5) - 6558/311505. Let q = -11/6 - -5/2. Factor -13/2*c**u + q - 35/6*c**3 + 0*c.
-(c + 1)*(5*c + 2)*(7*c - 2)/6
Let b(u) = -u**4 + 40*u**3 - 161*u**2 + 238*u - 102. Let w(m) = -5*m**4 + 204*m**3 - 803*m**2 + 1190*m - 509. Let h(f) = 33*b(f) - 6*w(f). Factor h(n).
-3*(n - 26)*(n - 4)*(n - 1)**2
Determine i, given that -325/3*i + 1/3*i**2 + 0 = 0.
0, 325
Let i = 414385 - 1243147/3. Factor -4/3*q - 4/3*q**2 + i.
-4*(q - 1)*(q + 2)/3
Let d be 84/15 - 320/(-800). Factor -50/9*s**2 - 16/9*s - 22/9*s**4 - d*s**3 + 0 - 2/9*s**5.
-2*s*(s + 1)**3*(s + 8)/9
Let o = -190 - -422. Suppose -233*x + o*x = -2. Determine h, given that -4*h - 2/5*h**x - 10 = 0.
-5
Let z(q) = -2*q**3 + 15*q**2 - 5*q - 11. Let o be z(7). Factor 24*s**3 - 24 - 21*s**3 - 5*s**o + 32*s - 6*s**2.
-2*(s - 2)*(s - 1)*(s + 6)
Suppose 761318*s = 761231*s + 174. Let x = -61/24 - -8/3. Find n, given that x*n**s + 1/4 - 3/8*n = 0.
1, 2
Let k(g) be the second derivative of g**5/50 + 41*g**4/10 + 1681*g**3/5 + 68921*g**2/5 + 2*g - 805. Factor k(o).
2*(o + 41)**3/5
Factor 12*z + 3*z**2 + 14*z**2 - 180 + z - 128*z + 23*z**2.
5*(z - 4)*(8*z + 9)
Let b be 366/(-427) - 57/(-42). Find a, given that 7 + 3/2*a**2 - b*a**4 - 23/2*a + 7/2*a**3 = 0.
-2, 1, 7
Determine y, given that -62/7*y**3 + 2*y**4 + 0*y + 24/7*y**2 + 0 = 0.
0, 3/7, 4
Let d(a) be the second derivative of a**5/4 + 245*a**4/12 + 350*a**3/3 + 230*a**2 - 29*a - 8. Factor d(b).
5*(b + 1)*(b + 2)*(b + 46)
Let 1/7*s**2 + 24/7*s + 23/7 = 0. Calculate s.
-23, -1
Let q(a) be the first derivative of a**5 - 15*a**4/4 - 5*a**3 + 55*a**2/2 - 30*a + 1495. Factor q(z).
5*(z - 3)*(z - 1)**2*(z + 2)
Let l(z) be the third derivative of z**6/600 + 3*z**5/20 - 2*z**4/5 - 46*z**3/15 + 38*z**2 - 26*z. Factor l(b).
(b - 2)*(b + 1)*(b + 46)/5
Let w(s) be the first derivative of -2*s**3/3 - 2*s**2 - 2*s - 1207. Factor w(q).
-2*(q + 1)**2
Let f(j) be the first derivative of -j**6/4 + 39*j**5/5 - 81*j**4 + 281*j**3 + 651*j**2/4 - 882*j - 3215. Find a such that f(a) = 0.
-1, 1, 7, 12
Let q(j) = -j**2 + 3*j + 4. Let v be q(5). Let u be 56/3 - v/18. Let 0*s + 9*s - u*s - 2*s**2 = 0. What is s?
-5, 0
Let r(z) be the second derivative of -5/8*z**2 + 74 - 2*z - 1/48*z**4 - 1/4*z**3. Let r(m) = 0. Calculate m.
-5, -1
Let y be (-8 - (-23)/3)/((-1)/9). Factor 3*h + 116*h**y - 21*h**2 - 131*h**3 - 9*h.
-3*h*(h + 1)*(5*h + 2)
Let t be ((-36)/54)/(508/12). Let d = 1514/635 - t. Factor 18/5*y**2 - 3/5*y**3 - 27/5*y + d.
-3*(y - 4)*(y - 1)**2/5
Let n(i) = 9*i**3 + i**2 - 15*i. Let j(h) = -5*h**3 - h**2 + 7*h. Let r be 34/14 - 4/(-7). Let q(g) = r*n(g) + 7*j(g). Factor q(z).
-4*z*(z + 1)*(2*z - 1)
Let x(d) be the second derivative of -5*d**4/12 - 55*d**3/6 - 45*d**2 + 59*d - 2. Factor x(q).
-5*(q + 2)*(q + 9)
Suppose -2*x + y = -2512, -2*y + 1616 = x + 350. Let d = x + -1253. Solve -1/6 - 1/3*p**2 + 1/2*p**4 - 1/3*p**3 + 1/2*p - 1/6*p**d = 0 for p.
-1, 1
Let d(r) be the second derivative of -2*r**7/147 - 106*r**6/105 - 904*r**5/35 - 776*r**4/3 - 24992*r**3/21 - 19360*r**2/7 + 5*r - 194. Solve d(o) = 0 for o.
-22, -5, -2
Let t(w) be the second derivative of w**5/16 - 2105*w**4/24 - 8435*w**3/24 - 1055*w**2/2 - 2540*w - 1. Solve t(n) = 0 for n.
-1, 844
Factor -712*r**3 - 117*r**4 + 136*r**2 - 110*r**4 - 514*r**3 - 119*r**4 + 364*r**4.
2*r**2*(r - 68)*(9*r - 1)
Let c = -7597 + 7602. Let b(w) be the second derivative of -4*w - 1/10*w**c + 0 + 9*w**2 + 7/6*w**4 - 5*w**3. Suppose b(l) = 0. Calculate l.
1, 3
Let k(g) be the second derivative of 151*g + 1144/5*g**5 + 38*g**4 - 62/3*g**3 + 256/7*g**7 + 4288/15*g**6 + 0 - 10*g**2. Find m, given that k(m) = 0.
-5, -1/4, 1/6
Factor 56 + 48/5*m + 2/5*m**2.
2*(m + 10)*(m + 14)/5
Factor -17*i**3 + 42*i - 3*i + 27*i + 28*i**2 + 60 + i**3 + 38*i.
-4*(i + 1)**2*(4*i - 15)
Let s be ((-9)/18 - 1)*(-10)/3. Find u, given that 4*u**s + 16*u**4 + 87*u**3 - 157*u**3 + 86*u**3 = 0.
-2, 0
Let c(k) = 5*k**4 + 158*k**3 - 19*k**2 - 53*k. Let z(j) = 3*j**4 + 110*j**3 - 13*j**2 - 35*j. Let p(h) = 5*c(h) - 7*z(h). Solve p(m) = 0.
-5, -1, 0, 1
Factor 1000 + 2/5*g**3 + 202/5*g**2 + 1040*g.
2*(g + 1)*(g + 50)**2/5
Suppose -5 = 3*n - 17. Suppose u - n*i + 14 = 0, -7 - 5 = -3*i. Factor -4*c + 6 - 21*c**u - 19*c + 8*c.
-3*(c + 1)*(7*c - 2)
Suppose -2*o = 5*o + 378. Let n = -51 - o. Factor 2 + 1 - 8*j - j**n + 5*j**2 + 1.
-(j - 2)**2*(j - 1)
Let d = 23707/55643 + 20/7949. Factor 0 - d*y**5 + 48/7*y + 12/7*y**4 - 48/7*y**2 + 0*y**3.
-3*y*(y - 2)**3*(y + 2)/7
Let x(f) be the second derivative of -f**5/20 - 5*f**4/4 - 13*f**3/3 - 391*f. Factor x(s).
-s*(s + 2)*(s + 13)
Let k(p) be the third derivative of 0*p**5 - p**2 - 1/42*p**7 + 0*p**3 + 5/6*p**4 + 0*p - 1/8*p**6 + 2. Let k(j) = 0. Calculate j.
-2, 0, 1
Let m(i) be the first derivative of -9*i**6/20 - 13*i**5/10 - 10*i**4/9 - 4*i**3/9 + 2*i**2 - 13*i + 10. Let u(l) be the second derivative of m(l). Factor u(z).
-2*(z + 1)*(9*z + 2)**2/3
Let r be 73/57 + (1768/494)/68. Suppose 1/3*b**4 - r*b**3 + 0 + 1/6*b**5 + 0*b + 0*b**2 = 0. Calculate b.
-4, 0, 2
Let h = 1005 - 1003. Let u(c) be the first derivative of -6/7*c**h - 12 + 2/21*c**3 + 0*c. Factor u(q).
2*q*(q - 6)/7
Let f(a) be the first derivative of -2*a**6 - 348*a**5/5 - 663*a**4/4 - 136*a**3 - 81*a**2/2 + 1408. Suppose f(v) = 0. What is v?
-27, -1, -1/2, 0
Solve 723*z**2 + 25*z**3 + 1296 + 4*z**4 + 567*z + 51*z**3 + 693*z + 72*z - 231*z**2 = 0 for z.
-9, -4, -3
Let n be ((-165)/(-990) + (-151)/42)*14/(-5). Solve -18/5*o**4 + 0 - n*o**3 - 24/5*o**2 + 0*o = 0 for o.
-2, -2/3, 0
Let m(t) be the first derivative of t**6/39 - 898*t**5/65 - 1353*t**4/26 - 2710*t**3/39 - 452*t**2/13 + 1994. Factor m(l).
2*l*(l - 452)*(l + 1)**3/13
Let n = -10048 - -10053. Let t(g) be the first derivative of -23 - 9/2*g**2 - g**3 + 5/4*g**4 - 1/5*g**n + 0*g. Factor t(s).
-s*(s - 3)**2*(s + 1)
Let z(n) be the second derivative of -2*n + 1/4*n**4 + 9*n**3 - 57/2*n**2 + 2. Factor z(t).
3*(t - 1)*(t + 19)
Let m = -66 + 72. Suppose 11*c - 10 = m*c. Let 8*u**c + 34 - 4 + u**3 - 38*u**2 - 5*u + 4*u**3 = 0. What is u?
-1, 1, 6
Let k(r) be the second derivative of -11 - 3*r - r**2 + 11/18*r**3 + 7/36*r**4. Factor k(s).
(s + 2)*(7*s - 3)/3
Let i be 2035/310 + (-284)/4402. What is z in 1/2*z**2 + i*z + 6 = 0?
-12, -1
Factor -2*l**3 - 680*l - 8506*l**2 + 4006*l**2 - 3*l**3 + 4150*l**2.
-5*l*(l + 2)*(l + 68)
Suppose -3*i - 31 = -4*y, 7*i + 2915 - 2860 = 5*y. Factor -60/11*t**2 - 48/11 - 2/11*t**y - 18/11*t**3 - 8*t.
-2*(t + 2)**3*(t + 3)/11
Let i(x) be the third derivative of x**5/12 - 1405*x**4/24 - 1415*x**3/3 + 707*x**2. Factor i(f).
5*(f - 283)*(f + 2)
Suppose -459 = 11*d - 30. Let s = d - -353/9. Factor 2/3*i**2 - 8/9*i + 8/9*i**3 - 8/9 + s*i**4.
2*(i - 1)*(i + 1)*(i + 2)**2/9
Suppose -839 = -242*t + 129. Factor 0*h - 1/7*h**3 - 1/7*h**t + 0 + 2/7*h**2.
-h**2*(h - 1)*(h + 2)/7
Let r(n) = -3*n**2 + 3*n + 4*n + 18 + 7*n + n**2. Let z be r(8). Suppose 5/4*g**4 + 1/2*g - z*g**3 + 0 + 1/4*g**2 = 0. What is g?
-2/5, 0, 1
Let 6/11 - 60/11*q + 54/11*q**2 = 0. What is q?
1/9, 1
Let h = -994038/7 + 142011. Let 0 + h*y + 3/7*y**2 = 0. Calculate y.
-13, 0
Let v = 309946/33 - 103308/11. Let 14/3 + 4*x - v*x**2 = 0. Calculate x.
-1, 7
Factor 4/9*r + 1/3*r**5 + 4/9 + 1/9*r**4 - 11/9*r**3 - r**2.
(r - 2)*(r + 1)**3*(3*r - 2)/9
Let b = -54 - -52. Let f be 78/24 - b/(-8). Let o - 54*o**f + 58*o**3 - o + 4*o**2 = 0. What is o?
-1, 0
Let b be ((-105)/(-63))/((-15)/(-27)). Let m(d) be the second derivative of -1/24*d**4 + 0*d**2 + 1/40*d**5 + 0 + 12*d + 1/36*d**b - 1/180*d**6. Factor m(n).
-n*(n - 1)**3/6
Let r = 14916/65 - 103372/455. Factor 2*o**2 + 2/7 - r*o.
2*(o - 1)*(7*o - 1)/7
Determine q so that -2/7*q**4 - 1420/7*q**3 + 0*q + 0 - 252050/7*q**2 = 0.
-355, 0
Let c(m) = 78*m + 106. Let n be c(-12). Let k = -827 - n. Factor -24/7*y - 12/7*y**2 - 2/7*y**k - 16/7.
-2*(y + 2)**3/7
Let r = -235 - -234. Let a(m) = -4*m**3 + 25*m**2 - 14*m - 45. Let g(q) = -q**3 - q. Let s(l) = r*a(l) - g(l). Factor s(o).
5*(o - 3)**2*(o + 1)
Let t = 1076 + 593. Factor -1669 - 5*n**3 - 10*n**2 + t + 40*n.
-5*n*(n - 2)*(n + 4)
What is t in -215*t - 816 + 1625 + 38*t - t**2 - 631 = 0?
-178, 1
Let -44/5*k**2 - 24 - 2/5*k**5 - 206/5*k + 48/5*k**3 + 4/5*k**4 = 0. What is k?
-4, -1, 3, 5
Let l(w) = 20*w**3 - 1964*w**2 - 268240*w - 786