+ 1/3*n**2 + h.
(n + 1)*(n + 3)/3
Let t(c) be the second derivative of -16/21*c**3 + 31/42*c**4 + 2 - 1/5*c**5 + 12*c - 1/105*c**6 + 0*c**2. Solve t(h) = 0 for h.
-16, 0, 1
Let j(v) = 7*v**3 + 5*v**2 - 5*v - 3. Let l(h) = -2*h**3 - 3*h**2 - 2*h - 1. Let d(x) = 2*j(x) + 6*l(x). Factor d(r).
2*(r - 6)*(r + 1)**2
Let v(h) = -1794*h**4 + 16032*h**3 + 17120*h**2 + 5272*h + 480. Let w(q) = q**4 + 2*q**3 - 10*q. Let k(b) = v(b) + 12*w(b). Suppose k(a) = 0. What is a?
-6/11, -2/9, 10
Let b(l) be the third derivative of -l**7/140 - 33*l**6/80 + 7*l**5/8 + 33*l**4/16 - 17*l**3/2 + 1363*l**2. Suppose b(p) = 0. Calculate p.
-34, -1, 1
Let p(u) be the third derivative of -1/98*u**7 + 0 - 1/28*u**4 - 1/20*u**5 + 0*u - 155*u**2 - 9/280*u**6 - 1/784*u**8 + 0*u**3. Factor p(k).
-3*k*(k + 1)**3*(k + 2)/7
Determine p, given that -353*p - 300*p**2 - 22*p - 611*p**5 + 12*p**4 + 90*p**3 + 608*p**5 = 0.
-5, -1, 0, 5
Suppose 160*z + 172*z - 318*z = 70. Let u(v) be the first derivative of 0*v - z + 3*v**4 + 4/5*v**5 + 0*v**3 - 8*v**2. Suppose u(y) = 0. Calculate y.
-2, 0, 1
Let i(z) = z**2 - 17*z + 5. Let s(y) = y**3 + 13*y**2 - 15*y + 3. Let r be s(-14). Let p be i(r). Determine x so that -p*x**2 + 20*x + 27*x - 15 - 27*x = 0.
1, 3
Suppose 0 = -9*f + 34 + 11. Factor 61*b**f - 16*b**5 - 20*b**2 - 105*b**4 + 90*b**3 - 37*b**3 + 27*b**3.
5*b**2*(b - 1)*(3*b - 2)**2
Solve 17/3*t**2 + 1/3*t**3 + 520/3 - 214/3*t = 0 for t.
-26, 4, 5
Suppose -9*b = -6*b - 114. Find m such that -15*m**2 - 25*m**2 - b*m - 10 - 2*m**4 - 18*m**3 - 10*m**2 - 2 + 8*m**2 = 0.
-6, -1
Let x(w) be the first derivative of -w**6/30 - 12*w**5/5 - 117*w**4/20 - 58*w**3/15 - 2185. Solve x(f) = 0 for f.
-58, -1, 0
Let v = 75 + -8. Let h = -63 + v. Suppose h*m**2 + 3*m - 8 + 5*m - 6*m**2 + 0*m**2 = 0. What is m?
2
Let h(a) be the third derivative of 1/630*a**5 - 1 - 1/42*a**4 + 20*a**2 + 0*a - 1/9*a**3. Solve h(s) = 0 for s.
-1, 7
Suppose 5*o = -5*l + 10, 40 = -20*o + 24*o - 4*l. Let d(n) = -n + 1. Let i be d(-4). Find s such that 14*s**3 - 4*s + 11*s**2 + o*s - i*s**3 = 0.
-1, -2/9, 0
Factor 472*s**2 + 1282*s**4 + 1 - 126*s**3 - 1 + 1263*s**4 - 2543*s**4.
2*s**2*(s - 59)*(s - 4)
Let l(h) = 206*h + 2063. Let x be l(-10). Let o(p) be the third derivative of 1/4*p**x + 2*p**2 + 1/240*p**5 + 0*p + 5/96*p**4 + 0. Factor o(n).
(n + 2)*(n + 3)/4
Suppose -3*z - 57835 = 4*n, n + 5 = 2*n. Let i be -3 + 54/15 - z/25. Find m such that -13*m**2 - 32*m**3 + i - 6*m**5 - 26*m**4 + 5*m**2 - 772 = 0.
-2, -1/3, 0
Let a be (-84)/(-5)*189/(-6468)*-40. Determine p so that -384/11*p + 96/11*p**2 + 6*p**4 + 0 + 6/11*p**5 + a*p**3 = 0.
-4, 0, 1
Let v(k) = -64 - 2*k**3 + k**3 + 32*k**2 + 18*k - 41*k - 12*k + 2*k**3. Let z be v(-33). Factor 0*c + 6/7 - 6/7*c**z.
-6*(c - 1)*(c + 1)/7
Let h(o) = -32*o**3 + 326*o**2 - 652*o - 218. Let w(g) = 322*g**3 - 3259*g**2 + 6516*g + 2181. Let x(a) = -21*h(a) - 2*w(a). Factor x(z).
4*(z - 9)*(z - 3)*(7*z + 2)
Let a(n) be the first derivative of 122 + 0*n + 8/15*n**3 + 1/20*n**4 + 7/10*n**2. Factor a(u).
u*(u + 1)*(u + 7)/5
Let b(q) = -12*q**2 - 72*q + 5. Let m be 0 + -5 + 72/(-72). Let w be b(m). Determine f so that 1/3*f**2 - f**4 - 2/3*f**w + 0*f**3 + 0 + 0*f = 0.
-1, 0, 1/2
Let p(t) be the second derivative of -5*t**4/12 + 5*t**3/6 + 765*t**2 + 10*t - 3. Suppose p(i) = 0. What is i?
-17, 18
Let o(p) be the first derivative of 28*p + 5*p**3 - 100 + 5*p**4 - 30*p**2 - 3/5*p**5. Suppose o(w) = 0. What is w?
-2, 2/3, 1, 7
Let a(y) = -y**4 - 32*y**3 - 369*y**2 - 1428*y - 1086. Let j(n) = 3*n**4 + 95*n**3 + 1107*n**2 + 4286*n + 3257. Let d(z) = 14*a(z) + 4*j(z). Factor d(s).
-2*(s + 1)*(s + 8)**2*(s + 17)
Let x(p) be the first derivative of -p**4/4 - 13*p**3/3 + 109*p**2/2 - 95*p + 1174. Factor x(d).
-(d - 5)*(d - 1)*(d + 19)
Factor 1325 + 30*o + 124*o - 5*o**2 + 87*o + 4*o - 5*o.
-5*(o - 53)*(o + 5)
Factor 76/3*s**2 + 0 + 24*s + 4/3*s**3.
4*s*(s + 1)*(s + 18)/3
Let 196*g**5 + 1210*g + 1643*g - 22*g**3 - 4464*g**2 - 17*g**3 + 15*g**3 + 1820*g**4 - 261*g = 0. Calculate g.
-9, -2, 0, 6/7
Let 3/2 - 3/4*n**4 - 3/4*n**2 - 9/4*n + 9/4*n**3 = 0. What is n?
-1, 1, 2
Suppose 0 = 158*l + 67 - 184 - 357. Determine j, given that -1/7*j**l + 4/7*j**2 - 1/7*j - 6/7 = 0.
-1, 2, 3
Let b(y) be the third derivative of -y**5/140 + 88*y**4/7 - 61952*y**3/7 + 844*y**2. Factor b(l).
-3*(l - 352)**2/7
Let a(m) = 123*m**2 + 995*m + 1197 + 46*m**2 + 293 - 44*m**2. Let o(s) = -9*s**2 - 71*s - 106. Let b(u) = -4*a(u) - 55*o(u). Factor b(d).
-5*(d + 2)*(d + 13)
Let x(g) be the first derivative of -g**4/7 - 20*g**3/7 + 74*g**2/7 + 204*g/7 + 6390. Factor x(d).
-4*(d - 3)*(d + 1)*(d + 17)/7
Let j(d) = 8*d**4 + 17*d**3 + d**2 - 31*d - 23. Suppose 6*c + 44 = 17*c. Let m(s) = 4*s**4 + 8*s**3 - 16*s - 12. Let f(z) = c*j(z) - 7*m(z). Factor f(t).
4*(t - 1)*(t + 1)**2*(t + 2)
Let -272/7*c - 16/7*c**3 - 148/7*c**2 + 4/7*c**4 - 144/7 = 0. Calculate c.
-2, -1, 9
Let p(o) be the first derivative of o**4/4 + 17*o**3/3 + 71*o**2/2 + 55*o + 2087. Factor p(z).
(z + 1)*(z + 5)*(z + 11)
Suppose -110*g - 24 = -102*g. Let o be (g/(-6))/((-5 - -10)/50). Factor 0*z**2 - 2/15*z**3 + 8/15*z**o - 2/5*z**4 + 0 + 0*z.
2*z**3*(z - 1)*(4*z + 1)/15
Let i be ((-196040)/(-728) + -269)/(0 - (-4)/42). Let h be 4/(-2) + 4/1. What is x in -2/5*x**i + 0 + 4/5*x**h + 6/5*x = 0?
-1, 0, 3
Let k(d) = 7*d**2 + 601*d + 382. Let a(g) = -4*g**2 - 300*g - 192. Suppose 30 = -6*t + 90. Let q(m) = t*a(m) + 4*k(m). Factor q(b).
-4*(b + 49)*(3*b + 2)
Let l be (-214)/(-20) + (-33)/(-110) + 1*-6. Let s(y) be the second derivative of -17*y + 1/100*y**l + 0*y**2 + 0*y**3 + 0*y**4 + 0. Factor s(z).
z**3/5
Let k(x) be the third derivative of x**6/300 + 61*x**5/150 - 1001*x**4/60 + 245*x**3 + 60*x**2 - 2*x - 3. Factor k(m).
2*(m - 7)**2*(m + 75)/5
Let z = 172848 + -172845. Factor -2/13*h**z + 0 - 6/13*h + 8/13*h**2.
-2*h*(h - 3)*(h - 1)/13
Let m = -32158 - -32160. What is w in -1/2*w**m - 73/6*w + 25/3 = 0?
-25, 2/3
Let g(c) = 12*c - 4. Let k be g(2). Suppose -2*p = -8 - 2, -k = -3*d - 4*p. Factor -3*z**2 + d*z**2 + 157*z**5 - 9*z**4 - 160*z**5 - 9*z**3.
-3*z**2*(z + 1)**3
Let d(k) = 9*k**2 + 23*k**2 + 243*k - 9*k**3 + 512 + 212. Let n(s) = 7*s**3 - 31*s**2 - 243*s - 725. Let m(w) = -4*d(w) - 5*n(w). Factor m(g).
(g + 9)**3
Let q(s) = -18*s**3 + 182*s**2 + 1218*s - 1394. Let w(h) = -40*h**3 + 362*h**2 + 2434*h - 2783. Let m(g) = 9*q(g) - 4*w(g). Solve m(p) = 0 for p.
-7, 1, 101
Determine t, given that -488*t**3 + 52*t - 52*t - 38*t**4 + 10132*t**2 - 10580*t**2 + 0*t**5 + 2*t**5 = 0.
-8, -1, 0, 28
Let k(v) = -1. Let s(h) = -10*h**2 + 74*h - 15. Let d(j) = -j**2. Let p(n) = d(n) - s(n). Let z(l) = -5*k(l) + 5*p(l). What is q in z(q) = 0?
2/9, 8
Suppose -5 = 14*o - 19*o. Suppose -4*v + 3*a = v - o, -4*v + 5*a - 7 = 0. Factor -30*m**2 + 4 - 28*m**v + 59*m**2 - 4*m.
(m - 2)**2
Let -56/9*g**2 + 106/9*g - 52/9 + 2/9*g**3 = 0. Calculate g.
1, 26
Factor 36/11 - 2/11*d + 2/11*d**3 - 36/11*d**2.
2*(d - 18)*(d - 1)*(d + 1)/11
Let d(t) be the first derivative of -t**6/3 - 34*t**5/5 - 31*t**4/2 + 970*t**3/3 + 1000*t**2 + 1000*t + 287. Determine x, given that d(x) = 0.
-10, -1, 5
Suppose -4*a + 75 - 71 = 0. Let q(d) = d**2 + d + 2. Let p(v) = 14*v**2 - 91*v + 266. Let l(x) = a*p(x) - 5*q(x). Determine u, given that l(u) = 0.
16/3
Let j(o) = -5*o**4 + 13*o**3 - 30*o**2 + 4*o + 28. Let b(l) = -l**4 + l**3 - 2*l**2 + l - 1. Let h = -139 - -159. Let n(w) = h*b(w) - 5*j(w). Factor n(q).
5*(q - 4)**2*(q - 2)*(q + 1)
Let c(v) be the first derivative of v**8/336 - v**7/42 + v**6/15 - v**5/15 + 29*v**2 + 135. Let d(z) be the second derivative of c(z). Factor d(y).
y**2*(y - 2)**2*(y - 1)
Let q(h) be the first derivative of -h**4/8 - 182*h**3 - 99372*h**2 - 24114272*h + 1971. Factor q(b).
-(b + 364)**3/2
Let j(w) = w**3 - 28*w**2 + 54*w + 56. Let a be j(26). Find g, given that -6 + 32*g**2 + 88*g + 22 + 50*g**3 + a*g**2 = 0.
-2, -2/5
Factor 1/7*o**3 + 12100/7 + 11880/7*o - 219/7*o**2.
(o - 110)**2*(o + 1)/7
Suppose 4*g + 199 + 2321 = 0. Let o be 240/g*21/(-18). Determine j so that 4/9 - 4/9*j**3 + o*j - 4/9*j**2 = 0.
-1, 1
Let x = 4056536/7 + -579505. Factor 0 - 1/7*m - x*m**2.
-m*(m + 1)/7
Let p(b) = -30*b - 24. Let i(c) = c**2 + 29*c + 24. Suppose 10 = 2*s - n + 1, 0 = 2*s + 3*n + 11. Let k(v) = s*p(v