uppose -l*y**4 + 4/9*y + 2/9*y**2 + 2/9*y**5 - 2/3*y**3 + 0 = 0. Calculate y.
-1, 0, 1, 2
Let t(a) be the first derivative of a**6/2 - 24*a**5/5 + 63*a**4/4 - 14*a**3 - 30*a**2 + 72*a - 3286. Suppose t(q) = 0. Calculate q.
-1, 2, 3
Let a be 38/1 - (383 + -345). Factor -3/4 + 1/4*u**4 + a*u**3 - 3/2*u**2 - 2*u.
(u - 3)*(u + 1)**3/4
Let j be (15/9)/((-50)/(-90)). Let d(m) = 9*m**5 + 7*m**4 - 5*m**3 - 3*m**2 - 8*m. Let w(i) = i**5 + i**4 - i. Let r(x) = j*d(x) - 24*w(x). Factor r(s).
3*s**2*(s - 3)*(s + 1)**2
Suppose 5*c - 436 = 3*w, -4*w = 2*c - w - 187. Let v = c + -443/5. Let 4/5*a**3 - 4/5*a + 2/5 - v*a**4 + 0*a**2 = 0. What is a?
-1, 1
Let d(k) be the third derivative of -k**7/126 + k**6/72 + k**5/36 - 5*k**4/72 - 81*k**2. Factor d(c).
-5*c*(c - 1)**2*(c + 1)/3
Factor 30*m - 5364 + 5364 + 2*m**2.
2*m*(m + 15)
Let p(w) be the third derivative of -w**7/70 - w**6/5 + 3*w**5/2 - 4*w**4 + 11*w**3/2 + 6*w**2 - 38*w. Solve p(n) = 0.
-11, 1
Let i = -4145 + 111917/27. Let m(n) be the second derivative of 2/15*n**5 + 0 - i*n**3 + 8*n - 1/18*n**4 + 0*n**2 - 7/135*n**6. Suppose m(a) = 0. What is a?
-2/7, 0, 1
Suppose 2552*v - 2388*v - 1 + 1 = 0. Factor -8*d - 4/5*d**2 + v.
-4*d*(d + 10)/5
Let c = -54/89 + 13086/445. Factor -1/5*g**2 + 24/5*g - c.
-(g - 12)**2/5
Let q(p) be the first derivative of p**4/6 + 8*p**3/9 - 77*p**2/3 - 6613. What is b in q(b) = 0?
-11, 0, 7
Let i(b) = -70*b**2 - 2*b + 66. Let h(k) = -117*k**2 - 4*k + 131. Let r(n) = 6*h(n) - 10*i(n). Factor r(g).
-2*(g - 7)*(g + 9)
Suppose -4*k = 5*s - 28, -5*s - 7*k + 12*k = -10. Let i(b) = 240*b + 4569. Let r(p) = p**2 - 242*p - 4571. Let c(z) = s*i(z) + 3*r(z). Factor c(m).
3*(m + 39)**2
Let r(j) be the second derivative of -j**5/190 - 977*j**4/38 - 715408*j**3/19 + 2149156*j**2/19 - 465*j. Suppose r(m) = 0. What is m?
-1466, 1
Find n such that 325*n**3 - 60*n**2 - 653*n**3 - 4*n + 240 + 16*n + 325*n**3 = 0.
-20, -2, 2
Suppose -2*d + 139 = w - 82, -5*w = 4*d - 1081. Factor -w*i + 12*i**2 - 4*i**3 + 517*i - 264*i.
-4*i*(i - 5)*(i + 2)
Let f = -1383 + 1386. Suppose g + i - 2 = 5*i, g = -5*i + 2. Factor 0*s**2 + 2*s**2 - 2*s**2 + f - 3*s**g.
-3*(s - 1)*(s + 1)
Suppose 0 = -1284*t + 1077*t + 80 + 748. Solve -4/3*k**t + 0*k - 2/3*k**5 + 0 + 2/3*k**3 + 4/3*k**2 = 0.
-2, -1, 0, 1
Let w(c) = -16*c**2 + 32*c - 8. Let b(v) be the first derivative of -v**3/3 + v**2/2 - 2*v + 102. Let z(r) = 28*b(r) - 2*w(r). Solve z(p) = 0 for p.
-1, 10
Suppose -379*i - 716 = -998*i + 522. Determine m, given that 39*m**i + 0 - 1521/2*m - 1/2*m**3 = 0.
0, 39
Suppose -345 = -41*o - 345. Let p(m) be the first derivative of -13 - 4*m**3 + 6*m**4 + 0*m**2 + o*m + 1/2*m**6 - 3*m**5. Factor p(f).
3*f**2*(f - 2)**2*(f - 1)
Let u(k) = -5*k**2 + 66*k + 326. Let j be u(17). Find p, given that 0*p**2 - 2/13*p**j - 2/13*p**5 + 0 + 0*p + 4/13*p**4 = 0.
0, 1
Suppose 0 = 25*i - 11279 + 2879. Let y = 675/2 - i. Factor -r**2 - 3/2*r - 1/4*r**4 + y*r**3 + 5/4.
-(r - 5)*(r - 1)**2*(r + 1)/4
Let w(s) = 4*s**2 + s - 4. Let a be w(-2). Suppose -8 = a*o - 14*o. Solve 2*y**o + 8*y + 9*y + 32 - y = 0 for y.
-4
Suppose -2*m**3 - 77*m - 100*m**2 - 644*m - 23*m + 6*m**3 = 0. Calculate m.
-6, 0, 31
Let i(o) = -o - 3. Let y be i(6). Let l(j) = -3*j - 12. Let a be l(y). Solve a*w**3 - 5*w**3 - 26*w**4 - 6*w**4 + 7*w**4 = 0 for w.
0, 2/5
Let i(z) = -21*z - 252. Let w(r) = -3*r - 37. Let y(l) = -4*i(l) + 27*w(l). Let b be y(-3). Factor -4/11*k**2 + b + 0*k + 0*k**4 + 6/11*k**3 - 2/11*k**5.
-2*k**2*(k - 1)**2*(k + 2)/11
Let j(o) be the first derivative of 7*o**3/4 - 87*o**2/4 + 12*o + 428. Factor j(t).
3*(t - 8)*(7*t - 2)/4
Let q(s) = -6*s**3 + 8*s**2 - 2*s. Suppose 0*v + 4*v = 76. Suppose 21 = -z + v. Let i(r) = 7*r**3 - 9*r**2 + 2*r. Let h(m) = z*q(m) - 3*i(m). Factor h(a).
-a*(a - 1)*(9*a - 2)
Suppose 0 = 3*v - 26 - 10. Let d be (-2)/(40/v + -4). Find l, given that -2*l**d - l**3 + 17*l**2 + 2*l**2 - 48 + 2*l**2 - 24*l = 0.
-1, 4
Let b(n) = -3*n**2 - n + 6. Let v(f) = 28*f**2 + 242*f + 174. Let i(u) = -10*b(u) - v(u). Suppose i(k) = 0. Calculate k.
-1, 117
Determine s so that -227*s**2 - 277*s + 16*s**3 - 13*s + 14*s**3 - 35*s**3 - 68*s**2 = 0.
-58, -1, 0
Factor -1/5*g**3 - 22/5*g - 13/5*g**2 + 0.
-g*(g + 2)*(g + 11)/5
Let d be (-1 - (-11)/6)*26/13. Let l(u) be the first derivative of 16*u - d*u**3 - 23 + 19*u**2. Factor l(n).
-(n - 8)*(5*n + 2)
Let n = 50 - -6. Let w be 47/15 + (n/60)/(-7). Let v**3 - 6*v + 10*v**w - 21*v**2 - 5*v**3 + 21*v**4 = 0. Calculate v.
-1, -2/7, 0, 1
Let o(b) be the second derivative of -b**7/84 - 19*b**6/60 + 9*b**5/4 - 25*b**4/12 - 89*b**3/12 + 69*b**2/4 - 2877*b. Solve o(a) = 0 for a.
-23, -1, 1, 3
Factor 1/2*g**2 - 1/2 + 0*g.
(g - 1)*(g + 1)/2
Solve -2/3*l**4 - 52/3*l**3 - 312 - 1112/3*l - 418/3*l**2 = 0.
-13, -9, -2
Let a(p) be the third derivative of -p**10/831600 - p**9/110880 - p**5/20 + 17*p**3/6 + 197*p**2. Let b(k) be the third derivative of a(k). Factor b(v).
-2*v**3*(v + 3)/11
Let x(d) be the third derivative of 2*d**7/105 + 2*d**6/5 + 41*d**5/15 + 7*d**4 + 467*d**2 + 3*d. Factor x(q).
4*q*(q + 2)*(q + 3)*(q + 7)
Suppose 4*f + 2945*x = 2941*x, 2*x = 5*f - 28. Factor 1/6*b + 0*b**3 + 1/3*b**f + 0 - 1/6*b**5 - 1/3*b**2.
-b*(b - 1)**3*(b + 1)/6
Let b(u) = 4*u**4 + 2*u**3 - 6*u**2 - 9*u. Let n(l) = -l**4 + l**2 + 2*l. Let m(k) = -2*b(k) - 9*n(k). Solve m(f) = 0.
0, 1, 3
Let k be (5 + 3 - 5) + 8/(-2). Let r be (k/(-3))/((-4)/(-36)). Factor 2*d - 10*d + 7 + 5 - 4*d**2 - 2*d + 2*d**r.
2*(d - 3)*(d - 1)*(d + 2)
Suppose 3*u + 53 = 5*g, -3*g + u + 43 = 2*u. Suppose 3*x + 5 = 5*i, 3 = -2*x + g. Factor -16 + 5*j - j - i*j**2 + 12*j.
-4*(j - 2)**2
Let c(j) be the second derivative of -506*j**3 - 21*j**5 + 3/10*j**6 - 1587/2*j**2 + 46 + j + 839/2*j**4. Solve c(r) = 0 for r.
-1/3, 1, 23
Let y(r) be the first derivative of -7*r**6/120 + 9*r**5/40 - r**4/4 - 17*r**3/3 + 56. Let f(k) be the third derivative of y(k). Factor f(u).
-3*(u - 1)*(7*u - 2)
Let w(u) be the second derivative of u**6/10 + 3*u**5/4 - 33*u**4/4 - 77*u**3/2 - 60*u**2 - 7*u - 253. Solve w(p) = 0 for p.
-8, -1, 5
Let z(v) = 2*v**2 + v + 1. Let b(f) = -f**5 - 11*f**4 + 3*f**3 + 307*f**2 + 500*f + 10. Let k(x) = -b(x) + 10*z(x). What is q in k(q) = 0?
-7, -2, 0, 5
Let i(f) be the second derivative of 15*f**7/14 + 14*f**6/5 + 9*f**5/20 - 9*f**4/2 - 4*f**3 - 18*f + 1. Let i(z) = 0. Calculate z.
-1, -2/3, 0, 4/5
Let c(t) be the second derivative of t**8/2240 + t**7/280 - t**6/40 - t**5/5 + 8*t**4/3 + 9*t. Let j(g) be the third derivative of c(g). What is y in j(y) = 0?
-4, -1, 2
Suppose 9 = -13*t + 35. Let -4*o**2 + t*o**4 - 86*o**2 - 7*o**4 + 30*o**3 + 50*o**2 = 0. What is o?
0, 2, 4
Let k(i) = 2*i**3 + i**2 + i. Let a be (-4)/7 + (-850)/(-238). Let d(u) = -3*u**3 - 8*u**2 - 7*u. Let l(s) = a*k(s) + 3*d(s). Solve l(n) = 0 for n.
-6, -1, 0
Let x(h) be the first derivative of -3*h**4/10 + 2*h**3 + 66*h**2/5 + 96*h/5 - 3378. Factor x(d).
-6*(d - 8)*(d + 1)*(d + 2)/5
Suppose -548*k**3 + 176*k**2 - 644 + 178*k + 203 + 6*k**4 + 370*k + 259 = 0. Calculate k.
-1, 1/3, 1, 91
Let u(b) be the second derivative of -b**5/90 + b**4/12 + 4*b**3/9 + 151*b**2/2 + 2*b - 8. Let n(q) be the first derivative of u(q). Factor n(z).
-2*(z - 4)*(z + 1)/3
Let d(c) be the second derivative of -9*c**5/5 + 992*c**4/3 - 440*c**3/3 + 9225*c. Factor d(y).
-4*y*(y - 110)*(9*y - 2)
Suppose 90*z**2 + 213*z**3 - 12*z + 57/2*z**5 + 0 + 279/2*z**4 = 0. What is z?
-2, -1, 0, 2/19
Let q = -5/38951 + 77917/116853. Factor 0*l**2 + q + 4/3*l - 2/3*l**4 - 4/3*l**3.
-2*(l - 1)*(l + 1)**3/3
Let c be (60/(-36))/(4/(-12)*5). Suppose 0 = -24*x + 22*x + 6. Factor c + 15*z + x*z**2 - z - 19 + z.
3*(z - 1)*(z + 6)
Suppose 25*b = 33*b - 48. Suppose -3*n = 2*r - r + 6, -r + b = -n. Suppose -27/8*d**5 - 27/4*d**2 + 0*d**4 - 9/2*d + 93/8*d**r + 3 = 0. What is d?
-2, -2/3, 2/3, 1
Suppose u - 21*y = -15*y - 16, 0 = 3*u + y - 85. Factor -16/3*z**4 - 1/3*z**5 - 112/3*z**2 - u*z**3 - 49/3*z + 0.
-z*(z + 1)**2*(z + 7)**2/3
Suppose u - 14 = -5. Suppose 0 + 18 = u*c. Suppose 21*j**2 - 9 - 12*j - j**c + 1 = 0. What is j?
-2/5, 1
Let f(y) be the second derivative of -y**6/120 + 119*y**5/80 - 117*y**4/16 + 349*y**3/24 - 29*y**2/2 + 169*y. Factor f(q).
-(q - 116)*(q - 1)**3/4
Let i be 25/(-20)*(-5 - (-8 + 7)). Let w(l) be the