 5*p**4 - 35*p**2 + 38*p**3 - r*p**4 - 109 - 5*p + 109.
-5*p*(p - 1)**2*(9*p + 1)
Let m(g) = 4*g**3 + 11*g**2 - 265*g + 890. Let r(k) = -18*k**3 - 48*k**2 + 1192*k - 4006. Let u(j) = 44*m(j) + 10*r(j). Suppose u(c) = 0. What is c?
-9, 5
Let y(p) = p**2 - 3*p - 68. Let o be y(-7). Let 22*h + 7*h**2 - 30*h - h**2 - 4*h**o - h**2 = 0. Calculate h.
0, 8
Let x(o) = -5 - 93*o + 48*o + 49*o. Let i be x(11). Factor -37*b**2 + 2 + 81*b**2 - 7*b - i*b**2.
(b - 1)*(5*b - 2)
Let d = -6843 - -12317399/1800. Let x = 489/200 + d. Determine y so that 10/9*y**2 + 4/3 + x*y = 0.
-6/5, -1
Let u(a) be the first derivative of 1/14*a**4 - 5/14*a**2 + 1/14*a**6 - 1/7*a + 1/5*a**5 - 2/7*a**3 - 57. Factor u(w).
(w - 1)*(w + 1)**3*(3*w + 1)/7
Let k(d) be the second derivative of d**4/18 + 14*d**3/9 - 117*d**2 - 958*d - 3. Factor k(j).
2*(j - 13)*(j + 27)/3
Let l(f) be the second derivative of -2*f**7/7 + 388*f**6/5 + 7089*f**5/20 + 209*f**4/4 - 1184*f**3 + 1182*f**2 - 14156*f. Solve l(v) = 0 for v.
-2, 1/2, 197
Let o(s) be the first derivative of -1/48*s**4 - 5/36*s**3 - 1/3*s**2 - 1/3*s - 54. Factor o(k).
-(k + 1)*(k + 2)**2/12
Solve -464*u + 164*u**3 + 23 + 145 - 37469*u**2 + 36987*u**2 + 14*u**4 = 0 for u.
-14, -1, 2/7, 3
Let t(u) be the third derivative of -1/12*u**6 + 1/105*u**7 + 1/10*u**5 + 1/168*u**8 + 0*u**4 - u + 0*u**3 + 29*u**2 + 0. Suppose t(v) = 0. Calculate v.
-3, 0, 1
Factor 2/9*a**3 + 278/9*a + 142/9*a**2 + 46/3.
2*(a + 1)**2*(a + 69)/9
Let q(t) be the third derivative of t**5/80 + 17*t**4/2 + 7*t**2 + 187. Factor q(n).
3*n*(n + 272)/4
Let f be 0/(-5 - (-1 - 3)). Suppose 4*b = 2*s - b - 35, 3*b + 15 = f. Suppose 0 + 0*v + 3/4*v**4 - 3/4*v**s + 3/4*v**3 - 3/4*v**2 = 0. What is v?
-1, 0, 1
Let v be (24/210)/(2/5)*(60 - 53). Find r, given that -7 + 1/3*r**v - 20/3*r = 0.
-1, 21
Let r be -4 + 13 + -3 + -2. Suppose -37 - 5 = -21*j. Factor -16/7*o + 20/7*o**3 + 4/7*o**r - 32/7 + 24/7*o**j.
4*(o - 1)*(o + 2)**3/7
Let n(u) be the first derivative of 4/21*u**3 - 1/21*u**6 + 1/7*u**2 - 59 - 4/35*u**5 + 0*u**4 + 0*u. Factor n(i).
-2*i*(i - 1)*(i + 1)**3/7
Let i(c) be the second derivative of -c**7/147 - 47*c**6/105 + 445*c. Determine q so that i(q) = 0.
-47, 0
Let a = 1216 + -1204. Let w be (3 - (7 + 0))*(-2)/a. Factor 5/3*p + 4/3*p**4 - 2/3 - 1/3*p**5 - w*p**2 - 4/3*p**3.
-(p - 2)*(p - 1)**3*(p + 1)/3
Suppose 0 = -d - 246 + 97. Let k = -149 - d. Find o such that -11/5*o**2 - 6/5*o - 3/5*o**3 + k = 0.
-3, -2/3, 0
Determine g, given that 2/15*g**4 + 34/15*g**3 - 256/5 - 64/15*g + 148/15*g**2 = 0.
-8, -3, 2
Suppose -25 = -4*z - 13. Factor -9*s**2 - 15*s - 12*s**3 - 5*s**z + 42*s**2 - 4*s**3 + 3*s**4 + 0*s**2.
3*s*(s - 5)*(s - 1)**2
Let v(p) be the second derivative of p**4/60 + 104*p**3/15 - 209*p**2/10 - 296*p + 1. Determine h so that v(h) = 0.
-209, 1
Let n be (4352/(-8160))/((-3)/5 + (-24)/40). Find y such that -10/9*y**2 + 2/3*y**3 + 0 + n*y = 0.
0, 2/3, 1
Let g(u) be the first derivative of -u**4/26 + 10*u**3/13 - 48*u**2/13 + 88*u/13 + 1461. Factor g(f).
-2*(f - 11)*(f - 2)**2/13
Suppose -5*x + 20*x + 48 = 39*x. Let k(f) be the second derivative of 0 + 0*f**4 + 2/5*f**5 - 2/15*f**6 + 0*f**3 + 0*f**x - f. Let k(h) = 0. Calculate h.
0, 2
Let z(t) = -8*t + 2. Let u(i) = -i**2 - 9*i - 21. Let x be u(-6). Let p be z(x). Determine r so that -p + 10 - 2*r**2 + 16*r - 16 = 0.
4
Let l(c) be the first derivative of -4*c**3/15 - 54*c**2/5 - 104*c/5 - 399. Factor l(r).
-4*(r + 1)*(r + 26)/5
Let a be (4/(-10))/(1/(-95)). Determine v so that -340 - v**4 - 14*v**3 + 768*v + a*v**3 - 208*v**2 - 684 = 0.
4, 8
Let b = -65616/7 - -9375. Find k such that -6/7*k + 3/7*k**2 - b = 0.
-1, 3
Suppose 74*k - 20076 = 53*k. Let v = -14332/15 + k. Factor 0 + 2/15*m + 2/3*m**2 + v*m**3.
2*m*(m + 1)*(4*m + 1)/15
Let b(x) = -43*x**2 + 231*x - 3. Let r(p) = 55*p**2 - 229*p + 4. Let j(i) = 4*b(i) + 3*r(i). Factor j(c).
-c*(7*c - 237)
Let j(y) = 35*y**3 - 440*y**2 + 1665*y - 1260. Let l(c) = 5*c**3 - 63*c**2 + 238*c - 180. Suppose -72*m + 58 = -43*m. Let w(b) = m*j(b) - 15*l(b). Factor w(k).
-5*(k - 6)**2*(k - 1)
Let m = 4752 + -4748. Let f(s) be the third derivative of -1/20*s**5 - 1/200*s**6 - 39*s**2 - 3/10*s**3 + 0*s - 7/40*s**m + 0. Let f(k) = 0. Calculate k.
-3, -1
Factor -1626*r + 214*r + 3*r**4 + 1947*r**2 + 1953*r**3 - 757*r - 1950 + 216*r.
3*(r - 1)*(r + 1)**2*(r + 650)
Let v be (-15)/(-4) - (-2)/8. Suppose -14*a + r = -15*a + 3, -5*r = 2*a + 6. Let -5*n**5 + 4*n**v - a*n**4 - 6*n**4 - 21*n**4 - 45*n**3 = 0. What is n?
-3, 0
Let k = 8632707/7 - 1233240. Let p be (1 + (-20)/14)/(-1). Find s such that k + p*s**2 - 18/7*s = 0.
3
Let z = 329 + -299. Factor 2*f**2 - 840*f + 831*f + z - 5*f**2.
-3*(f - 2)*(f + 5)
Suppose 501*u - 499*u - 44 = 0. Let i be u/(-33) + 2/(-2 - -4). Let -i*k**2 + 2/3*k + 1 = 0. Calculate k.
-1, 3
Let x(j) = j**3 - 22*j**2 - 51*j + 75. Let l be x(24). Let s(i) be the third derivative of 0 - 25/24*i**4 - 8*i**2 + 1/4*i**5 + 0*i + 5/3*i**l. Factor s(f).
5*(f - 1)*(3*f - 2)
Suppose -4*a + 5*y = -1, -1 = -6*a + 7*a - y. Let u be (a/21)/(11/(-77)). Factor 2/9 - 5/9*l - 1/3*l**u.
-(l + 2)*(3*l - 1)/9
Determine q, given that -11/4*q**3 + 4 + 5*q + 1/4*q**5 - 2*q**2 + 1/2*q**4 = 0.
-4, -1, 2
Suppose 732*n + 12 = 738*n. Determine p, given that -67*p**4 - 24*p**5 + 28*p**5 + 128*p**4 - 73*p**4 + 12*p**3 - 4*p**n = 0.
0, 1
Let h(s) = -9*s**3 - 20*s**2 + 361*s - 316. Let w(l) = -24*l**3 - 54*l**2 + 963*l - 843. Let d(v) = 21*h(v) - 8*w(v). Solve d(k) = 0 for k.
-9, 1, 4
Let g(r) be the first derivative of -3*r**4/4 - 4*r**3/3 - r**2/2 - 2*r + 36. Let d be g(-2). Factor -20*j**3 + 2*j**4 + 12*j**3 - 16*j - 6 + d*j**3 - 12*j**2.
2*(j - 3)*(j + 1)**3
Suppose -4930 - 1928 - 452*h + 310 - 1157*h + 4*h**2 - 4935*h = 0. Calculate h.
-1, 1637
Factor 186/7*u**2 + 2/7*u**3 - 376/7 - 192/7*u.
2*(u - 2)*(u + 1)*(u + 94)/7
Let g(y) be the third derivative of 13/18*y**4 - 178*y - 1/90*y**5 + 0 - 169/9*y**3 + y**2. Factor g(i).
-2*(i - 13)**2/3
Let u = 232 - 230. Solve -6*p**u + 21*p + 38*p + 7*p**2 + 10*p + 66 + 2*p**2 = 0.
-22, -1
Let b(r) be the second derivative of -5*r**7/42 + 8*r**6/3 + 98*r**5 - 1055*r**4/6 - 1955*r**3/6 + 1015*r**2 - 11388*r. Find l, given that b(l) = 0.
-14, -1, 1, 29
Let j = 2626 + -2626. Let a(h) be the first derivative of 2*h**5 + j*h**4 + 5/6*h**6 - 5/2*h**2 + 9 + 0*h - 10/3*h**3. Solve a(r) = 0.
-1, 0, 1
Let n(f) be the first derivative of -1/120*f**6 + 0*f**3 - 15/2*f**2 + 1/12*f**4 + 0*f - 13 + 1/60*f**5. Let g(v) be the second derivative of n(v). Factor g(c).
-c*(c - 2)*(c + 1)
Let k(d) be the third derivative of d**7/17640 - d**6/2520 - 35*d**4/8 - 16*d**2. Let q(f) be the second derivative of k(f). Factor q(t).
t*(t - 2)/7
Suppose 3*g - 1146*a = -1147*a, -a + 15 = 8*g. Factor -288*c - 384 - 3/2*c**4 - 6*c**2 + 18*c**g.
-3*(c - 8)**2*(c + 2)**2/2
Suppose 8*o + 615 = 79. Let s = o + 67. Let -1/4*b**3 - 1/4*b**2 + 0 + s*b = 0. What is b?
-1, 0
Let k = -7841/1407916 - 7/2092. Let s = k - -2734/4711. Suppose 0*g - s*g**2 + 0 - 2/21*g**3 = 0. What is g?
-6, 0
Factor -5120/3*w**2 - 40/3*w**4 - 800/3*w**3 + 1/3*w**5 - 14080/3*w - 14336/3.
(w - 56)*(w + 4)**4/3
Let r(k) be the third derivative of -1/2*k**3 + 2*k + 3/16*k**5 + 2*k**2 - 1/80*k**6 - 1/56*k**7 - 1/8*k**4 + 0. Let r(u) = 0. Calculate u.
-2, -2/5, 1
Let s(o) = -13*o**4 - 115*o**3 + 128*o**2 - 51*o + 17. Let r(z) = -7*z**4 - 57*z**3 + 64*z**2 - 27*z + 9. Let t(j) = 17*r(j) - 9*s(j). Factor t(c).
-2*c**2*(c - 32)*(c - 1)
Factor 1/4*d**4 + 41/2*d**2 + 0 + 83/4*d**3 + 0*d.
d**2*(d + 1)*(d + 82)/4
Let q(u) = u**3 - u**2 + 5*u - 2. Let f be q(2). Let h = 14 - f. Let -2*s**3 - 7*s**3 + s + 25*s**2 - 7*s**2 - h = 0. Calculate s.
-1/3, 1/3, 2
Let f(z) be the third derivative of -z**5/60 - z**4/24 + z**3/3 - 2636*z**2 - 2*z. Factor f(m).
-(m - 1)*(m + 2)
Let m(v) be the third derivative of -182*v**2 + 0*v - 1/180*v**5 - 1/3*v**3 - 7/72*v**4 + 0. Solve m(z) = 0 for z.
-6, -1
Let y = 169 + -155. Suppose y*f - 32 = -4. Let 4/5*o**5 + 4/5*o**4 - 4/5*o**3 - 4/5*o**f + 0 + 0*o = 0. What is o?
-1, 0, 1
Let h = 84247 + -84244. What is n in -10 + 15/2*n**2 + 5/2*n**h + 0*n = 0?
-2, 1
Let l(a) be the third derivative of a**5/80 - 235*a**4/32 - 59*a**3/2 - 105*a**2 - 1. Let l(m) = 0. Calculate m.
-1, 236
Let 0*h - 194/1