-9*p**4 - 71*p**3 - 121*p**2 - 46*p + 23. Let a(r) = -2*m(r) + 10*w(r). Find i such that a(i) = 0.
-3, -1, 2/9
Let p(l) be the second derivative of l**10/90720 + l**9/11340 + l**8/4032 + l**7/3780 - 7*l**4/6 + 13*l. Let i(s) be the third derivative of p(s). Factor i(u).
u**2*(u + 1)**2*(u + 2)/3
Let x be -2*4/10*(-250)/800. Factor 0 - 1/2*z - 3/4*z**2 - x*z**3.
-z*(z + 1)*(z + 2)/4
Let m(b) = b**3 - 7*b**2 + 3. Suppose -2*x = -3*l - 2, 5*x - 4*l - l = 15. Let g be m(x). Factor -2*j**g + 6*j**2 + 4*j**3 + 0*j - 3*j**3 - 9*j.
-j*(j - 3)**2
Let o(w) be the second derivative of -w**6/630 - 2*w**5/105 - 2*w**4/21 - 17*w**3/6 + 10*w. Let m(d) be the second derivative of o(d). Factor m(s).
-4*(s + 2)**2/7
Solve 16/7 + 12/7*m + 2/7*m**2 = 0 for m.
-4, -2
Let f(a) be the first derivative of 1/8*a**4 + 10 + 0*a**3 - 1/4*a**2 - 1/20*a**5 + 1/4*a. Let f(y) = 0. Calculate y.
-1, 1
Let r(v) be the third derivative of 1/60*v**7 + 0 + 13/120*v**6 + 0*v + 9/40*v**5 - 1/3*v**3 + 8*v**2 + 1/12*v**4. Find z such that r(z) = 0.
-2, -1, 2/7
Let s(w) = w + 6. Let c be ((-1)/(-3))/((-1)/6). Let u be s(c). Let 1/2*a**5 + 0 + 0*a**2 + 0*a**u - 1/2*a**3 + 0*a = 0. What is a?
-1, 0, 1
Let i = 19 + -17. Factor -8*t + 4 - 4*t**2 + 0*t + 5*t + t**3 + i*t.
(t - 4)*(t - 1)*(t + 1)
Let c(y) = -y**2 + y - 4. Let h(w) = w - 1. Let x(v) = c(v) - 4*h(v). Let o be x(-2). Factor -n**3 - 69*n**2 + 73*n**o - 3*n**3.
-4*n**2*(n - 1)
Factor 0 - 18/5*y**3 - 27/5*y**4 - 12/5*y**5 - 3/5*y**2 + 0*y.
-3*y**2*(y + 1)**2*(4*y + 1)/5
Determine x, given that 86 + 33 + 2*x**2 - 56*x + 5 - 20 = 0.
2, 26
Let s(f) be the third derivative of f**8/336 - 2*f**7/105 - f**6/60 + f**5/5 + 3*f**4/8 + 9*f**2 + 6*f. Factor s(r).
r*(r - 3)**2*(r + 1)**2
Let r(k) be the first derivative of 49*k**3 + 252*k**2 + 432*k + 62. Factor r(v).
3*(7*v + 12)**2
Let w(d) be the first derivative of 1/48*d**4 - 4 + 0*d**3 - 1/8*d**2 + 7*d. Let j(x) be the first derivative of w(x). Find i, given that j(i) = 0.
-1, 1
Let z(v) be the first derivative of -5*v**4/12 - 40*v**3/9 - 85*v**2/6 - 50*v/3 - 725. Factor z(y).
-5*(y + 1)*(y + 2)*(y + 5)/3
Let q(b) = -5*b**3 - 5*b**2 + 5*b - 6. Let g(m) = 5*m - 2*m**2 - 6*m - 2*m - 2 - 2*m**3 + 5*m. Let w(a) = 11*g(a) - 4*q(a). Suppose w(j) = 0. What is j?
-1, 1
Factor 22*c - 1/4*c**2 + 89/4.
-(c - 89)*(c + 1)/4
Let g(m) be the second derivative of m**4/48 + 5*m**3/4 + 225*m**2/8 - 24*m. Factor g(h).
(h + 15)**2/4
Let l(a) be the first derivative of a**3/30 - a**2/4 - 12*a/5 - 115. What is s in l(s) = 0?
-3, 8
Let o(a) be the third derivative of 0 + 0*a + 5/4*a**3 - 10*a**2 + 3/40*a**5 + a**4. Factor o(v).
3*(v + 5)*(3*v + 1)/2
Factor -21*p**3 - 17*p**3 - 20*p**2 + 43*p**3 + 5*p + 30.
5*(p - 3)*(p - 2)*(p + 1)
Let h = -2572 - -2574. Factor 16/5 + 1/5*k**h - 8/5*k.
(k - 4)**2/5
Let c(m) be the third derivative of m**8/131040 - m**6/4680 - m**5/5 + 19*m**2. Let a(s) be the third derivative of c(s). Factor a(o).
2*(o - 1)*(o + 1)/13
Let h(z) = 21*z**2 + 135*z + 6. Let s(r) = 17*r**2 + 137*r + 5. Let i(y) = 5*h(y) - 6*s(y). Determine a, given that i(a) = 0.
0, 49
Let q(o) be the first derivative of o**4/4 - 8*o**3 + 96*o**2 - 512*o - 57. Suppose q(a) = 0. What is a?
8
Determine h, given that -186*h + 45/2*h**3 + 6*h**5 + 87/2*h**4 - 165*h**2 - 36 = 0.
-6, -2, -1, -1/4, 2
Let u(i) be the second derivative of i**7/21 - 2*i**6/5 + 6*i**5/5 - 4*i**4/3 + 4*i + 3. Factor u(s).
2*s**2*(s - 2)**3
Suppose -1125*g + 1126*g = 3. Find u such that 3/5*u**2 - 3/5*u**g - 3/5 + 3/5*u = 0.
-1, 1
Let 412*z - 189*z**4 + 60*z**4 + 164616 + 62*z**4 + 64*z**4 - 12654*z**2 - 152032*z - 339*z**3 = 0. What is z?
-38, 1
Suppose 0 = 91*t - 117 + 114 - 179. Factor -1/3*v + 2/3 - 1/3*v**t.
-(v - 1)*(v + 2)/3
Determine m, given that -11/3*m**2 + 2/3*m**4 - 19/3*m**3 + 10/3*m + 0 = 0.
-1, 0, 1/2, 10
Let k = 95 - 36. Let w = 415/7 - k. Factor -2/7*d**2 + 0 - w*d.
-2*d*(d + 1)/7
Let c = -157 + 160. Let d(o) be the first derivative of 0*o - 2/5*o**5 + 5 - 1/3*o**c - 5/4*o**4 + o**2. Factor d(w).
-w*(w + 1)*(w + 2)*(2*w - 1)
Let o = -52 + 54. Let f be ((-4)/6)/(8/(-36)). Solve 4*a**3 + 0*a**3 - 2*a**2 - 2*a**o - 6*a**f = 0.
-2, 0
Let w = -3 + 2. Let r = 1 - w. Determine y so that -y**2 - 3 + 1 - r*y + 1 = 0.
-1
Suppose -36 = -264*q + 258*q. Let f(t) be the second derivative of 0*t**2 - 2/3*t**4 + 2/5*t**q - 5*t + 0*t**3 - 1/5*t**5 + 0. Factor f(r).
4*r**2*(r - 1)*(3*r + 2)
Suppose -5*l - c - 3*c - 14 = 0, -4*l - 5 = -3*c. Let h be 3 + (2 - l) - 3. Factor -14 + 13 + 6*u**4 - 5*u**h + 2*u - 2*u**3.
(u - 1)**3*(u + 1)
Let u(r) be the third derivative of r**5/90 + 11*r**4/36 - 26*r**3/9 + 152*r**2. Factor u(w).
2*(w - 2)*(w + 13)/3
Factor 2*l**2 + 0 - 4/3*l - 2/3*l**3.
-2*l*(l - 2)*(l - 1)/3
Let p(k) be the third derivative of 169/12*k**3 + 0 + 13/24*k**4 + 0*k + 46*k**2 + 1/120*k**5. Factor p(x).
(x + 13)**2/2
Let h(p) be the third derivative of p**8/2184 - 2*p**7/273 + 7*p**6/156 - 5*p**5/39 + 2*p**4/13 + 13*p**2 - 6*p. Find k such that h(k) = 0.
0, 1, 2, 3, 4
Let l(z) be the third derivative of -z**5/45 + 17*z**4/72 - 2*z**3/9 + 106*z**2. Solve l(j) = 0.
1/4, 4
Factor 4*r**4 - 136 + 212*r - 75*r**3 - 66729*r**2 + 66717*r**2 + 7*r**3.
4*(r - 17)*(r - 1)**2*(r + 2)
Determine c so that 22*c**2 - 2*c + 15*c**4 + 20*c**5 - c + 35*c**2 - 49*c**3 - 19*c - 21*c**5 = 0.
0, 1, 2, 11
Let t(v) be the third derivative of v**8/588 - 8*v**7/735 + v**6/105 + 4*v**5/105 - v**4/14 - v**2 - 17. Find u, given that t(u) = 0.
-1, 0, 1, 3
Let p(t) = t**3 + 32*t**2 + 10*t + 320. Let m be p(-32). Suppose 0 + 6/13*w**3 + 2/13*w**4 + 4/13*w**2 + m*w = 0. Calculate w.
-2, -1, 0
Let c(o) be the first derivative of o**5/2 + 205*o**4/8 - 235*o**3/6 - 1065*o**2/4 - 315*o - 170. Suppose c(w) = 0. What is w?
-42, -1, 3
Let s = -30781 + 30797. Factor s*o - 128 - 1/2*o**2.
-(o - 16)**2/2
Let x = -5/9 - -8/9. Suppose -x*s**2 + 1/6*s**3 + 0*s + 1/6*s**4 + 0 = 0. Calculate s.
-2, 0, 1
Let t(w) be the first derivative of 6*w - 29 + 0*w**3 + 9/2*w**2 - 3/4*w**4. Factor t(v).
-3*(v - 2)*(v + 1)**2
Let j(d) be the third derivative of d**8/672 - 13*d**7/1260 + 17*d**6/720 - d**5/120 - d**4/18 + d**3/9 + d**2 + 23*d. Let j(g) = 0. What is g?
-2/3, 1, 2
Let d(h) be the third derivative of 0*h**3 + 0 + 0*h**4 + 4/385*h**7 + 2*h**2 + 0*h + 1/165*h**5 - 3/220*h**6 - 5/1848*h**8. Let d(g) = 0. What is g?
0, 2/5, 1
Suppose 649 = -10*j + 689. Factor 0*g - g**2 + 1/2*g**j + 0 + 1/2*g**3.
g**2*(g - 1)*(g + 2)/2
Let b(n) be the first derivative of -n**8/5040 + n**7/2520 + n**6/270 - n**5/90 + 3*n**3 + 4. Let t(w) be the third derivative of b(w). Factor t(y).
-y*(y - 2)*(y - 1)*(y + 2)/3
Let n(l) = l**3 - 11*l**2 + 5*l. Let m(o) = -3*o**2 - 4*o**2 + 2*o**2 + 23*o**3 - 22*o**3 + 3*o. Let g(t) = -10*m(t) + 6*n(t). Factor g(i).
-4*i**2*(i + 4)
Let d(t) be the second derivative of t**6/90 - t**4/4 + 2*t**3/9 + 2*t**2 + 68*t. Factor d(z).
(z - 2)**2*(z + 1)*(z + 3)/3
Suppose -256 = 5*j - j + 4*s, 0 = -2*s. Let p = j - -66. Solve -1/2*y**2 - 2*y - p = 0 for y.
-2
Suppose 4*n + n + 30 = 0. Let h be (3/n)/(-3 - (-24)/9). Factor h*t**2 + 0 + 0*t + 3/2*t**3.
3*t**2*(t + 1)/2
Let t(r) = 2*r**2 + r - 4. Let u be t(-3). Suppose -82*x + 84*x = 12. Let u*j**3 + 29 + 3*j**3 - 8*j - x*j**4 - 29 = 0. What is j?
-2/3, 0, 1, 2
Let x be (-36)/(1944/(-450))*(-36)/(-10). Factor 0*v + x*v**3 - 39*v**4 + 12*v**2 + 21/2*v**5 + 0.
3*v**2*(v - 2)**2*(7*v + 2)/2
Let i(g) be the second derivative of g**7/84 - 13*g**5/40 - 2*g**4/3 + g**3 + 4*g**2 + 45*g + 4. Find z, given that i(z) = 0.
-2, -1, 1, 4
Let z(g) be the second derivative of 5/3*g**3 + 15/2*g**2 - 5/12*g**4 - 2*g + 0. Factor z(h).
-5*(h - 3)*(h + 1)
Let x(j) be the third derivative of j**8/112 - 2*j**7/35 + j**6/10 + j**5/10 - 5*j**4/8 + j**3 + 25*j**2. Factor x(a).
3*(a - 2)*(a - 1)**3*(a + 1)
Let q(h) = h**3 - 4*h**2 - 2*h - 3. Let l be q(4). Let v be l/((-132)/(-8))*6/(-10). Factor 2/5 - 6/5*x - v*x**3 + 6/5*x**2.
-2*(x - 1)**3/5
Suppose -3*v = 9, 5*v + 62 - 17 = 5*s. Solve 48*m - s*m**4 + 8*m**3 - 6 + 4*m**2 - 56*m + 8*m**4 = 0 for m.
-3, -1, 1
Suppose 24*w + 3499 = 3571. What is b in -1/4*b**w - 5/4*b**2 - 3/4 - 7/4*b = 0?
-3, -1
Let y(i) be the first derivative of -147*i**4/16 + 105*i**3 - 171*i**2/2 + 24*i + 84. Determine h, given that y(h