1820/56). Factor -3*j - 1/4*j**3 + 7/4*j**d + 0.
-j*(j - 4)*(j - 3)/4
Let j(t) be the third derivative of -t**8/84 - 32*t**7/15 - 1568*t**6/15 - 2484*t**2. Factor j(z).
-4*z**3*(z + 56)**2
Let t = 64605 - 64605. Factor 1/2*m + t - 1/4*m**2 - 1/4*m**3.
-m*(m - 1)*(m + 2)/4
Let p(x) be the first derivative of 2*x**3/21 + 293*x**2/7 - 84*x - 5379. Determine u so that p(u) = 0.
-294, 1
Factor 7412/9*z - 2/9*z**2 - 6867218/9.
-2*(z - 1853)**2/9
Let o(y) be the third derivative of y**6/1020 + y**5/30 - 21*y**2 - 31*y. Factor o(q).
2*q**2*(q + 17)/17
Let l = 11897/7 - 1689. Let n = 305533 + -2138711/7. Suppose -104/7*g**2 - 20/7 - 68/7*g**3 - l*g - n*g**4 - 2/7*g**5 = 0. Calculate g.
-5, -2, -1
Let u(b) = 2*b**2 + 35*b - 49. Let i be u(-19). Suppose -6*o - 2*r + 8 = -i*o, -2*r = -10. Factor t**2 + 5/2*t - o - 5/2*t**3.
-(t - 1)*(t + 1)*(5*t - 2)/2
Let f = 602803/54 - 11163. Let m(c) be the second derivative of 0 + f*c**4 + 1/135*c**6 + 0*c**3 - 20*c + 1/45*c**5 + 0*c**2. Factor m(g).
2*g**2*(g + 1)**2/9
Suppose 490*i + 54 = 508*i. Factor -144/5 - 8*o**2 - 132/5*o - 4/5*o**i.
-4*(o + 3)**2*(o + 4)/5
Let g(n) be the first derivative of 2*n**3/39 - 342*n**2/13 + 58482*n/13 + 896. Factor g(s).
2*(s - 171)**2/13
Suppose 0 = 26*f - 65 + 13. Let z be (f/7)/((-78)/(-546)). Solve 0*m**4 + 0*m**z - 1/5*m**5 + 0*m + 0 + 1/5*m**3 = 0 for m.
-1, 0, 1
Let x(n) be the third derivative of 2*n**7/105 - 11*n**6/15 - 157*n**5/15 - 151*n**4/3 - 112*n**3 + 962*n**2. Solve x(m) = 0 for m.
-3, -2, -1, 28
Let w(t) be the second derivative of -t**7/504 - 25*t**6/72 - 625*t**5/24 + 113*t**4/12 + 136*t. Let j(x) be the third derivative of w(x). Factor j(u).
-5*(u + 25)**2
Let q(d) be the third derivative of 21*d**2 + 486/5*d**4 + 0 + 16/525*d**7 + 324/25*d**5 + 2187/5*d**3 + 0*d + 24/25*d**6. Factor q(b).
2*(2*b + 9)**4/5
Let y(l) be the second derivative of -19/42*l**4 - 22/21*l**3 - 31*l - 1/14*l**5 + 0 - 8/7*l**2. Suppose y(c) = 0. What is c?
-2, -1, -4/5
Let w(l) = -5*l**2 - 15*l - 3. Let s(v) = 5*v**2 + 15*v + 4. Let z be ((-6)/(-7))/(42/196). Let j(d) = z*w(d) + 3*s(d). Factor j(a).
-5*a*(a + 3)
Let c(l) be the third derivative of 13/60*l**4 + 0*l + 0 + 1/1050*l**7 - 26*l**2 - 2/25*l**5 - 3/10*l**3 + 1/100*l**6. Determine i, given that c(i) = 0.
-9, 1
Let c be 22352/7920 + 6/(-10). Factor -2/3 - c*b - 8/3*b**2 - 4/3*b**3 - 2/9*b**4.
-2*(b + 1)**3*(b + 3)/9
Let o = 17827 + -17827. Let h(w) be the third derivative of -1/150*w**5 - 17*w**2 + 1/30*w**4 + o*w**3 + 0*w + 0. Let h(t) = 0. Calculate t.
0, 2
Suppose 78*a = -4*s + 73*a + 6, 0 = 7*a + 14. Let g(r) be the first derivative of 3/10*r**s - 7/5*r**2 + 33 - 6/5*r + 14/15*r**3. Factor g(z).
2*(z - 1)*(z + 3)*(3*z + 1)/5
Let q = -5114 - -61369/12. Let f(v) be the first derivative of 0*v**4 + 1/48*v**6 - q*v**3 + 0*v + 1/20*v**5 - 1/16*v**2 + 21. Factor f(t).
t*(t - 1)*(t + 1)**3/8
Let v(y) = -y**5 - 65*y**4 - 1650*y**3 - 13340*y**2 - 2644*y + 73003. Let r(f) = 5*f**4 + f + 1. Let d(h) = -2*r(h) + 2*v(h). Let d(b) = 0. What is b?
-23, -3, 2
Let m be (-8 - -8)*(-24)/(-42 - -18). What is s in 3/7*s**3 + 0 - 12/7*s**2 + m*s = 0?
0, 4
Determine g so that -851*g - g + 55892 - 55043 + 3*g**2 = 0.
1, 283
Let z(p) = 8*p**2 + 4*p + 12. Let w(j) = -j**2 - j. Suppose -3*d = 26*d - 29. Let m(h) = d*z(h) + 12*w(h). Determine y, given that m(y) = 0.
-3, 1
Let r(z) = 12*z**2 + 80*z - 72. Let b(l) = 5*l**2 + 40*l - 37. Let o = 325 + -335. Let f(w) = o*b(w) + 4*r(w). Find t such that f(t) = 0.
-41, 1
Let m be (-18)/21 - (-36)/14*9231/153. What is w in -m*w + 48600/7 + 6/7*w**2 = 0?
90
Suppose -2*u - 3*p + 1 = 0, -6 + 0 = -2*u + 2*p. Let c be -1*(-90 + 42)/96. Suppose 5*w + c*w**u + 25/2 = 0. Calculate w.
-5
Let m(n) be the second derivative of 1/90*n**6 - 1/15*n**5 + 1/12*n**4 + 0*n**2 + 25*n + 0*n**3 + 1. Factor m(w).
w**2*(w - 3)*(w - 1)/3
Let k(w) = w**2 + 41*w - 331. Let u be k(-48). Suppose -22 = -3*f - 4*j + 8*j, u*j = 4*f - 28. Factor -4/5 - 6/5*m - 2/5*m**f.
-2*(m + 1)*(m + 2)/5
Let b(y) be the first derivative of -3*y**5/5 + 141*y**4/2 - 2472*y**3 + 18480*y**2 - 46464*y + 13789. Factor b(i).
-3*(i - 44)**2*(i - 4)*(i - 2)
Suppose -1076/3*a**2 - 4/3*a**3 - 3200/3*a - 2128/3 = 0. Calculate a.
-266, -2, -1
Let n(h) be the first derivative of 1/60*h**5 + 1/24*h**4 + 0*h - 1/9*h**3 - 1/3*h**2 - 54. What is z in n(z) = 0?
-2, 0, 2
Let c(n) = 7824*n - 31286. Let g be c(4). Factor 104/3*x - 28*x**2 + g*x**3 - 4/3*x**4 - 16.
-2*(x - 2)**3*(2*x - 3)/3
Let r be 25 + 1 + 88/(-22). Determine f, given that -r*f**2 - 30*f + 42*f + 14*f**2 - 4*f**3 = 0.
-3, 0, 1
Let v be 4 + (-75)/40 + 2/(-16). Let s be 2/v - 20/(-5). Let -6*y**4 - 27*y**5 + 3*y**4 + 14*y**s + 10*y**5 = 0. What is y?
-1, 0
Let x(c) = -12*c - 5. Let g be x(-4). Solve 31*w**2 - g*w**2 + 14*w - 36*w**3 + 67*w**2 = 0.
-2/9, 0, 7/4
Let m(b) be the first derivative of -12005/2*b**2 + 0*b - 89 - 735/2*b**4 - 5/6*b**6 - 28*b**5 - 6860/3*b**3. Solve m(c) = 0 for c.
-7, 0
Suppose 3*n = 9, 1334*l - 26*n = 1336*l - 84. Solve -432 + 141/4*d**2 + 396*d + 3/4*d**l = 0.
-24, 1
Let s be ((-84)/343)/((-73)/1022). Solve 4*y - 4/7*y**2 - s = 0.
1, 6
Let k be (-2 - 3)*38/(-95). Let x(g) be the first derivative of -1/2*g**4 + 2/5*g**5 + 0*g**k + 0*g**3 + 0*g + 30. Factor x(q).
2*q**3*(q - 1)
Let s(z) be the first derivative of -4*z**5/5 + 17*z**4 + 104*z**3/3 - 264*z**2 - 864*z + 1682. Let s(t) = 0. What is t?
-2, 3, 18
Solve 0 - 934/5*n**4 + 0*n - 9/5*n**5 + 2116/5*n**3 - 424/5*n**2 = 0 for n.
-106, 0, 2/9, 2
Let o(q) be the second derivative of -2*q**7/21 - 16*q**6/15 - q**5 + 38*q**4/3 - 16*q**3 - 961*q. Determine m so that o(m) = 0.
-6, -4, 0, 1
Let d(s) be the third derivative of -s**7/630 + 47*s**6/90 - 3007*s**5/60 + 961*s**4/4 - 7356*s**2. Find r such that d(r) = 0.
0, 2, 93
Let 2/11*p**2 - 48/11 + 20/11*p = 0. What is p?
-12, 2
Let m(z) be the first derivative of -z**6/3 + 2*z**5/5 + 5*z**4 - 20*z**3/3 - 9*z**2 + 18*z - 406. What is q in m(q) = 0?
-3, -1, 1, 3
Factor -6*t**3 - 33*t - 186 + 255 - 258 - 9*t**3 + 141*t**2.
-3*(t - 9)*(t + 1)*(5*t - 7)
Let c(h) be the first derivative of 4*h**6/45 - 82*h**5/75 - 3*h**4 + 26*h**3/9 + 86*h**2/15 - 16*h/5 - 1930. Solve c(i) = 0 for i.
-2, -1, 1/4, 1, 12
Let n(z) be the second derivative of z**5/80 + 19*z**4/48 + 21*z**3/8 + 45*z**2/8 + 3442*z. Suppose n(r) = 0. What is r?
-15, -3, -1
Let t(d) be the first derivative of -d**5/20 + 47*d**4/8 + 25*d**3 - 439*d**2/4 + 485*d/4 + 6808. What is j in t(j) = 0?
-5, 1, 97
Let v be ((-8)/(-14))/((-828)/(-966)). Let d(l) be the first derivative of 12 + v*l**3 + 0*l**2 + 0*l. Factor d(t).
2*t**2
Solve -67*m**2 + 94*m - 40*m**2 - 180 + 105*m**2 = 0.
2, 45
Let p(q) = 9*q**2 - 594*q + 1168. Let d(b) = -6*b**2 + 396*b - 778. Let t(h) = -8*d(h) - 5*p(h). Determine c so that t(c) = 0.
2, 64
Factor 101*c**2 + 66*c**2 + 2*c**4 + 136*c**2 - 1365 + 64*c + 149 - 75*c**2 - 50*c**3.
2*(c - 19)*(c - 4)**2*(c + 2)
Let t(w) be the third derivative of w**5/240 + 11*w**4/48 + 39*w**3/8 + 13*w**2. Factor t(a).
(a + 9)*(a + 13)/4
Let a(f) be the second derivative of f**6/15 - 32*f**5/5 + 60*f**4 - 704*f**3/3 + 464*f**2 - 7602*f. Factor a(i).
2*(i - 58)*(i - 2)**3
Factor 1/3*f**3 + 18*f**2 - 3*f - 162.
(f - 3)*(f + 3)*(f + 54)/3
Solve -514*x**2 + 977*x**2 + 1440 - 466*x**2 + 156*x = 0 for x.
-8, 60
Suppose 180*j**2 - 1 + 1 + 117234*j**4 + 532*j - 372*j**3 - 117254*j**4 = 0. What is j?
-19, -1, 0, 7/5
Factor 2*a**2 - 48 - 41*a - 6*a**2 - 104 + 197*a.
-4*(a - 38)*(a - 1)
Let k(f) be the second derivative of f**7/70 + 51*f**6/50 + 537*f**5/25 + 384*f**4/5 - 1152*f**3/5 + 336*f. Suppose k(h) = 0. Calculate h.
-24, -4, 0, 1
Suppose 50*g - 134 = 16. Let p(i) be the third derivative of 0*i - 4/15*i**g + 1/150*i**5 + 1/20*i**4 - 24*i**2 + 0. Factor p(h).
2*(h - 1)*(h + 4)/5
Suppose 88*s - 9 = 85*s + z, s - 3 = -3*z. Suppose -3*b + s*i + 21 = 0, 3*b - 4*i - 22 = 2. Find c, given that 1/2*c**2 + 1/2 - 9/4*c - c**b + 9/4*c**3 = 0.
-1, 1/4, 1, 2
Let h be 32/20 + 154/264*709/35. Let h*i**2 - 343/3 + 196/3*i - 17/12*i**4 - 67/12*i**3 - 1/12*i**5 = 0. What is i?
-7, 2
Let r be (-56)/(-60)*-2*(-920)/644. Suppose r*j - 20/3 + 1/3*j**2 = 0. What is j?
-10, 2
Suppose 0 - 4/5*k**4 + 194*k + 1934/5*k**3 + 2908/5*k**2 = 0. Calculate k.
-1, -1/2, 0, 4