1)/7
Let r be (8 - 87/10)*(-10)/84. Let p(g) be the third derivative of g**2 - 1/120*g**6 + 1/80*g**5 + 3/32*g**4 + 0*g + r*g**3 + 0. Factor p(f).
-(f - 2)*(f + 1)*(4*f + 1)/4
Let g(i) be the second derivative of -5*i**7/42 + 5*i**6/6 + i**5 - 25*i**4/3 + 1379*i. Find r, given that g(r) = 0.
-2, 0, 2, 5
Suppose 3*l = 2*j + 4, 0 = -21*l - 205*j + 206*j + 41. Let d(f) be the third derivative of -2*f + 0*f**4 + 0 + 1/24*f**3 - 1/240*f**5 - 7*f**l. Factor d(r).
-(r - 1)*(r + 1)/4
Let f(j) be the third derivative of 2 - 1/14*j**7 + 11/12*j**5 - 41/24*j**6 + 10/3*j**3 + 15/112*j**8 + 59*j**2 + 0*j + 25/6*j**4. Let f(m) = 0. What is m?
-2, -1/3, 1, 2
Let k(w) be the first derivative of w**5/170 - w**4/102 - 2*w**3/51 + 150*w - 67. Let z(f) be the first derivative of k(f). Determine c, given that z(c) = 0.
-1, 0, 2
Factor 466*r - 71*r + 7*r**3 + 468*r - 86*r + 576 + 268*r**2 - 3*r**3.
(r + 64)*(2*r + 3)**2
Find o, given that -75/2 - 1/4*o**2 + 35/4*o = 0.
5, 30
Factor -1680/13 - 2/13*x**2 - 142/13*x.
-2*(x + 15)*(x + 56)/13
Factor -18169563/5*f**2 + 0 + 0*f + 14766/5*f**3 - 3/5*f**4.
-3*f**2*(f - 2461)**2/5
Let f(q) be the first derivative of q**3/2 + 231*q**2/4 + 1908*q - 2140. Solve f(v) = 0 for v.
-53, -24
Factor -5*v**5 - 203539*v**3 - 5624320*v - 494*v**4 - 408 + 39739*v**3 + 5786560*v**2 + 2059*v**4 + 408.
-5*v*(v - 104)**3*(v - 1)
Let x = 25 - 8. Suppose -3*i - 5 = -x, -5*t + 5*i + 5 = 0. Factor t*d**4 - d**3 + 2*d**3 + 7*d**3 - 3*d**3.
5*d**3*(d + 1)
Suppose -4*n - 5 = 5*t, -1110 = -5*t - 5*n - 1130. Determine x, given that 34/3*x - 1/3*x**2 - t = 0.
1, 33
Let z(r) be the first derivative of -2*r**5/5 - r**4/8 - 11*r**2/2 - 38. Let a(p) be the second derivative of z(p). Solve a(d) = 0 for d.
-1/8, 0
Find z such that 2/7*z - 2/7*z**3 + 16/7 - 16/7*z**2 = 0.
-8, -1, 1
Let f be (-6678)/(-2968) - (-134)/(-88). Solve 50/11*d**4 - f - 16/11*d + 100/11*d**3 + 42/11*d**2 = 0 for d.
-1, -2/5, 2/5
Factor 2/5*m + 0 + 1/5*m**3 - 3/5*m**2.
m*(m - 2)*(m - 1)/5
Let v = 442 + -438. Let -1 - 4089*s**5 + 1 + 64*s**v + 4091*s**5 - 66*s**3 = 0. What is s?
-33, 0, 1
Factor -26 + 58/3*q - 7/3*q**3 + 5/6*q**2 + 1/6*q**4.
(q - 13)*(q - 2)**2*(q + 3)/6
Suppose f + 29 = 31. Suppose 5 = -f*n + 3*n. What is a in 2*a**2 + n - 21 - 6*a**2 - 16*a = 0?
-2
Let x(v) be the third derivative of v**6/120 - 2*v**5/15 + v**4/2 - 19*v**2 - 140*v. Factor x(u).
u*(u - 6)*(u - 2)
Let s(h) be the first derivative of -3*h**5/25 + 119*h**4/20 - 341*h**3/5 + 561*h**2/2 - 290*h - 1364. Suppose s(j) = 0. Calculate j.
2/3, 5, 29
Let v be (54/12)/(30/(-20)). Let n(y) = -4*y**2 - y. Let c(o) = 9*o**2 + 63*o - 108. Let p(b) = v*n(b) - c(b). Factor p(u).
3*(u - 18)*(u - 2)
Determine g, given that -31752/11*g - 508/11*g**4 - 32762/11*g**3 + 0 - 2/11*g**5 - 64008/11*g**2 = 0.
-126, -1, 0
Factor -34*k + 2/5*k**3 + 40 - 32/5*k**2.
2*(k - 20)*(k - 1)*(k + 5)/5
Let p = -58 + 67. Let j = 4 - p. Let t(c) = -10*c**3 + 25*c**2 + 15*c - 15. Let d(w) = w**4 + w**2 + w. Let v(s) = j*d(s) + t(s). Factor v(g).
-5*(g - 1)**2*(g + 1)*(g + 3)
Let p = -417 - -426. Let i be p/(-6)*(-192)/84. Determine m so that -i*m - 12/7 - 15/7*m**2 - 3/7*m**3 = 0.
-2, -1
Let b be (-2 + 6)*5/10. Factor -u**2 - 68 - 74*u + 46 - b*u**2 + 47.
-(u + 25)*(3*u - 1)
What is q in 48*q**3 - 2061/2*q**2 - 3/4*q**4 - 91875/4 + 8400*q = 0?
7, 25
Let d(b) be the third derivative of -5*b**8/336 - b**7/3 - 19*b**6/8 - 19*b**5/3 - 20*b**4/3 + 2763*b**2. Let d(g) = 0. What is g?
-8, -4, -1, 0
Let d(j) = -7*j**4 - 129*j**3 + 370*j**2 - 234*j + 12. Let r(k) = 75*k**4 + 1420*k**3 - 4070*k**2 + 2575*k - 130. Let b(l) = -65*d(l) - 6*r(l). Factor b(p).
5*p*(p - 24)*(p - 2)*(p - 1)
Find m, given that -9*m**3 + 7*m**4 + 42*m - 82*m**2 + 17*m**3 - 8*m**3 - 5*m**4 + 38*m**3 = 0.
-21, 0, 1
Suppose 0 = -72*j + 4*j. Suppose -5*y + 15 = j, -17*u - y = -12*u - 13. Find m such that 2/7*m**u + 4/7*m + 2/7 = 0.
-1
Let n(c) be the first derivative of 2*c**3/27 - 64*c**2/9 - 146*c + 4183. Factor n(a).
2*(a - 73)*(a + 9)/9
Let h be 1*((-216)/(-5) - 1/5). Suppose 10*z = -3 + h. Factor -z*q**3 + 18*q + 0*q - 2*q.
-4*q*(q - 2)*(q + 2)
Suppose 0 = 2*u + 2*k, 3*k - 1 = 4*u - 36. Solve 730*y - 645*y - 75 - u - 5*y**2 = 0.
1, 16
Let u(p) be the third derivative of -1/3*p**4 + 1/15*p**5 - 6*p**2 + 1/60*p**6 + 0*p - 6 - 8/3*p**3. Factor u(h).
2*(h - 2)*(h + 2)**2
What is z in -136*z**3 + 14*z**4 + 193*z + 119*z - 406*z**2 - 2*z**4 - 144*z**3 - 438*z**2 = 0?
-3, 0, 1/3, 26
Let -5*s**2 - 3344 - 424 - 96*s - 2037 + 446*s = 0. Calculate s.
27, 43
Suppose -5*i + 14*i + 42 = 78. Let u(o) be the first derivative of 0*o**3 + 0*o**i + 0*o**2 - 1/18*o**6 + 1/5*o**5 - 2 + 0*o. Factor u(c).
-c**4*(c - 3)/3
Suppose -3*u = -55 + 22. Let g = 12 - 2. Suppose -3*l**2 - 4*l**2 + 2*l**2 + u + 4 - g*l = 0. What is l?
-3, 1
Let o(h) be the second derivative of h**6/75 + h**5/50 - 2*h**4/15 - 4*h**3/15 + h + 422. Factor o(d).
2*d*(d - 2)*(d + 1)*(d + 2)/5
Let j(t) be the third derivative of t**5/240 + 11*t**4/96 - 389*t**2 - 2. Determine f, given that j(f) = 0.
-11, 0
Let k(l) be the third derivative of -l**5/20 - 343*l**4/2 - 235298*l**3 + 2412*l**2. Let k(i) = 0. What is i?
-686
Find m, given that 22/3*m - 16 - 2/3*m**2 = 0.
3, 8
Let o(v) be the first derivative of v**4 - 277*v**3 - 522*v**2 - 209*v - 510. Solve o(a) = 0.
-1, -1/4, 209
Find z such that 0 - 3/4*z**2 + 1977/4*z = 0.
0, 659
Factor -100*a**3 - 613*a**2 + 105*a**3 + 593*a**2 - 10 + 25*a.
5*(a - 2)*(a - 1)**2
Suppose 0 = -8*m - x + 3, -3*x = 3*m - 11 + 2. Let a(u) be the third derivative of 0 + m*u**3 + 1/105*u**5 + 0*u + 1/42*u**4 - 5*u**2. Factor a(j).
4*j*(j + 1)/7
Let d be 1 + (-64)/(-11) - 86/(-473). Factor -44*b - 83*b**2 + 16 + 101*b**3 + d*b**2 - 117*b**3.
-4*(b + 1)*(b + 4)*(4*b - 1)
Let s(t) = -39*t**4 + 135*t**3 + 537*t**2 + 405*t. Let y(d) = -72*d**4 + 268*d**3 + 1073*d**2 + 810*d. Let n(k) = -11*s(k) + 6*y(k). Factor n(g).
-3*g*(g - 45)*(g + 1)*(g + 3)
Factor -g**3 - 427 + 432*g - 131*g**2 + 14*g**2 + 23*g**2 - 11*g**2 - 9.
-(g - 2)**2*(g + 109)
Let -3*j**3 + 657*j**2 - 1085*j + 76*j + 663 - 296*j - 12 = 0. What is j?
1, 217
Suppose n + 34 = -3*h, -3*n + 3*h - 114 = -0. Let g be (6/16)/(n/(-74)). Factor 0 + 1/4*q**5 - 3/4*q**4 + g*q**3 + 0*q - 1/4*q**2.
q**2*(q - 1)**3/4
Factor 0 + 13/3*u**3 + 0*u + 14/3*u**2 - 1/3*u**4.
-u**2*(u - 14)*(u + 1)/3
Let b(n) be the second derivative of -8*n**7/147 + 2*n**6/15 + 22*n**5/35 - 19*n**4/21 - 4*n**3/7 + 10*n + 273. Let b(a) = 0. Calculate a.
-2, -1/4, 0, 1, 3
Let d(z) be the second derivative of z**5/40 - 17*z**4/24 - 50*z + 30. Factor d(c).
c**2*(c - 17)/2
Factor -46372*v**4 + 195264*v**3 - 46268*v**4 - 3*v**5 + 24*v**5 + 88599*v**4 - 82944*v**2.
3*v**2*(v - 96)**2*(7*v - 3)
Let x(b) be the third derivative of b**7/1785 - b**6/17 - 7793*b**2. Solve x(r) = 0.
0, 60
Let k(z) be the second derivative of -z**5/30 - z**4/9 + 73*z**3/9 - 70*z**2/3 + 441*z - 1. Suppose k(n) = 0. Calculate n.
-10, 1, 7
Let l(g) be the second derivative of 1/6*g**3 - 1/80*g**5 + 0 + 0*g**4 + 0*g**2 - 22*g. Factor l(v).
-v*(v - 2)*(v + 2)/4
Let w(m) be the second derivative of -1/54*m**4 + 0 + 0*m**2 + 1/27*m**3 + 82*m. Determine c so that w(c) = 0.
0, 1
Let d be (5 - 3)*(-1)/2. Let q(f) = -2*f**3 - f**2 + 2. Let g be q(d). Factor -v**2 - 4*v - 2*v + g*v + 0*v.
-v*(v + 3)
Let i(q) be the second derivative of -q**8/112 - q**7/70 + 3*q**6/10 + 91*q**2 - 214*q. Let k(x) be the first derivative of i(x). Let k(d) = 0. What is d?
-4, 0, 3
Let h(p) = -52*p + 3. Let c be h(0). Factor 70*y - c*y**3 + 71*y - 138*y - y**4 + y**2.
-y*(y - 1)*(y + 1)*(y + 3)
Let n = 88 - 85. Let k be n - ((-198)/(-76) + (-14)/133). Suppose 0*m**2 - 1/4 + k*m - 1/2*m**3 + 1/4*m**4 = 0. What is m?
-1, 1
Let m(c) be the first derivative of c**5/10 + 79*c**4/8 + 13*c**3 + 10651. Let m(k) = 0. What is k?
-78, -1, 0
Let m = -1 - -3. Let w = -78641 + 78644. Find p such that 0 + 4/3*p - 1/3*p**w + 0*p**m = 0.
-2, 0, 2
Factor 4808/3*f - 1444804/3 - 4/3*f**2.
-4*(f - 601)**2/3
Let h(j) = -1129*j + 264284. Let d be h(234). Factor d + 9*n**2 - 105/2*n - 1/2*n**3.
-(n - 7)**2*(n - 4)/2
Let r(g) be the third derivative of g**8/1344 + g**7/126 - 5*g**6/144 + 17*g**4/24 + g**2 - 26*g. Let k(b) be the second derivative of r(b). Factor k(y).
5*y*(y -