- 71. Let l be b(-8). Let d be -9 - (-10 + l/44). Suppose 0 + 1/2*q + d*q**2 - 1/4*q**3 = 0. What is q?
-1, 0, 2
Let u = 41 + -6. Let d = 39 - u. Determine c so that 0*c - 2/5*c**3 - 4/5*c**d + 4/5*c**2 + 0 + 2/5*c**5 = 0.
-1, 0, 1, 2
Let u = 2721595/1166394 + -3/388798. Let 1/3*h**2 + 10/3 + u*h = 0. What is h?
-5, -2
Let y(f) = -f**2 - 18*f - 62. Let t be -4 - (-111)/(-12) - (-2)/8. Let v be y(t). Solve 42*r**5 + 124*r**4 + 111*r**3 - 23*r**v - 10*r**2 + 26*r**2 = 0.
-2, -2/3, -2/7, 0
Let a(z) = -20*z**3 + 377*z**2 + 775*z + 404. Let u(w) = -6*w**3 + 126*w**2 + 258*w + 134. Let j(g) = -8*a(g) + 26*u(g). Factor j(c).
4*(c + 1)**2*(c + 63)
Let p(l) be the second derivative of 7 - 2/9*l**4 - 7/9*l**3 + 3*l + 2/3*l**2. Let p(m) = 0. Calculate m.
-2, 1/4
Let u = -354 - -356. Solve a**2 - 120*a - 12*a**u + 5*a**3 - a**2 + 0*a**2 - 13*a**2 = 0 for a.
-3, 0, 8
Let v(b) be the second derivative of -b**6/75 + b**5/50 + b**4/15 + 2*b + 1072. Factor v(d).
-2*d**2*(d - 2)*(d + 1)/5
Let o(n) be the third derivative of 3*n**7/70 - 19*n**6/20 + 42*n**5/5 - 36*n**4 + 64*n**3 + 2*n**2 + 5*n - 57. Factor o(f).
3*(f - 4)**3*(3*f - 2)
Solve 29/5*a**3 - 2*a**4 + 12/5*a + 0 - 32/5*a**2 + 1/5*a**5 = 0 for a.
0, 1, 2, 6
Let i = -51 - -56. Factor b**2 - 15*b + 8*b + i + 4*b - 3.
(b - 2)*(b - 1)
Factor 0 - 4/5*j**4 - 1/5*j**5 + 18/5*j**2 + 3/5*j**3 + 0*j.
-j**2*(j - 2)*(j + 3)**2/5
Let z(d) be the third derivative of d**5/300 + 71*d**4/120 + 34*d**3/5 + 1364*d**2 - 2*d. Factor z(n).
(n + 3)*(n + 68)/5
Suppose 0 = -3*b + 1340 - 1181. Determine l, given that -33*l - 52 - 48*l**2 + 2*l**3 - 34*l - 88*l + b*l = 0.
-1, 26
Let b = 5398/5975 - -90/239. Let n = b + 398/275. Factor -2/11*v**3 - n*v - 50/11 + 18/11*v**2.
-2*(v - 5)**2*(v + 1)/11
Find y, given that 41/7*y**4 - 20/7 - 16*y - 131/7*y**2 - 2/7*y**3 + 4/7*y**5 = 0.
-10, -1, -1/4, 2
Suppose 5*m - 21 = -0*f + 2*f, -30 = -4*m - 5*f. Find u such that 6*u**3 - 6*u - 8*u**2 + 4*u**4 - u - 5*u + 4*u - 2*u**m = 0.
-1, 0, 2
Let v(a) be the third derivative of a**5/480 - 713*a**4/192 - 119*a**3/8 + 4676*a**2. Factor v(q).
(q - 714)*(q + 1)/8
Let d = 139581 - 139581. What is i in 1/8*i**2 + d - 1/8*i**3 + 0*i = 0?
0, 1
Let y(g) be the third derivative of 0*g - 1/30*g**6 + 0*g**3 - 267*g**2 + 0 - 1/5*g**5 - 1/3*g**4. Factor y(x).
-4*x*(x + 1)*(x + 2)
Let q(i) = i**3 - i**2. Let s(j) = -4*j**3 - 8*j**2 - 6*j. Suppose -d + 3*w = -4, -4*w + 5*w + 1 = 0. Let g(p) = d*s(p) + q(p). Factor g(b).
-3*b*(b + 1)*(b + 2)
Suppose 2*w - 5*z + 16 + 6 = 0, 5*w + 34 = 2*z. Let r be w/27 - (-252)/162. What is k in -13/3*k**4 + 1 + 8/3*k - 4*k**3 - r*k**5 + 2/3*k**2 = 0?
-1, 3/4
Let h(t) = 4*t**2 - 4*t + 2. Let v be h(1). Factor -5*k**2 - k**2 + v*k**2 - 16*k - 4*k - 16*k.
-4*k*(k + 9)
Solve -496680*k**2 + 330341328*k + 9*k**4 + 1498063*k**2 + 109783104 + 1977653*k**2 + 8967*k**3 = 0.
-332, -1/3
Let s(g) be the third derivative of g**7/210 + 51*g**6/40 + 88*g**5 - 5600*g**4/3 + g**2 + 1719*g. Factor s(l).
l*(l - 7)*(l + 80)**2
Let b(z) be the first derivative of -z**4/26 + 2*z**3/39 + 49*z**2/13 - 98*z/13 - 2891. Factor b(s).
-2*(s - 7)*(s - 1)*(s + 7)/13
Let f(o) = 3*o**2 - 4*o. Let s(c) = -4*c**2 + 7*c. Let g = -26 + 22. Let y(v) = g*s(v) - 7*f(v). Factor y(b).
-5*b**2
Let j be 34/(-8)*(-6628)/140845. Let z be (1 + 0)*(-3 - -5). Factor j*h**3 + 1/5*h**z - 6/5*h + 0.
h*(h - 2)*(h + 3)/5
Let l(v) = -8*v**3 + 8*v - 4. Let k(x) = x**4 - 9*x**3 + x**2 + 9*x - 5. Let g = 29 + -18. Suppose -7*c = -g*c + 12. Let i(j) = c*l(j) - 4*k(j). Factor i(r).
-4*(r - 2)*(r - 1)**2*(r + 1)
Let q be 1161/(-7740) - (-63)/20. Factor -3/4*v**2 + 3 + q*v - 3/4*v**3.
-3*(v - 2)*(v + 1)*(v + 2)/4
Suppose 3*g - 132 = -2*s + 2*g, 4*s = 2*g + 248. Factor -12*n**2 + 72*n**2 + s*n**3 + 4*n**5 - 27*n**2 + 15*n**2 + 28*n**4.
4*n**2*(n + 2)**2*(n + 3)
Factor 111*f**4 + 175*f**3 + 2160 + 3144*f**2 + 174*f**3 - 8*f**5 + 194*f**3 + 5*f**5 + 4272*f + 465*f**3.
-3*(f - 45)*(f + 2)**4
Find j such that -351*j - 303*j + 2*j**2 - 262*j - 1 + 1008*j + 259 = 0.
-43, -3
Let z = -51376 + 51380. Solve 0 - 6/5*h + 3/5*h**3 + 3/5*h**5 + 9/5*h**z - 9/5*h**2 = 0 for h.
-2, -1, 0, 1
Let a(o) be the third derivative of 1/120*o**5 + 1/18*o**3 + 0 - 5/144*o**4 + 66*o**2 + 0*o. Factor a(j).
(j - 1)*(3*j - 2)/6
What is s in -153/5*s - 162/5 - 3/5*s**3 - 42/5*s**2 = 0?
-9, -3, -2
Let q(s) be the third derivative of s**6/210 - 104*s**5/21 - 149*s**4/6 - 348*s**3/7 - 420*s**2. Determine r, given that q(r) = 0.
-1, 522
Factor 39*t - 80*t**2 + 0*t**3 + 4*t**3 - 256 + 408 + 29*t.
4*(t - 19)*(t - 2)*(t + 1)
Let r = 468 - 323. Factor 2113*f + 12*f**3 - 92 - 20 - 175*f**2 - r*f**2 - 2557*f.
4*(f - 28)*(f + 1)*(3*f + 1)
Let d(u) be the third derivative of -1/16*u**5 + 0 + 150*u**2 + 1/32*u**4 + 5/8*u**3 + 0*u - 1/160*u**6. Factor d(b).
-3*(b - 1)*(b + 1)*(b + 5)/4
Let z = 39 + -81. Let k be (z/18 - -3)*6/2. Find t, given that 2*t**2 - 5*t**3 + 10*t - 2*t**2 - t**2 - 4*t**k = 0.
-2, 0, 1
Factor 3288*c**4 - c**5 - 3259*c**4 - 103*c - 250*c**3 + 38 - 430*c + 586*c**2 + 131.
-(c - 13)**2*(c - 1)**3
Find a such that a**2 - 43387 + 43030 + 86*a + 30*a = 0.
-119, 3
Let u = 13/720 + 563/720. Factor u*s**3 - 2/5*s**5 + 2/5*s**4 + 2/5 - 4/5*s**2 - 2/5*s.
-2*(s - 1)**3*(s + 1)**2/5
Let b be ((-390)/(-52))/(870/232). What is y in -10*y**4 + 0 + 10*y**b + 75/2*y**3 + 0*y = 0?
-1/4, 0, 4
Let n(s) be the first derivative of -2/7*s**3 - 1/28*s**4 + 153 + 0*s**2 + 0*s. Factor n(b).
-b**2*(b + 6)/7
Let x(j) be the second derivative of j**6/40 + 9*j**5/10 + 89*j**4/8 + 60*j**3 + 975*j**2/8 - 1138*j. Let x(m) = 0. Calculate m.
-13, -5, -1
Let n = 157812 - 157812. Factor -28/9*t - 2*t**2 + n - 2/9*t**3.
-2*t*(t + 2)*(t + 7)/9
Let m be (-7)/3*40/280*(-2 + 2). Find k, given that -1/4*k**5 - 9/4*k**3 + 7/4*k**2 + m + 5/4*k**4 - 1/2*k = 0.
0, 1, 2
Suppose -3*a = -2*l - 6, -2*a + 8 = 3*l - 9. Let -18*s - 11*s**2 - a*s**2 - 287 + 284 = 0. Calculate s.
-1, -1/5
Let m(f) = -f**3 + 40*f**2 - 38*f + 8. Let w be m(39). Let u(t) = t**2 - 54*t + 333. Let y be u(w). Factor 9 + 21/2*h**3 + 51/2*h**2 + 3/2*h**y + 51/2*h.
3*(h + 1)**2*(h + 2)*(h + 3)/2
Let u = 2427476/5 + -485492. Let -2/5*w**4 + 0 - 28/5*w**2 - u*w - 14/5*w**3 = 0. Calculate w.
-4, -2, -1, 0
Let j(o) = -12*o**2 - 96*o - 291. Let c(q) = 15*q**2 + 92*q + 289. Let n(b) = -3*c(b) - 4*j(b). Factor n(l).
3*(l + 3)*(l + 33)
Let n(k) be the first derivative of -k**2/2 + k + 28. Let m(u) = 4*u**2 - 5*u + 1. Let i(a) = m(a) + 4*n(a). Factor i(v).
(v - 1)*(4*v - 5)
Factor 6/5 - 4/5*f - 2/5*f**2.
-2*(f - 1)*(f + 3)/5
Suppose y = -4*y + 125. Solve 2*h**3 - 57*h - 20*h**2 + 57*h - y*h**5 - 82*h**3 - 85*h**4 = 0 for h.
-2, -1, -2/5, 0
Let s = 44705/536 - 2682/67. Let 41/2*d + 5/2 + 63/8*d**3 + s*d**2 = 0. What is d?
-5, -2/7, -2/9
Factor -2/5*a**3 + 10*a - 8/5*a**2 + 56/5.
-2*(a - 4)*(a + 1)*(a + 7)/5
Let v(q) = -17*q**3 - 355*q**2 + 1348*q - 1368. Let a(y) = -70*y**3 - 1425*y**2 + 5390*y - 5470. Let j(u) = 6*a(u) - 25*v(u). Factor j(r).
5*(r - 2)**2*(r + 69)
Let x = 184 + -172. Solve 10*s**2 + 25*s + 42 - x*s**2 - 33*s = 0.
-7, 3
Let s = -21 + 23. Factor -6*k**2 + 5120 + 4*k**2 + 320*k - s*k**2 + 9*k**2.
5*(k + 32)**2
Let y(d) be the second derivative of 8*d + 17/2*d**2 + 0*d**3 - 1/8*d**6 + 0 + 3/10*d**5 - 1/8*d**4. Let w(i) be the first derivative of y(i). Factor w(g).
-3*g*(g - 1)*(5*g - 1)
Suppose -1540/3*d**3 - 85*d**4 - 1040*d**2 - 80/3 - 720*d = 0. What is d?
-2, -2/51
Let i be (8 + -4)*(28/8 - 3). Let u be ((-20)/175)/(i/(-14)). Factor u*j - 2/5*j**2 + 6/5.
-2*(j - 3)*(j + 1)/5
Let j = -17 + 19. Factor 35 - 52 + 4*f**4 + 10 + 43 + 32*f**3 + 96*f + 88*f**j.
4*(f + 1)**2*(f + 3)**2
Let c(t) be the first derivative of -2*t**6/21 + 36*t**5/35 - 26*t**4/7 + 136*t**3/21 - 6*t**2 + 20*t/7 + 2630. Let c(l) = 0. What is l?
1, 5
Suppose -657*h - 311 + 894 = -731. Suppose -2/3*m**4 + 2*m**h + 14/15*m - 4/15 + 2/15*m**3 = 0. What is m?
-1, 1/5, 2
Let k be 6/((-13)/((-8905)/10)). Factor k*y + 6*y**2 - y**2 - 3*y**3 + 4*y**5 - 5*y**4 - 204*y - 208*y.
y*(y - 1)**2*(y + 1)*(4*y - 1)
Let c(d) be the first derivative of 1/2*d**3 - 15/2*d + 29 + 3*d**2. Suppose c(h) = 0. What is h?
-5, 1
Let y(a) be the third derivative of -a**6/30 + 41*a**5/60 + a**4/6 - 41*a**3/6 + 130*a**2 + 2. Determine v, given t