05 + 955. Factor 3*u**3 - 2*u + 205*u**2 - f*u**2 - u + 48.
3*(u - 16)*(u - 1)*(u + 1)
Let c(s) be the third derivative of -s**8/6720 - 19*s**7/1680 + 5*s**5/6 - 128*s**2. Let w(u) be the third derivative of c(u). Factor w(b).
-3*b*(b + 19)
Let d(v) = -4*v - 193. Let a be d(-55). Suppose -18 = a*k - 99. Find h, given that 10/7*h**2 + 0 + 2/7*h**k + 0*h = 0.
-5, 0
Let m be (-44)/720*-4 - (-140)/(-1050). Let l(x) be the second derivative of m*x**3 + 1/90*x**4 + 0 + 4/15*x**2 - 21*x. Factor l(h).
2*(h + 1)*(h + 4)/15
Let r(v) = 105*v**3 + 2*v**2 - v - 6. Let d be r(2). Suppose -f = 2*f + 3, -4*n + 4*f + d = 0. Suppose -n*a + 209*a + 8*a**3 - 4*a**4 - 4*a**2 = 0. Calculate a.
0, 1
Let r = -4 + 18. Suppose -2*l = 2 - r. Suppose 25*t**3 - l*t + 25*t**2 - 80*t**4 + 55*t**4 - 4*t - 15*t**5 = 0. Calculate t.
-2, -1, 0, 1/3, 1
Let o be (-6)/(-27)*(-684)/1748 - 18260/(-506). Find q such that -3/2*q**2 + 75/2 - o*q = 0.
-25, 1
Let k(l) = -3*l**2 - 122*l - 37. Let y be k(-42). Let p = y - -205. Factor -14/9*m**3 + p - 8/9*m**4 - 4/9*m**2 + 2/9*m.
-2*m*(m + 1)**2*(4*m - 1)/9
Let s be (5 - 170/(-4)) + (-1)/(-2). Solve s*y - 3*y**2 + 612 + 96*y - 1301 - 1039 = 0.
24
Let t(r) be the first derivative of -r**3/30 - r**2 + 261*r/10 + 2764. Find a, given that t(a) = 0.
-29, 9
Let w(o) be the first derivative of -o**5/30 + o**4/6 - o**3/3 + o**2/3 + o - 2. Let u(z) be the first derivative of w(z). Find j, given that u(j) = 0.
1
Let a(i) = -2*i**2 + 1489*i - 11780. Let f be a(8). Solve -4/3*d + 2/3*d**5 + 0 + 2*d**2 + 2/3*d**3 - 2*d**f = 0 for d.
-1, 0, 1, 2
Let k be 4/18 - 129/(-27). Suppose 4*g - 8 = 4*x, g - x + 8 = k*g. Find w, given that -40*w**g + w + 15*w + 4*w - 5 + 10*w = 0.
1/4, 1/2
Let y = 1643/3 - 67390/123. Let n = y - -241/164. Suppose 0*q - 1 - 1/4*q**4 + n*q**2 + 0*q**3 = 0. What is q?
-2, -1, 1, 2
Suppose -4*y + 18 = i - 1, 2*y + 4*i = 6. Determine n so that -24*n - 3*n - 69*n + 12*n**4 + 21*n**2 + 93*n**3 + 3*n**y + 27*n**4 - 60 = 0.
-10, -2, -1, 1
Let x(s) = 4*s**4 - 47*s**3 + 30*s**2 + 26*s - 26. Let y(i) = i**4 - 11*i**3 + 7*i**2 + 6*i - 6. Let a(n) = 6*x(n) - 26*y(n). Factor a(f).
-2*f**2*(f - 1)**2
Let s be 36/(-8)*(-84)/9. Determine o so that -57 + s - 4*o + 12*o - o**2 = 0.
3, 5
Let y(b) be the third derivative of -2/15*b**5 + 49*b**2 + 0*b**3 + 4/3*b**4 + 0*b - 1/30*b**6 + 0. Factor y(c).
-4*c*(c - 2)*(c + 4)
Factor 3/8*g**2 + 0 - 57/8*g.
3*g*(g - 19)/8
Factor -441*d + 30*d**4 - 3*d**5 - 109*d**3 + 360*d + d**3 + 162*d**2.
-3*d*(d - 3)**3*(d - 1)
Let k be (-22308)/1690*(-35)/56. Determine q so that 1/4*q**2 + 31/2 - k*q = 0.
2, 31
Let b(k) = -225*k - 2250. Let p be b(-10). Let y(w) be the first derivative of p*w + 3/20*w**4 + 27/10*w**2 - 13 + 6/5*w**3. Suppose y(f) = 0. What is f?
-3, 0
Let p(o) be the second derivative of -o**10/70560 + o**9/8820 - o**8/3920 + 5*o**4/12 + 8*o - 2. Let d(y) be the third derivative of p(y). Factor d(u).
-3*u**3*(u - 2)**2/7
Let s(o) be the second derivative of 0*o**4 - 1/14*o**7 + 1/6*o**3 + 8*o - 3/10*o**5 + 0*o**2 + 4/15*o**6 + 1. Solve s(i) = 0 for i.
-1/3, 0, 1
Let z = -199523 + 199525. Factor 3*m**3 + 1/5*m**5 - 8/5*m**z - 16/5*m + 8/5*m**4 + 0.
m*(m - 1)*(m + 1)*(m + 4)**2/5
Let m = 9299 + -27887/3. Solve -m + 3*d + 1/3*d**2 = 0 for d.
-10, 1
Suppose k - 39 = -4*r, 4*r + 3*k - 8 - 21 = 0. Factor r*l**3 + 83*l**4 - 85*l**4 - 360*l - 122*l**2 + 25*l**3 - 200.
-2*(l - 10)**2*(l + 1)**2
Let g be 2*((-72)/14 + 6)*(-14)/(-8). Let x = 163/18 + -80/9. Solve 1/6*h**g - 1/6*h**2 + x - 1/6*h = 0.
-1, 1
Let j = 201296/3 - 201295/3. Factor -11/3*t - 26/3 + j*t**2.
(t - 13)*(t + 2)/3
Suppose -9 = -75*f + 66*f. Let v(y) = y**4 - y**3 - y**2 + y. Let p(n) = 7*n**4 - 5*n**3 - 11*n**2 + 9*n. Let h(o) = f*p(o) - 6*v(o). Factor h(w).
w*(w - 1)**2*(w + 3)
Let s be 32/154*481/1036. Let p = s - 2/1617. Factor 0*m + 0*m**2 + 0*m**3 + 0 - p*m**5 - 2/21*m**4.
-2*m**4*(m + 1)/21
Let k = 385/17 + -1109/85. Let w = -2/9162891 - -219909394/45814455. Solve -w*h - 3/5*h**2 - k = 0 for h.
-4
Let d be 885*(36/80)/((-12)/(-16)). Let j be 7/(-1) + d/63. Factor -8/7*x**2 - 4/7 + j*x + 2/7*x**3.
2*(x - 2)*(x - 1)**2/7
Let w(l) be the second derivative of 1/15*l**6 + 0*l**4 + 0 - 4/3*l**3 - 2/7*l**7 + 134*l + l**5 - l**2. Let w(v) = 0. What is v?
-1, -1/2, -1/3, 1
Let b(d) = -33*d**3 + 337*d**2 - 1014*d + 511. Let i(c) = -44*c**3 + 450*c**2 - 1353*c + 682. Let r(j) = -9*b(j) + 7*i(j). Factor r(l).
-(l - 5)**2*(11*l - 7)
Let c(n) be the third derivative of n**7/840 + n**6/120 - n**5/8 - 25*n**4/24 + 125*n**3/24 - 681*n**2. Factor c(k).
(k - 5)*(k - 1)*(k + 5)**2/4
Let b be 4/14 + (-137)/(-35). Let h = -408061/45 + 81623/9. Factor 21/5*v**2 - b*v + 6/5 - h*v**3.
-3*(v - 2)*(v - 1)*(2*v - 1)/5
Let d(o) be the third derivative of o**7/1260 + 11*o**6/720 - 29*o**5/36 + 119*o**4/12 - 50*o**3 - 2*o**2 - 5*o - 2. Solve d(n) = 0 for n.
-25, 2, 6
Let q(s) = s**2 + 38*s - 2037. Let m be q(-68). Suppose 0 = a - 2 - 3. Factor 13*b**2 - 9*b**2 + b**m - a*b**2.
b**2*(b - 1)
Suppose 486*x - 491*x + 20 = 0. Suppose -5*q - 8 = x*l, -4*l = -q - 3*q - 28. Find i such that 8/9*i - 2/9 + 8/9*i**l - 4/3*i**2 - 2/9*i**4 = 0.
1
Let z = 314 + -303. Let m(r) = -r**2 + 19*r - 85. Let w be m(z). Suppose 0 + 0*t**w + 0*t + 1/5*t**4 - 1/5*t**2 = 0. Calculate t.
-1, 0, 1
Let n(a) be the third derivative of -a**6/40 - 59*a**5/140 + 39*a**4/56 + 27*a**3/14 + 572*a**2 - 5*a. Factor n(m).
-3*(m - 1)*(m + 9)*(7*m + 3)/7
Let n(d) = -9*d**3 + 3*d**2 - 31*d - 92. Let x be n(-3). What is g in 281*g + 5*g**2 - 562*g + x*g = 0?
0, 2
Let p(v) be the second derivative of 45*v**6/4 + 153*v**5/8 + 31*v**4/8 + v**3/4 - 84*v. Find q such that p(q) = 0.
-1, -1/15, 0
Let v(t) be the second derivative of 5*t**3/6 - t**2 - 5*t. Let z be v(3). Factor 11*k**4 - 27*k**3 - 10*k**4 - z*k**4 - 9*k**4 - 6*k**2.
-3*k**2*(k + 1)*(7*k + 2)
Let m = -389/143 + 33/13. Let l = 58/77 + m. Let -l*b + 2/7*b**2 - 6/7 = 0. What is b?
-1, 3
Let d(r) be the first derivative of -r**3 - 3565*r**2/2 - 1188*r - 5731. Factor d(l).
-(l + 1188)*(3*l + 1)
Let g be 0 + (-58)/(-6) - -49*(-765)/4165. Suppose 194/3*w + g*w**3 - 100/3*w**2 - 32 = 0. Calculate w.
1, 48
Let m be -1 + 0/(1 + -4). Let o(p) = 15*p**2 + 27*p - 99. Let w(z) = 2*z**2 - z + 1. Let s(c) = m*o(c) + 9*w(c). Factor s(k).
3*(k - 6)**2
Let q(n) be the second derivative of n**6/30 - 11*n**5/10 + 13*n**4 - 60*n**3 + 92*n - 1. Factor q(g).
g*(g - 10)*(g - 6)**2
Let b(d) = 10*d**2 - 1508*d + 1502. Let g(s) = -43*s**2 + 6032*s - 6007. Let w(h) = 9*b(h) + 2*g(h). Factor w(i).
4*(i - 376)*(i - 1)
Let m = -5 + 11. Suppose 0 = 33*d - 50*d + 68. Suppose -12*s**2 - 2*s - 278*s**5 + 6*s**d + 275*s**5 + 6*s**3 - s + m = 0. Calculate s.
-1, 1, 2
Let g = 52 + -49. Suppose g*s = -2*k + 10, k + s = -4*s + 12. Solve -16*r**2 - 2 + k*r**3 + 13*r + 2*r**3 + r**3 = 0.
1/5, 1, 2
Determine m, given that -2070/11*m**2 + 122/11*m**3 - 2/11*m**4 + 194672/11 - 1058/11*m = 0.
-8, 23
Factor 49*h + 671*h - 30*h**2 + 2402*h + 7 - 215.
-2*(h - 104)*(15*h - 1)
Let d be -2 + -3 - (-2120)/280. Factor 20/7 + 2/7*z**4 + 50/7*z**2 + 54/7*z + d*z**3.
2*(z + 1)**2*(z + 2)*(z + 5)/7
Let n(a) = -a**2 + 41. Let y be n(0). Suppose -y*p + 37*p = -12. Factor 30*k + 228*k**3 - 268*k**p + 5*k**5 + 50*k.
5*k*(k - 2)**2*(k + 2)**2
Let r(g) = -13*g**4 - 111*g**3 + 25*g**2 + 23*g - 50. Let k(b) = -b**4 - 9*b**3 + 2*b**2 + 2*b - 4. Let m(j) = 25*k(j) - 2*r(j). Factor m(u).
u*(u - 2)**2*(u + 1)
Let q(v) = -v**2 + 5*v - 3. Let p(w) = 16*w**2 + 3 - 7 - 11*w**2 + 5*w - 6*w**2. Let h(z) = -3*p(z) + 4*q(z). Determine m, given that h(m) = 0.
0, 5
Let z(x) be the second derivative of x**4/32 - 111*x**3/2 + 36963*x**2 - 142*x. Factor z(w).
3*(w - 444)**2/8
Let r(h) = h**3 + 6*h**2 - h - 4. Let a be r(-6). Factor -4*x**5 - 8*x**3 + 2445*x**a - 12*x**4 - 2445*x**2.
-4*x**3*(x + 1)*(x + 2)
Let x = 4547/11255 - 9/2251. Determine s, given that 16/5*s + 0 + 24/5*s**2 + x*s**4 + 12/5*s**3 = 0.
-2, 0
Let i(d) be the second derivative of 92/21*d**4 + 0 - 54/35*d**5 + 0*d**2 - 2/147*d**7 - 16/3*d**3 + 26/105*d**6 - 149*d. Factor i(s).
-4*s*(s - 7)*(s - 2)**3/7
Let k be (-25 - -3) + (7 - 1). Let u be k/4 + 1 + (-40)/(-12). Suppose -1/3 + 1/6*t - 1/6*t**3 + u*t**2 = 0. What is t?
-1, 1, 2
Let z(o) be the third derivative of