 2*c - b - 12 = 0. Factor c*p**4 + 4*p**2 - 8 - 4*p**5 - 20*p - 40*p**3 + 12 + 36*p**2.
-4*(p - 1)**5
Let u(p) be the third derivative of -p**7/1785 - p**6/170 - 3*p**5/170 + 247*p**2 - 15. Let u(k) = 0. Calculate k.
-3, 0
Let r(h) be the first derivative of -h**6 - 16*h**5 - 463*h**4/6 - 104*h**3 - 140*h**2/3 + 1739. Determine t so that r(t) = 0.
-7, -5, -2/3, 0
Let p(n) be the third derivative of n**5/15 - 50*n**4/3 - 202*n**3/3 - 1555*n**2. Factor p(l).
4*(l - 101)*(l + 1)
Suppose -47*f + 52*f - 240 = 0. Suppose -r + f - 41 = 0. Solve 14*k - k**2 + 9*k - 15*k - r = 0.
1, 7
Factor -206/15*u**2 - 68/5*u - 2/15*u**3 + 0.
-2*u*(u + 1)*(u + 102)/15
Let x(o) be the third derivative of -o**5/18 + 103*o**4/9 - 164*o**3/9 + 3*o**2 + 439. Factor x(c).
-2*(c - 82)*(5*c - 2)/3
Let v(n) be the first derivative of -106 + 3/2*n**2 + 1/12*n**3 + 11/4*n. Let v(c) = 0. What is c?
-11, -1
Let x(b) be the third derivative of 20/33*b**3 - 1/330*b**5 + 0 + 62*b**2 + 0*b + 19/132*b**4. Factor x(z).
-2*(z - 20)*(z + 1)/11
Let s(m) be the first derivative of 15*m**4 + 964*m**3/3 + 28*m**2 - 128*m + 1753. Solve s(c) = 0.
-16, -2/5, 1/3
Suppose 0 = 17*p - 45 - 6. Let n be (-3)/(-11) + 1349/781. Factor -2/17*w**p + 4/17 + 0*w**n + 6/17*w.
-2*(w - 2)*(w + 1)**2/17
Let b be (-172)/(-130) - ((-23)/(-1196))/((-2)/8). Factor 0*s + 0 + 1/5*s**3 - b*s**2.
s**2*(s - 7)/5
Let j(z) = -2*z**3 + 81*z**2 - 13*z + 178. Let x be j(40). Suppose x = 17*q + 1207. Determine i, given that 1/4*i**5 - 4*i**2 + 5/4*i**4 - 4 + i**q - 8*i = 0.
-2, -1, 2
Let n be 6/((-18)/(-57)) - 4. Find r such that -16 - 78*r**2 - 77*r**2 + 156*r**2 + n*r = 0.
-16, 1
Let q be ((-62)/(-6) - (24 - 392/28))*0. Find n, given that 80/7*n + q + 92*n**3 + 64*n**2 + 60/7*n**4 = 0.
-10, -2/5, -1/3, 0
Let n(z) = -z**3 - z. Let r(j) = 1. Let u(b) = 11*b**3 - 7*b**2 + 2*b + 12. Let k(q) = -6*r(q) + u(q). Let d(g) = -5*k(g) - 35*n(g). Factor d(v).
-5*(v - 2)*(v + 1)*(4*v - 3)
Let c(p) be the second derivative of -p**10/22680 + p**8/1680 - p**7/945 + 11*p**4/4 + 2*p - 6. Let g(t) be the third derivative of c(t). Factor g(x).
-4*x**2*(x - 1)**2*(x + 2)/3
Let g(l) be the first derivative of -l**4/16 - 5*l**3 + 63*l**2/8 + 61*l/2 + 3810. Factor g(o).
-(o - 2)*(o + 1)*(o + 61)/4
Let x(c) = c**2 + 1360*c + 1361. Let z be x(-1). Factor 0 - 3/4*i**3 + 3/4*i + 7/4*i**z - 7/4*i**4.
-i*(i - 1)*(i + 1)*(7*i + 3)/4
Suppose y = 5*l - 12, 0 = l + 248*y - 249*y - 4. Let b(w) be the first derivative of -43 - 18/17*w - 32/51*w**3 + 24/17*w**l. Suppose b(m) = 0. What is m?
3/4
Let c be ((-462)/60 + (-32)/(-4))/(6/10). Factor -c*l**2 - 3/4*l + 9/4.
-(l + 3)*(2*l - 3)/4
Let g be 56/(-252)*(-3)/9 + 6368/1512. Factor g + 3/7*v**2 - 33/7*v.
3*(v - 10)*(v - 1)/7
Let q(z) = -7*z**3 + 107*z**2 - 258*z - 24. Let c(o) = -3*o**3 + 54*o**2 - 129*o - 6. Let n(t) = -13*c(t) + 6*q(t). Factor n(a).
-3*(a - 1)**2*(a + 22)
Let 48/5 - 2/5*z**2 - 46/5*z = 0. Calculate z.
-24, 1
Suppose 9 = -4*h + 6*h + 5*o, -o + 9 = 4*h. Factor 20*u**h + 16*u**2 + 10*u - 35*u**2 + 5*u**3 + 14*u**2.
5*u*(u + 1)*(u + 2)
Suppose -258*r - 43*r**2 + 68*r - 30*r - 41*r**2 + 96 = 0. What is r?
-3, 8/21
Factor -2400*p + 200/7*p**3 - 1828/7*p**2 - 4032 - 4/7*p**4.
-4*(p - 28)**2*(p + 3)**2/7
Let m(u) be the first derivative of -63 - 6*u**2 + 27/4*u**4 + 12*u - 9*u**3. What is h in m(h) = 0?
-2/3, 2/3, 1
Suppose -12*l + 10 = -9*l - c, 0 = 2*l - 4*c. What is h in 3*h - 35 - l*h - 6*h - 39*h + 2*h**2 - 13 = 0?
-1, 24
Let c(f) = -6*f**4 + 52*f**3 - 642*f**2 - 1602*f - 2. Let y(g) = -8*g**4 + 40*g**3 - 643*g**2 - 1603*g - 3. Let z(n) = 6*c(n) - 4*y(n). What is t in z(t) = 0?
-2, 0, 20
What is p in -1410 + 5448*p**2 + 1567 - 36*p**3 + 2486*p + 2243 - 9702*p = 0?
2/3, 150
Suppose -27*i + 97*i - 610 + 470 = 0. Factor 476/3*h**i - 1200 + 2320*h + 8/3*h**3.
4*(h + 30)**2*(2*h - 1)/3
Let r be ((-11 - -2)/(-3))/(138/184). Let m(c) be the third derivative of -2*c**r + 0 + 2*c**3 + 17*c**2 - 9/20*c**5 + 0*c. Factor m(d).
-3*(d + 2)*(9*d - 2)
Let n be ((1160632/654)/(1/9))/(2 + 8/(-18)). Factor -6534/7*c - 198/7*c**2 - n - 2/7*c**3.
-2*(c + 33)**3/7
Let w be 3*3 + (-25543)/2870. Let i(g) be the third derivative of 3/10*g**5 - w*g**6 + 0 + 1/2*g**3 + 1/70*g**7 + 0*g + 20*g**2 - 1/2*g**4. Factor i(t).
3*(t - 1)**4
Suppose -7 = -5*h + 4*p, 16*p = 15*p + 2. Factor 21*c**h + 3*c + 4*c**4 + 2*c**4 + 3*c + 24*c**2 - 3*c**2.
3*c*(c + 1)*(c + 2)*(2*c + 1)
Suppose -2*v - 2*f + 6 = -5*v, -10 = 4*v - 3*f. Let n(j) be the second derivative of -1/4*j**5 + 9*j + 25/12*j**4 + 10*j**v + 0 - 20/3*j**3. Factor n(o).
-5*(o - 2)**2*(o - 1)
Determine u, given that -120 - 302*u - 343*u + 33*u**3 - 397*u + 345*u**2 + 1060*u - 267*u - 9*u**4 = 0.
-5, -1/3, 1, 8
Let f(x) be the first derivative of x**5/5 - 667*x**4/2 + 446221*x**3/3 - 444222*x**2 + 443556*x + 469. Factor f(o).
(o - 666)**2*(o - 1)**2
Determine p so that -21/2*p + 0 + 21*p**4 - 66*p**3 + 9/2*p**5 + 51*p**2 = 0.
-7, 0, 1/3, 1
Suppose 0 = -33*s + 31*s + 28. Factor -s*p**2 + 5*p**2 + 7*p**2 + 3*p**2.
p**2
Find k such that -276/7*k - 90/7*k**5 - 342/7*k**2 + 201/7*k**3 - 24/7 + 201/7*k**4 = 0.
-1, -2/3, -1/10, 2
Let g(n) = -4*n**3 - 540*n**2 - 36440*n - 6. Let w(u) = 9*u**3 + 1080*u**2 + 72875*u + 15. Let b(i) = -5*g(i) - 2*w(i). Let b(f) = 0. What is f?
-135, 0
Let w(s) be the first derivative of 6/5*s**2 + 0*s + 1/15*s**3 - 1/25*s**5 - 3/5*s**4 + 96. Suppose w(t) = 0. Calculate t.
-12, -1, 0, 1
Let i(c) = 3*c - 29. Let n be i(13). Suppose -n*j + 9*j = -2. Solve 59*x**4 - 2*x**2 - 5*x + 0*x**2 + 5*x**3 - 54*x**4 - 3*x**j = 0.
-1, 0, 1
Let o(x) be the third derivative of -x**6/480 + 13*x**5/240 + 25*x**4/96 - 325*x**3/24 + 4*x**2 - 198*x. Determine i so that o(i) = 0.
-5, 5, 13
Suppose -v = 4, 2*q + 10*v - 20 = 5*v. Let k(h) = -h**3 + 21*h**2 - 16*h - 43. Let m be k(q). Factor 23*s + 160 + 5*s**2 + 20 + m*s.
5*(s + 6)**2
Let j = -85 - -45. Let r = -38 - j. Factor -3 + z - 1 + r*z**3 - 7*z.
2*(z - 2)*(z + 1)**2
Let x(k) = -k**2 - 20*k + 15. Suppose 0 = 3*n - 63 + 72. Let y be n*4/(36/39). Let o(v) = 3*v**2 + 40*v - 30. Let w(h) = y*x(h) - 6*o(h). Factor w(d).
-5*(d - 3)*(d - 1)
Let d(y) be the first derivative of -3*y**4/4 + 296*y**3 + 1785*y**2/2 + 894*y - 1627. Factor d(c).
-3*(c - 298)*(c + 1)**2
Let l be (-3683)/(-1218) - (-5)/(-210). Let x(r) be the first derivative of -8/3*r**3 - 42 + 2*r + l*r**2. Let x(k) = 0. What is k?
-1/4, 1
Factor 1892/19*j - 2/19*j**2 - 447458/19.
-2*(j - 473)**2/19
Let i(k) be the third derivative of -k**7/945 + k**6/54 - 7*k**5/90 + 4993*k**2. Factor i(b).
-2*b**2*(b - 7)*(b - 3)/9
Solve -146/5*g**2 + 2/5*g**4 + 288/5 + 4/5*g**3 - 148/5*g = 0 for g.
-9, -2, 1, 8
Determine o, given that -16*o**3 - 3 + 64*o + 124*o**2 - 120*o**2 + 51 - 4*o**4 = 0.
-3, -2, -1, 2
Solve 1136 + 1070*u**2 - 299*u**2 - 1134*u - 773*u**2 = 0 for u.
-568, 1
Let k(d) be the second derivative of -d**5/5 + 85*d**4/3 - 332*d**3/3 + 36*d + 10. Determine w so that k(w) = 0.
0, 2, 83
Let n(l) be the first derivative of 4*l**3/5 - 488*l**2/5 + 324*l/5 + 376. Factor n(b).
4*(b - 81)*(3*b - 1)/5
Solve 81/4*j - 9/2 - 28*j**2 + 49/4*j**3 = 0.
3/7, 6/7, 1
Let a(h) = -h**4 - h**3 + 4*h + 1. Let v(b) = -18*b**4 + 48*b**3 - 54*b**2 - 60*b + 15. Let x(l) = 15*a(l) - v(l). Solve x(u) = 0 for u.
-1, 0, 2, 20
Let x(g) be the first derivative of g**3/9 + 9*g**2 + 51*g - 897. Suppose x(s) = 0. What is s?
-51, -3
Find z, given that 0 - 22/5*z**3 + 4/5*z - 18/5*z**2 = 0.
-1, 0, 2/11
Let a(l) = l**3 - 36*l**2 - 192*l - 222. Let g(t) = -t**3 + 10*t + 2. Let k(y) = a(y) + 3*g(y). Factor k(s).
-2*(s + 3)**2*(s + 12)
Let i(g) be the first derivative of 2*g**5/45 + 37*g**4/18 + 310*g**3/9 + 2119*g**2/9 + 3380*g/9 - 375. Let i(q) = 0. Calculate q.
-13, -10, -1
Let k(v) be the first derivative of v**6/33 - 238*v**5/55 + 1856*v**4/11 - 20176*v**3/33 - 464*v**2/11 + 26912*v/11 + 12350. Find g, given that k(g) = 0.
-1, 2, 58
Find t such that 0*t**4 + 24 - 12*t**4 + 92*t**3 - 6*t**2 - 136*t + 156*t - 118*t**2 = 0.
-1/3, 1, 6
Let a = -51 + 75. Suppose 5*x - z = a, -x + 0*x + 3*z + 16 = 0. Factor 12*o**3 + 4*o**3 - 18*o**3 - 2*o**x + 4*o**2.
-2*o**2*(o - 1)*(o + 2)
Find h, given that -24*h**2 + 11*h + h - 17*h**3 + 15*h**3 + 3*h + 11*h = 0.
-13, 0, 1
Let t(p) be the second derivative of 0 +