*d**2 - d**2 + 450 - 71*d = 0.
-2, 75
Let p = -4 - 2. Let k be (-5)/((-21)/p - 4). Factor -5*m**5 + k*m**3 - 11*m**3 - 24*m**3 - 10*m**2 - 7*m**4 - 13*m**4.
-5*m**2*(m + 1)**2*(m + 2)
Let o(n) be the second derivative of n**8/2240 - n**6/480 - 28*n**3/3 + 4*n + 9. Let b(s) be the second derivative of o(s). Solve b(p) = 0.
-1, 0, 1
Solve -2563201/5*a + 0 - 1/5*a**3 + 3202/5*a**2 = 0 for a.
0, 1601
Let f = -231185/11 - -21017. Factor -90/11*p + 24/11*p**2 + 100/11 - f*p**3.
-2*(p - 5)**2*(p - 2)/11
Suppose -1712*p - 4068*p**2 + 157 + 4611*p**3 - 100*p**4 - 2508*p**2 + 1109*p**3 - 1949 - 6320*p = 0. What is p?
-2/5, 2, 56
Let l(r) be the second derivative of -5*r**4/16 + 1677*r**3/8 - 1005*r**2/4 - 467*r. Solve l(d) = 0 for d.
2/5, 335
Factor -552/17*n + 2/17*n**2 + 38088/17.
2*(n - 138)**2/17
Factor 9*u**2 - 2152*u - 19*u**2 - 42 - 8*u**3 + 2328*u - 20*u**2.
-2*(u - 3)*(u + 7)*(4*u - 1)
Let m(f) be the third derivative of f**6/1080 + f**5/45 + 47*f**4/216 + 10*f**3/9 + 2*f**2 + 173*f - 6. Let m(w) = 0. What is w?
-5, -4, -3
Let d(j) be the first derivative of -j**5/180 - 7*j**4/36 - 4*j**3/3 - 32*j**2 + 21. Let m(y) be the second derivative of d(y). Factor m(q).
-(q + 2)*(q + 12)/3
Let j(g) = g**2 - 2*g + 13. Let t(d) = -3*d**3 + 34561*d**2 - 132710402*d + 169869312013. Let h(k) = j(k) - t(k). Suppose h(b) = 0. What is b?
3840
Let k(a) be the first derivative of a**6/75 + 2*a**5/25 + a**4/15 - 4*a**3/15 - 3*a**2/5 + 42*a + 6. Let s(f) be the first derivative of k(f). Factor s(h).
2*(h - 1)*(h + 1)**2*(h + 3)/5
Factor 3*a**2 - 149 + 149 - 16138*a + 21820*a.
3*a*(a + 1894)
Let z(x) be the third derivative of 0 - 71/10*x**5 - 143/30*x**6 - 121/105*x**7 - 13/3*x**4 - 4*x - 2*x**2 - 4/3*x**3. Factor z(s).
-2*(s + 1)**2*(11*s + 2)**2
Solve -797*k**2 + 819*k + 497/4*k**3 - 9/4*k**4 - 144 = 0 for k.
2/9, 1, 6, 48
Let g(z) be the second derivative of z**6/90 - 9*z**5/20 + 37*z**4/18 - 8*z**3/3 - 1663*z + 1. Factor g(k).
k*(k - 24)*(k - 2)*(k - 1)/3
Factor -4999442*d + 2*d**3 + 4999598*d - 782*d**2 + 8*d**3.
2*d*(d - 78)*(5*d - 1)
Factor -5*r**3 + 0*r - 13/5*r**4 + 2/5*r**2 + 0.
-r**2*(r + 2)*(13*r - 1)/5
Let g(o) = 5*o**2 - 565*o + 1122. Let b(c) = 4*c**2 - 566*c + 1124. Let k(t) = 6*b(t) - 4*g(t). Factor k(d).
4*(d - 282)*(d - 2)
Let h(f) be the third derivative of -f**5/45 + 220*f**4/9 - 584*f**3/3 + 17*f**2 + 2*f + 94. Factor h(c).
-4*(c - 438)*(c - 2)/3
Let n be (312/15 - (4 - -6)) + 4. Suppose n*b + 66/5*b**2 + 28/5 + 2/5*b**4 + 22/5*b**3 = 0. What is b?
-7, -2, -1
Let u(i) be the first derivative of -8*i - 1/5*i**2 + 1/5*i**4 - 8/5*i**5 - 1/15*i**6 - 51 + 16/3*i**3. Let u(t) = 0. Calculate t.
-20, -1, 1
Let d(t) be the first derivative of -5*t**4/4 - 110*t**3/3 + 235*t**2/2 - 120*t - 347. Factor d(x).
-5*(x - 1)**2*(x + 24)
Let l(p) be the second derivative of p**4/4 - 5*p**3/2 - 36*p**2 + 139*p. Factor l(a).
3*(a - 8)*(a + 3)
Let m(a) be the third derivative of -a**6/160 - 17*a**5/80 - 55*a**4/32 - 39*a**3/8 - 7557*a**2. What is r in m(r) = 0?
-13, -3, -1
Let g(f) be the third derivative of f**7/840 + 29*f**6/480 - f**5/80 - 85*f**4/96 + 29*f**3/12 + 592*f**2. Determine p so that g(p) = 0.
-29, -2, 1
Let a(y) be the second derivative of -2*y**7/3 + 16*y**6/3 + 208*y**5/5 - 658*y**4/3 - 1606*y**3 - 1260*y**2 - 1239*y. Let a(l) = 0. Calculate l.
-3, -2/7, 5, 7
Suppose 4*g = -5*l - 5, l + 4*g = -3*l - 8. Let r(n) be the second derivative of -n**l - 1/6*n**4 - 2*n**2 + 0 - 6*n. What is w in r(w) = 0?
-2, -1
Let l(g) be the third derivative of -g**8/336 + 2*g**7/15 + g**6/20 - 8*g**5/3 - 221*g**4/24 - 14*g**3 + 825*g**2. Solve l(s) = 0 for s.
-1, 3, 28
Factor -35/12*b + 1/12*b**2 + 31/3.
(b - 31)*(b - 4)/12
Let i = -710/7 - -2158/21. Let g(o) be the third derivative of 1/12*o**6 - 5/12*o**4 + 19*o**2 - i*o**3 + 0 + 1/105*o**7 + 0*o + 1/10*o**5. Factor g(k).
2*(k - 1)*(k + 1)**2*(k + 4)
Suppose 0 = 25*d - 97*d - 29*d + 202. Suppose 2 + 12/5*f + 2/5*f**d = 0. Calculate f.
-5, -1
Solve 66557/3*v**2 + 1/3*v**4 + 65365*v + 43350 + 171*v**3 = 0 for v.
-255, -2, -1
Suppose -t - 2 = -4*u + 3*u, -2 = u - 2*t. Let y be (-9)/u*2 + (-115)/(-35). Let -y*c**5 - 8/7*c**2 + 6/7*c**4 + 0*c + 0*c**3 + 0 = 0. Calculate c.
-1, 0, 2
Let o(w) = 221*w**2 + 5*w - 5. Let l be o(1). Suppose 225*k = l*k + 8. Find v such that 0 + 4/3*v - 1/3*v**k = 0.
0, 4
Solve 7948/5*k**3 + 7932/5*k**2 + 2628/5*k + 2652/5*k**4 - 8/5 = 0 for k.
-1, 2/663
Let x(k) = k**5 - 2*k**3 + 12*k**2 - 5*k - 6. Suppose 4*z = -12*z - 16. Let i(a) = 2*a**2 - a - 1. Let h(o) = z*x(o) + 6*i(o). Find v, given that h(v) = 0.
-1, 0, 1
Let z(k) be the first derivative of -k**8/12600 + k**7/6300 + 2*k**6/675 - k**5/75 - 2*k**3 - k**2 + 58. Let y(v) be the third derivative of z(v). Factor y(t).
-2*t*(t - 2)**2*(t + 3)/15
Factor 0 + 0*l**3 + 2/19*l**4 - 112/19*l - 6*l**2.
2*l*(l - 8)*(l + 1)*(l + 7)/19
Factor 39200/9 + 2/9*c**3 + 16*c**2 - 1736/3*c.
2*(c - 14)**2*(c + 100)/9
Factor -4/3*n**3 + 196/3*n + 16*n**2 - 80.
-4*(n - 15)*(n - 1)*(n + 4)/3
Let u(c) be the first derivative of 22801*c**3/12 - 1359*c**2/4 + 81*c/4 - 8734. Factor u(x).
(151*x - 9)**2/4
Suppose 30 = 2*r - 22. Let y = 28 - r. Factor 8*z - 2*z**y + 4 + 8*z**2 + 0*z**2 - 2*z**2.
4*(z + 1)**2
Factor 3*u**2 - 65*u + 2540 - 5094 + 2486.
(u + 1)*(3*u - 68)
Let u(y) be the third derivative of 0 - 11/42*y**4 + 0*y - 172*y**2 - 1/105*y**5 + 8/7*y**3. Factor u(x).
-4*(x - 1)*(x + 12)/7
Let z be (-200)/(-65)*(-18048)/(-1880). Suppose -2/13*v**3 - z - 224/13*v - 38/13*v**2 = 0. Calculate v.
-8, -3
Suppose -38*g + 34*g + 8 = 0. Determine t, given that -7*t**4 + 291*t - 25*t**g - 88*t**4 - 301*t + 105*t**3 + 25*t**5 = 0.
-1/5, 0, 1, 2
Factor 44/7*h**2 - 48/7 + 64/7*h.
4*(h + 2)*(11*h - 6)/7
Suppose -3*q = -173 - 1711. Let s = 632 - q. Let -2/5*n**s + 0*n**3 + 0*n**2 + 0*n + 0 - 2/5*n**5 = 0. Calculate n.
-1, 0
Let i(q) be the second derivative of 256/3*q**4 + 0*q**2 + 1/90*q**6 + 280*q - 16384/9*q**3 - 8/5*q**5 + 0. Find f, given that i(f) = 0.
0, 32
Let j be (-8 - 612/(-85))/(-6). Factor 2/5*q**2 + 4/15*q**3 + 0 - j*q**4 + 0*q.
-2*q**2*(q - 3)*(q + 1)/15
Suppose 163 - 490/3*v + 1/3*v**2 = 0. What is v?
1, 489
Let v = 153654 - 153651. Let 10/3*u**2 - 10/3*u - 4 + 10/3*u**v + 2/3*u**4 = 0. Calculate u.
-3, -2, -1, 1
Let s(l) be the first derivative of -7*l**6/3 + 16*l**5 + 173*l**4/2 - 748*l**3/3 + 104*l**2 + 128*l - 620. Find v such that s(v) = 0.
-4, -2/7, 1, 8
Let c(g) = g**4 - 58*g**3 - 654*g**2 - 10*g + 10. Let v(x) = 2*x**3 + x**2 + 2*x - 2. Let d(i) = c(i) + 5*v(i). Find t, given that d(t) = 0.
-11, 0, 59
Let m = 309756 + -309753. Factor 35/3*o**m + 125/3*o - 50*o**2 + 625/6 - 5/6*o**4.
-5*(o - 5)**3*(o + 1)/6
Let z(l) be the first derivative of -5*l**6/6 - 16*l**5 - 120*l**4 - 450*l**3 - 1755*l**2/2 - 810*l - 1011. Let z(s) = 0. Calculate s.
-6, -3, -1
Factor -160/7 + 3/7*i**3 + 192/7*i + 10*i**2.
(i + 4)*(i + 20)*(3*i - 2)/7
Suppose 3*p - 2 = 4*p - r, -3*p + 26 = 5*r. Factor -8*a**3 + p*a**5 + 4*a**2 - 4 + 22*a - 14*a - 2*a.
2*(a - 1)**3*(a + 1)*(a + 2)
Let a(o) be the third derivative of 0 + 2*o**4 + 30*o**2 + 0*o - 8/3*o**3 - 1/5*o**5 - 1/6*o**6. Factor a(g).
-4*(g - 1)*(g + 2)*(5*g - 2)
Let d(v) = -1191*v**3 + 1254*v**2 - 3*v - 6. Let n(k) = 1191*k**3 - 1264*k**2 + 3*k + 7. Let h(w) = -7*d(w) - 6*n(w). What is l in h(l) = 0?
0, 1/397, 1
Let s be (1/15)/((-29)/(-145)). Factor 7/3*z**2 - 7/3 + 1/3*z**3 - s*z.
(z - 1)*(z + 1)*(z + 7)/3
Let x(d) be the second derivative of -d**5/90 + 1207*d**4/18 - 1456849*d**3/9 + 1758416743*d**2/9 + 4*d - 353. Solve x(h) = 0.
1207
Let d be (-8)/(-10)*(-360)/144. Let z(v) = -v**3 - v**2 - 3*v. Let g(m) = -m**3 + m**2 - 4*m. Let j(u) = d*z(u) + 3*g(u). Find n, given that j(n) = 0.
0, 2, 3
Factor -15 + 1/8*s**3 - 17/2*s - 1/4*s**2.
(s - 10)*(s + 2)*(s + 6)/8
Let r = 11/2193 + 11641/10965. Find k, given that 0 + r*k - 2/15*k**2 = 0.
0, 8
Let f = -581 + 585. Let t(m) be the third derivative of 0 + 0*m + 1/480*m**5 + 0*m**3 - 2*m**2 + 1/48*m**f. Factor t(y).
y*(y + 4)/8
Suppose -13 = -k + 4*w, 4*w - 2 = -5*k + 3*w. Let q be k/(4 - 3) + 1. Factor 2*g**3 + 2*g**4 + 3*g**q + 2*g - 4*g - 5*g**2.
2*g*(g - 1)*(g + 1)**2
Determine c, given that 9*c**3 + 41*c + 43*c - 102*c**2 - 8*c**2 - 3*c**5 + 242*c**2 - 42*c**4 = 0.
-14, -1, 0