5. Let q = z - 374. Determine r, given that 88/5*r**2 - q*r**3 + 4 - 94/5*r = 0.
2/7, 1, 5
Factor -34*f - 353*f**2 + 855 + 174*f + 358*f**2.
5*(f + 9)*(f + 19)
Let h(a) be the first derivative of a**5/20 - 43*a**4/16 + 10*a**3/3 + 21*a**2/2 + 5104. Find k, given that h(k) = 0.
-1, 0, 2, 42
Let x(u) be the second derivative of -u**8/1680 + u**7/315 - 3*u**4 + 3*u - 5. Let w(k) be the third derivative of x(k). Factor w(m).
-4*m**2*(m - 2)
Let l be 12/(45/(-20) - -3). Let h(c) = -c**2 + 91 - 3*c**2 - 99 + l*c - 4*c**3. Let u(n) = n - 1. Let w(d) = h(d) - 8*u(d). Factor w(i).
-4*i*(i - 1)*(i + 2)
Let c(y) be the first derivative of -y**3/3 - 2087*y**2/2 - 2086*y + 1920. Suppose c(s) = 0. Calculate s.
-2086, -1
Let f(j) be the third derivative of j**6/12 + j**5/30 - 15*j**4/4 - 3*j**3 - 1166*j**2. Factor f(p).
2*(p - 3)*(p + 3)*(5*p + 1)
Factor 15/4*c**3 - 27/4*c - 9/4*c**2 - 3/4*c**4 + 0.
-3*c*(c - 3)**2*(c + 1)/4
Factor 163*g - 28*g + 136 + 93663*g**2 - 93664*g**2.
-(g - 136)*(g + 1)
Factor -1767 + 1864*s - 5020 - 4*s**2 + 3075.
-4*(s - 464)*(s - 2)
Let w = -59 + 75. Suppose w = -3*p + 11*p. Factor -29*n + 12 + 46*n + 3*n**p - 29*n.
3*(n - 2)**2
Let p(v) be the first derivative of 4*v**3/3 + 192*v**2 - 784*v + 2440. What is q in p(q) = 0?
-98, 2
Let h(w) = -6 + 10 + 4*w + w**2 + 4*w. Let r(l) = -10*l - 5. Let s(c) = 5*h(c) + 4*r(c). Factor s(t).
5*t**2
Let l(b) = -54*b**3 + b**2 - 1. Let c be l(1). Let y = c - -59. Factor 12*x + 8*x**2 + 4 + 4*x**3 - 12*x**4 - 4*x**y - 11*x**3 - x**3.
-4*(x - 1)*(x + 1)**4
Let i(c) be the first derivative of 89 - 4/11*c + 14/55*c**5 + 15/22*c**4 - 2/11*c**6 - 10/33*c**3 - 9/11*c**2. Solve i(a) = 0.
-1, -1/2, -1/3, 1, 2
Let y = -479 - -500. Let a be -2*y/(-18)*(-35)/(-49). Solve a*x**3 + 1/3*x**4 + 0 - 5/3*x - 1/3*x**2 = 0.
-5, -1, 0, 1
Factor 1/7*d**2 - 60/7*d - 124/7.
(d - 62)*(d + 2)/7
Let -1/5*u**2 + 74/5 + 7*u = 0. What is u?
-2, 37
Determine c, given that -42/5*c + 0 + 171/5*c**3 - 1191/5*c**2 = 0.
-2/57, 0, 7
Let n = -1/8818 + 2205/4409. Let f(u) be the third derivative of 0 + 3/10*u**5 + 1/3*u**3 + n*u**4 + 1/15*u**6 + 31*u**2 + 0*u. Factor f(t).
2*(t + 1)**2*(4*t + 1)
Suppose 3*v - 7 = c, 0 = 5*c - 10*c - 5. Factor 36*y**2 - 7 - 73*y**v + 39*y**2 - 5 + 2*y.
2*(y - 2)*(y + 3)
Let z(u) = 1761*u**2 - 1758*u + 42. Let j(q) = -439*q**2 + 439*q - 10. Let g(b) = 9*j(b) + 2*z(b). What is o in g(o) = 0?
2/143, 1
Let -7*c**3 - 663*c**2 + 256348*c + 372 - 128942*c - 128518*c = 0. Calculate c.
-93, -2, 2/7
What is u in 7/3*u**4 + 0 + 3761/3*u**3 + 0*u + 358*u**2 = 0?
-537, -2/7, 0
Suppose 0 = 4*z + r - 23, 5 = z - 4*r + 5*r. Suppose -3*f + 3*q = -z, -f + 9*q = -10 + 8. Find k such that -2/5*k**f + 0 + 2/5*k = 0.
0, 1
Let d(o) be the third derivative of -o**7/980 + o**6/630 - 21*o**4/8 + 35*o**2. Let b(v) be the second derivative of d(v). Factor b(u).
-2*u*(9*u - 4)/7
Let v = -1419 - -1609. Let o = 192 - v. Factor -8/7 - 8/7*y + 2/7*y**o + 2/7*y**3.
2*(y - 2)*(y + 1)*(y + 2)/7
Let q(s) be the third derivative of s**8/2016 + 11*s**7/1260 + 7*s**6/720 - 143*s**5/360 + 7*s**4/18 + 49*s**3/9 + 2598*s**2. Let q(y) = 0. What is y?
-7, -1, 2
Let l = -10 + 17. Suppose -r + 0*r = 4*f - 11, -f + 3*r = l. Let -27*v**5 + v**f - 17*v**2 + 35*v**3 - 10*v + 2*v**5 + v**2 + 15*v**4 = 0. What is v?
-1, -2/5, 0, 1
Find y such that 94/3*y**2 - 12*y**3 + 0 + 2/3*y**4 - 20*y = 0.
0, 1, 2, 15
Let s(a) be the third derivative of -a**5/72 - 517*a**4/144 - 103*a**3/18 + 4198*a**2. Let s(n) = 0. What is n?
-103, -2/5
Let c be 43/15 + 3/(-15). Let y be 7*440/2100 + (-8)/60. Factor y*z**4 - 4*z - c + 4*z**3 + 4/3*z**2.
4*(z - 1)*(z + 1)**2*(z + 2)/3
Let n(q) = q - 25. Let t be n(20). Let z = 5 - t. Solve 0 - 15*s + 6*s**2 + 3*s**4 + 2*s**4 - z - s**2 + 15*s**3 = 0.
-2, -1, 1
Let 326/5*b**3 + 430/3*b - 188/5 + 22/15*b**4 - 862/5*b**2 = 0. Calculate b.
-47, 6/11, 1
Let c(p) = -p. Let w(b) be the first derivative of -b**3/3 + 15*b**2 + 39*b - 189. Let k(n) = -40*c(n) + 5*w(n). Factor k(v).
-5*(v - 39)*(v + 1)
Let x(r) = 10*r**3 + 21*r**2 + 117*r - 341. Let t(b) = 3*b**3 - b**2 - 1. Suppose 30 = -7*d - 12. Let z(c) = d*t(c) + 2*x(c). Factor z(k).
2*(k - 2)*(k + 13)**2
Let w(n) be the third derivative of -87808/9*n**3 + 1/360*n**6 - 14/15*n**5 + 0*n + 392/3*n**4 + 0 - 238*n**2. Suppose w(p) = 0. Calculate p.
56
Suppose -5*n = 27*r - 25*r - 56, -7*r + 71 = 5*n. Factor 2/13*t**2 + 2/13*t - 2/13 - 2/13*t**r.
-2*(t - 1)**2*(t + 1)/13
Let o(l) = l**3 + l**2 + 3*l - 2. Let g(a) = -196*a**3 + 379*a**2 - 194*a + 2. Let v(t) = g(t) + 3*o(t). Solve v(n) = 0.
-4/193, 1
Let w be 8/14*(((-52)/8)/1 - -10). Suppose -30/7 - 2/7*g**4 - 96/7*g**w - 92/7*g - 36/7*g**3 = 0. Calculate g.
-15, -1
Suppose 5*s + 6010 = 3*d, -3*d = 18*s - 22*s - 4808. Let f = s + 3638/3. Determine n, given that 64/9*n**2 + f*n + 4 = 0.
-3/4
Let p be (3/3 - 1)*2/4. Let k be -1 + 0 - (-4 - p)/1. Factor k*u - 46*u**2 - 15*u + 42*u**2.
-4*u*(u + 3)
Let z(i) be the first derivative of 5*i**6/18 - 2*i**5 - 15*i**4/4 + 290*i**3/9 - 10*i**2 - 120*i - 2485. Suppose z(n) = 0. What is n?
-3, -1, 2, 6
Let v(u) be the third derivative of -2*u**7/105 + 491*u**6/30 - 977*u**5/15 - 491*u**4/6 + 652*u**3 - 1149*u**2. Find r such that v(r) = 0.
-1, 1, 2, 489
Suppose 0 = 21*f + 28*f. Suppose 3*u - 2 = 4*l + 5*u, f = -5*l - 11*u - 11. Suppose 4/5*d**2 + 0*d + l - 6/5*d**3 + 2/5*d**4 = 0. Calculate d.
0, 1, 2
Let d(s) be the first derivative of -4*s**3/9 - 922*s**2/3 + 616*s - 690. Suppose d(x) = 0. Calculate x.
-462, 1
Let m(n) = 6*n**2 - 40*n - 36. Let s(c) = -28*c**2 + 200*c + 180. Let p be 1/6 - (-145)/30. Let d(k) = p*s(k) + 24*m(k). Factor d(f).
4*(f + 1)*(f + 9)
Let c = -171595948/2797 + 61350. Let i = 22398/30767 - c. Find r such that 8/11*r - 2/11*r**2 - i = 0.
2
Let h(a) be the third derivative of -5*a**3 + 0*a + 331*a**2 - 103/24*a**4 + 0 - 17/15*a**5 + 1/24*a**6. Find k such that h(k) = 0.
-1, -2/5, 15
Solve -123/2*p + 1/2*p**2 - 62 = 0.
-1, 124
Let c(n) = -n**3 + n**2 + 4*n. Let f(i) = 5*i**3 + 3878*i**2 + 5023292*i + 2166720184. Let x(k) = -8*c(k) - 2*f(k). Factor x(h).
-2*(h + 1294)**3
Let x(n) = n**5 - n**4 - n**3 - n**2 + 2. Let p(j) = 2*j**5 - 8*j**4 - 2*j**2 + 7 + 3 - 513*j**3 + 511*j**3. Let w(k) = p(k) - 5*x(k). Solve w(l) = 0.
-1, 0, 1
Let u(s) = s**4 - 60*s**3 + 2*s**2 + 192*s - 120. Let o(g) = -g**4 + 60*g**3 - g**2 - 190*g + 120. Let r(x) = -15*o(x) - 12*u(x). Factor r(b).
3*(b - 60)*(b - 1)**2*(b + 2)
Suppose -84 = -37*l + 9*l. Let w(u) be the first derivative of -2/9*u**l - 1/3*u**2 + 4/3*u + 27. Determine d, given that w(d) = 0.
-2, 1
Let b(z) be the second derivative of 3*z**5/16 - 3*z**4 - 875*z**3/8 - 513*z**2/4 + 112*z - 22. Find h such that b(h) = 0.
-9, -2/5, 19
Let x(c) = 4*c**2 + 5*c + 19. Suppose 4*b + b = -3*a + 11, a = -4*b + 13. Let m(t) = -t**2 + t - 1. Let g(l) = a*m(l) - x(l). Suppose g(v) = 0. What is v?
-4
Let j be 18/24*((-72)/(-1485))/(7/70). Let a = 3/17 - -1/187. Solve -2/11*l**4 + 0*l + 0 + j*l**2 + a*l**3 = 0 for l.
-1, 0, 2
Let z(u) be the first derivative of 5*u**3/3 - 715*u**2 + 102245*u - 1276. Factor z(l).
5*(l - 143)**2
What is l in 0 + 0*l + 82/9*l**3 + 80/9*l**4 - 2/9*l**5 + 0*l**2 = 0?
-1, 0, 41
Let d(h) be the second derivative of h**5/5 + 83*h**4/18 - 14*h**3/9 - 313*h - 1. Factor d(p).
2*p*(p + 14)*(6*p - 1)/3
Let 56*d**2 + 480/7*d + 20/7*d**4 - 192/7*d**3 - 100 = 0. What is d?
-7/5, 1, 5
Let h be 2/(-32)*-38 - (-2145)/(-5720). Factor 44/3*o + 0 - 4/3*o**3 + 40/3*o**h.
-4*o*(o - 11)*(o + 1)/3
Suppose -7 = -w - 2*d, -2*w = -w - 3*d + 18. Let t be w + 2 + 0 + 3. Determine q so that 125*q**2 - t*q**4 - 63*q**2 - 60*q**2 = 0.
-1, 0, 1
Let b(c) be the second derivative of 0 - 5*c**4 + 22*c**3 - 34*c**2 + 95*c - 1/5*c**5. Factor b(n).
-4*(n - 1)**2*(n + 17)
Let v(b) be the first derivative of b**5/36 + 5*b**4/12 - 40*b**3/9 + b**2/2 - 34*b - 8. Let x(z) be the second derivative of v(z). Suppose x(f) = 0. What is f?
-8, 2
What is o in -71*o**2 + 29 - 23 - 6*o**4 + 21*o**4 + 41*o**3 - 8*o**4 - 14*o**4 + 31*o = 0?
-1/7, 1, 2, 3
Factor -24 + 4*c - 332*c**2 + 23*c**4 - 9*c**3 + 350*c**2 - 22*c**4.
(c - 6)*(c - 2)**2*(c + 1)
Let p(z) be the second derivative of z**7/210 + z**6/24 + 2*z**5/15 + z**4/6 + 255*z**2/2 + 22*z + 5. Let q(w) be the first derivative