19. Factor y(p).
3*(p + 54)**2/5
Let c(q) be the third derivative of -q**8/1680 + q**7/630 + q**6/90 + q**4/6 + 38*q**2. Let u(g) be the second derivative of c(g). Factor u(o).
-4*o*(o - 2)*(o + 1)
Let q(i) be the third derivative of -i**4/24 - 7*i**3/6 + i**2. Let o be q(-12). Find c such that 0 + c**2 + o*c - 4*c + 0 = 0.
-1, 0
Let m(b) = -b**2 + 15*b - 9. Let n be m(14). Factor -21*v**4 + 19*v**4 + v**n + 2*v**2 + 2*v**3 - 3*v**3.
v**2*(v - 2)*(v - 1)*(v + 1)
Let k = 222 + -220. Let w be (k/(-2))/((-32)/64). Factor -10/9*l**w + 4/9*l + 0 - 2/3*l**3.
-2*l*(l + 2)*(3*l - 1)/9
Let d(l) be the third derivative of l**6/160 + 11*l**5/48 + 19*l**4/16 + 4*l**3/3 + 3*l**2 - 36*l. Factor d(u).
(u + 2)*(u + 16)*(3*u + 1)/4
Let t be ((-92)/115)/(4/(-10)). Let p(x) be the first derivative of 2 - 3/2*x**t - 1/5*x**5 + 2*x + 3/4*x**4 - 1/3*x**3. Factor p(r).
-(r - 2)*(r - 1)**2*(r + 1)
Let o(y) be the first derivative of -2*y**3 + 63*y**2/10 - 6*y/5 - 58. Determine s so that o(s) = 0.
1/10, 2
Let y(r) be the first derivative of r**5/55 + 3*r**4/44 + 2*r**3/33 + 42. Factor y(w).
w**2*(w + 1)*(w + 2)/11
Let a be (210/(-63))/(4/(-102)). Let p be ((-216)/a)/(-4) - 20/50. Factor 2/17*t**5 - 4/17*t**3 + 2/17*t**4 + 2/17 + 2/17*t - p*t**2.
2*(t - 1)**2*(t + 1)**3/17
Let z(o) be the second derivative of -5*o**7/42 + o**6 - 13*o**5/4 + 5*o**4 - 10*o**3/3 - 240*o. Suppose z(m) = 0. What is m?
0, 1, 2
Let j = -154038/11 + 14004. Factor 30/11*n**2 - j*n**3 - 48/11*n + 24/11.
-6*(n - 2)**2*(n - 1)/11
Factor 2/9*f**3 + 256/9 + 64/3*f + 4*f**2.
2*(f + 2)*(f + 8)**2/9
Let z = 15 - 13. Let l(t) = 2*t**2 - 2*t + 1. Let g be l(z). Factor f**4 + 5*f**5 - 2*f**3 + 2*f**2 - 3*f**4 - 5*f**5 + 2*f**g.
2*f**2*(f - 1)**2*(f + 1)
Let c(n) be the first derivative of 2*n - 1/3*n**6 - n**4 + 5 - 6/5*n**5 + 3*n**2 + 4/3*n**3. Factor c(a).
-2*(a - 1)*(a + 1)**4
Let h be (-12)/20 - (-1)/(40/264). Let p(n) be the third derivative of 7*n**2 - 2/105*n**7 + 1/30*n**h + 0*n + 0*n**3 - 1/6*n**4 + 1/15*n**5 + 0. Factor p(b).
-4*b*(b - 1)**2*(b + 1)
Let j(f) be the first derivative of -10/19*f + 11/19*f**2 - 14/57*f**3 + 55 + 1/38*f**4. Factor j(b).
2*(b - 5)*(b - 1)**2/19
Let q(b) be the third derivative of b**6/24 - b**5/3 - 145*b**4/24 - 20*b**3 + 199*b**2. Solve q(v) = 0.
-3, -1, 8
Let d(j) = 2*j**3 + 27*j**2 + 90*j + 16. Let f be d(-8). Let 0 + 2/5*u**4 + f*u**3 + 0*u + 2/5*u**5 + 0*u**2 = 0. What is u?
-1, 0
Factor 64/3*x + 0 - 1/3*x**4 - 4/3*x**3 + 16/3*x**2.
-x*(x - 4)*(x + 4)**2/3
Let a = 1448 - 8687/6. Let c(v) be the second derivative of 0*v**2 - 1/3*v**3 + a*v**4 + 0 - v. Factor c(s).
2*s*(s - 1)
Let n(g) be the third derivative of -g**5/150 + 13*g**4/60 - 22*g**3/15 - 140*g**2. Let n(d) = 0. Calculate d.
2, 11
Let r(s) = -2*s - 4. Let t be r(14). Let g be (-34)/(-8) - (-8)/t. Find h, given that 3*h**3 + 3*h**2 - h**5 - 3*h**4 - 4*h**5 - 2*h**5 + g*h**5 = 0.
-1, 0, 1
Let k(x) = -8*x**3 - x**2 - 10*x + 1. Let o(i) = -i**3 - i. Let p(y) = -2*k(y) + 18*o(y). Factor p(b).
-2*(b - 1)**2*(b + 1)
Let l(y) be the first derivative of -y**8/18480 + y**7/4620 + 13*y**3/3 + 14. Let s(p) be the third derivative of l(p). Determine o so that s(o) = 0.
0, 2
Let l = 5/8 + -11/24. Let j = 236 + -234. Find y such that -l*y**j - 1/3*y + 0 + 1/6*y**3 = 0.
-1, 0, 2
Let b(l) = 9*l**3 - 1746*l**2 - 338728*l - 21904152. Let x(u) = -3*u**3 + u. Let a(g) = -b(g) - 4*x(g). Factor a(q).
3*(q + 194)**3
Let v(h) be the first derivative of 10*h**2 + 27 - 15*h - 5/3*h**3. Factor v(q).
-5*(q - 3)*(q - 1)
Suppose -12 = -4*k + 4*t, t - 3*t + 2 = 0. Let n(p) be the third derivative of 1/72*p**4 - 1/90*p**5 + 1/360*p**6 + 0 + 0*p**3 + 0*p + k*p**2. Factor n(u).
u*(u - 1)**2/3
Suppose 0 = 5*k - 5*x - 25, 5*k + 3*x + 0*x = -15. Let t(u) be the third derivative of -1/18*u**4 + 3*u**2 + 1/180*u**5 + k*u + 1/6*u**3 + 0. Factor t(m).
(m - 3)*(m - 1)/3
Suppose -5*n = 20, 2*n = -2*z - 12 + 172. Factor 2 + z*y**2 - 2 + 4*y - 90*y**2.
-2*y*(3*y - 2)
Let l(a) = -2*a**2 + 28*a + 32. Let z be l(15). Let d(v) be the second derivative of 1/40*v**5 + 0 + 1/2*v**z - 7*v - 1/12*v**4 - 1/12*v**3. Factor d(c).
(c - 2)*(c - 1)*(c + 1)/2
Let m(w) be the third derivative of -w**8/84 + 26*w**7/105 - 23*w**6/30 + 11*w**5/15 + 13*w**2. Determine d so that m(d) = 0.
0, 1, 11
Let q(l) be the second derivative of 39*l**4/4 - l**3 - 6*l - 3. Solve q(s) = 0.
0, 2/39
Let l be -7 + 116/15 - (-10)/(-25). Factor -l*p**5 - 1/3*p + 1/3 + 2/3*p**3 - 2/3*p**2 + 1/3*p**4.
-(p - 1)**3*(p + 1)**2/3
Suppose 3*b = -3*b + 1548. Let p = -1289/5 + b. Factor 0 + p*j**2 + 2/5*j.
j*(j + 2)/5
Let n = -13876 - -27757/2. Suppose 25/4 + 1/4*f**2 - n*f = 0. Calculate f.
5
Let n be ((-5)/(-15))/((-20)/(-30))*(4 + 0). Factor -2*z - 1/2*z**2 - n.
-(z + 2)**2/2
Let h(z) be the third derivative of 1/15*z**6 - 2/105*z**7 + 1/12*z**4 - 8*z**2 + 1/504*z**8 + 0*z + 0*z**3 - 1/9*z**5 + 0. Let h(j) = 0. What is j?
0, 1, 3
Let k(v) be the third derivative of -v**6/8 + 17*v**5/10 - 53*v**4/8 - 6*v**3 - 363*v**2. Solve k(z) = 0 for z.
-1/5, 3, 4
Let k = -13 - -10. Let w be ((-3)/9)/((-22)/6 - k). Suppose 0*g - w*g**2 + 0 = 0. Calculate g.
0
Let p = -9773 - -9773. Let -4/7*k**3 + 6/7*k**4 + p - 2*k**2 - 4/7*k = 0. Calculate k.
-1, -1/3, 0, 2
Let k = 332 + -181. Let v = k + -151. Suppose 24/7*s - 33*s**4 + 198/7*s**3 + 156/7*s**2 - 21*s**5 + v = 0. Calculate s.
-2, -2/7, 0, 1
Suppose -7*u = 2*u - 27. Determine f so that -3*f**5 - 4*f**4 - 4*f + 2*f**u + 3*f**2 + 7*f**2 + 4*f**5 - 8 - f**3 = 0.
-1, 2
Let d be (-5)/(-4) + -20 + 150/8. Suppose d - 10*x**2 - 15*x - 5/3*x**3 = 0. Calculate x.
-3, 0
Let y(n) be the third derivative of 46*n**2 + 0*n**3 + 0 - 1/140*n**5 + 5/28*n**4 + 0*n. Let y(h) = 0. What is h?
0, 10
Suppose 6*b = 11*b - 15. Let -20*a - 7 - 2 - b*a**2 + 32*a = 0. Calculate a.
1, 3
Let v(s) be the second derivative of 8*s**2 + 12/5*s**5 - 2*s - 8*s**3 - 11/3*s**4 + 14/15*s**6 + 0. Suppose v(n) = 0. What is n?
-2, -1, 2/7, 1
Let f(n) be the first derivative of -n**4/38 - 16*n**3/57 - 13*n**2/19 - 12*n/19 - 28. Find a such that f(a) = 0.
-6, -1
Let k(s) be the first derivative of 3*s**4/4 + 4*s**3 - 33*s**2/2 - 90*s - 576. Find m, given that k(m) = 0.
-5, -2, 3
Factor -155*x**4 + 54*x**4 - 100 + 304*x - 312*x**2 + 45*x**4 + 52*x**4 + 112*x**3.
-4*(x - 25)*(x - 1)**3
Suppose x + 2*b + 0*b - 12 = 0, 4*x = -2*b + 66. Suppose -x*m + 3 + 6*m**2 + 0*m - 9*m**4 + 3*m**5 + m + 8*m + 6*m**3 = 0. What is m?
-1, 1
Let s = 1923/6706 + -1/958. Solve 6/7*z**2 + 4/7*z + 0 + s*z**3 = 0 for z.
-2, -1, 0
Let m(s) = s**4 - s**3. Let n(x) = -x + 1. Let d be n(-1). Let k(a) = -8*a**4 + 12*a**3 + 22*a**2 + 6*a. Let v(h) = d*m(h) + k(h). Factor v(g).
-2*g*(g - 3)*(g + 1)*(3*g + 1)
Factor -108*w - 270*w**2 - 277*w**2 + 549*w**2.
2*w*(w - 54)
Factor 9/8*l**2 - 1/8*l**3 - 7/4*l + 0.
-l*(l - 7)*(l - 2)/8
Let g(v) be the third derivative of -v**6/720 - v**5/90 - v**4/36 - 2*v**2 + 11. Factor g(k).
-k*(k + 2)**2/6
Let v(j) = -10*j**4 + 12*j**3 - 3*j**2 - 16*j - 13. Let n(d) = -d**4 + d**3 - d - 1. Let g(r) = -22*n(r) + 2*v(r). Factor g(t).
2*(t - 2)*(t + 1)**3
Factor 0*f - 3/8*f**3 + 0 - 1/8*f**5 + 3/8*f**4 + 1/8*f**2.
-f**2*(f - 1)**3/8
Solve -83 + 2*m + 115 - 10*m - 16*m + 4*m**2 = 0.
2, 4
Let o(r) be the first derivative of 2*r**5 + 27*r**4/2 + 20*r**3/3 - 477. Find j such that o(j) = 0.
-5, -2/5, 0
Let b(n) be the second derivative of -n**6/210 + 3*n**5/140 - n**4/42 + 71*n. Solve b(m) = 0.
0, 1, 2
Let q(d) = -d**3 + 3*d**2 + 3*d + 2. Let u be q(-1). Let l be (0 + 8/6)*3. Solve 2*c**3 - 2*c**4 + 7*c**4 - 2*c**5 - c**4 - l*c**u = 0.
0, 1
Let u(h) = -7*h**5 + 2*h**4 - 15*h**3 + h**2 - 5*h. Let i(l) = l**5 - 2*l**4 + l**3 - l**2 + l. Let p(y) = -10*i(y) - 2*u(y). Factor p(a).
4*a**2*(a + 1)**2*(a + 2)
Factor 4*j**2 - 221*j**4 + 3*j + 2*j**3 - 6*j + 217*j**4 + j**5.
j*(j - 3)*(j - 1)**2*(j + 1)
Let q = 251 + -752/3. What is n in -1/3*n + 1/3*n**3 + q*n**2 - 1/3 = 0?
-1, 1
Let o(x) be the third derivative of x**7/70 - 3*x**6/20 + 3*x**5/20 + 5*x**4/4 + 159*x**2. Let o(f) = 0. Calculate f.
-1, 0, 2, 5
Let k(i) = -4*i**2 + 27*i + 31. Let p(t) = -10*t**2 + 51*t + 61. Let o(u) = -7*k(u) + 3*p(u). Factor o(v).
-2*(v + 1)*(v + 17)
Let o(b) = -5*b**2 + 6*b - 1. Let k(a) = -a + 1. Suppose 2 = -2*p + p + v, 4*v = -8