7)/7
Let f(c) be the third derivative of c**7/1470 + c**6/140 + 11*c**5/420 + c**4/28 - 126*c**2 - 3. Factor f(v).
v*(v + 1)*(v + 2)*(v + 3)/7
Let t(a) = -a**3 + 22*a**2 - 17*a - 81. Let g be t(21). Determine r so that 0 + 3*r**4 + 137*r**3 - 125*r**g + 0 = 0.
-4, 0
Let m = 165946 - 165944. Factor 0 + 18/11*v + 6/11*v**5 - 36/11*v**4 + 72/11*v**3 - 60/11*v**m.
6*v*(v - 3)*(v - 1)**3/11
Let n(v) be the third derivative of 0*v**3 + 0*v - 2/105*v**7 - 45*v**2 + 0 + 1/15*v**5 + 1/3*v**4 - 1/15*v**6. Factor n(t).
-4*t*(t - 1)*(t + 1)*(t + 2)
Factor 81/5*j**2 + 231/5 + 311/5*j + 1/5*j**3.
(j + 1)*(j + 3)*(j + 77)/5
Let r(n) = 3*n**2 + 116*n - 1692. Let p(y) = 238*y**2 + 957 - 58*y - 240*y**2 - 110. Let d(t) = 10*p(t) + 6*r(t). Factor d(i).
-2*(i - 29)**2
Solve -27*f**2 - 23*f**2 + 90*f - 11*f - 45*f = 0 for f.
0, 17/25
Factor 68/3*r + 720 - 2/3*r**2.
-2*(r - 54)*(r + 20)/3
Let d be (57/912)/((-21)/(-56)). Let j(f) be the second derivative of 1/6*f**2 - 2/9*f**3 + d*f**4 + 1/90*f**6 + 13*f + 0 - 1/15*f**5. Factor j(c).
(c - 1)**4/3
Factor -330*n**3 + 292*n**3 + 12*n**4 + 111*n**2 + 448*n**3 - n**4.
n**2*(n + 37)*(11*n + 3)
Let w(f) be the first derivative of f**9/3780 - 4*f**8/525 + 32*f**7/525 + 11*f**3 + 53. Let m(b) be the third derivative of w(b). Solve m(r) = 0 for r.
0, 8
Let b(a) = -276 - 64*a + 306 - a**2 + 6*a**2. Let r(t) = -14*t**2 + 193*t - 91. Let j(n) = 8*b(n) + 3*r(n). Factor j(m).
-(m - 33)*(2*m - 1)
Let u(i) be the first derivative of i**7/4620 + 17*i**6/1980 + 21*i**5/220 - 27*i**4/44 + 81*i**3 + 130. Let t(g) be the third derivative of u(g). Factor t(x).
2*(x - 1)*(x + 9)**2/11
Suppose 5 = 3*v - f, -3*v + 3 = -0*f - 3*f. Solve 25*p**3 - 4*p**v - p**3 + 3*p**4 - 16*p**3 - 7*p**4 = 0.
0, 1
Let q(f) be the first derivative of 2*f**3/3 + 299*f**2 - 1812*f + 7772. Factor q(n).
2*(n - 3)*(n + 302)
Let z(m) = m**4 - m**3 + 2*m**2 + 1. Let o = -135 + 120. Let a(l) = 66*l**3 + 18*l**2 + 12*l - 15. Let s(k) = o*z(k) - a(k). Solve s(w) = 0 for w.
-2, -1, -2/5, 0
Let i(d) be the first derivative of 31/5*d**4 + 56/15*d**6 + 216/25*d**5 + 6/5*d**3 + 0*d - 212 - 1/5*d**2. Determine a, given that i(a) = 0.
-1, -1/2, 0, 1/14
Let l(k) be the third derivative of 67*k**2 + 217/75*k**6 - 2 - 372/5*k**4 + 0*k - 7/150*k**7 - 216/5*k**3 - 3718/75*k**5. Solve l(b) = 0 for b.
-2/7, 18
Let r(h) be the first derivative of h**5/60 + h**4/6 + 2*h**3/3 + h**2/2 - 19*h - 16. Let j(z) be the second derivative of r(z). Factor j(y).
(y + 2)**2
Let s = 180 - 207. Let c be (s/30)/(5/(-20)). Factor 2/5*g**4 - 8/5*g**3 + 24/5*g - 4/5*g**2 + c.
2*(g - 3)**2*(g + 1)**2/5
Let m be 3/5*(5 + (6 - 21))/((-120)/30). Factor -48*s**3 + 24 + 27/2*s**4 + 84*s**2 - 72*s - m*s**5.
-3*(s - 2)**4*(s - 1)/2
Let j(m) = -279*m**2 + 93*m + 600. Let b(g) = -232*g**2 + 92*g + 599. Let v(f) = 6*b(f) - 5*j(f). Suppose v(s) = 0. What is s?
-18, -11
Let g(u) be the first derivative of 15*u**4/8 - 27*u**3 - 15*u**2/4 + 81*u - 1945. Let g(v) = 0. What is v?
-1, 1, 54/5
Suppose -5*h + h - 32 = 4*g, 5*h = 3*g. Let x be (-6 - (0 + -3)) + g/(-1). Factor 3*l**4 - 52*l**3 + 9*l - 6 + 18*l**3 + 25*l**3 + 3*l**x.
3*(l - 2)*(l - 1)**2*(l + 1)
Let t(h) be the second derivative of -25*h**5/4 - 3275*h**4/2 + 2630*h**3 - 1580*h**2 + 32*h - 36. Find m such that t(m) = 0.
-158, 2/5
Let h(y) = -2*y**2 + 30*y - 20. Let o be h(14). Factor -4*q**4 + 54*q**2 - o*q**3 - 8*q - 42*q**2 + 19*q + 21*q + 16.
-4*(q - 2)*(q + 1)**2*(q + 2)
Let d(h) be the first derivative of 25/3*h + 5/3*h**2 - 32 + 1/9*h**3. Factor d(n).
(n + 5)**2/3
Factor 138*i + 0 + 1/2*i**4 - 41/2*i**3 - 118*i**2.
i*(i - 46)*(i - 1)*(i + 6)/2
Determine n so that -564*n + 2044*n + 1139*n + 5*n**2 - 169*n = 0.
-490, 0
What is c in 2/7*c**4 + 44/7*c**3 + 48 - 404/7*c + 22/7*c**2 = 0?
-21, -4, 1, 2
Let u(h) be the second derivative of -h**6/20 - 21*h**5/8 - 44*h**4 - 192*h**3 - 9*h - 12. Factor u(l).
-3*l*(l + 3)*(l + 16)**2/2
Let v(h) = 39*h**3 - 553*h**2 + 2356*h - 1332. Let q(g) = -113*g**3 + 1661*g**2 - 7067*g + 3994. Let z(n) = 6*q(n) + 17*v(n). Factor z(f).
-5*(f - 33)*(f - 4)*(3*f - 2)
Suppose 4*c = 169 - 1121. Let v = c + 238. Suppose -6/11*l**2 + 10/11*l**3 + 0 - 2/11*l**5 - 2/11*l**4 + v*l = 0. What is l?
-3, 0, 1
Let p = 1363204 - 1363093. What is u in -219/2*u - 3/2*u**2 + p = 0?
-74, 1
Let w = 1/84539 + 1521697/422695. Factor -w*f + 4/5 + 14/5*f**2.
2*(f - 1)*(7*f - 2)/5
Let g(k) = -15*k**4 - 8*k**3 + 2*k**2 + 7. Let s(f) = -13*f**4 - 8*f**3 + 3*f**2 + 6. Let t(y) = -6*g(y) + 7*s(y). Factor t(l).
-l**2*(l - 1)*(l + 9)
Let m(o) be the second derivative of o**8/40320 + o**7/5040 - 11*o**4/6 - o**3/3 - 3*o + 14. Let l(y) be the third derivative of m(y). Factor l(w).
w**2*(w + 3)/6
Let b(m) be the second derivative of -m**4/4 + 35*m**3 + 657*m**2/2 - 38*m - 2. Solve b(u) = 0 for u.
-3, 73
Let n(s) = -2*s**3 + s + 2. Let z(b) = 21*b**3 - 4653*b**2 + 2405592*b - 414565257. Let l(t) = -9*n(t) - z(t). Solve l(r) = 0 for r.
517
Suppose 0*z + 84 = 6*z. Suppose -5*k - z + 1 = -o, -2*k = -2*o + 10. Determine p so that p**2 - 6*p**3 + 11*p**o + 6*p**2 - 2*p**2 = 0.
-1, 0
Let a(f) be the third derivative of 0 + 0*f + 1/20*f**4 - 95*f**2 + 1/50*f**5 - 2/5*f**3. Factor a(u).
6*(u - 1)*(u + 2)/5
Let h(l) be the second derivative of l**5/40 + 3*l**4/8 + 23*l**3/12 + 15*l**2/4 - 3*l - 14. Factor h(v).
(v + 1)*(v + 3)*(v + 5)/2
Suppose 0 = 3*i - 15, 3*q - 2*i = 540 - 58. Solve -2*z + 110*z**2 - z - q*z**2 + 27 - 3*z**5 + 6*z**3 + 27*z**4 = 0.
-1, 1, 9
Let r(l) be the third derivative of 5/8*l**4 - 1/8*l**6 - 1/70*l**7 + 0*l**3 + 1/20*l**5 + 0*l - 190*l**2 + 0. Suppose r(u) = 0. Calculate u.
-5, -1, 0, 1
Let r(y) be the third derivative of -y**8/3024 + 2*y**7/105 - 143*y**6/540 - 19*y**5/15 - 361*y**4/216 - 2132*y**2. Factor r(w).
-w*(w - 19)**2*(w + 1)**2/9
Let i(j) be the first derivative of 0*j + 40 + 9/2*j**2 + 0*j**3 - 1/4*j**4. Let i(v) = 0. What is v?
-3, 0, 3
Let y(h) be the first derivative of h**3 - 480*h**2 + 76800*h - 404. Factor y(v).
3*(v - 160)**2
Let r(f) be the third derivative of -f**8/672 + f**7/84 + 23*f**6/240 + 11*f**5/120 - 11*f**4/24 - 4*f**3/3 - 668*f**2. Suppose r(y) = 0. Calculate y.
-2, -1, 1, 8
Let b(j) = -303*j**2 - 141*j - 12. Let a(t) = t**3 - t**2 + t - 2. Suppose 0 = -21*i + 11*i - 10. Let q(p) = i*b(p) + 6*a(p). Suppose q(g) = 0. What is g?
-49, -1/2, 0
Let x(p) be the second derivative of p**6/75 + 17*p**5/50 - 37*p**4/30 + 19*p**3/15 - 78*p - 5. Factor x(k).
2*k*(k - 1)**2*(k + 19)/5
Suppose -50*w = -5*m - 54*w - 22, -w - 4 = 2*m. Let n(g) be the third derivative of 1/180*g**5 - 1/18*g**3 + 23*g**m + 0 + 0*g + 0*g**4. Factor n(u).
(u - 1)*(u + 1)/3
Let r(m) be the second derivative of -m**9/3780 - m**8/1680 + m**7/630 + m**6/180 + 11*m**4/4 - 55*m. Let i(v) be the third derivative of r(v). Factor i(j).
-4*j*(j - 1)*(j + 1)**2
Let z be (1*3)/(4968/230 + -21). Factor 1/4*c**z - c**3 + 0 - 1/2*c**4 + 1/2*c**2 + 3/4*c.
c*(c - 3)*(c - 1)*(c + 1)**2/4
Let x be ((-14325)/17190)/((-3)/80). Factor x*p + 5000/9 + 2/9*p**2.
2*(p + 50)**2/9
Let o be ((-138)/(-60))/23*-302. Let q = o - -31. Factor 12/5 + q*x**2 + 16/5*x.
4*(x + 1)*(x + 3)/5
Suppose -d + 3580*a - 3576*a = 36, 5*a = -3*d + 62. Find p such that 10/7*p**d - 4/7*p**3 - 4*p**2 + 18/7 - 2/7*p**5 + 6/7*p = 0.
-1, 1, 3
Suppose 0 = -309*m + 697*m - 315*m. Let 6*g**2 + m*g + 3/2*g**3 + 0 = 0. What is g?
-4, 0
Let m(c) be the first derivative of -c**6/6 + 38*c**5/5 - 71*c**4/2 + 208*c**3/3 - 137*c**2/2 + 34*c + 2992. Let m(b) = 0. Calculate b.
1, 34
Let a(i) be the second derivative of 35/2*i**2 - 20/3*i**3 + 172*i + 0 + 5/12*i**4. Factor a(n).
5*(n - 7)*(n - 1)
Let m = 42164/7 - 379336/63. Determine o, given that -34/9*o + m + 2/3*o**2 = 0.
2/3, 5
Factor -3/2*q**2 - 273*q - 24843/2.
-3*(q + 91)**2/2
Let v(g) = g**3 + 49*g**2 - 101*g + 67. Let x be v(-51). Suppose 5*m - 15 = -4*b, -x*m + 18*m = b + 6. Find u, given that 1/3*u**2 + 0 + 1/3*u**3 + b*u = 0.
-1, 0
Suppose 0 + 0*w - 78/7*w**3 - 32/7*w**4 - 2/7*w**5 + 0*w**2 = 0. What is w?
-13, -3, 0
Let b(w) = -w**4 + 5*w**3 + w**2 + 1. Let c(n) = -8*n**4 + 372*n**3 + 530*n**2 + 120*n - 6. Let v(x) = -12*b(x) - 2*c(x). What is l in v(l) = 0?
-1, -2/7, 0, 30
Let c be (-1368 - -1383 - 84/5)/((-42)/20). Suppose -2/7*b**2 - c*b - 4/7 = 0.