9*c**3/3 + 61*c**2 - 1. Let h(q) be the first derivative of p(q). Solve h(j) = 0 for j.
-9, -1
Let r be (66 - (-668)/(-10))*(-5)/24*3*4. Factor -54*y + 108 + 27/4*y**r - 1/4*y**3.
-(y - 12)**2*(y - 3)/4
Let s(o) = o**4 + o**2 - 4. Let x(p) = -6*p**4 + 36*p**3 + 120*p**2 + 72*p - 204. Let w(j) = -9*s(j) - x(j). Factor w(f).
-3*(f - 1)*(f + 4)**2*(f + 5)
Let r be (4/(-8))/((-5)/50). Let -36 - 15*d**2 - 12*d**3 - 2*d**5 - r*d**2 + 12*d**4 + 44*d + 34*d - 20*d**2 = 0. What is d?
-2, 1, 3
Let x(h) be the second derivative of h**2 + 0*h**3 + 0 + 2/3*h**5 + 11*h - 5/2*h**4 - 1/24*h**6. Let m(r) be the first derivative of x(r). Factor m(z).
-5*z*(z - 6)*(z - 2)
Let o(b) = 415*b**2 + 242*b + 37. Let y(a) = 208*a**2 + 120*a + 18. Let z = 690 - 680. Let h(t) = z*y(t) - 4*o(t). Factor h(l).
4*(7*l + 2)*(15*l + 4)
Let l(b) be the first derivative of 2*b**5 - 7*b**4/2 + 12*b**3/5 - 4*b**2/5 + 16*b + 66. Let w(m) be the first derivative of l(m). Find t such that w(t) = 0.
1/4, 2/5
Solve -12/19*o**4 + 8/19*o + 2/19*o**5 + 0 - 24/19*o**2 + 26/19*o**3 = 0.
0, 1, 2
Let c(d) be the second derivative of d**4/72 + 197*d**3/18 - 5*d - 331. Factor c(j).
j*(j + 394)/6
Solve -186/5*z - 4/5*z**2 - 92/5 = 0 for z.
-46, -1/2
Let g(j) = 41*j**3 - 123*j**2 + 245*j - 62. Let t(k) = 8*k**3 - 25*k**2 + 48*k - 12. Let y(v) = 6*g(v) - 31*t(v). Factor y(u).
-u*(u - 18)*(2*u - 1)
Let r(f) = 2*f + 13. Let m be r(-4). Suppose -m*q = -5*j - 5 - 5, -2*j - q + 11 = 0. Solve -y**4 - 6*y**4 - 4*y + 0*y**3 + 4*y**3 + j*y**4 + 4*y**2 = 0 for y.
-1, 0, 1
Let i(b) be the third derivative of -2*b**6/165 + 13*b**5/30 - 251*b**4/66 - 65*b**3/33 - 5651*b**2. Suppose i(j) = 0. Calculate j.
-1/8, 5, 13
Let z(k) = 2*k**2 + 14*k + 6. Let h(u) = u**2 + 8*u + 3. Suppose 14 = -4*a - 10. Let t(v) = a*z(v) + 11*h(v). Factor t(i).
-(i - 3)*(i - 1)
Let k(u) = 3*u**4 - 560*u**3 - 49*u**2 + 6*u + 3. Let y(t) = 19*t**4 - 3361*t**3 - 309*t**2 + 34*t + 17. Let z(p) = 34*k(p) - 6*y(p). Solve z(j) = 0.
-1/6, 0, 94
Let f be ((-650)/(-30))/(-13) - 2/132*-122. Let j(t) be the first derivative of -10 + 2/33*t**3 - f*t + 0*t**2. Find b, given that j(b) = 0.
-1, 1
Let j be (-95 - -93)*(98/63 + -2). Determine g so that -8/9 - 2/9*g**2 + j*g = 0.
2
Let y(m) = m**3 - 37*m**2 + 110*m - 39. Let o be y(34). Factor -o*i - 5*i**3 - 504*i**2 - 76*i**3 - 293*i - 430*i + 172*i.
-i*(9*i + 28)**2
Factor -12*h**2 + 29*h**2 + 468 - 20*h**2 - 105*h.
-3*(h - 4)*(h + 39)
Let h be (-2)/(-12) - ((-100)/(-336)*-34 + 0). Let i be 1*(-155)/(-7) - (5 + -6). Factor -h*p - 8/7 - i*p**2.
-2*(9*p + 2)**2/7
Let d(i) be the second derivative of 1/60*i**5 + 0 + 0*i**2 + 0*i**3 - 18*i + 0*i**4. Factor d(x).
x**3/3
Let g be ((-715)/39 - -18) + 2/6. Let l(y) be the third derivative of g + 1/15*y**5 - 14/3*y**3 - y**4 + 0*y + 41*y**2. Factor l(p).
4*(p - 7)*(p + 1)
Let h(p) be the second derivative of -p**7/189 - 11*p**6/45 - 31*p**5/30 - 91*p**4/54 - 10*p**3/9 + 15*p + 48. Determine q, given that h(q) = 0.
-30, -1, 0
Let g(y) be the first derivative of 2*y**3/3 + 963*y**2 - 1928*y - 4443. Find b, given that g(b) = 0.
-964, 1
Let m be (3 + -5)/(-1) - ((-195)/15)/13. Let k(o) be the second derivative of -1/4*o**5 + 0*o**2 + 0 + 0*o**m + 0*o**4 + 2*o. Suppose k(v) = 0. Calculate v.
0
Let h(j) be the second derivative of -j**5/210 + j**4/42 - j**3/21 - 23*j**2 + j - 19. Let w(p) be the first derivative of h(p). Factor w(n).
-2*(n - 1)**2/7
Factor 0 - 1/2*o**4 + 3/2*o**2 + 0*o**3 + o.
-o*(o - 2)*(o + 1)**2/2
Factor -93285*i - 93303*i - 66 + 3*i**2 + 186561*i.
3*(i - 11)*(i + 2)
Let m be -1 - (-1020)/525 - (-4)/(-5). Let h(q) be the first derivative of -3 + m*q**2 + 0*q + 2/21*q**3. Factor h(n).
2*n*(n + 1)/7
Let z be (-1)/(15/6) + (-472)/(-5). Let t = z - 87. Find j, given that 15*j**3 - 2*j - t*j + 15*j**2 - j + 3*j**4 - 13*j**4 = 0.
-1, 0, 1/2, 2
Suppose -86 = 3*o - 3*x - 89, -9 = -3*x. Let j(p) be the first derivative of 0*p - 8/13*p**2 - 3/26*p**o - 28/39*p**3 - 1. Factor j(t).
-2*t*(t + 4)*(3*t + 2)/13
Suppose 340 = 22*n - 2*n. Factor 59*a**2 + 372*a**3 + n*a**2 - 376*a**3.
-4*a**2*(a - 19)
Let r(i) be the third derivative of -i**6/840 - 2*i**5/15 - 1792*i**2. Suppose r(u) = 0. What is u?
-56, 0
Let q(v) be the first derivative of -8/11*v**2 - 24/11*v - 50 - 2/33*v**3. Factor q(y).
-2*(y + 2)*(y + 6)/11
Let k(x) be the second derivative of x**7/42 + x**6/3 + 27*x**5/20 + 3*x**4/2 + 6*x + 46. Factor k(d).
d**2*(d + 1)*(d + 3)*(d + 6)
Suppose 6*x - 109 + 19 = 54. Let h(i) be the second derivative of -1/5*i**2 + x*i + 1/5*i**3 - 1/25*i**5 + 0 - 1/15*i**4 - 1/105*i**7 + 1/25*i**6. Factor h(n).
-2*(n - 1)**4*(n + 1)/5
Solve 78/7 + 129/7*l**2 + 345/7*l - 12/7*l**3 = 0.
-2, -1/4, 13
Suppose 34/7*t**4 + 120/7 + 54/7*t**3 + 2/7*t**5 - 14*t**2 - 16*t = 0. What is t?
-15, -2, 1
Let k be 11*2/(-110)*(21/18 - 2). Factor -1/3*u**2 + 1/3 + 1/6*u - k*u**3.
-(u - 1)*(u + 1)*(u + 2)/6
Let r(n) be the first derivative of -2*n**3/13 - 4235*n**2/13 + 2824*n/13 + 1900. Factor r(q).
-2*(q + 1412)*(3*q - 1)/13
Let y(g) = 19*g**2 + 4*g - 10. Let k be y(-2). Suppose 2*n - k + 50 = 0. What is z in -2/3*z**3 + 0 + 0*z**n + 0*z**2 + 1/3*z + 1/3*z**5 = 0?
-1, 0, 1
Let 82*b + 55076*b**2 - 55050*b**2 - 270*b = 0. What is b?
0, 94/13
Let q(s) = 3*s**3 - 33*s**2 - 42*s + 48. Let p(b) = b**3 - 4*b**2 + 8*b - 9. Let a be p(2). Let j(v) = -v**3 - v**2. Let u(k) = a*q(k) + 12*j(k). Factor u(o).
-3*(o - 2)*(o - 1)*(5*o + 8)
Suppose -33*q = -28*q + 50. Let s be (-32)/q + (2 - 4). Let 9/5*k + s*k**2 - 21/5*k**3 + 0 + 6/5*k**4 = 0. What is k?
-1/2, 0, 1, 3
Let q(w) be the third derivative of -w**7/70 - 11*w**6/20 - 137*w**5/20 - 53*w**4/2 - 48*w**3 - 1950*w**2. Factor q(d).
-3*(d + 1)**2*(d + 8)*(d + 12)
Determine s, given that 13/2*s**3 + 147/2*s - 135/4 - 1/4*s**4 - 46*s**2 = 0.
1, 9, 15
Suppose 9*j = 2*j + 385. Suppose 9*f**3 - 8*f - 3*f**3 + 2*f**4 - 55 + j = 0. What is f?
-2, 0, 1
Suppose 235 = -19*b - 5693. Let m be (-1)/5 - b/360. Let m*u + 16/3*u**3 - 10/3*u**2 - 8/3*u**4 + 0 = 0. Calculate u.
0, 1/2, 1
Let s(h) be the second derivative of h**4/42 - 1250*h**3/21 + 390625*h**2/7 - 20*h - 10. Solve s(v) = 0.
625
Let n(r) be the third derivative of r**5/210 - 5*r**4/21 + 13*r**3/3 + 11*r**2 - 73*r. Suppose n(h) = 0. What is h?
7, 13
Let y(w) be the second derivative of -w**4/12 + w**3/6 - 73*w. Let x(g) = -8*g**2 + 24*g + 24. Let f(j) = -x(j) + 4*y(j). Factor f(z).
4*(z - 6)*(z + 1)
Factor 12/11 + 14/11*f + 2/11*f**2.
2*(f + 1)*(f + 6)/11
Let g = 29687 - 207751/7. Factor 54/7*i + g*i**2 - 4/7.
2*(i + 1)*(29*i - 2)/7
Suppose 5*z = -6*x + 30, -5*z = -194*x + 199*x - 25. Let 8/11*f**x - 254/11*f**3 - 80/11 + 54/11*f**4 + 92/11*f**2 + 312/11*f = 0. What is f?
-10, -1, 1/4, 2
Let h(n) be the first derivative of -n**6/51 + 24*n**5/85 - 57*n**4/34 + 268*n**3/51 - 156*n**2/17 + 144*n/17 + 1682. Suppose h(x) = 0. What is x?
2, 3
Factor -2396*t**2 - 211*t**3 - 7576*t + 205*t**3 - 230824*t + 160000.
-2*(t + 200)**2*(3*t - 2)
Suppose 0 = 5*y + 3*m - 378, -3*y - 2*m = -4*y + 73. Determine u, given that -15625 + 2*u**3 - y*u**2 - 12*u**3 + 15*u**3 - 4*u**3 + 1875*u = 0.
25
Let r = -995546 - -995551. Factor -72/7*x**2 - 26/7*x**4 + 2/7*x**r + 80/7*x**3 + 0*x + 0.
2*x**2*(x - 9)*(x - 2)**2/7
Let k(q) be the second derivative of -q**3 - 57*q**2/2 - 25*q. Let y be k(-10). Solve -15*u**y + 117*u**2 + 5*u**5 + 113*u**2 - 240*u**2 = 0 for u.
-1, 0, 2
Let i(t) be the first derivative of -t**7/350 + t**6/25 + 24*t**2 - 30. Let g(a) be the second derivative of i(a). Factor g(d).
-3*d**3*(d - 8)/5
Let n(z) be the first derivative of -z**5/300 + z**4/40 + 2*z**3/15 - 29*z**2/2 - 6. Let f(r) be the second derivative of n(r). Let f(b) = 0. What is b?
-1, 4
Let c be (11 - 12)/((-2)/802). Suppose -c = -13*x - 375. Factor -5/2*z + 5/2*z**3 - 1/2 + 2*z**4 - 3/2*z**x.
(z - 1)*(z + 1)**2*(4*z + 1)/2
Let p(y) be the second derivative of 0 + 1/2*y**4 + 0*y**2 + 18*y - 9/50*y**5 + 1/75*y**6 - 7/15*y**3. Let p(h) = 0. Calculate h.
0, 1, 7
Let k = 288 + -276. Factor -k*h**3 - 6*h**4 + 42*h + 3 + 71*h**2 - 12*h**5 + 14*h**5 + 15 - 51*h**2.
2*(h - 3)**2*(h + 1)**3
Suppose -4*t = g - 66, 5*g - 102*t - 90 = -107*t. Solve 10*c + 77/4*c**g - 1/2*c**3 - 39/4 = 0 for c.
-1, 1/2, 39
Let z(p) be the first derivative of -84 - 4/7*p*