35. Suppose 8/5*k**4 + 24/5*k - 2/15*k**5 - 112/15 + 76/15*k**p - 82/15*k**3 = 0. What is k?
-1, 2, 7
Let j be 7/3*(-31)/(1612/29055). Let m = j - -1309. Find g, given that m*g**2 + 5 - g**3 - 9*g = 0.
5/4, 2
Let n(g) = 16893*g**2 - 5*g + 1. Let r be n(-2). Factor -67583 - 10*x + r - 5*x**2.
-5*x*(x + 2)
Let s = 3623 - 3620. Let r(t) be the second derivative of -8/5*t**4 - 2/75*t**6 + 7*t + 64/15*t**s - 32/5*t**2 + 8/25*t**5 + 0. Factor r(d).
-4*(d - 2)**4/5
Let p be 6/(-15) - (-12)/5. Suppose -2*t = 2*b - 14, p = b + b. Let t*h + 2*h**2 - 8*h**2 + 3*h**2 - 3 = 0. Calculate h.
1
Factor -529/3*i**2 - 1/3*i**3 + 530/3*i + 0.
-i*(i - 1)*(i + 530)/3
Let g = -759 + 855. Suppose 31*u - g = -34. Factor -10/3*p + 2/3*p**u + 0.
2*p*(p - 5)/3
Suppose 5*g = 7 - 12. Let k(a) = 24*a**2 - 2*a - 1. Let v be k(g). Factor 52*f - v*f**4 - 114*f**2 + 95*f**3 - 17 - 1 + 10.
-(f - 2)*(f - 1)*(5*f - 2)**2
Suppose 0 = f - 68*f + 402. Let u(l) be the third derivative of 0*l - 8*l**2 + 1/240*l**f + 0 - 1/840*l**7 + 0*l**3 - 1/48*l**4 + 1/240*l**5. Solve u(x) = 0.
-1, 0, 1, 2
Let i = -3/12698 - -14515/12698. Factor -i*k + 2/7*k**2 - 10/7.
2*(k - 5)*(k + 1)/7
Find x such that 82*x**3 - 252*x**2 + 20*x**4 - 16*x**4 + 32*x - 4*x**3 + 96*x + 42*x**3 = 0.
-32, 0, 1
Let y be (28/(-20) + 2)/(5/25). Factor 11*b + 20*b**2 - 20 + 2*b**y - 11*b - 2*b.
2*(b - 1)*(b + 1)*(b + 10)
Let a(z) be the second derivative of 2*z**6/45 - 317*z**5/60 + 233*z**4/12 - 463*z**3/18 + 77*z**2/6 + 2*z + 1469. Determine o so that a(o) = 0.
1/4, 1, 77
Let s(j) = j**3 - 8*j**2 + 8*j + 30. Let a be s(6). Factor -18 + a + 0*m**2 - m**4 + 3*m**3 - 7*m**2 - 17*m + 2*m**3 + 8*m**2.
-(m - 4)*(m - 3)*(m + 1)**2
Let c be 14846/527033 - 31946/(-142). Solve c*z + 10125/2 + 5/2*z**2 = 0.
-45
Let x(b) = -7*b**3 + 3*b**3 - 3*b**2 + 2*b**3 + 0*b**3. Let n be x(-2). Factor 2*u + 3*u + u + n*u**2 - 1 + 3.
2*(u + 1)*(2*u + 1)
Let w be (30/(-16))/(-5) + 1391/(-4280). Let c(n) be the second derivative of 16*n + 0 + 0*n**4 + 2/3*n**3 - w*n**5 + 0*n**2. Suppose c(h) = 0. What is h?
-2, 0, 2
Let n(v) be the first derivative of -v**9/6048 + v**8/1680 + 7*v**3/3 - 4*v + 93. Let w(r) be the third derivative of n(r). Factor w(y).
-y**4*(y - 2)/2
Suppose 986/15*u + 2/15 - 986/15*u**3 - 66*u**2 + 988/15*u**4 = 0. Calculate u.
-1, -1/494, 1
Let z(r) be the second derivative of -r**7/210 + 11*r**6/150 + r**5/100 - 11*r**4/60 + 695*r. Suppose z(b) = 0. Calculate b.
-1, 0, 1, 11
Factor -96*x**2 - 104 + 13 + 183*x + 3*x**3 + 1.
3*(x - 30)*(x - 1)**2
Factor 24 + t**4 + 106418*t - 6*t**2 - 106395*t - 19*t**2 - 23*t**3.
(t - 24)*(t - 1)*(t + 1)**2
Find q, given that -3/7*q**4 + 0*q + 6/7*q**2 + 0 - 3/7*q**3 = 0.
-2, 0, 1
Let t(a) be the first derivative of -95 + 1/2*a**3 + 3/4*a**2 + 3/32*a**4 + 0*a. Determine k so that t(k) = 0.
-2, 0
Let d(y) be the second derivative of -9*y**5/7 + 479*y**4/14 - 272*y**3 - 192*y**2/7 - 41*y - 34. Factor d(g).
-6*(g - 8)**2*(30*g + 1)/7
Let n(f) = -2*f**4 - f**3 - f + 1. Let l be (-3)/((-1 - -4) + 0). Let w(i) = 3*i**4 - 13*i**3 - i**2 + 15*i - 1. Let q(h) = l*n(h) - w(h). Factor q(m).
-m*(m - 14)*(m - 1)*(m + 1)
Let y = -41533 - -41535. Determine b so that 2/11*b**3 - 26/11 - y*b**2 - 50/11*b = 0.
-1, 13
Let 1344/5*s**4 + 0 - 21904/5*s + 66304/5*s**2 - 51064/5*s**3 - 9/5*s**5 = 0. What is s?
0, 2/3, 74
Factor -257762/21 - 2/21*g**2 - 1436/21*g.
-2*(g + 359)**2/21
Let r(d) be the first derivative of 4/35*d**5 + 0*d**2 - 1/14*d**4 - 1/21*d**6 + 0*d + 0*d**3 + 294. Solve r(n) = 0 for n.
0, 1
Let w(a) be the second derivative of a**5/330 + 2*a**4/33 - 3*a**3/11 + 45*a**2/2 + 50*a. Let d(x) be the first derivative of w(x). Factor d(t).
2*(t - 1)*(t + 9)/11
Let i(y) be the second derivative of y**4/3 + 386*y**3/3 + 408*y**2 + 75*y. Let g(d) = -d**2 - 154*d - 163. Let p(j) = -24*g(j) - 5*i(j). Factor p(t).
4*(t - 42)*(t + 1)
Factor -213 + 184*h**2 - 5/2*h**3 - 917/2*h.
-(h - 71)*(h - 3)*(5*h + 2)/2
Let r = -171219 + 171222. Factor -12*n**2 - 3/5*n**4 - 36/5*n - 27/5*n**r + 0.
-3*n*(n + 1)*(n + 2)*(n + 6)/5
Let i(l) = l**3 - 51*l**2 + 50*l - 4. Let c be i(50). Let f(y) = 2*y**3 + 8*y**2 - 6*y - 21. Let s be f(c). What is h in 21/5*h + 3/5*h**3 + 9/5 + s*h**2 = 0?
-3, -1
Let g(t) = t**3 - 4*t**2 + 4*t - 1. Let c be g(3). Suppose 4*j - u = u, c*j + 5*u = 0. Factor 3/5*a**5 - 6/5*a**3 + j*a**2 + 0*a**4 + 3/5*a + 0.
3*a*(a - 1)**2*(a + 1)**2/5
Suppose -3*f = -2*h + 75, -2*f = -5*h - 44 + 94. Let i be (f/(-15))/((-30)/(-24)). Let i*r + 0 - 3*r**2 = 0. Calculate r.
0, 4/9
Suppose 4*s = 5*k - 221, 22*k = 21*k + 5*s + 40. Factor 9/2*x**3 - 1/4*x**4 - k*x - 25 - 61/4*x**2.
-(x - 10)**2*(x + 1)**2/4
Let h(v) be the second derivative of -4*v**7/21 - 13*v**6/15 + 73*v**5/10 + 31*v**4/6 - 23*v**3 - 18*v**2 + 518*v. Suppose h(u) = 0. What is u?
-6, -1, -1/4, 1, 3
What is q in 332 + 34 - 5*q**4 - 41 + 95 - 210*q**3 + 15*q**2 + 640*q = 0?
-42, -1, 2
Let m be 64218/25020 + (9/(-30) - (-4)/10). Let m*u - 32/3 + 8/3*u**2 - 2/3*u**3 = 0. What is u?
-2, 2, 4
Let z(a) be the first derivative of 12/5*a**5 + 63/4*a**4 - 80 - 9*a**2 - 19*a**3 + 0*a. Find n, given that z(n) = 0.
-6, -1/4, 0, 1
Let z(d) be the third derivative of -d**5/30 - 17*d**4/12 + 6*d**3 - 1028*d**2. Solve z(m) = 0 for m.
-18, 1
Let z(u) be the first derivative of u**8/560 + 27*u**7/280 - u**6/120 - 27*u**5/40 + 130*u**3/3 - 232. Let r(k) be the third derivative of z(k). Factor r(f).
3*f*(f - 1)*(f + 1)*(f + 27)
Factor 90 - 6*t**2 - 129/2*t.
-3*(t + 12)*(4*t - 5)/2
Suppose -8*a = 25 - 49. Let d(r) be the second derivative of 1/18*r**a + 0*r**2 - 15*r - 1/36*r**4 + 0. Factor d(p).
-p*(p - 1)/3
Let p(s) be the first derivative of s**3 - 1611*s**2 + 865107*s - 3431. Factor p(t).
3*(t - 537)**2
Let j(p) = -768*p + 3843. Let q be j(5). Let z(i) be the first derivative of 2/5*i**5 + 54*i**2 - 162*i + 0*i**q - 3*i**4 - 44. Suppose z(x) = 0. What is x?
-3, 3
Let p(k) be the third derivative of k**7/17640 - k**6/1260 + k**5/210 + 61*k**4/12 - 34*k**2 + 1. Let q(z) be the second derivative of p(z). Factor q(r).
(r - 2)**2/7
Let j(m) be the second derivative of -7*m**5/450 + 41*m**4/90 + 8*m**3/15 + 120*m**2 - 183*m. Let l(d) be the first derivative of j(d). Factor l(s).
-2*(s - 12)*(7*s + 2)/15
Suppose -115*n + 228*n - 107*n = 0. Let c = -12 + 38/3. Factor 2/3*s**2 + n*s + 0 - 4/3*s**3 + c*s**4.
2*s**2*(s - 1)**2/3
Factor 67/2 - 1/10*q**2 + 31/5*q.
-(q - 67)*(q + 5)/10
Let y be (-12)/8*(4488/(-18) + -6). Let i = y - 1909/5. Find c such that i*c - 9/5 - 1/5*c**2 = 0.
3
Let y = -2/788323 + 9459898/8671553. Solve 6/11 + 4/11*d**2 - y*d**3 - 2/11*d**5 - 10/11*d**4 + 14/11*d = 0 for d.
-3, -1, 1
Let l(m) be the second derivative of m**4/48 + 5*m**3/2 - 31*m**2/2 - 263*m + 3. Factor l(s).
(s - 2)*(s + 62)/4
Let m = 16874/49 - 83929/245. Suppose 8 + 2 = 2*w. Let 0 - m*v**2 + 3/5*v**3 - 6/5*v + 3/5*v**w + 9/5*v**4 = 0. Calculate v.
-2, -1, 0, 1
Factor 200*o + 8165*o**3 + 6*o**4 - 8050*o**3 - 11*o**4 - 310*o**2.
-5*o*(o - 20)*(o - 2)*(o - 1)
Let r(t) = -712*t**2 - 935*t + 11. Let b(q) = 358*q**2 + 457*q - 5. Let k(n) = 9*b(n) + 4*r(n). Factor k(y).
(y + 1)*(374*y - 1)
Let i(f) be the first derivative of -f**4/66 - 4*f**3/33 - 81*f - 109. Let g(w) be the first derivative of i(w). Factor g(r).
-2*r*(r + 4)/11
Let w(y) be the first derivative of 3*y**4/8 - 54*y**3 - 3*y**2/4 + 162*y - 3215. Factor w(k).
3*(k - 108)*(k - 1)*(k + 1)/2
Find n, given that 6165725*n**2 - 6165661*n**2 + 26*n**3 + 2*n**4 + 40*n - 2 + 2 = 0.
-10, -2, -1, 0
Let h be (-81550)/140*(-8)/10. Let z = h - 461. What is r in -2/7*r**z - 4/7*r**4 - 2/7*r**3 + 0 + 0*r**2 + 0*r = 0?
-1, 0
Let u(h) = -h**2 - 7*h + 19. Let s be u(-9). Let q be -4*((-6)/4 + s). Factor 0*k**2 - 373*k + 3*k**q + 403*k + 75.
3*(k + 5)**2
Let a(s) = -s**3 + 2*s**2 + 1. Let p(c) = -8*c**3 + 40*c**2 - 204*c + 372. Let q(n) = -47*n + 12. Let d be q(0). Let t(y) = d*a(y) - p(y). Factor t(l).
-4*(l - 3)**2*(l + 10)
Factor 11*l**2 - 16*l**3 + 4*l**4 - 8*l**4 + 17*l**2 + 20*l - 14*l**3 + 10*l**3 - 24.
-4*(l - 1)**2*(l + 1)*(l + 6)
Suppose 4263*g + 925 = 4300*g. Let t(p) be the first derivative of -48/7*p**2 - g + 8/7*p**3 - 1/14*p**4 + 128/7*p. Find n, given that t(n) = 0.
4
Let j(o) be the third derivative of 2*o**6/45 - o**5/30 - 2*o**4/9 + o**