-1, 0, 1, 2
Let x(m) = -3*m + 21. Let v be x(6). Let q(r) = 2*r**2 + 3*r + 2. Let l be q(-2). Determine w so that 3 - 5*w**4 + 2 + 2*w**4 - 2*w**l + 10*w**v - 10*w = 0.
-1, 1
Let k(v) be the third derivative of v**5/80 - 3*v**4/32 + v**3/4 - 460*v**2 + 1. Factor k(m).
3*(m - 2)*(m - 1)/4
Let n(w) be the first derivative of -49*w**6/15 + 42*w**5 - 284*w**4/5 - 1256*w**3/5 + 1472*w**2/5 + 4608*w/5 + 4079. Determine o so that n(o) = 0.
-8/7, 2, 9
Let o(n) = 2*n**2 + 353*n - 30477. Let l be o(-240). Suppose 4 + 1/2*b**2 + l*b = 0. What is b?
-4, -2
Let x(d) = 67*d**2 - 934*d - 54. Let b be x(14). Let 16/5*t - 4/5*t**4 + 16/5*t**b - 4/5*t**3 + 0 = 0. Calculate t.
-2, -1, 0, 2
Let i(k) = 2*k + 2. Let h be i(-1). Suppose 3*p - 5*m + 14 = h, 3*p - 2*m = -p. Solve 13*b + 0*b - b - 3*b**p - 12 = 0.
2
Let d be 122*12/(-168) - (-6 - 3). Factor -d*s**2 + 30/7 - 4/7*s.
-2*(s - 3)*(s + 5)/7
Suppose 7/4*d**4 - d**2 + 0 - 1/2*d**5 + 0*d - d**3 = 0. What is d?
-1/2, 0, 2
Let t(s) = -s - 14. Let o be t(-21). Suppose -2*n + 3*f + 140 = 0, -4*f + o + 52 = n. Factor 5 + n*v - 85*v - 5 - 12*v**2 - 2*v**3.
-2*v*(v + 3)**2
Factor 11062272/7*s + 4/7*s**3 - 11048976/7 - 1900*s**2.
4*(s - 1662)**2*(s - 1)/7
Let r(b) be the second derivative of -4*b**7/147 - 18*b**6/35 + 62*b**5/7 - 40*b**4/7 - 88*b**3/3 + 42*b**2 + 6*b - 269. Determine g so that r(g) = 0.
-21, -1, 1/2, 1, 7
Let o = 27290 + -271149/10. Let n = o - 853/5. Solve n*t + 1/4 + 81/4*t**2 = 0 for t.
-1/9
Factor 25/2 + 51/4*i**3 - 1/4*i**4 - 49/4*i**2 - 51/4*i.
-(i - 50)*(i - 1)**2*(i + 1)/4
Let a(q) be the third derivative of 2 - q**3 + 1/24*q**4 + 0*q + 1/60*q**5 - q**2. Factor a(n).
(n - 2)*(n + 3)
Let j(y) be the first derivative of y**5/30 + 35*y**4/6 + 1225*y**3/3 - 39*y**2 - 5. Let r(h) be the second derivative of j(h). Factor r(w).
2*(w + 35)**2
Let x(i) be the third derivative of -55*i**2 + 0*i**3 - 1/4*i**4 + 1/120*i**6 + 0 + 1/12*i**5 + 0*i. Factor x(l).
l*(l - 1)*(l + 6)
Let -987/2 + 3/4*k**2 + 1971/4*k = 0. Calculate k.
-658, 1
Let s(u) be the second derivative of -u**6/120 + 7*u**5/80 - u**4/24 - 8*u**3/3 + 12*u**2 + 141*u + 1. Suppose s(n) = 0. Calculate n.
-3, 2, 4
Solve 660*j**2 + 3*j**4 + 39*j**3 + 76*j**3 + 170*j + 530*j - 5*j**5 - 33*j**4 = 0.
-7, -2, 0, 5
Factor 9*f**3 + f**4 - 35*f**2 + 63*f**2 + 2*f**4 - 22*f - 31*f**2 + 13*f.
3*f*(f - 1)*(f + 1)*(f + 3)
Let c(k) be the second derivative of 0*k**3 - 2/15*k**6 + 0*k**4 + 0*k**2 + 0 + 5/126*k**7 + 1/15*k**5 - 5*k. Determine y so that c(y) = 0.
0, 2/5, 2
Factor -38/17*s**2 - 10/17*s**3 - 28/17*s + 0.
-2*s*(s + 1)*(5*s + 14)/17
Suppose 0 = 50*k - 62*k. Let b(f) be the second derivative of k - 1/4*f**5 + 9*f + 5/3*f**4 + 0*f**2 + 0*f**3. Find y, given that b(y) = 0.
0, 4
Suppose -23*g - 75 - 40 = 0. Let d be 0 + (g - (-7)/1) + 0. Factor -4/7 - 4/7*u**3 - 2*u - 16/7*u**d + 2/7*u**5 + 4/7*u**4.
2*(u - 2)*(u + 1)**4/7
Suppose 162 = 51*o + 43*o - 120. Determine q so that 0 + 6*q**2 + 0*q + 3/2*q**o = 0.
-4, 0
Let s(n) be the third derivative of -n**7/840 + n**6/240 + 19*n**5/80 + 9*n**4/16 + 476*n**2 - 2*n. Factor s(f).
-f*(f - 9)*(f + 1)*(f + 6)/4
Suppose 471/2*o + 1/4*o**2 + 221841/4 = 0. Calculate o.
-471
Determine l, given that 0 - 1/4*l**2 - 1907/4*l = 0.
-1907, 0
Let u be (-56)/44 - (-24)/88. Let j be (-4 + 5)/((0 - u) + 1). Factor -j*n - 3/2*n**2 + 3/2 + 1/2*n**3.
(n - 3)*(n - 1)*(n + 1)/2
Let f(g) = -g**3 - g**2 - g. Let k(h) = 14*h**3 - 2*h - 20*h**3 - 38*h**2 - 2*h**4 + 28*h**3 - 2*h**4. Let s(a) = 2*f(a) - k(a). Factor s(u).
4*u**2*(u - 3)**2
Let i(b) = -b**2 - 17*b - 27. Let p be (328/902)/((-4)/22). Let v be i(p). Determine d, given that 6/7*d**2 + 2/7*d**v + 0*d - 8/7 = 0.
-2, 1
Let b(y) = -27*y**3 - 241*y**2 + 1136*y - 240. Let t(x) = 24*x**3 + 240*x**2 - 1136*x + 240. Let a(j) = 4*b(j) + 3*t(j). Factor a(r).
-4*(r - 3)*(r + 10)*(9*r - 2)
Let m(d) be the third derivative of -d**6/24 + d**5 + 35*d**4/6 - 1169*d**2. Factor m(c).
-5*c*(c - 14)*(c + 2)
Let r = -73/958 - -8175/6706. Factor -1/7*l**2 - r*l - 16/7.
-(l + 4)**2/7
Let x(v) be the second derivative of v**7/840 + 11*v**6/240 + 7*v**4/4 + v**2 - v + 25. Let y(w) be the third derivative of x(w). Suppose y(f) = 0. What is f?
-11, 0
Let c = -590249 + 590251. Solve 8/3 - 50*r**3 + 410/3*r**c + 352/9*r = 0 for r.
-2/15, 3
Let r(w) = -2*w**3 - w - 6. Let t(h) = -22*h**3 + 312*h**2 + 5027*h + 23122. Let k(x) = -13*r(x) + t(x). Suppose k(p) = 0. What is p?
-58, -10
Let m(f) = -57*f**3 - 6243*f**2 - 12489*f. Let i(p) = 11*p**3 + 1249*p**2 + 2498*p. Let c(a) = 21*i(a) + 4*m(a). Factor c(b).
3*b*(b + 2)*(b + 417)
Let 702*x**2 - 2013*x - 63*x**4 - 2*x**5 + 209*x**3 + 261*x**3 - 188*x**3 + 5*x**5 + 1089 = 0. Calculate x.
-3, 1, 11
Find q such that -182503 + 50*q**3 - 70*q + 34*q**4 + 182743 + 13*q**4 - 305*q**2 - 2*q**4 = 0.
-3, -1, 8/9, 2
Let w(x) be the second derivative of -x**7/280 + x**6/120 + 3*x**5/20 - x**3/3 + 18*x**2 - 13*x. Let n(u) be the second derivative of w(u). Factor n(m).
-3*m*(m - 3)*(m + 2)
Suppose 11*c - 1518 = 3762. Let g = 485 - c. Factor -2/3*w**g - 2*w**3 + 0*w + 2/3*w**2 + 2*w**4 + 0.
-2*w**2*(w - 1)**3/3
Suppose 0*r + 0*r**2 - 200/17*r**3 + 0 + 2/17*r**5 + 30/17*r**4 = 0. What is r?
-20, 0, 5
Let p(y) be the first derivative of -19 + 1/10*y**4 - 18*y + 1/75*y**6 + 3/50*y**5 + 0*y**2 + 1/15*y**3. Let b(u) be the first derivative of p(u). Factor b(o).
2*o*(o + 1)**3/5
Let m(d) be the second derivative of -d**5/5 + 91*d**4/3 + 1154*d**3/3 + 970*d**2 + 7*d - 58. Factor m(h).
-4*(h - 97)*(h + 1)*(h + 5)
Let c(p) = -4*p**3 - 2282*p**2 - 870970*p - 110612682. Let y(r) = r**3 - 2*r**2 + 2*r. Let k(i) = -c(i) - 2*y(i). Determine d, given that k(d) = 0.
-381
Let h(g) be the second derivative of -27*g**4/4 + 609*g**3 - 41209*g**2/2 + 9634*g. Determine v, given that h(v) = 0.
203/9
Determine g so that 0*g**4 + 32/3*g**2 + 0 + 8*g**3 - 4/3*g**5 + 4*g = 0.
-1, 0, 3
Let v(w) be the first derivative of 2*w**3/15 + 138*w**2/5 + 544*w/5 - 2466. Suppose v(h) = 0. What is h?
-136, -2
Let o(j) = -7*j**2 + 24378*j + 29743725. Let g(b) = -3*b**2 + 9751*b + 11897492. Let n(y) = 12*g(y) - 5*o(y). Factor n(k).
-(k + 2439)**2
Let y(g) be the third derivative of -g**8/224 + 23*g**7/280 - 3*g**6/10 + 13*g**5/40 + 5*g**4/16 - 9*g**3/8 - 12*g**2 - 134*g. Let y(q) = 0. Calculate q.
-1/2, 1, 9
Suppose 28 = -220*b + 227*b. Let x(a) = a**2 - 11*a - 6. Let g(o) = o**2 - 13*o - 5. Let z(w) = b*g(w) - 5*x(w). What is n in z(n) = 0?
-2, 5
Find l, given that 1617*l**2 - 5*l**3 + 38295*l + 73926 + 8*l**3 - 945*l**2 = 0.
-111, -2
Let s(i) be the first derivative of -2*i**3/3 + 13*i**2 + 180*i - 2011. Factor s(c).
-2*(c - 18)*(c + 5)
Let i(f) be the first derivative of f**4/18 + 7*f**3/3 + 110*f - 19. Let j(n) be the first derivative of i(n). Factor j(v).
2*v*(v + 21)/3
Suppose 30*n + 2*n = -n + 132. Let p(c) be the second derivative of 9/40*c**5 + 1/20*c**6 - 3/4*c**3 + 1/8*c**n + 0 + 8*c - 3/2*c**2. Solve p(x) = 0.
-2, -1, 1
Let u(s) be the second derivative of -s**4/54 + 88*s**3/3 - 17424*s**2 + 12*s + 16. Find b, given that u(b) = 0.
396
Let x = 255 + -76. Factor -3*u**3 - x*u**2 + 127*u**2 - 401 + 101 - u**3 - 220*u.
-4*(u + 3)*(u + 5)**2
Let h(w) = -3*w + 188. Let z be h(16). Factor -720 + 3*f**4 + 6*f**4 - 80*f**3 - z*f + 20*f**3 + 160*f**2 - 4*f**4 + 380*f.
5*(f - 6)**2*(f - 2)*(f + 2)
Let j(c) = 5*c**2 + 15*c - 42. Let u be j(4). Let p be u/80 + 9/24. Factor 0 - p*i + 8/5*i**3 - 2/5*i**2 + 2/5*i**4.
2*i*(i - 1)*(i + 1)*(i + 4)/5
Let y(d) = 5*d**3 + 30*d**2 - 125*d + 70. Let r(m) = -2*m**3 - 10*m**2 + 41*m - 23. Let f(s) = 10*r(s) + 3*y(s). Factor f(j).
-5*(j - 1)**2*(j + 4)
Let g(r) = 11*r**4 - 69*r**3 + 58*r**2 + 24*r + 6. Let y(z) = 12*z**4 - 68*z**3 + 60*z**2 + 24*z + 4. Let b(c) = -2*g(c) + 3*y(c). Find u such that b(u) = 0.
-2/7, 0, 2, 3
Let l(q) be the second derivative of -q**4/3 + 50*q**3 + 800*q**2 - 1083*q. Factor l(r).
-4*(r - 80)*(r + 5)
Let b(x) = 3*x**2 - 31*x - 1. Let l be b(13). Factor l*u**2 + 86*u + 31*u**4 - 9*u**4 + 44*u**3 + 24 - 6*u**4 - 13*u**4.
(u + 1)**2*(u + 12)*(3*u + 2)
Let p(u) be the third derivative of -1/60*u**5 - 2 + 7*u**2 + 5/24*u**4 + 0*u + 7/3*u**3. Factor p(t).
-(t - 7)*(t + 2)
Let w(x) = -2*x - 2. Let v be w(7). Let p be -3*(v/(-12) - 2). Let -12*s + 9*s +