 7*t**5/390 - t**4/39 - 4*t**3/39 - 70*t**2 - t. Factor s(p).
-2*(p - 2)**2*(2*p + 1)/13
Find n such that -2/9*n**3 + 80/9 + 158/9*n + 76/9*n**2 = 0.
-1, 40
Determine n, given that -572/17*n**2 - 13310/17 + 58/17*n**4 + 452/17*n**3 + 2/17*n**5 - 14278/17*n = 0.
-11, -1, 5
Suppose 6*p - y = 2*p + 12, -2*y - 6 = -2*p. Factor -51*s + 14*s**3 + 4*s**p - 22*s**3 + 7*s**3 + 7*s**2 - 4*s**2 + 45.
3*(s - 3)*(s - 1)*(s + 5)
Suppose 56510*t + 395*t**3 - 22*t**4 + 25337 - 9202*t**2 + 17*t**4 + 35913 - 4885*t - 23*t**2 = 0. What is t?
-1, 10, 35
Let g(r) be the second derivative of -r**7/630 - 7*r**6/180 + 11*r**4/3 + 34*r - 2. Let w(k) be the third derivative of g(k). Factor w(c).
-4*c*(c + 7)
Let r(m) be the first derivative of -2*m**5/25 + 19*m**4/5 - 134*m**3/5 + 288*m**2/5 + 643. Factor r(k).
-2*k*(k - 32)*(k - 3)**2/5
Let q(n) = -68*n + 15. Let v be q(0). Suppose -v*a + 6 = -24. Factor 24/5*k + 48/5 + 3/5*k**a.
3*(k + 4)**2/5
Let a = 1457721 + -1457719. Factor 148/13 + 6/13*c**a - 226/13*c.
2*(c - 37)*(3*c - 2)/13
Let d = 196/29 - 124/87. Let c(f) be the first derivative of 0*f**2 + d*f**3 - 12*f**4 + 6 + 0*f + 36/5*f**5. Determine y so that c(y) = 0.
0, 2/3
Suppose 7*n = 19*n - 57228. Suppose -n*y = -4772*y + 12. Find p such that 9/2*p**y - 15/2*p**2 + 6*p**3 - 15/4*p**5 + 3 - 9/4*p = 0.
-1, -4/5, 1
Let x(g) be the first derivative of 68*g + 205 - 1/2*g**4 + g**2 - 68/3*g**3. Factor x(n).
-2*(n - 1)*(n + 1)*(n + 34)
Let t = -11682/373 + 36538/1119. Factor -t*m**2 - 34/9*m + 2/3.
-2*(m + 3)*(6*m - 1)/9
Let o = -10 + 21. Suppose -4*v + 1 = -o. Solve -3*r**3 + 3*r**v - 16*r**4 + 12*r**4 + 4*r**3 = 0 for r.
0, 1
Suppose -2*n - 135 = 5*t, 5*n + 52 - 27 = 0. Let q be 28/10 + (-5)/t. Find k such that -k**2 - 4/3 - 2/3*k**q + 1/3*k**4 + 8/3*k = 0.
-2, 1, 2
Solve -18 + 4/5*l**3 + 96/5*l - 34/5*l**2 = 0.
5/2, 3
Let a(p) = -17*p**3 + 190*p**2 + 403*p - 85. Let z(b) = -25*b**3 + 286*b**2 + 604*b - 128. Let t(j) = -8*a(j) + 5*z(j). Factor t(q).
(q - 10)*(q + 2)*(11*q - 2)
Let f(o) = -11*o**2 + 1. Let b(c) = 43*c**2 - 155*c - 158. Let z(t) = -b(t) - 4*f(t). Find v such that z(v) = 0.
-154, -1
Let r(i) be the third derivative of i**9/672 + i**8/112 + 3*i**7/560 - i**3/6 + 62*i**2. Let f(h) be the first derivative of r(h). Solve f(u) = 0 for u.
-3, -1/3, 0
Let t(w) = 27*w**2 - 15285*w + 15201. Let l(c) = -3*c**2 + 1698*c - 1689. Let a(v) = -19*l(v) - 2*t(v). Let a(i) = 0. What is i?
1, 563
Factor -92/3*c**2 - 104/3*c + 32/3 - 16/3*c**3.
-4*(c + 2)*(c + 4)*(4*c - 1)/3
Let v be ((-1071999)/(-6560))/19 - 8. Let i = -1/1312 + v. Factor 3/5*o**3 + 3/5 - 3/5*o**2 - i*o.
3*(o - 1)**2*(o + 1)/5
Suppose 10*p - 637 = -3*p. Let s be (p/147)/(1/12*2). Factor 4*x**3 + 10/19*x**5 + 26/19*x - 4/19 - 44/19*x**4 - 64/19*x**s.
2*(x - 1)**4*(5*x - 2)/19
Let j(w) be the third derivative of -w**7/70 + 75*w**6/2 - 84375*w**5/2 + 52734375*w**4/2 - 19775390625*w**3/2 - 2017*w**2. Let j(p) = 0. What is p?
375
Suppose -3/2*w**4 - 15*w**3 + 15*w + 114*w**2 - 225/2 = 0. What is w?
-15, -1, 1, 5
Factor 1620*l**2 - 14*l**3 + 101728*l + 19*l**3 + 31097*l + 259210.
5*(l + 2)*(l + 161)**2
Suppose 22*a - 563 - 713 = 0. Factor -32*b**2 - 6 - 9 + 2*b**3 - 13 - 4*b**3 - a*b.
-2*(b + 1)**2*(b + 14)
Let x be 22 + 18/(18/(-19)). Let u(t) be the second derivative of -1/5*t**5 + 0 + 34*t + 0*t**2 - 1/3*t**4 + 4/3*t**x. Find n such that u(n) = 0.
-2, 0, 1
Let f(o) be the first derivative of -2*o**5/55 + 180*o**4/11 - 64076*o**3/33 - 65160*o**2/11 - 65522*o/11 - 1479. Factor f(b).
-2*(b - 181)**2*(b + 1)**2/11
Let l = 25361 + -608663/24. Let g(q) be the first derivative of -5/12*q**2 - 14 + 1/3*q + 1/6*q**3 - 1/30*q**5 + l*q**4. Factor g(u).
-(u - 1)**3*(u + 2)/6
Let n(k) = k**3 + 23*k**2 - 77*k + 72. Let j(a) = 4*a**3 + 68*a**2 - 230*a + 216. Let w(t) = -3*j(t) + 10*n(t). What is g in w(g) = 0?
2, 9
Let m be (199/(-3998))/(72/320). Let h = 2/1999 - m. Suppose h*z + 2/3 - 2/9*z**3 - 2/3*z**2 = 0. What is z?
-3, -1, 1
Let w(y) be the first derivative of 3*y**4/8 + 809*y**3/2 - 2384. Factor w(s).
3*s**2*(s + 809)/2
Suppose -22 = -12*m + 38. Find k, given that -21*k**3 - 5*k + k**5 + m*k**4 + 54*k**3 - k - 28*k**3 - 5*k**2 = 0.
-3, -2, -1, 0, 1
Let l = 411 + -426. Let s(x) = 5*x**2 + 29*x + 22. Let m(n) = 35*n**2 + 205*n + 155. Let f(y) = l*s(y) + 2*m(y). Factor f(z).
-5*(z + 1)*(z + 4)
Let f(x) be the first derivative of x**6/12 - x**5/10 - 1671. Factor f(l).
l**4*(l - 1)/2
Factor -2/23*x**2 - 236/23*x + 238/23.
-2*(x - 1)*(x + 119)/23
Let n be (-10 - -14)/(12/45). Suppose n*q = 16*q. Determine a, given that 0*a - 33/5*a**2 + 3/5*a**3 + q = 0.
0, 11
Suppose -3*a - 29*i = -30*i - 10, -5 = 3*a - 4*i. Suppose -2*o = -a*o. Let -4/7*g + o + 2/7*g**2 = 0. Calculate g.
0, 2
Let n(f) be the third derivative of f**5/60 - 13*f**4/3 - 35*f**3/2 - 372*f**2. Factor n(r).
(r - 105)*(r + 1)
Let s = -10052 - -80419/8. Let l(n) be the third derivative of -4/3*n**3 - 12*n**2 + 0 + 0*n - s*n**4 - 1/60*n**5. Suppose l(c) = 0. Calculate c.
-8, -1
Let s = 20915 - 230063/11. Let k(w) = w**2 + w. Let b be k(-1). Factor -s*n + 2/11*n**3 + 0*n**2 + b.
2*n*(n - 1)*(n + 1)/11
Let n be (-63)/105 - 4/10. Let u(g) = g**2. Let v(y) = 9*y**2 + 156*y - 2028. Let d(j) = n*v(j) + 12*u(j). Factor d(m).
3*(m - 26)**2
Let g(h) be the first derivative of 2*h**5/65 + h**4/2 + 80*h**3/39 + 36*h**2/13 - 1361. Factor g(w).
2*w*(w + 2)**2*(w + 9)/13
Let f be 13 + (-10 + (-713)/(-69))/(2/(-60)). Factor 0 + 3/2*d**f - 3*d + 3/2*d**2.
3*d*(d - 1)*(d + 2)/2
Let d(o) be the second derivative of 0 + 0*o**2 + 11/15*o**6 + 2/3*o**3 - 11/10*o**5 + 1/6*o**4 + 18*o - 1/7*o**7. Find f such that d(f) = 0.
-1/3, 0, 1, 2
Let y be 5 + 11/(77/(-14)). Factor -33*d + 3*d**5 - 13 - 2 - 818*d**3 + 848*d**y - 6*d**2 + 21*d**4.
3*(d - 1)*(d + 1)**3*(d + 5)
Let n be (-18*(-5)/900)/((-32)/(-2)). Let z(k) be the second derivative of 0 - 49/16*k**3 - 343/16*k**2 - 7/32*k**4 - 9*k - n*k**5. Factor z(w).
-(w + 7)**3/8
Let l(w) = -2*w**2 + 26*w + 2. Let h(z) be the third derivative of -z**5/60 + 25*z**4/24 + z**3/2 + 6*z**2. Let u(i) = 2*h(i) - 3*l(i). Factor u(o).
4*o*(o - 7)
Let x(i) be the third derivative of -4/35*i**7 + 2/15*i**5 + 236*i**2 + 8/3*i**3 + 1/84*i**8 + 0 + 0*i - 3/2*i**4 + 4/15*i**6. Let x(v) = 0. What is v?
-1, 1, 4
Let n(b) be the first derivative of 1/7*b**3 + 30/7*b - 145 - 3/2*b**2. Solve n(d) = 0 for d.
2, 5
Let y(n) be the second derivative of -n**5/60 + n**4/72 + n**3/9 + 109*n**2 + 219*n. Let r(b) be the first derivative of y(b). Suppose r(o) = 0. What is o?
-2/3, 1
Suppose 12 + 39/2*b**2 + 81*b = 0. What is b?
-4, -2/13
Let r(j) be the third derivative of 0 + j - 60*j**2 - 1/100*j**5 - 1/10*j**4 - 3/10*j**3. Factor r(o).
-3*(o + 1)*(o + 3)/5
Let v(o) be the third derivative of -o**8/1176 - o**7/105 + 6*o**5/35 - 20*o**2 - 5*o - 8. Find t, given that v(t) = 0.
-6, -3, 0, 2
Let g(d) be the first derivative of 8/3*d**3 + 41*d + 4 + 0*d**2 - 1/3*d**4 - 1/10*d**5. Let b(q) be the first derivative of g(q). Factor b(w).
-2*w*(w - 2)*(w + 4)
Suppose 4*d - 4*q = -4, -2*d - 3*q + 16 - 13 = 0. Let t(k) be the second derivative of 5/6*k**3 + 0 - 11*k + d*k**2 + 5/12*k**4. What is f in t(f) = 0?
-1, 0
Let u be ((-1)/4)/((-5)/(-4)) - 8/(-40). Let z(x) be the second derivative of u - 27*x**2 + 9/2*x**3 + 1/80*x**5 - 3/8*x**4 - 27*x. Factor z(b).
(b - 6)**3/4
Let z(u) be the first derivative of 80*u**2 - 155/3*u**3 + 180*u + 106 + 15/4*u**4. Factor z(l).
5*(l - 9)*(l - 2)*(3*l + 2)
Suppose 480 = 5*j - f, 0 = -j + 3*j + f - 192. Factor j*v**2 - v - 48*v**2 - 44*v**2.
v*(4*v - 1)
Let a(n) be the second derivative of 1 - 11/24*n**3 + 1/4*n**4 + 0*n**2 - 5*n - 1/80*n**5. Suppose a(t) = 0. Calculate t.
0, 1, 11
Suppose -599*d + 292*d + 293*d = -28. Let i(r) be the third derivative of 0 - 8/15*r**5 + 0*r + 6*r**d + 0*r**3 + 1/2*r**4. Determine m so that i(m) = 0.
0, 3/8
Let g(v) = 39 - 22*v + 92 + 21 + 11*v**2 + 68 + 2*v. Let u(o) = 2*o**2 + 2*o - 1. Let c(b) = g(b) - 5*u(b). Factor c(d).
(d - 15)**2
Suppose -4/5*n**2 + 5512/5*n - 1898884/5 = 0. Calculate n.
689
Let h = -837444 - -837444. Let d = 714/55 + -64/5. Suppose 0*n**2 + 2/11*n**3 + h - d*n = 0. Calculate n.
-1, 0, 1
Factor -39/4*t**2 - 18 - 21/4*t**3 + 3/4*t**4 + 129/4*t.
3*(t - 8)*(t - 1)**2*(t + 3)/4
Suppose -5