. Let k(b) be the second derivative of 2/3*b**2 - 5*b + r + 2/9*b**3 + 1/36*b**4. Factor k(i).
(i + 2)**2/3
Let r(t) = t**2 - 1. Let m(o) = -4*o**4 - 20*o**3 - 2*o**2 + 84*o + 70. Let u(j) = m(j) - 2*r(j). Factor u(d).
-4*(d - 2)*(d + 1)*(d + 3)**2
Let o be 51/(-45) - (-2)/15. Let m be (0 + o)*(0 + -3). Solve 8*s**4 + s**3 + 3*s**2 - s**2 + m*s**3 - 6*s**4 = 0.
-1, 0
Let v = 1 + 2. Suppose 16*y**5 - 20*y**2 - y**4 + 21*y**4 + 7*y**3 - 4*y - 13*y**v - 6*y**3 = 0. Calculate y.
-1, -1/4, 0, 1
Suppose -81*x + 78*x + 3 = 0. Let a(r) = 2*r - 2. Let b be a(x). Factor 6/7*q**2 + 0*q + b + 10/7*q**3.
2*q**2*(5*q + 3)/7
Let b be 2/(1 + 840/(-423) + 1). Let f = 145 - b. Determine q so that 0 - 6/5*q**3 + 8/5*q - 2/5*q**5 - 8/5*q**f + 8/5*q**2 = 0.
-2, -1, 0, 1
Let t(u) be the second derivative of u**8/112 - 2*u**7/35 + u**6/8 - u**5/10 + 3*u**2/2 + 7*u. Let q(j) be the first derivative of t(j). Factor q(v).
3*v**2*(v - 2)*(v - 1)**2
Let 0 - 2*h**3 + 0*h - 8/9*h**4 - 4/9*h**2 = 0. What is h?
-2, -1/4, 0
Let p(a) be the first derivative of -7 + 1/15*a**5 + 0*a - 2*a**2 + 2/15*a**3 - 3/20*a**4. Let q(b) be the second derivative of p(b). Factor q(c).
2*(2*c - 1)*(5*c - 2)/5
Let b = 380 - 379. Let f(w) be the first derivative of -b - 12/7*w + 4/7*w**2 + 4/21*w**3. Factor f(o).
4*(o - 1)*(o + 3)/7
Let u be (2 - 14/6)*-3*2. Solve -12*m**3 - 6*m**2 + 2*m**4 + 14*m**2 + u*m**4 = 0.
0, 1, 2
Let y(i) be the third derivative of -26*i**2 + 0 - 1/20*i**4 + 1/150*i**6 + 1/840*i**8 + 1/175*i**7 - 1/75*i**5 + 0*i - 1/15*i**3. Factor y(c).
2*(c - 1)*(c + 1)**4/5
Let v = 1813 - 1808. Let i(p) be the third derivative of 0*p**3 + 1/56*p**4 + 0*p - p**2 + 1/70*p**v + 0 - 1/56*p**6 - 3/245*p**7. Determine k so that i(k) = 0.
-1, -1/3, 0, 1/2
Let -15/7*z + 0 - 1/7*z**2 = 0. What is z?
-15, 0
Let g = 255946/287919 + -2/31991. Factor -10/9*l + g*l**2 - 2/9*l**3 + 4/9.
-2*(l - 2)*(l - 1)**2/9
Let q(j) be the third derivative of j**8/2352 + j**7/490 - j**6/140 - j**5/42 + j**4/8 - 3*j**3/14 - 352*j**2. Determine s so that q(s) = 0.
-3, 1
Let k = -324 + 324. Suppose k = -9*j + 5*j. Factor j*g - 2/7*g**4 - 2/7*g**3 + 4/7*g**2 + 0.
-2*g**2*(g - 1)*(g + 2)/7
Suppose -3*t = 4*f + t - 12, 3*f = -2*t + 8. Let 37 - 5*d**4 - 104*d**2 + 114*d**f + 37*d - 15*d**3 + 23*d + 3 = 0. Calculate d.
-2, -1, 2
Let w(d) be the first derivative of 8*d**5/45 + 7*d**4/18 + 4*d**3/27 - d**2/9 - 32. Determine x, given that w(x) = 0.
-1, 0, 1/4
Let g = 6/355 - -65651/1420. Let q = 47 - g. Factor 3/4*z**4 - q*z**2 + 0*z**3 + 0 + 0*z.
3*z**2*(z - 1)*(z + 1)/4
Let f = 66 + -64. Let h(n) = n**4 - 11*n**3 + 3*n**2 + 11*n - 4. Let i(u) = -3*u**4 + 45*u**3 - 12*u**2 - 45*u + 15. Let j(s) = f*i(s) + 9*h(s). Factor j(g).
3*(g - 2)*(g - 1)**2*(g + 1)
Suppose 0 - 1/3*y**3 - 75*y + 10*y**2 = 0. Calculate y.
0, 15
Suppose -8/9*x**3 - 2/9*x**4 + 8/9*x + 2/9*x**2 + 0 = 0. What is x?
-4, -1, 0, 1
Suppose 0*o = -6*o - 12. Let g(x) = 5*x**3 + 4*x**2 - 10*x - 24. Let i(u) = -26*u**3 - 19*u**2 + 49*u + 120. Let s(q) = o*i(q) - 11*g(q). Factor s(v).
-3*(v - 2)*(v + 2)**2
Factor 1082*q + 260*q**3 - 265*q**2 + 1077*q - 2154*q.
5*q*(q - 1)*(52*q - 1)
Let r(i) be the second derivative of -1/240*i**6 + 3*i**2 + 0 - 1/40*i**5 + 0*i**4 - 2*i + 1/3*i**3. Let u(y) be the first derivative of r(y). Factor u(b).
-(b - 1)*(b + 2)**2/2
Let k(z) be the third derivative of -z**8/4032 + z**7/120 - 23*z**6/240 + 149*z**5/360 - 29*z**4/32 + 9*z**3/8 + 49*z**2. Factor k(m).
-(m - 9)**2*(m - 1)**3/12
Let o = -8279 - -8279. Factor -1/4*p**3 - 1/4*p - 1/2*p**2 + o.
-p*(p + 1)**2/4
Let p(t) be the third derivative of 0 + 0*t + t**2 - 4/7*t**3 - 1/140*t**5 + 9/56*t**4. Factor p(g).
-3*(g - 8)*(g - 1)/7
Factor 0*w**2 + 0 + 1/2*w**3 + 1/2*w**5 + 0*w - w**4.
w**3*(w - 1)**2/2
Let s = -9 - -12. Determine c so that -c**4 + s*c**4 - 6*c**2 + 7*c**3 + 2*c**4 - 5*c**4 = 0.
0, 1, 6
Let k(t) be the first derivative of -1/2*t**6 - 9 + 3/2*t**4 + 6/5*t**5 + 21/2*t**2 - 6*t - 8*t**3. Solve k(y) = 0 for y.
-2, 1
Let h(r) = -r**4 + 55*r**3 - 225*r**2 + 396*r - 213. Let b(f) = 4*f**4 - 276*f**3 + 1124*f**2 - 1980*f + 1064. Let x(o) = -3*b(o) - 16*h(o). Factor x(d).
4*(d - 6)*(d - 3)**2*(d - 1)
Let y(v) be the second derivative of -v**5/45 - 2*v**4/3 - 8*v**3 + 11*v**2 + 3*v. Let a(o) be the first derivative of y(o). Factor a(p).
-4*(p + 6)**2/3
Let f(w) be the second derivative of 1/42*w**7 + 0 - 2*w**2 - 1/4*w**5 - 1/30*w**6 + 5/12*w**4 - 8*w + 2/3*w**3. What is h in f(h) = 0?
-2, -1, 1, 2
Factor 13/4*m + 11/2 + 1/4*m**2.
(m + 2)*(m + 11)/4
Factor 111*o**2 + 42*o**2 - 519*o + 169*o**2 + 258 - 58*o**2 - 2*o**3 - o**3.
-3*(o - 86)*(o - 1)**2
Suppose 3*o + b = 4*b + 18, 0 = -5*o + 4*b + 28. Factor 3*l**3 - l**2 + 2*l**o - 1 + 0*l - 3*l + l**4 - l**4.
(l - 1)*(l + 1)**2*(2*l + 1)
Let l(s) be the first derivative of 2/27*s**3 - 2/3*s - 3 + 2/9*s**2. Factor l(g).
2*(g - 1)*(g + 3)/9
Let z(d) be the first derivative of 3*d**4/4 + 2*d**3/7 + 58. Factor z(x).
3*x**2*(7*x + 2)/7
Let n(x) be the first derivative of 3*x**6/160 - x**5/10 + 7*x**4/32 - x**3/4 + 9*x**2/2 - 14. Let o(r) be the second derivative of n(r). Factor o(l).
3*(l - 1)**2*(3*l - 2)/4
Let a(l) be the second derivative of l**5/100 - 13*l**4/60 - 13*l**3/6 - 51*l**2/10 - 65*l - 9. Solve a(x) = 0.
-3, -1, 17
Determine q, given that -48/5*q + 2/5*q**5 - 18/5*q**4 + 104/5*q**2 - 128/5 + 4/5*q**3 = 0.
-2, -1, 2, 8
Let j(z) = z**4 - 101*z**3 - 787*z**2 - 2587*z - 2921. Let v(p) = p**4 - p**3 + p**2 + p - 1. Let n(i) = j(i) - 5*v(i). Determine h so that n(h) = 0.
-9, -3
Let f(p) be the first derivative of 16*p**2 + 1/10*p**5 + 8*p**3 + 0*p + 3/2*p**4 - 13. Determine s so that f(s) = 0.
-4, 0
Suppose -57*w + 18 = -77*w + 118. Find b such that 3 + 13/2*b + 5*b**4 + 7/6*b**w - 44/3*b**2 - b**3 = 0.
-3, -2/7, 1
Let r be 0/89 + (64/24 - (1 - -1)). Suppose r - 2/9*b**2 - 4/9*b = 0. What is b?
-3, 1
Factor -21*s**2 + 3*s**4 + 125*s**3 - 2*s**4 - 4*s**4 - 149*s**3.
-3*s**2*(s + 1)*(s + 7)
Let j be 21*(-6)/(-36)*(-68)/(-7). Factor -4*v**5 - 55*v**3 + 13*v**4 - 4 - 96*v**2 - 89*v**4 - j*v - 69*v**3 - 14*v**5.
-2*(v + 1)**4*(9*v + 2)
Suppose -4*g + 0*q = 2*q - 30, 2*g + 5*q = -5. Let d be (-6)/21 - g/14 - -4. Suppose -9/5*b**2 + 0*b + 3/5*b**d + 0 = 0. Calculate b.
0, 3
Let o be ((-2)/((-24)/(-18)))/((-85)/158). Let m = 78/17 - o. Factor 0*j**2 - 6/5*j**3 - 3/5*j**5 + 0 - m*j**4 + 0*j.
-3*j**3*(j + 1)*(j + 2)/5
Let t(n) be the first derivative of 5*n**4/4 + 175*n**3/3 + 335*n**2/2 + 165*n - 539. Find d such that t(d) = 0.
-33, -1
Let w(j) = 3*j**3 + j**3 - 2733 + 12*j**2 + 6*j + 2719. Let g(t) = -t**3 - t**2 - t + 1. Let u(m) = 12*g(m) + 2*w(m). What is x in u(x) = 0?
-1, 2
Let c = 207 - 207. Let k(f) be the second derivative of -7/20*f**5 + 1/3*f**3 + 0*f**2 + c - 5/12*f**4 - 2*f. Factor k(v).
-v*(v + 1)*(7*v - 2)
Let h(z) = -4*z**4 + 44*z**3 + 84*z**2 + 36*z - 16. Let m(p) = p**4 - 15*p**3 - 28*p**2 - 12*p + 5. Let u(a) = -5*h(a) - 16*m(a). Factor u(i).
4*i*(i + 1)**2*(i + 3)
Factor -16/3*m**2 - 94/9*m**3 + 2/9*m**5 - 44/9*m**4 + 0*m + 0.
2*m**2*(m - 24)*(m + 1)**2/9
Let y(i) be the third derivative of i**8/2016 + i**7/315 - i**6/90 + 29*i**5/60 + 15*i**2. Let a(t) be the third derivative of y(t). Let a(o) = 0. Calculate o.
-2, 2/5
Let v(d) be the second derivative of d**5/35 + 34*d**4/7 - 99*d. Factor v(p).
4*p**2*(p + 102)/7
Factor 50/3 - 13/3*w**3 - 95/3*w + 1/3*w**4 + 19*w**2.
(w - 5)**2*(w - 2)*(w - 1)/3
Let w(y) = 29 + 24 - y - 49. Let d be w(2). Factor 10*q - 17/2*q**2 - 2 + d*q**3.
(q - 2)**2*(4*q - 1)/2
What is w in 2/13*w + 310/13*w**2 + 0 = 0?
-1/155, 0
Determine o, given that 0 - 81/4*o + 27/4*o**2 + 9/4*o**3 - 3/4*o**4 = 0.
-3, 0, 3
Let c(s) = -17*s + 1056. Let j be c(62). What is u in 0 - 1/2*u - 1/2*u**j = 0?
-1, 0
Suppose -3*m - 5*h - 12 = -43, -m + 3*h + 29 = 0. Suppose -3 = -a + 5*f + m, -3*f = 9. Factor 0*d**2 + 0*d + 0*d**4 - 2/11*d**a + 0 + 2/11*d**3.
-2*d**3*(d - 1)*(d + 1)/11
Let m(s) = 8*s**3 - 537*s**2 + 19449*s - 233280. Let h(l) = -l**3 - l**2 - 3*l. Let r(u) = 3*h(u) + m(u). Determine v so that r(v) = 0.
36
Let f(o) be the second derivative of -o**7/15120 + o**6/432 + 11*o**5/720 + 19*o**4/12 + o**2 - 5*o - 1. Let m(r) be the third derivative of f(r). Factor m(j).
-(j - 11)*(j + 1)/6
Let w(m) be