t r(s) be the second derivative of s**5/100 - 3*s**4/10 + 77*s**3/30 - 6*s**2 - 172*s. Factor r(t).
(t - 12)*(t - 5)*(t - 1)/5
Let m(u) be the second derivative of u**7/147 - 48*u**6/35 + 2519*u**5/35 + 1752*u**4/7 + 5329*u**3/21 - 3*u + 10. Solve m(r) = 0.
-1, 0, 73
Let g(c) be the first derivative of c**4/36 - c**3/9 - 15*c - 4. Let v(x) be the first derivative of g(x). Determine d, given that v(d) = 0.
0, 2
Let b be (16/104)/(212/2067). Factor -b*n - 1/4*n**2 - 9/4.
-(n + 3)**2/4
Let t(l) = -l**2 - 4*l + 14. Let z be t(-6). Suppose -3*y + z*y = -2. Determine r so that r**3 + 4*r + 3*r**2 - 5*r - 3*r**y = 0.
-1, 0, 1
Let n be ((-9)/27)/((-1)/9). Let d = n - 3. Factor -2/7*u**3 - 4/7*u**2 + d + 2/7*u**4 + 0*u.
2*u**2*(u - 2)*(u + 1)/7
Let d(u) be the third derivative of 11*u**5/60 + 7*u**4/24 - 9*u**2. Let q(o) = -5*o**2 - 4*o. Let h(z) = -2*d(z) - 5*q(z). Solve h(c) = 0.
-2, 0
Let x be 72/27 - 5/(-15). Let d(a) be the first derivative of -a**3 + 3/2*a**4 + 3/5*a**5 + 0*a - 3 - x*a**2. Let d(j) = 0. Calculate j.
-2, -1, 0, 1
Let q = 9 - 5. Solve 4*d + 8*d**4 - 10*d**q + 3 - 1 - 4*d**3 = 0.
-1, 1
Suppose 0 = 4*z - 8, 1 = -v - z + 3. Let s be -2 - v - 15/(-3). Factor 6*n**5 - n**5 + 44*n**2 + 5 + 10*n**s + 4*n**4 - 34*n**2 - 19*n**4 - 15*n.
5*(n - 1)**4*(n + 1)
Let g = -21539/60 - -359. Let d(c) be the second derivative of 1/18*c**3 - g*c**5 + 1/3*c**2 - 1/18*c**4 + 2*c + 0. Factor d(p).
-(p - 1)*(p + 1)*(p + 2)/3
Let r(x) = -x**2 + 2. Let a be r(0). Factor -9*w**4 + 2*w**2 - 4*w**2 - 3*w**3 + 8*w**4 - w**a - w.
-w*(w + 1)**3
Let o(j) be the third derivative of 2*j**7/135 + j**6/27 + j**5/45 - 19*j**2 + 3*j. Determine b, given that o(b) = 0.
-1, -3/7, 0
Let o(y) be the first derivative of 9*y**5/10 + 363*y**4/8 + 620*y**3 + 300*y**2 + 512. Determine n, given that o(n) = 0.
-20, -1/3, 0
Let b = 21221 + -106101/5. Suppose 16/5*s - 16/5 + 4/5*s**2 - b*s**3 = 0. Calculate s.
-2, 1, 2
Determine g so that 2/17*g**2 - 12/17*g + 10/17 = 0.
1, 5
Let g(y) be the first derivative of -2*y**5/45 - y**4/9 + 2*y**2/9 + 2*y/9 - 534. Factor g(x).
-2*(x - 1)*(x + 1)**3/9
Let a be 4 + -9 + 1 + 4. Factor -2*v**2 + a*v**2 + v**5 + 41 + v**4 - 40 + v - 2*v**3.
(v - 1)**2*(v + 1)**3
Let c(v) be the third derivative of 0*v + 0*v**4 - 1/120*v**6 + 6*v**2 + 1/20*v**5 + 0 - 2/3*v**3. Factor c(y).
-(y - 2)**2*(y + 1)
Let y = -22422 - -22424. Let 40/13*q**y - 24/13*q + 10/13*q**4 + 0 + 46/13*q**3 = 0. Calculate q.
-3, -2, 0, 2/5
Let p(m) = -m**4 + 36*m**3 - 52*m**2 - 177*m + 197. Let u(x) = 3*x**4 - 72*x**3 + 104*x**2 + 355*x - 395. Let v(s) = -5*p(s) - 3*u(s). Factor v(h).
-4*(h - 5)**2*(h - 1)*(h + 2)
Let t(x) be the first derivative of -x**4/42 + 2*x**3/7 + x**2 - 13*x + 35. Let y(q) be the first derivative of t(q). Determine w so that y(w) = 0.
-1, 7
Let b(k) be the third derivative of -k**8/84 - 4*k**7/105 + k**6/10 + 4*k**5/15 - 2*k**4/3 - 4*k**2 + 29. Factor b(u).
-4*u*(u - 1)**2*(u + 2)**2
Let y = -837 + 842. Let i(w) be the second derivative of 0*w**2 + 8*w - 1/20*w**6 - 1/6*w**3 + 1/10*w**y + 1/24*w**4 + 0. Factor i(q).
-q*(q - 1)**2*(3*q + 2)/2
Let k be 56/70 - 381/(-5). Determine q, given that -12 + 50*q - 4*q**2 - k - q**2 - 36 = 0.
5
Let b be (11 - (-341)/(-33))*3. Factor -2/9*k**b - 8/9*k - 8/9.
-2*(k + 2)**2/9
Let l(q) be the second derivative of q**7/147 - 2*q**6/105 - q**5/35 + 4*q**4/21 - q**3/3 + 2*q**2/7 - 802*q. Factor l(x).
2*(x - 1)**4*(x + 2)/7
Suppose -12*a + 20 = 14 - 18. Factor -2/5*y**2 - a - 13/5*y + 1/5*y**3.
(y - 5)*(y + 1)*(y + 2)/5
Let d(x) be the third derivative of x**9/5040 + x**8/1680 - x**7/630 + x**4/6 - 4*x**2. Let w(f) be the second derivative of d(f). Factor w(n).
n**2*(n + 2)*(3*n - 2)
Let h(v) be the third derivative of v**8/6720 - v**7/840 - v**6/30 + 9*v**5/20 - 37*v**2. Let z(r) be the third derivative of h(r). Factor z(n).
3*(n - 4)*(n + 2)
Let n(a) be the first derivative of a**6/6 - 3*a**4/4 - 2*a**3/3 + 83. Suppose n(z) = 0. What is z?
-1, 0, 2
Let k(m) be the second derivative of -m**6/15 + 12*m**5/5 - 36*m**4 + 288*m**3 - 1296*m**2 - 95*m. Let k(c) = 0. Calculate c.
6
Let z(t) be the third derivative of -t**6/180 - t**5/18 - 2*t**4/9 - 4*t**3/9 - 2*t**2 + 86. Factor z(p).
-2*(p + 1)*(p + 2)**2/3
Let s(n) be the first derivative of -n**5/20 - 7*n**4/4 - 49*n**3/2 + 31*n**2/2 + 28. Let u(t) be the second derivative of s(t). Factor u(d).
-3*(d + 7)**2
Let w(m) be the first derivative of 33 - 1/10*m**2 + 1/15*m**3 + 0*m. Let w(z) = 0. What is z?
0, 1
Let m(y) be the first derivative of -2/7*y**2 + 3/7*y**4 + 0*y + 5 + 0*y**3 - 8/35*y**5. What is l in m(l) = 0?
-1/2, 0, 1
Let p(a) = a**3 - 10*a**2 + 10*a - 10. Let h be p(9). Let f be (3 + (-16)/5)*h. Factor f*d + 2/5 - 2/5*d**2 - 1/5*d**3.
-(d - 1)*(d + 1)*(d + 2)/5
Let d be (2/(-56) + 58/203)*1. Factor -1/4*x + d*x**2 - 1/2.
(x - 2)*(x + 1)/4
Factor -5 - 3 - 9819*t**3 - 3*t + 4*t + 9818*t**3 + 8*t**2.
-(t - 8)*(t - 1)*(t + 1)
Find q, given that -3/2 + 23/4*q + 11/2*q**4 - 5/4*q**5 - 4*q**2 - 9/2*q**3 = 0.
-1, 2/5, 1, 3
Let f = 201 - 199. Let k be f/6*(-30)/(-20). Determine p, given that -3/2 - 2*p - k*p**2 = 0.
-3, -1
Factor 49/2*g**4 + 14*g**3 - 56*g - 96*g**2 - 8.
(g - 2)*(g + 2)*(7*g + 2)**2/2
Let u(w) = -w**5 + 3*w**4 + 9*w**3 - 21*w**2 - 16*w + 22. Let g(z) = z**5 + 2*z**4 - z**3 + z**2 - 1. Let o(x) = -2*g(x) - u(x). Factor o(q).
-(q - 1)**2*(q + 2)**2*(q + 5)
Let c(i) = 9*i**2 - i + 1. Let d(l) = -50*l**2 - 395*l + 815. Let w(v) = 5*c(v) + d(v). Factor w(z).
-5*(z - 2)*(z + 82)
Let u = 7 - 3. Let b(v) = 9*v**3 - 17*v**2 + 3*v - 5. Let w(x) = -8*x**3 + 16*x**2 - 4*x + 4. Let d(a) = u*b(a) + 5*w(a). Factor d(f).
-4*f*(f - 2)*(f - 1)
Let n(l) = -l**2 - 2*l**2 + 8 + 2*l**2 + l - 9. Let d(q) = 2*q**2 - 4*q + 3. Let y(m) = 2*d(m) + 6*n(m). Factor y(h).
-2*h*(h + 1)
Let d = 28973/12 + -9655/4. Solve 2/3*z**4 - 4/15*z + 0 + 4/15*z**3 - d*z**2 = 0.
-1, -2/5, 0, 1
Let -12*x**3 - 2*x**4 + 4*x**3 + 28*x**3 - 2*x**2 - 16*x**2 = 0. What is x?
0, 1, 9
Factor 4418/9 + 188/9*h + 2/9*h**2.
2*(h + 47)**2/9
Let i(l) = l**3 + 33*l**2 + 121*l + 150. Let p be i(-29). Factor 24/11*d**3 + 20/11*d**2 + 0 + 6/11*d + 2/11*d**p + 12/11*d**4.
2*d*(d + 1)**3*(d + 3)/11
Suppose -39*p + 5*f + 30 = -34*p, 3*p = 2*f + 17. Let h(g) be the first derivative of -5 + 1/4*g**4 - 1/3*g**3 - 1/2*g**2 + 0*g + 1/5*g**p. Factor h(x).
x*(x - 1)*(x + 1)**2
Suppose 4*n + 2*t - 44 = 0, 2*n + 2*t = -0*t + 22. Let d = 14 - 5. Factor n - d*i**2 + 6*i**3 + 1 - 9*i**3.
-3*(i - 1)*(i + 2)**2
Let k(o) be the second derivative of -1/66*o**4 - 1/33*o**3 + o + 0 + 0*o**2. Suppose k(n) = 0. Calculate n.
-1, 0
Suppose -2*b = 8 - 18. Suppose 3 = -y - 4*n - 13, -y = -b*n - 29. Factor -6*l**3 - 2*l**y - 5*l**2 - 7*l**2 - 4 + l**4 - 12*l - l**2.
-(l + 1)**2*(l + 2)**2
Let a(s) be the first derivative of -13*s**6/720 + s**5/16 - s**4/24 + 32*s**3/3 + 29. Let h(d) be the third derivative of a(d). Factor h(o).
-(o - 1)*(13*o - 2)/2
Let t(c) = 6*c**2 - 3*c + 3. Let h(l) = 11*l**2 - 7*l + 6. Suppose -7*r = -2*r + 15. Let n(v) = r*h(v) + 5*t(v). Factor n(a).
-3*(a - 1)**2
Let s(u) be the third derivative of u**6/360 - u**4/18 + 35*u**2 + 2*u. Factor s(m).
m*(m - 2)*(m + 2)/3
Let b(y) = -6*y - 18. Let j be b(-9). Determine d so that -4*d**4 + j*d**2 + 3*d**4 - 35*d**2 = 0.
-1, 0, 1
Let g be (-12)/(-15)*(-135)/(-18). Suppose g*q**5 + 6*q + 24*q**2 - 33/2*q**4 - 9/2*q**3 + 0 = 0. What is q?
-1, -1/4, 0, 2
Let r = -2135 - -12811/6. Let s(y) be the second derivative of r*y**4 + 0 - 6*y + 4*y**2 - 5/3*y**3. Factor s(q).
2*(q - 4)*(q - 1)
Suppose -325*n**3 + 31 - 17 + 2*n**4 + 8*n**4 - 14 + 25*n**5 + 120*n + 170*n**2 = 0. What is n?
-4, -2/5, 0, 1, 3
Let 384/5 + 42/5*o**2 - 1356/5*o = 0. What is o?
2/7, 32
Let l(s) be the third derivative of s**8/336 - 13*s**7/210 + 19*s**6/40 - 19*s**5/12 + 25*s**4/12 + 848*s**2. Factor l(a).
a*(a - 5)**2*(a - 2)*(a - 1)
Let j(u) be the third derivative of -5*u**8/112 + u**7/6 + u**6/24 - 7*u**5/12 + 5*u**4/12 + 104*u**2. Find m, given that j(m) = 0.
-1, 0, 1/3, 1, 2
Factor -8978/17 + 268/17*y - 2/17*y**2.
-2*(y - 67)**2/17
Let h(d) be the third derivative of 5/6*d**3 - 3*d**2 - 1/252*d**6 - 1/42*d**4 + 0*d + 0 + 1/60*d**5. Let a(o) be the first derivative of h(o). Factor a(w).
-2*(w - 1)*(5*w - 2)/7
Let 