for f.
-11, 2
Let c be (1335/(-5340))/((2/2)/(-12)). What is j in 36/5*j + 34/5*j**4 - 38/5*j**c - 6/5*j**5 - 42/5*j**2 + 0 = 0?
-1, 0, 2/3, 3
Let b(s) = -s**3 - 1. Let v(r) = r**4 + r**3 - 5*r**2 + 3*r + 8. Suppose 5*g - 61 = -66. Let o(d) = g*v(d) - 4*b(d). Find j such that o(j) = 0.
-1, 1, 4
Let f(y) be the second derivative of y**4/12 - y**3/2 + 3*y**2/2 + 2*y. Let z be f(0). Solve 11*x**4 + z*x**4 - 33*x**3 + 6*x - 2*x**4 + 13*x**2 + 2*x**2 = 0.
-1/4, 0, 1, 2
Suppose -15 = 3*c - 8*c, -159 = 5*u + 2*c. Let h = 87 + u. Let -4*r**5 + 16*r**3 + 22*r**2 - 153*r**4 - h*r**2 + 161*r**4 = 0. Calculate r.
-2, 0, 2
Factor -11 - 519 + 1061*p + 0*p**3 + p**3 - 134*p**2 + 0*p**3 - 398*p**2.
(p - 530)*(p - 1)**2
Suppose h - 130 = 12*o - 7*o, -3*o + 3*h = 66. Let k be (-20)/(-42)*(4 + o/(-9)). Factor -16/3*r**2 - 2/3*r**4 + 8/3*r + k*r**3 + 0.
-2*r*(r - 2)**2*(r - 1)/3
Factor 0 - 696/7*v**2 - 99*v - 3/7*v**3.
-3*v*(v + 1)*(v + 231)/7
Let w(y) be the second derivative of y**5/140 - 29*y**4/28 - 59*y**3/14 - 89*y**2/14 + y + 977. Factor w(z).
(z - 89)*(z + 1)**2/7
Let v(d) be the first derivative of -d**6/12 - 5*d**5/2 + 485*d**4/8 + 13205*d**3/6 - 14440*d**2 - 877952*d + 3184. Factor v(s).
-(s - 16)**2*(s + 19)**3/2
Let f = -4662 + 4664. Determine k, given that -1/2*k**4 + 1/2*k**f + 0 + 6*k**3 - 6*k = 0.
-1, 0, 1, 12
Let v(o) be the second derivative of -o**5/40 + 13*o**4/24 + 161*o**3/12 + 147*o**2/4 + 181*o + 2. Factor v(h).
-(h - 21)*(h + 1)*(h + 7)/2
Let d(u) be the second derivative of 5*u**4/12 - 25*u**3/6 - 210*u**2 - 1565*u. Find x such that d(x) = 0.
-7, 12
Let i be (-8 + 1 + -2 + 85/9)*9. Let b(o) be the third derivative of 0*o + o**3 + 1/12*o**5 - 24*o**2 + 17/24*o**i + 0. Factor b(j).
(j + 3)*(5*j + 2)
Let p(n) = 2*n + 28. Let l be p(-10). Let l*v**3 - 13*v**2 - 1 + 93*v - v**3 + 4 - 109*v - v**3 = 0. Calculate v.
-1, 1/6, 3
Determine a so that 41877*a - 168 - 83694*a - 3*a**2 + 41988*a = 0.
1, 56
Let g(i) = i**3 - 27*i**2 + 28*i - 51. Let a be g(26). Determine t, given that -t**4 + 85*t**2 - 5*t**3 + 5 - a - 19*t - 2*t**4 - 62*t**2 = 0.
-4, 1/3, 1
Let f(n) be the third derivative of -n**7/70 + 9*n**6/5 - 277*n**5/20 + 171*n**4/4 - 68*n**3 - 8*n**2 - 40*n. What is p in f(p) = 0?
1, 2, 68
Let w(j) be the second derivative of j**4/6 + 2*j**3/3 - 99*j**2 + 5057*j. Let w(b) = 0. Calculate b.
-11, 9
Let c(z) = -13*z**2 - 842*z - 58798. Let i(h) = -135*h**2 - 8421*h - 587979. Let u(f) = 21*c(f) - 2*i(f). What is s in u(s) = 0?
-140
What is y in 33*y**3 + 108*y**2 + 345/2 - 1/2*y**4 - 313*y = 0?
-5, 1, 69
Solve 0 - 2601/8*m - 1/8*m**3 + 51/4*m**2 = 0 for m.
0, 51
Factor -52979055584/9 - 9464/3*d**2 + 4/9*d**3 + 22391824/3*d.
4*(d - 2366)**3/9
Let g(r) be the first derivative of -4*r**5/5 - 2*r**4 + 172*r**3/3 + 88*r**2 - 336*r + 2466. Suppose g(t) = 0. Calculate t.
-7, -2, 1, 6
Let t(v) be the second derivative of -39*v + 0*v**2 - 2/69*v**3 - 1/69*v**6 + 1/115*v**5 + 2 + 5/138*v**4. Let t(z) = 0. Calculate z.
-1, 0, 2/5, 1
Factor -9/7*a + 10/7*a**2 - 1/7*a**3 + 0.
-a*(a - 9)*(a - 1)/7
Let t(y) be the third derivative of -3*y**8/448 + 19*y**7/280 + 7*y**6/32 - 23*y**5/16 - 53*y**4/8 - 21*y**3/2 - 1698*y**2. What is r in t(r) = 0?
-2, -1, -2/3, 3, 7
Let c(q) be the third derivative of q**6/120 + 31*q**5/20 + 99*q**4 + 4840*q**3/3 - 273*q**2 - 2*q. Suppose c(i) = 0. Calculate i.
-44, -5
Let j(z) be the first derivative of 158 - 12/7*z**2 + 96/7*z + 3/35*z**5 - 12/7*z**3 + 3/14*z**4. Factor j(l).
3*(l - 2)**2*(l + 2)*(l + 4)/7
Let d(x) = -10*x**4 + 160*x**3 + 855*x**2 - 1020*x. Let y(i) = -5*i**4 + 80*i**3 + 427*i**2 - 508*i. Let v(o) = -2*d(o) + 5*y(o). What is w in v(w) = 0?
-5, 0, 1, 20
Suppose 4*p = -n + 3420, 4*n = 3 - 19. Factor 20*d**2 - 460*d + p*d - 444*d.
4*d*(5*d - 12)
Let l(q) be the second derivative of -34*q + 0 - 1/27*q**3 + 1/108*q**4 - 1/6*q**2. Find r such that l(r) = 0.
-1, 3
Suppose o - 9 = a, -3*a - o = 745 - 762. Suppose 8/7*h + 25/7*h**a + 1/7*h**5 + 27/7*h**3 + 0 + 11/7*h**4 = 0. Calculate h.
-8, -1, 0
Factor 136/13*f**2 + 14/13*f**3 + 310/13*f - 100/13.
2*(f + 5)**2*(7*f - 2)/13
Let j = -42471 + 976893/23. Determine s so that 48/23*s - 14/23*s**4 - 86/23*s**2 + j*s**3 - 8/23 = 0.
2/7, 1, 2
Let l(c) = 39*c + 9207. Let r be l(-236). Find o, given that -4/9*o**2 + 2/3 - 2/9*o**4 - 8/9*o + 8/9*o**r = 0.
-1, 1, 3
Let r(m) = 36*m + 504. Let v be 10 - (-1 - (-33 - -8)). Let o be r(v). Factor -2*a**2 + o - 4/5*a - 2/5*a**4 - 8/5*a**3.
-2*a*(a + 1)**2*(a + 2)/5
Let c = -18 - -16. Let p(x) = x. Let l(k) = 162*k**2 + 54*k + 8. Let n(g) = c*l(g) - 36*p(g). Factor n(j).
-4*(9*j + 2)**2
Let d(k) be the first derivative of -k**4/4 - 18*k**3 - 486*k**2 - 111*k + 68. Let j(i) be the first derivative of d(i). Factor j(u).
-3*(u + 18)**2
Let h(y) be the third derivative of -y**7/175 - 91*y**6/50 - 846*y**5/5 - 810*y**4 + 1682*y**2. Find i such that h(i) = 0.
-90, -2, 0
Suppose -10*s**4 + 25*s**3 + 4871 - 2402 - 2419 - s**2 - 95*s + 31*s**2 = 0. What is s?
-2, 1, 5/2
Let n(j) be the third derivative of j**10/151200 + j**9/20160 + j**8/10080 - 7*j**5/60 - 3*j**2 + 15*j. Let c(h) be the third derivative of n(h). Factor c(s).
s**2*(s + 1)*(s + 2)
Suppose -104 + 122 = 6*g. Factor -27*i**4 - i**3 + g*i**2 + i**3 - 34*i**3 + 10*i**3.
-3*i**2*(i + 1)*(9*i - 1)
Let d(p) be the third derivative of p**7/2100 - p**6/1200 - p**5/150 + p**4/60 + 6589*p**2. Suppose d(r) = 0. What is r?
-2, 0, 1, 2
Let p be ((-177)/(-1298))/((-126)/(-770)). Solve -5/6*n**3 - 1/6*n**4 + p*n - 5/6*n**2 + 1 = 0 for n.
-3, -2, -1, 1
Suppose q - 42 = 2*q + 3*q - 50. Factor 25/3*b**3 + 2 + 47/3*b**q + 31/3*b + b**4.
(b + 1)**2*(b + 6)*(3*b + 1)/3
Let h = -1903 + 1459. Let r be h/(-104) + 48/208. Factor 0 + r*q**3 + 27/4*q**2 + 3*q + 3/4*q**4.
3*q*(q + 1)**2*(q + 4)/4
Factor -67 + 3*x**2 + 201 + 77 + 189*x - 25.
3*(x + 1)*(x + 62)
Let m(u) be the first derivative of -5*u**6/6 + 7*u**5 - 45*u**4/4 - 35*u**3/3 + 25*u**2 - 211. Let m(l) = 0. What is l?
-1, 0, 1, 2, 5
Let u(j) = -8*j**3 - 14*j**2 - 134*j - 194. Let q(x) = -14*x**3 - 15*x**2 - 133*x - 195. Let p(i) = 2*q(i) - 3*u(i). Factor p(a).
-4*(a - 8)*(a + 2)*(a + 3)
Let k(p) = 2*p**2 - 5*p - 16. Let n be k(-2). Solve -56*a - 34 - 3 + 5 + 56*a**n - 2*a**3 - 8*a**3 = 0 for a.
-2/5, 2, 4
Let v(i) be the first derivative of i**4/12 - 49*i**3/3 + 2401*i**2/2 + 184*i + 109. Let z(n) be the first derivative of v(n). Let z(r) = 0. Calculate r.
49
Suppose 12*w = -w - 53885. Let c be 6*w/(-25) - (-1)/5. Factor 4*h**3 - 16*h**2 - c*h + 16 + 999*h - 8*h**3.
-4*(h - 1)*(h + 1)*(h + 4)
Let k(m) = -m**4 + m**3 + m**2 - 1. Let w = -3127 + 3128. Let h(y) = y**4 - 2*y**4 - 5*y**4 + 3 - y**2 + 4*y. Let p(i) = w*h(i) - 5*k(i). Factor p(o).
-(o - 1)*(o + 2)**3
Factor 6911*o - 13930*o + 192 - 2*o**2 + 6927*o.
-2*(o - 2)*(o + 48)
Factor 5186*c + 282*c**2 - 16*c**3 + 5308*c - 72*c**2 + 18*c**3 + 85750 - 3144*c.
2*(c + 35)**3
Let z = 75863 - 682705/9. What is d in 80/9*d + z*d**3 + 2*d**4 + 2/9*d**5 + 8/3 + 34/3*d**2 = 0?
-3, -2, -1
Suppose -8*s = -6*s + 40. Let j = s + 26. Factor 108*k**2 - 2*k + 86*k**3 + 32*k + 4 + j*k + 22*k**3.
4*(3*k + 1)**3
Suppose 51 - 636 = -15*u. What is y in -284*y + 191 - 38 + u + 0*y**2 - 2*y**2 - 4*y**2 = 0?
-48, 2/3
Let h = -3 - -5. Let r = -218166/35 + 43636/7. Suppose -8/5*o + r*o**h + 8/5 = 0. Calculate o.
2
Suppose 33*u + 250 = 382. Let v(z) be the first derivative of 0*z - 6 + 0*z**3 + 12/5*z**5 + 3/4*z**u + 0*z**2. Solve v(g) = 0 for g.
-1/4, 0
Let u(a) = 2*a**3 + 2*a**2 - 2*a - 5. Suppose 2*w = -4 + 8. Let h be u(w). Suppose h*i**2 - 20 + 3*i**3 - 8*i**3 + 0*i**3 + 0*i**3 = 0. Calculate i.
-1, 2
Suppose 0*h = 5*h + 10. Let p be (2 - (h + 1)) + 0. Factor -12*n**3 - p - 5*n**4 - 8*n**3 - 6 + 4 - 20*n - 30*n**2.
-5*(n + 1)**4
Let b = 956492 + -14356652/15. Let s = -618 - b. Let 0 - 2/15*y**4 + 0*y + 0*y**2 + s*y**5 - 4/15*y**3 = 0. Calculate y.
-1, 0, 2
Let d be (-2)/((-168)/(-36)) + (-888)/(-14). Suppose -92*g = -d*g. Factor y**2 + g + 5/4*y**3 - 1/4*y.
y*(y + 1)*(5*y - 1)/4
Let t be (-1 + 21/6)/(15/18). Let 8 - t*a**3 + 20*a**2 - 5*a**2 - 8 = 0. What is a?
0, 5
Let g be 14/(-70) + (0 - 26/(-5)). Let s be (-2)/(-9) - 38/(-171). Suppose -4/9*j**g - 4/9 - 4/9*j + 8/9*j**3 + 8/9*j**2 - s*j**4 = 0. What is j?
-1, 1
Let l