**4.
3*(j + 1)**3*(2*j + 1)**2
Let r(w) be the third derivative of 1/60*w**5 + 0*w - 1/210*w**7 + 0*w**4 + 0*w**3 - 26*w**2 + 0 + 0*w**6. Factor r(d).
-d**2*(d - 1)*(d + 1)
Factor 3/4*b**3 + 12*b + 51/4*b**2 + 0.
3*b*(b + 1)*(b + 16)/4
Factor -171*j**2 - 6192 - 38*j**2 - 2208*j - 4*j**3 - 87*j**2 + 76*j**2.
-4*(j + 6)**2*(j + 43)
Let i = -17021/2 + 8162. Let r = i - -352. Suppose 7/2*y**5 - 7*y**3 + r*y + 1 + y**4 - 2*y**2 = 0. What is y?
-1, -2/7, 1
Let i(a) be the first derivative of 2*a + 31 + 1/32*a**4 + 3/8*a**3 + 3/2*a**2. Let i(y) = 0. Calculate y.
-4, -1
Let k be (-9 - (-4577)/506)*(-4 + 36). Factor -2/11*d**3 - 2/11*d**4 + 0 + 24/11*d + k*d**2.
-2*d*(d - 3)*(d + 2)**2/11
Let r(x) be the third derivative of -x**2 + 3*x**3 - 51/20*x**5 + 1/14*x**7 + 0 + x + 19/8*x**4 + 21/40*x**6. Find m, given that r(m) = 0.
-6, -1/5, 1
Suppose -234*r + 106387 - 3091*r - 107217 - 20*r**2 = 0. Calculate r.
-166, -1/4
Let z(m) be the first derivative of -m**4/8 + 7*m**3/2 - 111*m**2/4 + 91*m/2 - 1083. Suppose z(k) = 0. Calculate k.
1, 7, 13
Determine i so that -2106/5*i**2 - 778383918/5 - 2217618/5*i - 2/15*i**3 = 0.
-1053
Let a(z) be the first derivative of 0*z - 4/3*z**3 - 27 + 1/4*z**4 + 0*z**2. Suppose a(t) = 0. Calculate t.
0, 4
Let m(c) be the second derivative of -2*c**6/15 - 6*c**5 - 23*c**4/3 + 116*c**3 - 8*c + 2. Find a such that m(a) = 0.
-29, -3, 0, 2
Let k(q) be the first derivative of 79 - 676/7*q - 793/7*q**2 - 5/14*q**4 + 256/21*q**3. Let k(z) = 0. What is z?
-2/5, 13
Let g = -452/15 - -472/15. Let y(t) be the first derivative of -2*t**4 - g*t**3 + 4/5*t**5 - 20 + 4*t**2 + 0*t. Determine a so that y(a) = 0.
-1, 0, 1, 2
Let c(h) be the second derivative of -h**7/273 - h**6/3 + 67*h**5/65 - 6043*h. Let c(y) = 0. Calculate y.
-67, 0, 2
Let g(o) be the second derivative of 2*o**7/27 + 71*o**6/45 + 326*o**5/45 - o**4/54 - 122*o**3/9 + 88*o**2/9 + 2*o + 40. Suppose g(a) = 0. What is a?
-11, -4, -1, 2/7, 1/2
Let h(s) = -s**3 + 23*s**2 + s - 5. Let n be h(23). Suppose -4*w = 5*w - n. Factor -3*o**w + 0*o - 9*o + o - 7*o - 6 + 6*o**3.
3*(o - 2)*(o + 1)*(2*o + 1)
Suppose 19*j = -12 + 50. Factor -37*m + 94*m + 4 - 4 + 3*m**j.
3*m*(m + 19)
Let h(g) be the second derivative of g**7/63 + 499*g**6/45 + 83659*g**5/30 + 535645*g**4/2 + 2032800*g**3 + 5989500*g**2 - 2*g - 230. Find j such that h(j) = 0.
-165, -2
Let f(o) = -11*o**4 - 155*o**3 - 555*o**2 - 713*o - 278. Let s(r) = 4*r**4 + 52*r**3 + 185*r**2 + 239*r + 93. Let h(w) = 9*f(w) + 24*s(w). Factor h(t).
-3*(t + 1)**2*(t + 2)*(t + 45)
Factor -34/3*r + 32/3*r**2 + 2/3*r**3 + 0.
2*r*(r - 1)*(r + 17)/3
Let n(g) be the second derivative of g**4/4 - 29*g**3/3 - 20*g**2 - 8467*g. Determine o, given that n(o) = 0.
-2/3, 20
Determine r, given that -3532/5 + 3534/5*r - 2/5*r**2 = 0.
1, 1766
Let i(z) be the first derivative of 10/9*z**3 + 25*z + 25/3*z**2 + 1/18*z**4 - 23. Let c(h) be the first derivative of i(h). Solve c(l) = 0 for l.
-5
Factor 88/9 + 89/9*z + 1/9*z**2.
(z + 1)*(z + 88)/9
Factor -100/3*g - 8*g**3 - 98/3*g**2 + 0.
-2*g*(g + 2)*(12*g + 25)/3
Find f, given that -28/5*f + 28/5*f**3 + 104/5*f**2 - 104/5 = 0.
-26/7, -1, 1
Let w(y) be the third derivative of y**5/120 + 185*y**4/48 + 5*y**2 + 30. What is p in w(p) = 0?
-185, 0
Solve 5*t**3 - 2780 - 5141*t**2 + 14*t**3 + 996*t**2 - 3038*t - 4*t**3 - 3902*t = 0 for t.
-1, -2/3, 278
Let s(d) be the first derivative of -9*d**3/2 - 6*d**2 - 3112. Let s(n) = 0. What is n?
-8/9, 0
Let r(z) be the first derivative of 3/20*z**6 - 3/10*z**5 - 54 - 19/20*z**4 + 1/15*z**3 + 13/20*z**2 - 3/10*z. Find d such that r(d) = 0.
-1, 1/3, 3
Let y be (589/(-1596) - (-8)/28)*10/(-6). Let s(r) be the third derivative of -4/9*r**3 + 0*r + y*r**4 - 13*r**2 + 1/60*r**5 + 0. Determine b so that s(b) = 0.
-4, 2/3
Let q(y) be the first derivative of 0*y**2 + 4*y - y**3 + 43 - 1/4*y**4. Factor q(m).
-(m - 1)*(m + 2)**2
Let y = 1671851/9 + -185761. Suppose 14/9*r - y*r**2 + 4 = 0. Calculate r.
-2, 9
Let q(z) = 3*z - 30. Let t be q(11). Let m(c) = 1 - 1 + c**2 + 1 - 2. Let y(a) = -3*a**2 + 3*a. Let l(s) = t*m(s) - y(s). Factor l(o).
3*(o - 1)*(2*o + 1)
Let z(l) be the second derivative of -l**4/3 + 140*l**3/3 + 288*l**2 - 2*l + 1066. Solve z(g) = 0 for g.
-2, 72
Let l = -533824 + 533832. Suppose -64/3 - l*v - 2/3*v**2 = 0. What is v?
-8, -4
Let a(y) = -y**3 - 17*y**2 - 16*y + 2. Let s be a(-16). Suppose -5*n + 21 - 6 = 0. Factor -24*j**3 + 18*j**s + j**n - 4*j + 9*j**3.
-2*j*(j - 1)*(7*j - 2)
Suppose -12*j + 10*j = -60. Suppose -2*i = -3*s + 1 + 2, -j = -5*s - 5*i. Solve -579*t**2 - 234*t - 2 + s - 6 - 48*t**4 - 22 - 312*t**3 = 0 for t.
-3, -1/4
Suppose 0 = -5*d + 16*d - 253. Suppose 384 + 288*q + 13*q**3 - 33*q**3 + d*q**3 + 54*q**2 = 0. Calculate q.
-8, -2
Let z(u) be the first derivative of 0*u - 12 - 13/3*u**3 - 7/1080*u**6 + 1/72*u**5 + 0*u**2 + 1/36*u**4. Let f(t) be the third derivative of z(t). Factor f(i).
-(i - 1)*(7*i + 2)/3
Let q be ((-195)/(-780))/(3/572). Factor 1/6*j**4 + q*j**2 - 16/3*j**3 + 75/2 - 80*j.
(j - 15)**2*(j - 1)**2/6
Let c(k) be the first derivative of 112 + 0*k**4 + 22/25*k**5 + 1/15*k**6 + 0*k + 0*k**2 + 0*k**3. Factor c(b).
2*b**4*(b + 11)/5
Let x(w) be the third derivative of -1/270*w**6 + 7/270*w**5 + 0*w**3 - 11*w**2 - 1/945*w**7 - 1/27*w**4 + 0*w + 1. Let x(k) = 0. Calculate k.
-4, 0, 1
Suppose -2*c - 1433 = 33*s - 38*s, -c - 710 = 4*s. Let g = c - -719. Solve 4/3*d**2 - 4/3*d**4 + 2/3*d**3 - 2/3*d**g + 0*d + 0 = 0 for d.
-2, -1, 0, 1
Let k be 7 - 2*(-7 + 8). Let h(u) be the third derivative of 0*u - 17*u**2 + 0*u**3 + 0 + 1/12*u**4 - 1/60*u**k. Factor h(f).
-f*(f - 2)
Let m(f) be the third derivative of -f**5/15 - 27*f**4 - 322*f**3/3 - 953*f**2. Determine b so that m(b) = 0.
-161, -1
Let z(o) be the second derivative of o**7/14 - 107*o**6/10 + 159*o**5/10 - 832*o. Let z(h) = 0. What is h?
0, 1, 106
Let w(m) be the second derivative of 3*m**6/50 - 4*m**5/5 - 3*m**4/10 + 8*m**3/3 + 9*m**2/10 + 1550*m. Let w(f) = 0. Calculate f.
-1, -1/9, 1, 9
Let j(z) be the first derivative of -8*z**6/9 - 116*z**5/15 + 179*z**4 - 1504*z**3/9 - 256*z**2/3 + 2633. Solve j(t) = 0.
-16, -1/4, 0, 1, 8
Suppose 145*d - 469 = 138*d. Factor -77*l**3 + 5*l**2 + 118*l**3 + 3*l**2 - d*l**3.
-2*l**2*(13*l - 4)
Let x(g) be the third derivative of g**7/490 - 11*g**6/40 + 73*g**5/35 + 4*g**2 + 117*g - 2. Find s, given that x(s) = 0.
0, 4, 73
Factor 0 - 16*g + 4/3*g**3 + 26/3*g**2.
2*g*(g + 8)*(2*g - 3)/3
Let c be (-2680)/(-1675) - (2/(-4) - (-633)/330). Solve 4/11 - c*i**2 + 2/11*i = 0.
-1, 2
Let s be ((-122)/6 - 1)/(33/(-38610)*75). Solve -224/5*l**4 - s*l + 12/5*l**5 + 252*l**3 + 1536/5 - 1704/5*l**2 = 0 for l.
-1, 2/3, 3, 8
Let z(t) be the first derivative of -t**4/22 + 14*t**3/3 - 74*t**2/11 - 304*t/11 + 3529. Factor z(p).
-2*(p - 76)*(p - 2)*(p + 1)/11
Let v(w) be the first derivative of w**3/2 - 2373*w**2/4 + 859. Solve v(y) = 0 for y.
0, 791
Let v = 304198 - 304198. Factor v*o + 0*o**3 + 1/5*o**4 + 0 - 1/5*o**2.
o**2*(o - 1)*(o + 1)/5
Let g = 19661 + -39315/2. Let p(f) be the second derivative of 20*f + 0 + 5*f**2 - 5/42*f**7 - g*f**5 + 20/3*f**4 - 15/2*f**3 + f**6. Find a such that p(a) = 0.
1, 2
Let o be ((-18)/12*1)/((-3)/(-4)). Let b(t) = 113*t**2 - 715*t. Let l(h) = 19*h**2 - 119*h. Let w(u) = o*b(u) + 13*l(u). Factor w(g).
3*g*(7*g - 39)
Let l(v) be the first derivative of -11*v**4/16 + 5*v**3/12 - 3097. Find r such that l(r) = 0.
0, 5/11
Solve -84 - 1/4*n**2 + 85/2*n = 0 for n.
2, 168
Let b(l) = -l**5 - 4*l**4 + 76*l**3 + 50*l**2 - 51*l - 46. Let f(z) = 3*z**3 - z**2 + 1. Let t(i) = b(i) - 8*f(i). What is r in t(r) = 0?
-9, -1, 1, 6
Let o(g) be the second derivative of g**7/14 - 737*g**6/10 + 552*g**5/5 - 3050*g. Solve o(l) = 0 for l.
0, 1, 736
Let j be (-8942)/(-30771) + 22/(-26) + 1. What is w in -16/9*w + 0 - 8/9*w**2 + 2/9*w**4 + j*w**3 = 0?
-2, 0, 2
Suppose -4*d - z + 42 = -13, 0 = 5*d + 2*z - 71. Suppose -6*q + d*q - 14 = 0. Factor -3*g**5 + 75*g**3 + 5*g**2 + 15*g**4 - 90*g**3 - q*g**5.
-5*g**2*(g - 1)**3
What is i in 40247296/3 + 2/3*i**3 + 544*i**2 + 147968*i = 0?
-272
Let h(j) be the second derivative of 1/24*j**4 - 90*j + 0 + 5041/4*j**2 + 71/6*j**3. What is c in h(c) = 0?
-71
Let r(t) be the third derivative of -t**8/1008 + 527*t**7/126 - 579041*t*