e of 0*k**2 - t*k + 0 - 1/4*k**3 + 1/8*k**4. Factor m(y).
3*y*(y - 1)/2
Factor -624/5*m - 1029/5*m**5 + 192/5 - 294/5*m**4 + 1491/5*m**3 - 12*m**2.
-3*(m + 1)**2*(7*m - 4)**3/5
Let i(a) be the third derivative of -a**8/48 + 2*a**7/105 + a**6/12 - a**5/15 - a**4/8 + 36*a**2. Let i(t) = 0. What is t?
-1, -3/7, 0, 1
Let a(z) be the first derivative of -5*z**6/21 - 106*z**5/35 + 27*z**4/14 + 106*z**3/21 - 22*z**2/7 + 55. Suppose a(q) = 0. Calculate q.
-11, -1, 0, 2/5, 1
Let d(v) be the first derivative of -3*v**5/5 + 21*v**4/4 - 6*v**3 - 48*v**2 + 96*v + 61. Factor d(m).
-3*(m - 4)**2*(m - 1)*(m + 2)
Let l(p) be the first derivative of -5/7*p**2 - 1/14*p**4 - 15 - 8/21*p**3 - 4/7*p. Find s such that l(s) = 0.
-2, -1
Let d(q) be the first derivative of -q**6/72 - q**5/6 - 5*q**4/8 - 20*q**3/3 + 26. Let l(w) be the third derivative of d(w). Factor l(z).
-5*(z + 1)*(z + 3)
Let a(d) be the first derivative of 1/50*d**5 + 0*d**4 + 13 + 2/5*d + 0*d**2 - 1/6*d**3. Suppose a(v) = 0. Calculate v.
-2, -1, 1, 2
Let i(h) = h**2 - 7*h + 9. Let m be i(7). Let x = -5 + m. Factor 8*a**2 + 2*a**4 - x*a**2 - 3*a**3 - 3*a**2 + 0*a**3.
a**2*(a - 1)*(2*a - 1)
Determine g, given that 979*g**4 - 492*g**4 + 16*g**3 - 20*g**2 - 491*g**4 + 8*g = 0.
0, 1, 2
Let i(v) be the second derivative of -4*v + 0 - 1/15*v**6 + 0*v**4 - 1/10*v**5 + 0*v**2 + 0*v**3. Factor i(w).
-2*w**3*(w + 1)
Let b = 55 - 78. Let k = 29 + b. Suppose 11*o**4 + 3 + 8*o**2 - 5*o - k + 2*o**5 + 18*o**3 + o = 0. Calculate o.
-3, -1, 1/2
Let d(l) = l + 1 - l + l - 3*l**2 + 2*l**2. Let z(n) = -2*n**3 - 6*n**2 - 20*n - 12. Let j(c) = 4*d(c) + z(c). Factor j(k).
-2*(k + 1)*(k + 2)**2
Factor -6*w**4 + 7*w**4 + 102*w**3 - 99*w**3 - 4*w**2.
w**2*(w - 1)*(w + 4)
Suppose 0 = -7*x - 6458 + 6458. Factor x*p + 0 + 3/8*p**2.
3*p**2/8
Let c(s) be the first derivative of 1/5*s**2 + 2/9*s**3 - 2/15*s - 16 - 8/75*s**5 - 1/10*s**4. Find a such that c(a) = 0.
-1, 1/4, 1
Let l(c) be the third derivative of c**8/211680 + c**7/6615 - 7*c**5/60 + 2*c**2. Let a(d) be the third derivative of l(d). Factor a(x).
2*x*(x + 8)/21
Let h(y) be the first derivative of 4*y**3/21 + 183*y**2/14 - 46*y/7 + 32. Let h(k) = 0. What is k?
-46, 1/4
Let m(v) = -10*v**4 - 10*v**3 + 10*v**2 + 10*v - 25. Let y(b) = b**4 + 2*b**3 + b**2 + 1. Let w(q) = m(q) + 25*y(q). Suppose w(l) = 0. What is l?
-1, -2/3, 0
Let u = 189456/17 - 11144. Determine i so that -10/17*i**3 + u + 16/17*i - 14/17*i**2 = 0.
-2, -2/5, 1
Let u be (18/(-8))/((-4)/(-48)*-3). Suppose 5*s = 2*s + u. Solve -o + 2/5 - 1/5*o**s + 4/5*o**2 = 0 for o.
1, 2
Factor 2/7*a**5 + 0 + 0*a + 0*a**2 + 0*a**3 + 2/7*a**4.
2*a**4*(a + 1)/7
Let v(u) = u - 1. Let z(d) = -4*d**2 + 40*d - 36. Let j(x) = -4*x**2 - 27*x + 6. Let q be j(-7). Let b(l) = q*z(l) + 20*v(l). Factor b(r).
4*(r - 4)*(r - 1)
Factor -8/5 - 7/5*q + 1/5*q**2.
(q - 8)*(q + 1)/5
Let x be 36/6 + (-377)/65. What is b in 1/5*b**2 - 2/5 + x*b = 0?
-2, 1
Suppose -18*p + 13*p = -240. Let h be 3 + 1 - p/14. Factor -4/7*d**3 + 2/7*d**4 + 2/7*d - h*d**2 + 2/7*d**5 + 2/7.
2*(d - 1)**2*(d + 1)**3/7
Let s(p) be the third derivative of 0*p**3 + 0*p - 1/3*p**5 + 1/24*p**6 + 5/6*p**4 - 3*p**2 + 0. Factor s(x).
5*x*(x - 2)**2
Let q = -463/3 + 3253/21. What is i in -2/7*i**2 - q*i + 0 + 2/7*i**4 - 2/7*i**5 + 6/7*i**3 = 0?
-1, 0, 1, 2
Let w(n) be the first derivative of 1/3*n**3 + 0*n**4 + n**2 - 9 - 1/120*n**5 + 0*n. Let c(v) be the second derivative of w(v). Factor c(f).
-(f - 2)*(f + 2)/2
Let d be (-2)/(-2) - (-5258)/(-5280). Let r(q) be the third derivative of 0*q**4 + 1/180*q**5 + 0*q - 6*q**2 + 0*q**3 + d*q**6 + 0 + 1/1260*q**7. Factor r(o).
o**2*(o + 1)*(o + 2)/6
Let v(c) be the third derivative of -c**10/982800 - c**9/131040 - c**8/65520 + 7*c**5/60 + 21*c**2. Let x(y) be the third derivative of v(y). Factor x(m).
-2*m**2*(m + 1)*(m + 2)/13
Let l be 1058/16 + (-2)/16. Let f = 68 - l. Factor -2/7*m**f + 0 - 2/7*m.
-2*m*(m + 1)/7
Let c be 3/5 + -2*95/25. Let y be c/(-6) + 24/(-36). Factor -1/4*b**2 - y*b - 1/4.
-(b + 1)**2/4
Let d(z) be the second derivative of -5*z**4/12 - 35*z**3/2 - 225*z**2 + 294*z. Determine k so that d(k) = 0.
-15, -6
Let u(f) be the second derivative of -5/42*f**7 - 1/4*f**5 + 0*f**4 - 25*f + 0*f**2 - 1/3*f**6 + 0*f**3 + 0. Determine n, given that u(n) = 0.
-1, 0
Let k(t) be the first derivative of -121*t**5/5 + 649*t**4/4 - 236*t**3 + 98*t**2 - 16*t + 977. Factor k(c).
-(c - 4)*(c - 1)*(11*c - 2)**2
Let i = -17 + 19. Suppose 6*w**5 - 10*w**4 - 22*w**3 - 8*w + 42*w**i - 8 - 4 + 4 = 0. What is w?
-2, -1/3, 1, 2
Determine m, given that -81/7*m**2 - 72*m + 84 - 3/7*m**3 = 0.
-14, 1
Let c(s) = -2*s**2 - 11*s - 12. Let v be c(-4). Factor -6*g**4 - 6 + v*g**4 + 8*g**2 + 2 + 2*g**4.
-4*(g - 1)**2*(g + 1)**2
Let l(x) = -x**2 - 9*x - 6. Let p be l(-8). Suppose -b**3 - 12*b**2 - p*b**4 - 7*b**3 + 6*b**4 = 0. Calculate b.
-1, 0, 3
Suppose 2*k + 9 = -k - 3*p, -4*k + p = 32. Let i = 7 + k. What is n in 4 + 6*n + i*n + n - 3*n + n**2 = 0?
-2
Suppose 2*u = -7*y + 4*y + 9, 2*y = 2. Find t such that u*t**3 + 8*t**2 - 12*t**2 - 11*t**2 + 17*t - 5*t = 0.
0, 1, 4
Let a(d) be the second derivative of -d**7/420 + d**6/90 + 8*d**3/3 + 8*d. Let o(q) be the second derivative of a(q). Factor o(b).
-2*b**2*(b - 2)
Suppose -5*m - 3*t = -2*t - 17, -2*m = -3*t. Let i(g) be the second derivative of -10*g + 1/2*g**m + 0 + 3/2*g**2 + 1/16*g**4. Factor i(v).
3*(v + 2)**2/4
Let r = -36645 + 36743. Determine n, given that 1/2*n**2 - 14*n + r = 0.
14
Let k(t) = 2*t**3 + 2*t**2 - 2*t. Let y be k(-2). Let l = -2 - y. Factor -2*a**l + a**2 + 2 - a - 2.
-a*(a + 1)
Let j(l) be the first derivative of -8*l**5/35 + 122*l**4/7 - 2398*l**3/7 - 3782*l**2/7 - 1922*l/7 + 1039. Let j(a) = 0. Calculate a.
-1/2, 31
Determine h, given that -5/2*h + 5/2*h**3 + 1/8*h**2 - 1/8 = 0.
-1, -1/20, 1
Let l(b) be the second derivative of -b**8/56 + 3*b**7/70 - b**5/20 - 5*b**2 + 34*b. Let n(p) be the first derivative of l(p). Let n(x) = 0. Calculate x.
-1/2, 0, 1
Let c be -1*-1*(-2)/(-8). Let u be -10*8/32 + (-38)/(-8). Factor u*v + c*v**4 - 5/4*v**3 + 3/4*v**2 + 0.
v*(v - 3)**2*(v + 1)/4
Let w(z) be the first derivative of -162*z - 2/3*z**3 - 11 + 18*z**2. Factor w(r).
-2*(r - 9)**2
Suppose 4*j + 70 = -3*j. Let p be (-5)/j*4*(-2)/(-16). Let -p*s**3 + 0 - s - 2*s**2 + 3/4*s**4 = 0. Calculate s.
-1, -2/3, 0, 2
Let l be -4 - (-46)/(-22)*-2. Factor l*a**3 + 0 + 8/11*a**2 + 8/11*a.
2*a*(a + 2)**2/11
Let l = -197 - -202. Let g(m) be the first derivative of 0*m**3 + 3/4*m**4 + 0*m**2 + 0*m - 3 + 0*m**l - 1/2*m**6. Find j, given that g(j) = 0.
-1, 0, 1
Let o be 2/(-20) + (2486/660 - 3). Factor 0 - 2/3*s**2 + 2/3*s**4 - 2/3*s + o*s**3.
2*s*(s - 1)*(s + 1)**2/3
Let r(a) be the first derivative of a**5/15 - 2*a**3/3 + 7*a**2 + 14. Let j(b) be the second derivative of r(b). Factor j(v).
4*(v - 1)*(v + 1)
Suppose 3*s - 12 = -3. Suppose d + 2 = s*p - 19, -18 = -5*p - 4*d. Factor -9/2 - p*f - 3/2*f**2.
-3*(f + 1)*(f + 3)/2
Suppose 40*n - 37*n = 4*q + 26, -23 = n + 5*q. Determine r so that -10/7 + 12/7*r**n - 8/7*r + 8/7*r**3 - 2/7*r**4 = 0.
-1, 1, 5
Let z(q) = 455*q**3 - 5785*q**2 + 8400*q + 2820. Let t(i) = -35*i**3 + 445*i**2 - 646*i - 217. Let r(p) = 40*t(p) + 3*z(p). Factor r(y).
-5*(y - 11)*(y - 2)*(7*y + 2)
Suppose 0 = 7*o - 11*o + 8, 4*o - 8 = -5*l. Factor 0*j + l*j**2 + 1/2*j**3 + 0.
j**3/2
Let h = 78 + -96. Let w be 48/h*(-2 + (-34)/(-20)). Factor 0 - 2*v**2 - w*v.
-2*v*(5*v + 2)/5
Suppose -5*v - 637 = -2*p - 2*p, -p + 178 = 5*v. Let k = p + -809/5. Factor -2/5*m**3 + 0*m + k*m**2 - 8/5.
-2*(m - 2)**2*(m + 1)/5
Let l(n) be the second derivative of -n**5/40 + 5*n**4/6 - 77*n**3/12 - 121*n**2/2 + 6*n - 3. Determine x so that l(x) = 0.
-2, 11
Let a(m) be the first derivative of -m**6/3 - 8*m**5/5 + 5*m**4 + 56*m**3/3 + 15*m**2 + 221. Let a(w) = 0. Calculate w.
-5, -1, 0, 3
Let h = -65 - 79. Let x = -70 - h. Factor -x - 3*j + 74 - 3*j**2.
-3*j*(j + 1)
Let n = -35 + 37. Suppose 2*a - a = n. Factor 2/11*m**3 - 2/11*m + 2/11*m**a - 2/11.
2*(m - 1)*(m + 1)**2/11
Let l(s) be the second derivative of 49*s**6/10 - 63*s**5/4 + 253*s**4/16 - 15*s**3/4 + 3*s**2/8 - 2*s - 88. Factor l(q).
3*(q - 1)**2*(14*q - 1)**2/4
Let z(p) be the first derivative of -p**4/20 - p**3/15 + p**2/10 + p/5 + 81. Factor z(