3*b**5 - 58829 + 56*b**5.
2*(b - 7)*(b + 2)*(b + 17)**3
Let g(w) = 3*w**4 + 6848*w**3 + 20554*w**2 + 20534*w + 6839. Let h(t) = -t**3 + t**2 - t - 1. Let b(o) = g(o) - 7*h(o). Determine x, given that b(x) = 0.
-2282, -1
Let h be 110/(-165) - (494/171*3/(-7) + -4). Suppose -20/7 - 4/7*k**4 + h*k**3 + 64/7*k - 72/7*k**2 = 0. Calculate k.
1, 5
Let s(f) be the third derivative of f**6/60 + f**5/6 - 83*f**4/6 + 160*f**3/3 - 950*f**2. Find c, given that s(c) = 0.
-16, 1, 10
Let y(i) = -i**3 + 245*i**2 + 4643*i + 27658. Let f(z) = -2*z**3 + 368*z**2 + 6968*z + 41488. Let j(h) = -5*f(h) + 8*y(h). Factor j(u).
2*(u + 12)*(u + 24)**2
Let k(a) be the third derivative of -1/4*a**3 + 1/448*a**8 + 1/40*a**5 + 0*a**7 - 1/40*a**6 + 3/32*a**4 + 2*a**2 - 20*a + 0. Suppose k(o) = 0. What is o?
-2, -1, 1
Determine a, given that 4743*a + 483 - 911 - 730 + a**2 + 2*a**2 - 3588*a = 0.
-386, 1
Let k = 9521426/11 - 866643. Let h = 1059 + k. Factor 0*x**2 + 2/11*x + 0 - h*x**3.
-2*x*(x - 1)*(x + 1)/11
Let d(m) be the second derivative of -m**4/60 - 41*m**3/3 - 408*m**2/5 - 4452*m + 1. Solve d(u) = 0.
-408, -2
Let d(u) = u**3 + u**2 + u. Let t(o) = -271 - 4*o**3 - 5*o + 8*o**2 + 271. Let v(b) = 5*d(b) + t(b). Factor v(w).
w**2*(w + 13)
Let m(n) be the second derivative of -n**7/28 + n**6/4 - 5*n**4/2 + 4*n**3 - 1417*n. Let m(x) = 0. What is x?
-2, 0, 1, 2, 4
Let g(u) be the first derivative of -27270901*u**5/5 - 26727295*u**4/4 + 179998*u**3 - 1802*u**2 + 8*u + 1540. Let g(v) = 0. Calculate v.
-1, 2/301
Let m(z) be the first derivative of z**6/42 - z**5/5 - 15*z**4/28 + 55*z**3/21 + z**2 - 48*z/7 - 7025. Suppose m(v) = 0. What is v?
-3, -1, 1, 2, 8
Let y = 2319 + -1559. Let k = 9882/13 - y. Determine a, given that -22/13*a - 12/13*a**3 - 28/13*a**2 + 2/13*a**4 - 6/13 + k*a**5 = 0.
-1, 3
Let b = -3/281851 + 6764457/3100361. Determine f so that 6/11 + 20/11*f + 12/11*f**3 + 2/11*f**4 + b*f**2 = 0.
-3, -1
Let w(j) be the second derivative of j**4/54 - 101*j**3/27 + 388*j**2/9 - 28*j - 62. Factor w(y).
2*(y - 97)*(y - 4)/9
Let k(q) be the first derivative of -q**5/80 + 5*q**4/32 + 3*q**3/4 + 239*q**2/2 + 74. Let n(c) be the second derivative of k(c). Factor n(w).
-3*(w - 6)*(w + 1)/4
Let f(h) = -3*h**3 + 3*h**2 - 28*h - 232. Let l(p) = p**3 + p**2 + p + 13. Let o(g) = -f(g) - 4*l(g). Factor o(z).
-(z - 5)*(z + 6)**2
Let f(t) be the third derivative of t**7/13860 - t**6/1320 + t**4/12 - 29*t**2. Let u(r) be the second derivative of f(r). Let u(n) = 0. Calculate n.
0, 3
Let x(i) be the third derivative of -i**6/60 - 191*i**5/5 - 1145*i**4/12 + 2849*i**2. Let x(p) = 0. What is p?
-1145, -1, 0
Let d(n) be the third derivative of 0*n**3 - 1/60*n**6 - 31*n**2 - 1/30*n**5 + 0*n + 0*n**4 + 0. What is c in d(c) = 0?
-1, 0
Factor -2/9*r**3 - 48 - 98/9*r**2 + 532/9*r.
-2*(r - 4)*(r - 1)*(r + 54)/9
Let h(l) = -2*l**3 + 8*l**2 - 34*l + 4. Let s(j) = 3*j**3 - 8*j**2 + 40*j - 5. Let b = 532 + -537. Let v(x) = b*h(x) - 4*s(x). Factor v(u).
-2*u*(u - 1)*(u + 5)
Determine k so that 102/11*k**2 + 72/11*k**3 - 180/11*k + 0 + 6/11*k**4 = 0.
-10, -3, 0, 1
Let r(g) be the second derivative of -g**5/50 + 87*g**4/10 - 5633*g**3/5 - 17161*g**2/5 + 3*g - 553. Factor r(w).
-2*(w - 131)**2*(w + 1)/5
Let u(f) be the first derivative of -5*f**3/3 + 2175*f**2 - 946125*f + 1135. What is w in u(w) = 0?
435
Let l be (2/(8/6))/(126/420). Let -3*b**2 - l*b**2 + 6*b**2 - 12*b - 18 = 0. What is b?
-3
Let c be ((-9)/132 + 0)/(11100/(-29600)). Solve 24/11 - 10/11*l - c*l**3 - 12/11*l**2 = 0.
-4, -3, 1
Let z = 131 - 129. Factor z*d**2 + 50*d - 4*d**2 + 2 - 57*d + 3 + 4*d**2.
(d - 1)*(2*d - 5)
Suppose -2*i - 18 = -4*j, 0*i + 15 = 3*j - 2*i. Suppose -j = l - 5. What is n in 33*n**l + 0 - 33*n**4 - 310*n**3 + 4 + 9*n**5 + 329*n**3 - 24*n = 0?
-1, 1/3, 2
Factor 72 + 40*o**3 - 34*o**2 + 12*o - 19*o**3 + o**5 + 4*o**4 - o**3 - 27*o**3.
(o - 2)**2*(o + 2)*(o + 3)**2
Let u(h) = 2*h**2 - 42606*h - 255705. Let p be u(-6). Let 2/9*y**p - 2/9*y + 8/9*y**2 - 8/9 = 0. What is y?
-4, -1, 1
Let g(w) be the first derivative of 4*w**3/3 + 12*w**2 - 64*w + 304. Suppose g(r) = 0. Calculate r.
-8, 2
Let p(n) be the first derivative of n**3/9 - 87*n**2/2 - 264*n + 1718. Factor p(o).
(o - 264)*(o + 3)/3
Let j = -266313 + 266321. Let -j*y + 26/3*y**2 + 0 - 2/3*y**3 = 0. Calculate y.
0, 1, 12
Let t be 205 + -201 + (1 - 0). Let s(l) be the third derivative of -5/8*l**4 + 5/6*l**3 + 0 - 1/24*l**6 + 1/4*l**t + 0*l - 5*l**2. Factor s(n).
-5*(n - 1)**3
Let p(i) be the first derivative of 7*i**5 + 535*i**4/4 + 785*i**3 + 2345*i**2/2 + 490*i + 4536. Factor p(q).
5*(q + 1)*(q + 7)**2*(7*q + 2)
Factor 0 - 3*t**2 - 1/5*t**3 + 324/5*t.
-t*(t - 12)*(t + 27)/5
Let d(m) be the first derivative of m**6/12 - 32*m**5/5 + 271*m**4/2 - 929*m**3/3 - 1085*m**2/4 + 961*m - 3614. Determine p, given that d(p) = 0.
-1, 1, 2, 31
Let l = 1/1363 + 2701/34075. Let c(q) be the second derivative of 5*q - 1/2*q**4 + 8/15*q**3 + l*q**5 + 3/5*q**2 + 0. Let c(d) = 0. Calculate d.
-1/4, 1, 3
Let k(i) be the first derivative of -57 + 8/9*i - 64/9*i**2 + 190/9*i**3 - 25/2*i**4. Factor k(a).
-2*(a - 1)*(15*a - 2)**2/9
Factor -43627081040*k**2 - 71286650419360*k - 13349780*k**3 - 1/8*k**5 - 4085/2*k**4 - 46592954714093696.
-(k + 3268)**5/8
Let d(p) be the second derivative of 784/15*p**2 + 59/30*p**4 + 18 + 1/225*p**6 + 7*p - 616/45*p**3 - 11/75*p**5. Find n such that d(n) = 0.
4, 7
Let g be (7 + -2)/(-2 - -3). Solve 25*b**2 + 16 - b**5 + 71*b**4 - 40*b + 67*b**4 - 143*b**4 + g*b**3 = 0.
-4, 1
Let n(q) be the first derivative of -9/5*q - 81/10*q**4 + 81/25*q**5 - 39/5*q**2 - 72/5*q**3 - 2. What is w in n(w) = 0?
-1/3, 3
Suppose -q = 3*m - 635 + 651, -q - m = 2. Let w(z) be the second derivative of -25/12*z**4 + 1/4*z**q - 25*z - 65/6*z**3 - 35/2*z**2 + 0. Factor w(y).
5*(y - 7)*(y + 1)**2
Let h = -1378/89 + 2845/178. Factor h*w**3 - 13/3*w - 4/3 - 5/6*w**2.
(w - 4)*(w + 2)*(3*w + 1)/6
Let b be 5/(-10)*2702/(-7105). Let h = 2/203 + b. Determine g so that 1/5 + 0*g - h*g**2 = 0.
-1, 1
Let l be (-413)/(-708)*(-2)/(-7). Let c(t) be the first derivative of -l*t**3 + 3/2*t**2 - 5/2*t - 46. Determine r, given that c(r) = 0.
1, 5
Let b(y) = 5*y**2 - 8*y - 9. Let f(m) = -4*m**2 + 7*m + 7. Let q(n) = -3*n**2 - 112*n - 31. Let v be q(-37). Let i(x) = v*f(x) + 5*b(x). Factor i(w).
(w - 1)*(w + 3)
Let j(x) be the third derivative of -x**7/735 + x**6/30 - 2*x**5/35 - x**4/6 + 13*x**3/21 + 4262*x**2. Suppose j(b) = 0. What is b?
-1, 1, 13
Let y = 359 + -354. Factor -4*k**4 + 124*k**3 - 8*k**3 - 6*k**5 - 385 - 1343 - 11*k**y + 13*k**5 + 180*k**2 - 864*k.
-4*(k - 4)**2*(k + 3)**3
Let q be (-162)/8 - 6/8. Let f = -19 - q. Let -8*a**f - 3*a - 2*a**5 + 3*a - 85*a**4 + 91*a**4 = 0. Calculate a.
-1, 0, 2
Suppose 5*k - 49 = 1564*p - 1561*p, k - 2*p = 28. Solve 0 - 2/3*z**4 + 2/3*z**3 + 0*z + 2/9*z**5 - 2/9*z**k = 0.
0, 1
Let d(z) be the first derivative of 3*z**4/8 + 25*z**3 + 141*z**2/4 - 147*z + 62. What is p in d(p) = 0?
-49, -2, 1
Let h be -3 - (-13)/4 - 3724/112. Let d be (h/6)/(-11)*0. Factor 0 + d*i**2 + 4/3*i - 4/3*i**3.
-4*i*(i - 1)*(i + 1)/3
Suppose -28 = -3*m - 13. Let f be ((-3899)/5013)/(14/(-8)). Suppose -1/3*t**3 - 1/9*t + 0 + 5/9*t**2 - 5/9*t**4 + f*t**m = 0. What is t?
-1, 0, 1/4, 1
Let i(r) = -2*r**3 - 287*r**2 + 1028*r - 146. Let v be i(-147). Factor -h**2 - v + 26/5*h.
-(h - 5)*(5*h - 1)/5
Let r(g) = -36*g**2 - 112*g - 36. Let s(n) = -n**3 + 107*n**2 + 327*n + 109. Let k(l) = 11*r(l) + 4*s(l). What is t in k(t) = 0?
-1, 10
Let g(b) = 13*b**3 + 11*b**2 - 10*b - 14. Let n(t) = -31*t**3 - 22*t**2 + 21*t + 27. Let r(v) = 5*g(v) + 2*n(v). Suppose r(h) = 0. Calculate h.
-4, -1, 4/3
Let f = -32 + 34. Factor -f*s**2 - 2*s**2 - 3 - 12 - 9 - 20*s.
-4*(s + 2)*(s + 3)
Let k(u) be the third derivative of 0 + 204*u**2 - 7/5*u**5 - 4/35*u**7 + 0*u**3 + 23/40*u**6 + 3/2*u**4 + 1/112*u**8 + 0*u. Factor k(v).
3*v*(v - 3)*(v - 2)**2*(v - 1)
Let 821*h + 1077*h - 3*h**2 - 2115 - 661*h + 881*h = 0. Calculate h.
1, 705
Let r(z) = z + 7*z + z - 8*z + 13*z**2 - 1 - 11*z**2. Let l(o) = -17*o**2 - 4*o + 20. Let t(f) = -3*l(f) - 24*r(f). Suppose t(u) = 0. What is u?
-2, 6
Let g = -131323 + 1181917/9. Factor -16/9 - g*j**3 + 8/9*j + 4/3*j**2 + 2/9*j**4.
2*(j - 2)**3*(j + 1)/9
Suppose -73/3*j - 107/3*j**2 