*a**3 - 20*a**2 - 28*a + 84. Let n(r) = -4*g(r) + 3*k(r). Factor n(m).
-5*(m - 4)*(m - 2)*(m + 2)
Let t(v) be the second derivative of -v**4/16 - v**3/2 + 15*v**2/8 - v + 2. Factor t(q).
-3*(q - 1)*(q + 5)/4
Let x(r) = 15*r - 325. Let u be x(22). Let h(z) be the second derivative of z**3 + 4/3*z**4 + 0 - 11/5*z**u - 2*z**2 - 5/21*z**7 + 2*z + 6/5*z**6. Factor h(i).
-2*(i - 1)**4*(5*i + 2)
Let x(u) be the second derivative of 11*u + 0*u**2 + 0 + 0*u**3 - 1/120*u**5 - 1/36*u**4. Let x(k) = 0. Calculate k.
-2, 0
Suppose -x = -v - 7, -v - 3*v = -x + 19. Solve -74*y**2 + 34*y**3 - 75*y + 29*y**2 - 7*y**x - 44*y**4 + 41*y**4 = 0 for y.
-1, 0, 5
Let d(o) be the third derivative of 0*o + 0*o**5 - 1/20*o**6 + 0*o**3 + 1/112*o**8 + 1/8*o**4 - 2*o**2 + 0 + 0*o**7. Factor d(b).
3*b*(b - 1)**2*(b + 1)**2
Factor -12*y - 2*y**3 - 233*y**2 + 102*y**2 + 117*y**2.
-2*y*(y + 1)*(y + 6)
Let q(j) be the third derivative of 1/3*j**6 + 5*j**4 - j**2 - 15/2*j**3 - 1/42*j**7 + 0 + 0*j - 11/6*j**5. Determine v so that q(v) = 0.
1, 3
Let c = 49816/187 - 4470/17. Solve 18/11 + 6/11*h**3 + c*h**2 + 6*h = 0.
-3, -1/3
Let p(z) = -18*z**4 - 115*z**3 + 865*z**2 + 2052*z + 1076. Let o(f) = -5*f**4 - 38*f**3 + 288*f**2 + 684*f + 359. Let y(h) = 14*o(h) - 4*p(h). Factor y(m).
2*(m - 19)**2*(m + 1)**2
Let a(q) = q**2 - 2*q - 1. Let z be a(3). Suppose -61*v + 77*v + 12*v**3 - 16*v**2 - 16*v**z = 0. What is v?
0, 2/3, 2
Let p(v) be the first derivative of -5/18*v**3 + 5/12*v**2 - 12 + 0*v. Let p(f) = 0. Calculate f.
0, 1
Factor -25/2*u**2 - 73/6 - 49/2*u - 1/6*u**3.
-(u + 1)**2*(u + 73)/6
Let f(m) be the third derivative of -m**9/3780 + m**8/840 - m**7/630 - m**4/2 - 6*m**2. Let s(y) be the second derivative of f(y). Factor s(r).
-4*r**2*(r - 1)**2
Let k(p) be the first derivative of -p**4/4 + p**3/3 - p + 2. Let w(t) = 15*t**3 - 9*t**2 - 6*t + 6. Let x(n) = 6*k(n) + w(n). Factor x(c).
3*c*(c - 1)*(3*c + 2)
Let q(v) = -v**3 - 5*v**2 - 2*v - 7. Let a be q(-5). Let l(p) = 51*p + 615. Let b be l(-12). Factor a*w**b + w**2 + 64*w**5 - 3*w**2 + 2*w**4 - 66*w**5 - w**3.
-2*w**2*(w - 1)**2*(w + 1)
Suppose -d + 3*i + 2 = 4*i, 0 = -d + 4*i + 2. Factor -35*b - 3*b**d + 4*b**2 + 39*b.
b*(b + 4)
Let g(s) = 3*s**3 - 11*s**2 - 5*s + 5. Let u(z) = -10*z**3 + 34*z**2 + 16*z - 16. Suppose 14*h - 6*h - 40 = 0. Let q(o) = h*u(o) + 16*g(o). Factor q(c).
-2*c**2*(c + 3)
Let l = -3039 + 3039. Factor 1/2*f**4 + 0*f**3 + 1/2*f**5 + l*f + 0 + 0*f**2.
f**4*(f + 1)/2
Let s(c) = c + 21. Let h be s(-18). Suppose 18*k**5 - 12*k + 60*k**h + 8*k**5 + 12 - 33*k**4 + 9*k**5 - 29*k**5 - 33*k**2 = 0. Calculate k.
-1/2, 1, 2
Suppose -5 = -n - f, 5*n + 0*n + f - 5 = 0. Suppose n*k - 10 = -2*k + 3*m, -5*m + 15 = 3*k. Factor 3*i**2 + k*i**3 + 9*i**4 - 3*i - 2*i**3 - 12*i**4.
-3*i*(i - 1)**2*(i + 1)
Determine j, given that -3/2*j**3 - 3/4*j**5 + 5/2*j**4 - 1/2 - 2*j**2 + 9/4*j = 0.
-1, 1/3, 1, 2
Let v(l) be the third derivative of -l**5/8 + 37*l**4/16 - 7*l**3/2 - 69*l**2. Find x such that v(x) = 0.
2/5, 7
Let j be 272/(-3672) + (-662)/(-189). Find v such that 4/7*v**2 + 20/7 + j*v = 0.
-5, -1
Suppose -2*h = 5*c + 3*h - 15, 0 = -3*c - 2*h + 9. Determine a, given that 2*a**c + 4*a**5 - 6*a**3 - a**4 - 5*a**4 = 0.
-1/2, 0, 2
Factor 90/7 + 54/7*l**2 - 141/7*l - 3/7*l**3.
-3*(l - 15)*(l - 2)*(l - 1)/7
Let o(w) be the third derivative of -w**7/1785 - w**6/170 - 3*w**5/170 - w**4/51 - 3*w**2. Factor o(b).
-2*b*(b + 1)**2*(b + 4)/17
Let z(a) be the second derivative of -1/2*a**2 + 0 + 7*a + 1/6*a**3 - 1/48*a**4. Suppose z(r) = 0. Calculate r.
2
Factor 2/3*r**2 - 46/3 - 44/3*r.
2*(r - 23)*(r + 1)/3
Suppose 5*r = -5*l + 519 - 84, 83 = l + 5*r. Let h = l - 88. Let 2/3*g**2 + h - 2/3*g = 0. Calculate g.
0, 1
Let m(u) be the first derivative of -u**6/12 + u**5/10 + 3*u**4/4 + u**3/3 - 5*u**2/4 - 3*u/2 + 10. Solve m(n) = 0 for n.
-1, 1, 3
Let a(u) = -u**3 + u**2. Let r(c) = -4*c**4 - 21*c**3 - 7*c**2. Let q(b) = 5*a(b) - r(b). Solve q(h) = 0 for h.
-3, -1, 0
Let j(o) be the first derivative of -9*o**5/5 - 15*o**4 - 39*o**3 - 27*o**2 + 7. Solve j(c) = 0 for c.
-3, -2/3, 0
Let v = 433 - 23809/55. Let f(d) be the first derivative of 0*d + 32/33*d**3 + v*d**5 - 13/22*d**4 - 2 - 4/11*d**2. Factor f(u).
2*u*(u - 2)**2*(3*u - 1)/11
Let n be 4/(-2) - (-16)/5. Let a = -210 - -212. Let -1/5*m + 0 + n*m**a = 0. What is m?
0, 1/6
Factor -297/5*v**2 - 107811/5 + 9801/5*v + 3/5*v**3.
3*(v - 33)**3/5
Determine w, given that -25/4*w**3 + 5/2*w - 15/4*w**2 + 0 = 0.
-1, 0, 2/5
Let m(x) be the third derivative of -x**9/5040 - 3*x**8/2240 + x**6/60 - x**4/4 - 2*x**2. Let u(t) be the second derivative of m(t). Factor u(p).
-3*p*(p - 1)*(p + 2)**2
Let b(n) be the first derivative of n**6/72 - n**5/8 - 5*n**4/6 + 17*n**3/3 - 2. Let v(c) be the third derivative of b(c). Factor v(y).
5*(y - 4)*(y + 1)
Suppose 79 = -p + 9. Let o = -60 - p. Find h, given that 0 - o*h**2 + 4/3*h = 0.
0, 2/15
Let k = 31 - 28. Factor 4*x**5 + x**3 - 12*x**4 - 12*x + 4 - 5*x**3 + 8*x**2 + 0*x**3 + 12*x**k.
4*(x - 1)**4*(x + 1)
Let x = 3061/2 - 1530. Factor x*l**2 + l - 3/2.
(l - 1)*(l + 3)/2
Let b(l) be the first derivative of -1 - 1/27*l**6 + 32/27*l**3 - 8/45*l**5 + 0*l + 16/9*l**2 + 0*l**4. Suppose b(r) = 0. Calculate r.
-2, 0, 2
Suppose 3*y - 3*n + 6 = 0, 5*y - 3*n - 5 = -n. Let l be 9 - (1 + (-1 - y)). Factor -8*u + l + u**2 + 2*u**2 + 4*u - 8*u.
3*(u - 2)**2
Let y(o) be the third derivative of o**6/10 - 31*o**5/20 - o**4 - 28*o**2. Suppose y(v) = 0. Calculate v.
-1/4, 0, 8
Let l be (-7)/(-21) - 10/(-6). Factor -2*y**4 + 40*y**l - 44*y**2 + 6*y**3 + 0*y**4.
-2*y**2*(y - 2)*(y - 1)
Let a(w) = -w**3 + 2*w**2 + 5*w - 4. Let l be a(3). Factor 64*i + 36*i**l + 15*i**3 + 32 - 96*i**4 + 97*i**4 - 4*i**3 + 6*i**2.
(i + 1)*(i + 2)*(i + 4)**2
Let l(q) be the second derivative of -10*q + 0 + 1/210*q**7 + 0*q**2 + 0*q**3 + 0*q**5 + 1/15*q**4 - 1/50*q**6. Factor l(r).
r**2*(r - 2)**2*(r + 1)/5
Factor -2/9*n**2 + 20/9*n - 16/9 - 2/9*n**3.
-2*(n - 2)*(n - 1)*(n + 4)/9
Let g(n) be the third derivative of -n**7/210 + n**6/40 + 11*n**5/60 - n**4/8 - 5*n**3/3 - 549*n**2. Suppose g(a) = 0. Calculate a.
-2, -1, 1, 5
Let v be 48/(-1)*2/4. Let a = v - -27. Determine j, given that 4/7*j**2 - 4/7*j**4 + 2/7*j**5 - 2/7*j**a + 0 + 0*j = 0.
-1, 0, 1, 2
Let j(f) be the second derivative of f**5/90 - 7*f**3/27 - 2*f**2/3 + 3*f - 64. Factor j(v).
2*(v - 3)*(v + 1)*(v + 2)/9
Suppose -53*c - 105/2 - 1/2*c**2 = 0. Calculate c.
-105, -1
Let 0 - 14/9*j**2 - 22/9*j**4 + 40/9*j**3 - 4/9*j = 0. What is j?
-2/11, 0, 1
Let a = 965 + -1929/2. Solve 3/2*h - 2*h**2 + a = 0 for h.
-1/4, 1
Let u(d) be the third derivative of d**7/350 - d**6/200 - d**5/100 + d**4/40 + 3*d**2 - 8*d. Suppose u(a) = 0. Calculate a.
-1, 0, 1
Let m = 4 - 10. Let l(k) = 3*k**2 - 12*k + 12. Let d(h) = 3*h**2 - 12*h + 12. Let r(i) = m*d(i) + 5*l(i). Let r(y) = 0. What is y?
2
Let h(s) be the first derivative of -s**3/4 - 3*s**2 - 21*s/4 - 89. Factor h(j).
-3*(j + 1)*(j + 7)/4
Let u(h) be the third derivative of 0 - 51/100*h**5 - 25*h**2 + 0*h + h**3 + 1/20*h**6 + 3/40*h**4. Suppose u(z) = 0. What is z?
-2/5, 1/2, 5
Let a(m) be the second derivative of -5/14*m**4 + 14*m + 0 + 3/14*m**3 + 9/35*m**5 + 1/98*m**7 + 0*m**2 - 3/35*m**6. Factor a(i).
3*i*(i - 3)*(i - 1)**3/7
Let z(d) be the second derivative of -d**5/450 + d**4/60 + 4*d**3/45 - 2*d**2 + 11*d. Let k(i) be the first derivative of z(i). Find y such that k(y) = 0.
-1, 4
Let c(t) be the third derivative of -t**7/630 - t**6/180 + 7*t**5/180 - t**4/18 + 13*t**2. Factor c(g).
-g*(g - 1)**2*(g + 4)/3
Suppose 2*z - 42 = -2. Factor -3*n**4 + n**3 + n**4 - 26*n**2 + 24 + 5*n**4 - z*n.
(n - 3)*(n + 2)**2*(3*n - 2)
Factor 0*f**3 + 424*f**2 - 430*f**2 - 2*f**3.
-2*f**2*(f + 3)
Let c(g) be the first derivative of -2*g**6/15 + 4*g**5/25 + g**4/5 - 4*g**3/15 - 794. Solve c(o) = 0 for o.
-1, 0, 1
Let b(d) = -231*d - 560 - 420*d**2 - 15*d**3 + 602*d + 384*d. Let a(p) = p**3 + 30*p**2 - 54*p + 40. Let o(i) = 85*a(i) + 6*b(i). Factor o(w).
-5*(w - 2)**3
Let h(k) be the third derivative of k**7/840 - k**6/80 + k**5/60 + k**4/16 - 5*k**3/24 - 92*k**2. Factor h(d).
(d - 5)*(d - 1)**2*(d + 1)/4
Let 3*b + 1/2*b**3 + 0 - 7/2*b**2 = 0. What is b?
0, 1, 6
Let o(q) be the second derivative of 2*q**3 - 2/3*q**4 + 0