t p(l) be the third derivative of 51/20*l**4 - 40*l**2 - 1/20*l**5 + 2 + 0*l - 4*l**3. Factor p(w).
-3*(w - 20)*(5*w - 2)/5
Let y(o) = 3*o**2 - 1240*o + 1217. Let u(t) = 2*t**2 - 1240*t + 1222. Let g(z) = -5*u(z) + 4*y(z). Let g(b) = 0. What is b?
-621, 1
Let v(b) be the third derivative of 0*b**3 + 0 + 0*b - 13/480*b**6 - 1/210*b**7 + 0*b**4 - 1/80*b**5 + 51*b**2. Factor v(j).
-j**2*(j + 3)*(4*j + 1)/4
Let f(v) = -2*v**2 + 40*v + 32. Let c(h) = -h**2 + 14*h + 11. Let y(z) = z**3 - 4*z**2 - z - 12. Let k be y(5). Let p(w) = k*c(w) - 3*f(w). Factor p(l).
-2*(l + 2)**2
Let o(z) = -3 + 7 - 3 - 3*z. Let y be o(-1). Factor -107*q**2 - 12 + 24*q**y + 60*q**3 - 19*q + 88*q - 19*q**2.
3*(q + 4)*(2*q - 1)**3
Factor 4/3*i**2 - 92/3*i - 560/3.
4*(i - 28)*(i + 5)/3
Let x(i) = 18*i**4 - 27*i**3 - 12*i**2 - 27*i + 30. Let s(u) = u**4 - 2*u**3 - u + 2. Let m(v) = -15*s(v) + x(v). Determine j, given that m(j) = 0.
-2, -1, 0, 2
Solve 0 - 476/9*i**2 + 0*i + 478/9*i**3 - 2/9*i**4 = 0.
0, 1, 238
Let g(t) = 13*t**3 - 24*t**2 - 105*t + 4. Let w(x) = -2*x**3 + x**2 - 1. Let b(r) = -g(r) - 4*w(r). Factor b(u).
-5*u*(u - 7)*(u + 3)
Suppose 0 = -2*m + 10, -27 = -i - 24*m + 19*m. Determine c, given that 0*c - 2*c**4 + c - c**3 - 2*c**i + 3*c**2 + c**2 = 0.
-1, -1/2, 0, 1
Let k be 0/(28 + -70 - -41). Factor 8/3*t + k + 1/3*t**2.
t*(t + 8)/3
Let h be (-1)/((-3)/(-18)*2) + 6 + -1. Let n(d) be the second derivative of 0 - 1/9*d**4 - 4/3*d**h + 2/3*d**3 + 14*d. Let n(w) = 0. What is w?
1, 2
Suppose 7 - 17 = -u + 5*v, -8 = 4*v. Let m(h) be the second derivative of 5/6*h**3 - 5/12*h**4 + u*h**2 + 15*h + 0. Factor m(f).
-5*f*(f - 1)
Let y(d) be the third derivative of d**5/540 - 65*d**4/72 - 500*d**3/27 + 32*d**2 + 2*d - 65. Factor y(u).
(u - 200)*(u + 5)/9
Suppose 96/7 + 2/7*l**3 + 58/7*l - 36/7*l**2 = 0. What is l?
-1, 3, 16
Suppose -6*q + 8*q + 6 = 3*t, 0 = 2*t - 4*q + 4. What is o in -13*o + o**2 + t + 2*o + 19*o + 3*o**2 = 0?
-1
Suppose -8*m + 468 = -5*m. Let j = -150 + m. Factor 2*i**3 + j*i**2 + 561*i - 558*i + i**3.
3*i*(i + 1)**2
Determine t, given that 1664*t**3 - 555*t**3 - 171*t + 3*t**2 - 555*t**3 - 553*t**3 - 13*t**2 = 0.
-9, 0, 19
Let p be (-13)/(-6) + -3 + 252/168. Let 10/9*x**5 + 32/3 - p*x**4 - 104/9*x**3 + 0*x**2 + 256/9*x = 0. What is x?
-2, -2/5, 2, 3
Let c(l) = l - 2. Let a be c(-1). Let t be (0 - -6)*5*a/(-30). Factor 3*v**t - 59 + 59 - v**4.
-v**3*(v - 3)
Let -5/6*t**2 - 168750 - 750*t = 0. Calculate t.
-450
Let j be (((-1156)/(-119))/17)/((-1)/(21/(-6))). Let w(x) be the first derivative of -4/7*x**j + 12/7*x + 10 - 4/21*x**3. Factor w(u).
-4*(u - 1)*(u + 3)/7
Suppose 22*f**2 - 2199*f - 22*f**2 + 32*f**2 + 13*f**2 - 366 - 540*f = 0. Calculate f.
-2/15, 61
What is d in 44712*d**2 + 1104 - 8959 + 10563*d**3 + 14103 + 57132*d + 18086 + 1101*d**3 = 0?
-23/18
Let a(b) be the third derivative of -b**5/20 - 15*b**4/2 - 112*b**3 + 2193*b**2. Find d, given that a(d) = 0.
-56, -4
Factor -8*k**3 - 18*k**2 - 28/3*k + 0 + 2/3*k**4.
2*k*(k - 14)*(k + 1)**2/3
Suppose -288*s - 853*s**3 - 272 - 84*s**2 - 850*s**3 + 3406*s**3 - 853*s**3 - 854*s**3 = 0. Calculate s.
-17, -2
Let z(k) = -k**2. Let f(d) = 5*d**4 - 20*d**3 - 130*d**2 - 190*d - 80. Let x(s) = -16*s - 193. Let g be x(-12). Let a(i) = g*f(i) - 5*z(i). Factor a(b).
-5*(b - 8)*(b + 1)**2*(b + 2)
Let n(x) be the first derivative of -5*x**4/4 + 785*x**3/3 - 15600*x**2 + 30420*x - 1901. Factor n(v).
-5*(v - 78)**2*(v - 1)
Let s be 66 + (-38 - (-8 + 33)). Factor 0*b**s - 3/2*b**4 + 0 - 3*b + 9/2*b**2.
-3*b*(b - 1)**2*(b + 2)/2
Find i, given that 129*i + 631*i**4 - 757*i**4 + 47*i**3 - 179*i**3 + 126*i**2 + 3*i**5 = 0.
-1, 0, 1, 43
Suppose -15 = -4*z - p, 0 = -3*z + 38*p - 34*p - 3. Factor -2/3*i**4 + 4/3*i**2 - 2/3 + 0*i**z + 0*i.
-2*(i - 1)**2*(i + 1)**2/3
Let y(r) = -r**3 - 20*r**2 + 5*r - 12. Let l be y(-20). Let f be -1 - -2 - 44/l*4. Determine t, given that -f*t**2 - 4/7 + 2*t + 10/7*t**3 - 2/7*t**4 = 0.
1, 2
Suppose -4*q + 40 = 5*f, -4*f - 3*q + 40 = 8. Let u = f - 6. Factor -15 + 25*v**u - 12*v**3 + 18*v + 6*v**3 + 2*v**2.
-3*(v - 5)*(v + 1)*(2*v - 1)
Let i = 42 - 39. Suppose 3*j - 11 = 2*r, 9 = -i*r + 4*j - 5. Suppose 4*h**4 - 6*h**r - 2*h**2 - 18*h**3 - 4*h**4 + 2*h**5 + 24*h = 0. What is h?
-2, 0, 1, 3
What is j in -534578 + 1034*j - 1/2*j**2 = 0?
1034
Let k(a) be the first derivative of 5*a**4 + 85*a**3 + 450*a**2 + 540*a - 756. Factor k(x).
5*(x + 6)**2*(4*x + 3)
Factor -127*r**3 - 5*r**4 - 494*r**3 - 2329*r**3.
-5*r**3*(r + 590)
Let n = 6669 + -80027/12. Let w(j) be the second derivative of 0 + 1/3*j**3 + 0*j**2 - 24*j - n*j**4. Factor w(b).
-b*(b - 2)
Let t(k) be the second derivative of 5/24*k**4 - 1/80*k**5 + 6*k - 3/8*k**3 + 0*k**2 + 1. Solve t(l) = 0.
0, 1, 9
Suppose 6*u - 50 = u - 5*u. Let v(p) be the third derivative of 0*p - 1/28*p**4 + 0*p**3 + 0 + 1/210*p**u + 3*p**2. Determine r so that v(r) = 0.
0, 3
Suppose -14*c + 6*c = -32. Solve -4*w**3 - 6*w**2 + w**2 - w**c - 1 - w**2 - 4*w = 0 for w.
-1
Let z(a) be the third derivative of 1/4*a**4 - 1/5*a**5 + 4/3*a**3 + 0*a - a**2 - 1/12*a**6 + 1. Determine b so that z(b) = 0.
-1, 4/5
Let f(z) be the first derivative of 9/4*z**2 - 24/5*z**5 + 72 - 25/2*z**3 + 21*z**4 + 0*z. Factor f(w).
-3*w*(w - 3)*(4*w - 1)**2/2
Let x be ((-124)/(-4))/31 - (0 - (-11)/12). Let b(a) be the third derivative of 5/96*a**4 + 1/120*a**5 + 0*a - 1/96*a**6 + 0 - a**2 - x*a**3. Factor b(i).
-(i - 1)*(i + 1)*(5*i - 2)/4
Suppose -4*g + 21789 - 475 = 5*x, 0 = 3*x + 4*g - 12790. Determine k so that 5*k**2 + x + 6813 - 50*k + 11370 + 423*k + 297*k = 0.
-67
Let n = -8944 + 8946. Let h(p) be the first derivative of 1/3*p**3 + n + 5/2*p**2 + 0*p. Let h(y) = 0. What is y?
-5, 0
Suppose 5*k = -2*w + 6*w - 23, 0 = 4*w - 3*k - 17. Determine j, given that 221*j**2 + 80*j**4 + 2744*j**w - 176*j**2 + 576*j**2 + 245 - 1080*j**3 + 1890*j = 0.
-1/4, 7
Let h(i) be the third derivative of i**5/90 + 23*i**4/36 - 12*i**3 - i**2 - 57. Factor h(o).
2*(o - 4)*(o + 27)/3
Suppose 0 = -5*u - 642 + 662. What is l in -3*l**5 + 5*l**3 + 10*l**2 - 10*l**u - 14*l**5 + 12*l**5 = 0?
-2, -1, 0, 1
Let s(r) = -r**3 - 68*r**2 - 3*r - 186. Let z be s(-68). Suppose p - 2*p + z = 3*d, -37 = -4*p - 5*d. Factor 1/4 + 1/8*o - 1/8*o**p - 1/4*o**2.
-(o - 1)*(o + 1)*(o + 2)/8
Suppose 0 = 3*n - x - 148, -5*n + 6*x - x = -260. Let l = n + -45. Determine g, given that -20*g**2 - 25*g - 11*g**l + 6*g**3 - 3 - 7 = 0.
-2, -1
Let s be (2 - -4) + (1 - (1 - -618)). Let k be (s/(-544))/((-3)/(-4)). Determine q so that 3/2 + k*q**2 - 3*q = 0.
1
Factor -5/2*c**5 + 0*c**2 + 0 - 180*c**3 + 0*c + 95*c**4.
-5*c**3*(c - 36)*(c - 2)/2
Let l(m) be the first derivative of m**8/420 - m**7/70 - 7*m**6/15 - 10*m**5/3 - 12*m**4 - 10*m**3/3 + 7. Let u(x) be the third derivative of l(x). Factor u(w).
4*(w - 9)*(w + 2)**3
Let g(b) be the first derivative of -5*b**3/3 + 113*b**2/2 + 48*b - 582. Let a be g(23). What is n in 2*n**a - 2*n - 2/3*n**3 + 2/3 = 0?
1
Let c(n) be the second derivative of -5*n**4/36 + 790*n**3/9 - 84*n - 10. Factor c(d).
-5*d*(d - 316)/3
Let z(n) be the third derivative of n**5/150 - 23*n**4/30 + 3*n**3 - 3*n**2 - 5*n. Factor z(w).
2*(w - 45)*(w - 1)/5
Find a, given that 1/2*a**5 - 10061824 - 274720*a**2 - 110*a**4 + 2959360*a + 8600*a**3 = 0.
8, 68
Let q = -3/3734 + 3761/33606. Let j(i) be the first derivative of q*i**2 + 0*i - 2/27*i**3 - 2. Suppose j(k) = 0. What is k?
0, 1
Let s(a) be the first derivative of 1/2*a**4 - a**2 - 1/5*a**5 + 1/3*a**3 + 61 + 0*a. Suppose s(d) = 0. What is d?
-1, 0, 1, 2
Let r be 1039/(-2)*(-48)/18. Let p = 1386 - r. Find s such that p*s + 4/9 + 2/9*s**2 = 0.
-2, -1
Let g be ((-61)/((-3294)/144))/((-8)/(-15)). What is q in 0 + 0*q - 13/2*q**3 - q**4 - 5*q**2 + 1/2*q**g = 0?
-2, -1, 0, 5
Let l(c) be the first derivative of 2/15*c**5 - 3/10*c**4 + 181 - 1/45*c**6 + 14/45*c**3 + 0*c - 2/15*c**2. Solve l(t) = 0 for t.
0, 1, 2
Let a(d) = 3*d**2 - 35*d + 220. Let l(z) = 7*z**2 - 73*z + 433. Let q(b) = -9*a(b) + 4*l(b). Determine u, given that q(u) = 0.
-31, 8
Suppose 28*d - 67*d = -429. Let l be -5 - (-16 + d - 1/2). Factor -1/4*w + 1/4*w**2 - l.
(w - 2)*(w + 1)/4
Suppose -3*n - 4*s = -26, -4*n + 5*s - 12 - 5 = 0. Suppose 6614*k = 6615*k - 2. Factor f**2 - 4*f**n + 6 - k*f - f + 0*f.
-3*(f - 1)*(f 