he third derivative of -k**8/294 + 34*k**7/735 + 29*k**6/210 + 2*k**5/21 - 107*k**2. Determine b, given that c(b) = 0.
-1, -1/2, 0, 10
Suppose -2*t + 47 = -5*q - 4*t, 0 = -2*q + t - 17. Let g = 12 + q. Determine p, given that -3*p**g + 9*p**2 - 9*p + 0 + 1 + 1 + 1 = 0.
1
Let 0 - 3/5*r**2 - 3/5*r**5 + 18/5*r - 31/5*r**3 + 19/5*r**4 = 0. Calculate r.
-2/3, 0, 1, 3
Find l such that -3/4*l**5 + 3*l**2 + 0*l - 9/4*l**4 + 0 + 0*l**3 = 0.
-2, 0, 1
Let y(a) be the first derivative of 2*a**6/3 + 16*a**5/5 - 6*a**4 - 128*a**3/3 - 70*a**2 - 48*a + 111. Suppose y(i) = 0. Calculate i.
-4, -1, 3
Factor -42*i**2 - 10*i + 20 + 22*i + 50*i**2 + 14*i.
2*(i + 2)*(4*i + 5)
Let r = -279 + 276. Let z be 32/20 + (-4 - r). Determine l, given that 6*l - 15 - z*l**2 = 0.
5
Suppose 0*r - 17 = -5*q - r, -r = 4*q - 13. Factor -97 - m + m**3 + 97 + m**2 - m**q.
-m*(m - 1)**2*(m + 1)
Let q(w) be the third derivative of 0 + 1/72*w**6 + 5/72*w**4 + 6*w**2 + 0*w + 0*w**3 + 1/18*w**5. Factor q(g).
5*g*(g + 1)**2/3
Let j = -225 - -229. Let i(y) be the second derivative of 2/3*y**3 + 3/10*y**5 + 0*y**2 - 7*y + 0 + 5/6*y**j. Solve i(n) = 0 for n.
-1, -2/3, 0
Let j(f) = -18*f - 12. Let n be j(-4). Factor -11*g**2 + n*g + 51*g**2 + 24 - 29*g**3 + 3*g**4 + 14*g**2 + 50*g**3.
3*(g + 1)*(g + 2)**3
Let x(o) be the first derivative of -3*o**4/16 - 117*o**3/4 - 693*o**2/8 - 345*o/4 + 521. Let x(w) = 0. What is w?
-115, -1
Let s(i) be the third derivative of i**6/360 - i**5/45 + i**4/18 + 89*i**2. Factor s(j).
j*(j - 2)**2/3
Let p(o) be the first derivative of -o**4/16 - o**3/6 + 19*o**2/8 + 5*o + 293. Factor p(f).
-(f - 4)*(f + 1)*(f + 5)/4
Let z(p) be the third derivative of -p**8/15680 + p**7/5880 - 7*p**5/12 - 7*p**2. Let j(d) be the third derivative of z(d). Solve j(i) = 0 for i.
0, 2/3
Let z(k) = 1693*k**2 + 1704*k**2 + 20*k - 3433*k**2 - 5*k. Let i be 2/(14/(-10) + 1). Let y(j) = -7*j**2 + 3*j. Let t(c) = i*z(c) + 24*y(c). Factor t(r).
3*r*(4*r - 1)
Let m(o) be the first derivative of 25*o**3/3 - 70*o**2 + 115*o - 19. What is x in m(x) = 0?
1, 23/5
Let p(r) = r**3 + r**2 - 3. Suppose -3*h + 12 = -9*h. Let u(y) = -2 + y**3 + 0*y**3 + y**2 + 0*y**2. Let z(i) = h*p(i) + 3*u(i). What is v in z(v) = 0?
-1, 0
Factor -1/5*i**3 + 4*i - 24/5 - 2/5*i**2.
-(i - 2)**2*(i + 6)/5
Let o(v) = 9*v**3 - 101*v**2 + 43*v. Let a(h) = -3*h. Let q(x) = 21*a(x) + 3*o(x). Determine n, given that q(n) = 0.
0, 2/9, 11
Let f(g) be the first derivative of 0*g - 2/3*g**3 - 2/15*g**5 - 1/3*g**2 - 1/2*g**4 - 17. Solve f(p) = 0.
-1, 0
Suppose 4*v + 2*s = -10, -v - 4 = -5*s + 15. Let q be 980/455 - v*1/(-26). Factor 2/3*g**3 + 0 + 2/3*g - 4/3*g**q.
2*g*(g - 1)**2/3
Let r(s) be the second derivative of 1/60*s**5 + 0 + 0*s**4 + 4*s - 1/3*s**2 - 1/6*s**3. What is l in r(l) = 0?
-1, 2
Let l(v) = -v**3 + 4*v**2 + v + 4. Let h(z) = -5*z**3 + 25*z**2 + 5*z + 25. Let a(k) = -4*h(k) + 25*l(k). Determine y, given that a(y) = 0.
-1, 0, 1
Let c be ((-28)/8 + 28/7)*0/(-5). Factor -8/9*h**2 + 2/9*h + c.
-2*h*(4*h - 1)/9
Let i = 5115/533 - 138/41. Let t = i - 813/143. Factor t*m**3 + 4/11 + 6/11*m - 16/11*m**2.
2*(m - 2)*(m - 1)*(3*m + 1)/11
Let c(x) = 10*x**2 + 24*x - 22. Let d(k) = 21*k**2 + 52*k - 45. Let g(o) = 13*c(o) - 6*d(o). Factor g(s).
4*(s - 2)*(s + 2)
Let l = -280 - -1121/4. Let p(n) be the first derivative of -1/4*n - 1 + 7/12*n**3 - 1/4*n**4 - l*n**2. Let p(g) = 0. What is g?
-1/4, 1
Suppose -4*n + z + 8 = 5*z, 0 = -2*n + 4*z + 22. Let q(a) = a**2 - 1. Let b(w) = -5*w**2 - 3*w + 6. Let x(c) = n*b(c) + 30*q(c). Factor x(h).
5*h*(h - 3)
Determine j so that 85/4*j**2 + 25 + 0*j**3 - 5/4*j**4 + 45*j = 0.
-2, -1, 5
Let u(j) = -17*j**2 - 1548*j - 66516. Let t(r) = 11*r**2 + 1032*r + 44346. Let z(k) = -8*t(k) - 5*u(k). Solve z(n) = 0 for n.
-86
Let b(w) = -382*w**2 + 699*w + 53. Let s(a) = 255*a**2 - 465*a - 35. Let i(o) = 5*b(o) + 7*s(o). Suppose i(y) = 0. What is y?
-2/25, 2
Let d(u) = u**3 - 14*u**2 + 14*u - 13. Let a be d(13). Let x(i) be the first derivative of 1/3*i**3 + a*i - 1/2*i**2 + 5. Find b such that x(b) = 0.
0, 1
Solve 2*r**2 + 3/7*r - 17/7*r**3 + 0 = 0.
-3/17, 0, 1
Let o be 10/2 + (-1)/(6/30). Let -1/2*j**3 + 1/2*j**2 + 0*j + o = 0. Calculate j.
0, 1
Find r, given that -8/5*r**2 + 4*r**3 - 84/5*r - 2/5*r**4 - 54/5 = 0.
-1, 3, 9
Let s(u) = u + 12. Let w be s(-6). Factor l**3 + 0*l**3 - w*l**3 + 12*l**2 + 2*l**3.
-3*l**2*(l - 4)
Suppose 1369/4 + 1/4*k**2 + 37/2*k = 0. What is k?
-37
Suppose 2*g = -3*v + 24, -1275*v - g = -1270*v - 26. Factor s**v - 1/2*s**3 + 0*s + 0*s**2 + 0.
s**3*(2*s - 1)/2
Suppose 0 = -16*w + 94 - 46. Factor 4/13 + 0*b**2 + 2/13*b**w - 6/13*b.
2*(b - 1)**2*(b + 2)/13
Solve 159/5*f**3 + 114/5*f**4 + 0 + 12/5*f + 84/5*f**2 + 27/5*f**5 = 0.
-2, -1, -2/9, 0
Let l(d) be the second derivative of -d**4/66 - 5*d**3/11 + 16*d**2/11 - 42*d. Solve l(i) = 0.
-16, 1
Let t(r) be the first derivative of 3/4*r**4 + 6*r - 3/2*r**2 + 5 - 3*r**3 + 3/5*r**5. Solve t(c) = 0.
-2, -1, 1
Let f(l) be the first derivative of 21*l**4/4 - 23*l**3/3 - 62*l**2 + 12*l + 230. Factor f(u).
(u - 3)*(u + 2)*(21*u - 2)
Let f(a) be the second derivative of -a**6/90 - 8*a**5/15 - 32*a**4/3 + 8*a**3/3 + 28*a. Let v(c) be the second derivative of f(c). Factor v(d).
-4*(d + 8)**2
Let l(n) be the first derivative of -1 - 1/6*n**5 + 3/2*n**2 + 0*n + 4/3*n**4 - 19/6*n**3. Determine r, given that l(r) = 0.
0, 2/5, 3
Let t = -2053/5 + 411. Let n(w) be the first derivative of 0*w**2 + 1 - 4/15*w**3 + 2/25*w**5 + t*w + 0*w**4. Let n(d) = 0. Calculate d.
-1, 1
Factor -64*z + 64 + 24*z**2 + 1/4*z**4 - 4*z**3.
(z - 4)**4/4
Let r(a) = -4*a**2 - 8*a. Let y(c) = c**3 + c**2 - c. Let p = 21 - 20. Let s(i) = p*r(i) - 4*y(i). Let s(j) = 0. What is j?
-1, 0
Let x(u) be the second derivative of -1/80*u**5 + 0 - 10/3*u**3 - 30*u + 17/48*u**4 + 8*u**2. Solve x(o) = 0 for o.
1, 8
Let o(f) be the third derivative of -13*f**5/50 - 2*f**4/3 - f**3/15 + f**2 + 153*f. Find g such that o(g) = 0.
-1, -1/39
Let z = -5235 - -5238. What is f in -1/3*f**4 - f**z + 2/3*f**2 + 1 + 13/6*f + 1/6*f**5 = 0?
-1, 2, 3
Suppose 0*o + 3*o = 0. Let k(f) = o + 12*f - 5 + f**2 + 9*f - 12. Let q(n) = n**2 + 31*n - 25. Let y(i) = -7*k(i) + 5*q(i). Factor y(h).
-2*(h - 3)*(h - 1)
Let h = -28 + 41. Let d(g) = -4*g - 2*g + 7*g**2 - 8 + h - g. Let b(z) = 11*z**2 - 11*z + 8. Let r(l) = 5*b(l) - 8*d(l). Let r(a) = 0. Calculate a.
0, 1
Let g(a) be the second derivative of a**4/114 + 17*a**3/57 + 16*a**2/19 - 2*a. Let g(t) = 0. Calculate t.
-16, -1
Suppose -9*y + 16 = -2. Let 0*x + 2/9*x**5 + 0 + 2/9*x**3 + 0*x**y - 4/9*x**4 = 0. Calculate x.
0, 1
Suppose o = a - 41, 2*o + 45 + 52 = 5*a. Let g be 24/(-9)*3/o. Factor 2/3*t**4 + 0 - g*t**2 + 4/9*t - 8/9*t**3.
2*t*(t - 1)**2*(3*t + 2)/9
Suppose 5*a - 26 = -3*v, -a = 2*v + 2*v - 12. Suppose -2 = 2*y - 3*p, 3*y + 4*p - 1 = 6*y. Find b such that 0*b**4 - 4*b**3 - b + v - 2*b**4 + y*b + 0*b**3 = 0.
-1, 1
Let q(h) be the third derivative of -h**7/2205 + 19*h**6/1260 + 23*h**5/315 - 19*h**4/63 - 8*h**3/3 - 9*h**2 - 28*h. Find a, given that q(a) = 0.
-2, 2, 21
Factor -17*q**2 + 233*q**3 + 42*q**2 - 248*q**3 - 40*q**4.
-5*q**2*(q + 1)*(8*q - 5)
Find g such that -g - 13506 - 15*g**2 + 13506 - 64*g**2 = 0.
-1/79, 0
Let a be 9/(-21) - (-1)/1. Let k(t) = 10*t**2 + 305*t - 153. Let o be k(-31). Let a*v**3 + 10/7*v**o + 1/7*v - 2/7 - 8/7*v**4 - 5/7*v**5 = 0. What is v?
-1, 2/5, 1
Factor -7/2*l**3 - 27/2*l**2 + 1/2*l**4 - 29/2*l - 5.
(l - 10)*(l + 1)**3/2
Let r be ((-40)/2)/2 - (19 + -31). What is o in 0 + 1/5*o**4 + 0*o - 1/5*o**5 - 1/5*o**r + 1/5*o**3 = 0?
-1, 0, 1
Let u be (-375)/10*16/(-10). Find v, given that -6 + 9 + 5 - 15*v - u*v**2 + 2 - 35*v**3 = 0.
-1, 2/7
Let a(i) be the third derivative of i**5/150 + 31*i**4/60 + 2*i**3 + 31*i**2. Solve a(r) = 0 for r.
-30, -1
Suppose -2*f + 1 = -7. Suppose 0 = -4*d + 12, 0*d - f*d = -2*l - 2. Factor 7*v**2 - l*v**2 + 2*v**2.
4*v**2
Let h(k) be the second derivative of -k**7/42 - k**6/12 + k**5/12 + 5*k**4/12 + k**2/2 - k - 2. Let g(b) be the first derivative of h(b). Factor g(d).
-5*d*(d - 1)*(d + 1)*(d + 2)
Let l be (5 + 2 - 6) + 2. Let h(y) be the first derivative of 1/2*y**4 + 0*y + 4/3*y**l + y**2 - 3. Factor h(z).
2*z*(z + 1)**2
Let u(k) be the second derivative of -k**5/35 - 17*k**4/21 - 40*k**