. Suppose -8 = 30*u - 32*u + 2*m, -4*m = p. Determine z so that 0*z + u + 5/2*z**2 = 0.
0
Let v = 9073/672 - 27/2. Let d(q) be the third derivative of -15*q**2 + v*q**8 + 1/40*q**6 + 0*q + 1/30*q**5 + 0 + 0*q**3 + 1/48*q**4 + 1/105*q**7. Factor d(k).
k*(k + 1)**4/2
Let l(w) = 9*w**3 + 5*w**2. Let m = 124 + -120. Let h(g) = -5*g**3 - 3*g**2. Let n(j) = m*l(j) + 7*h(j). Factor n(o).
o**2*(o - 1)
Let q = 32 + -4. Suppose -j - 10 - 10 = -4*i, j = -4*i + q. Factor -3*c**4 + i*c**3 - 2*c**5 + 6*c**4 - 3*c**4 + 4*c**2.
-2*c**2*(c - 2)*(c + 1)**2
Suppose -2*b - 34 = -5*d + 2*b, -4*d - b + 23 = 0. Let q = 8 - d. Factor 6 + 1 - 6*v - 4 - v**2 + 4*v**q.
3*(v - 1)**2
Suppose -34234 + 6315*q**4 - 8*q**5 - 34233 + 2454*q**2 + 68467 + 8578*q**3 - 1226*q - 1425*q**4 = 0. What is q?
-1, 0, 1/4, 613
What is g in -1/2*g**5 - 19*g**3 + 15/2*g**4 - 116*g**2 + 384*g - 256 = 0?
-4, 1, 2, 8
Factor -2*l**2 + 910 - 2*l**2 + 38*l - 34*l - 550.
-4*(l - 10)*(l + 9)
Let z = 2/132195 - -132191/264390. What is q in -16/5*q - 1/10*q**4 - 16/5 + 3/5*q**2 + z*q**3 = 0?
-2, -1, 4
Let a(g) be the first derivative of -48*g - 141 + 32*g**2 + 92/3*g**3 - 12*g**4 + 4/3*g**6 - 4*g**5. Solve a(c) = 0 for c.
-2, -1, 1/2, 2, 3
Suppose -4*j = 4*q - 7*j + 165, -2*q - 2*j - 100 = 0. Let y be (-145)/q + 4/(-18). Factor 2*c**3 - c**3 + c + 2 - 2*c**y + 29*c**2 - 31*c**2.
-(c - 1)*(c + 1)*(c + 2)
Suppose -606 = 159*t - 308*t - 154*t. Suppose 24/5*g**t + 0 + 9/5*g - 9/5*g**3 - 24/5*g**4 = 0. Calculate g.
-1, -3/8, 0, 1
Let d(b) be the second derivative of -2/39*b**4 + 1/130*b**5 + 1/13*b**3 + 0*b**2 - 35*b - 1. Find x such that d(x) = 0.
0, 1, 3
Let f(h) be the third derivative of h**6/30 + 16*h**5/15 - 61*h**4/6 - 152*h**3/3 + 983*h**2. Solve f(t) = 0 for t.
-19, -1, 4
Suppose -1 = -c + s, 3*c - 7*s + 10*s - 33 = 0. Factor 3*k + c*k**2 - 22466*k**3 + 22466*k**3 - 3*k**5 - 6*k**4.
-3*k*(k - 1)*(k + 1)**3
Let m = 228 - 200. Let k be -3*63/m + 7. Suppose k*b**3 - 5/4*b + 1/4*b**2 + 3/4 = 0. Calculate b.
-3, 1
Let 171/2*b + 3/2*b**3 + 48*b**2 - 135 = 0. Calculate b.
-30, -3, 1
Suppose -52/7*w**2 - 338/7*w - 2/7*w**3 + 0 = 0. Calculate w.
-13, 0
Suppose -57*a - 249 + 591 = 0. Let n(y) be the second derivative of 1/9*y**4 + 1/9*y**2 + 26*y + 0 + 1/135*y**a + 4/27*y**3 + 2/45*y**5. Factor n(x).
2*(x + 1)**4/9
Solve -6428/17*a - 5164898/17 - 2/17*a**2 = 0 for a.
-1607
Let u be (117/(-39))/(12/(-8) - 0). Solve -8/3*g - 4/3 - 4/3*g**u = 0 for g.
-1
Let u(p) = 2*p**3 - p**2 + p + 2. Let t(j) = 23*j**3 - 81*j**2 + 11*j + 38. Let n(f) = 2*t(f) - 38*u(f). Determine k, given that n(k) = 0.
-4, -2/15, 0
Let v be (4/(-45))/((-1042)/42201). Factor v - 18/5*a**2 - 8/5*a + 8/5*a**3.
2*(a - 1)*(a + 1)*(4*a - 9)/5
Let z = -874 - -830. Let b = -219/5 - z. Suppose 7*x + 11/5*x**2 + 5 + b*x**3 = 0. Calculate x.
-5, -1
Let h be (-3000)/(-2000) + 2/4. Suppose 12/5 - 1/5*q**3 + 8/5*q - 1/5*q**h = 0. Calculate q.
-2, 3
Suppose 0 + 7115526/13*m**2 - 6534/13*m**3 - 2582935938/13*m + 2/13*m**4 = 0. Calculate m.
0, 1089
Let g be (5/(400/24))/((-18)/83685). Let k = -1394 - g. Factor 3/4*l**2 + 3/2*l + k.
3*(l + 1)**2/4
Let k be 5/(-3)*(91 + -92). Let u(n) be the first derivative of -1/6*n**4 + 8/9*n**3 - 36 - k*n**2 + 4/3*n. Factor u(d).
-2*(d - 2)*(d - 1)**2/3
Factor -82*x**3 + 0 + 0*x + 18/13*x**4 + 236/13*x**2.
2*x**2*(x - 59)*(9*x - 2)/13
Suppose j**3 + 5*j**2 + 2 + 17/3*j - 1/3*j**4 = 0. Calculate j.
-1, 6
Suppose -42 = 258*j - 261*j - 2*o, 17*j - 2*o = -2. Factor 2/17*y**j - 30/17 - 4/17*y.
2*(y - 5)*(y + 3)/17
Let f(z) be the second derivative of z**5/50 - 17*z**4/30 - 27*z**3/5 - 63*z**2/5 - 217*z + 6. Solve f(l) = 0 for l.
-3, -1, 21
Determine h so that -5/2*h**2 + 50*h - 95/2 = 0.
1, 19
Let m(v) be the third derivative of v**6/120 - 19*v**5/12 + 31*v**4/4 + 10*v**2 + 13*v. Factor m(z).
z*(z - 93)*(z - 2)
Let d be (-276)/(-27) + (-2)/9. Let b(v) be the first derivative of 1/3*v**3 - v - 1/4*v**4 - d + 1/2*v**2. Find f such that b(f) = 0.
-1, 1
Let s = 93 - 89. Solve 393*y + 2*y**3 - y**3 - y**4 + s + 3*y**2 - 401*y + y**3 = 0.
-2, 1, 2
Let s(h) be the second derivative of 0 + 1/2*h**4 - 3/2*h**3 + 3/20*h**5 - 54*h + 0*h**2. Factor s(w).
3*w*(w - 1)*(w + 3)
Let s(b) be the third derivative of -b**6/72 - 14*b**5/3 - 1960*b**4/3 - 439040*b**3/9 + 4*b**2 + 96. Factor s(y).
-5*(y + 56)**3/3
Let r(p) be the third derivative of 11/40*p**6 + 6*p**2 + 2*p**4 - 31/20*p**5 + 2*p**3 + 0 - 3*p. Find o, given that r(o) = 0.
-2/11, 1, 2
Let o be -114*3/(-105) + 316/(-5530). Let 12/5 + 7/5*b**2 + o*b + 1/5*b**3 = 0. What is b?
-3, -2
Let t(w) be the second derivative of -w**6/10 + 27*w**5/4 - 133*w**4/2 - 8938*w. Factor t(i).
-3*i**2*(i - 38)*(i - 7)
Let z(s) be the second derivative of -s**4/21 - 172*s**3/21 - 48*s**2 + s - 29. What is h in z(h) = 0?
-84, -2
Let s(y) be the first derivative of -2*y**3/3 + 114*y**2 + 464*y + 823. Factor s(l).
-2*(l - 116)*(l + 2)
Let z(m) = -53*m - 70. Let h be z(3). Let x = h + 231. Suppose 4/11*u + 2/11 + 2/11*u**x = 0. Calculate u.
-1
Solve 4*d**3 + 2*d**2 + 8 - 2/3*d**4 - 40/3*d = 0.
-2, 1, 6
Let h(q) be the second derivative of -q**5/90 + 37*q**4/54 - 455*q**3/27 + 1859*q**2/9 + 666*q - 4. Factor h(n).
-2*(n - 13)**2*(n - 11)/9
Suppose -29*k = -25*k - 5*m + 31, -5*k - 45 = -5*m. Let d be (5/(-20))/((21/k)/3). Factor 1/4*z**3 + 0 + 1/4*z - d*z**2.
z*(z - 1)**2/4
Let s(c) = 25*c**2 - 20*c. Let p be s(0). Determine v, given that -10*v**2 - 15*v + 5/4*v**4 + 5/4*v**3 + p