2*s**3 - s**2 - 4*s**4.
-4*s**2*(s - 1)*(s + 2)
Let a(w) be the first derivative of -1/20*w**5 + 0*w + 3/2*w**2 - 1/4*w**4 + 0*w**3 + 2. Let g(y) be the second derivative of a(y). Factor g(k).
-3*k*(k + 2)
Let r = -14 - -21. Factor r - 6 + 2 - 6 - 3*q**2 + 6*q.
-3*(q - 1)**2
Let n = -196 + 1374/7. Let k be (-2)/(-3) - (-80)/105. Find b, given that -8/7 - k*b**2 - n*b**3 - 16/7*b = 0.
-2, -1
Factor -2*t**2 - 4970*t**3 + 16 + 4972*t**3 - 2*t**2 - 8*t.
2*(t - 2)**2*(t + 2)
Let g(f) be the second derivative of -f**8/23520 + f**7/2940 - f**6/1260 + 17*f**4/12 - 10*f. Let o(k) be the third derivative of g(k). Factor o(y).
-2*y*(y - 2)*(y - 1)/7
Let l(h) = -96*h**4 + 38*h**3 + 234*h**2 + 103*h + 5. Let j(d) = 144*d**4 - 56*d**3 - 351*d**2 - 154*d - 8. Let i(p) = 5*j(p) + 8*l(p). Factor i(m).
-3*m*(m - 2)*(4*m + 3)**2
Let b be -4 + (4 - 0 - -2). Determine d so that 0 + 4/11*d - 2/11*d**b = 0.
0, 2
Factor -135/2*c + 243 - 3/2*c**3 - 24*c**2.
-3*(c - 2)*(c + 9)**2/2
Let b(i) be the first derivative of 3*i**5/5 - 3*i**4/2 - 3*i**3 - 26. Factor b(n).
3*n**2*(n - 3)*(n + 1)
Let d be (28/2)/(9/(-54)*-12). Let f(m) = m**3 - 7*m**2. Let j be f(d). Determine l so that 1/4*l + j - 1/8*l**2 = 0.
0, 2
Let p = -15 - -21. Suppose -i + p = -0. Factor -s + 1 - s**3 - 8*s**2 - 1 + i*s**2.
-s*(s + 1)**2
Let v(n) be the second derivative of n**5/12 - 10*n**3/3 - n**2 + 3*n. Let q(i) be the first derivative of v(i). Solve q(m) = 0.
-2, 2
Suppose 4*c + c + 20 = -5*a, 2*a + 3*c = -12. Let x(m) be the second derivative of -1/100*m**5 - 7/30*m**3 + m + a - 1/12*m**4 - 3/10*m**2. Factor x(b).
-(b + 1)**2*(b + 3)/5
Suppose -5*i - x = -49, 4*i - x = 2*x + 43. Let -3*w**2 - i*w - 11*w**2 + 8*w**4 - 3*w**4 - w**2 = 0. What is w?
-1, 0, 2
Let z = -6857 + 20581/3. Factor 4 - z*h - 2/3*h**2.
-2*(h - 1)*(h + 6)/3
Solve -20*u + 25/2*u**4 + 20*u**3 - 45/2*u**2 + 10 = 0 for u.
-2, -1, 2/5, 1
Factor 116*t + t**2 + 27*t**2 - 32*t**2.
-4*t*(t - 29)
Let h(l) = -l**2 - 7*l - 5. Let x be h(-5). Factor x*n**2 - 4*n**3 + 2*n - 6*n**2 + 5*n**2 + 6*n.
-4*n*(n - 2)*(n + 1)
Let k = -1089 + 5563/5. Let p = k - 23. Find y, given that -3/5*y**2 + p*y + 0 = 0.
0, 1
Let f(z) be the first derivative of -z**4/4 - 7*z**3/3 - 6*z**2 - 258. Factor f(h).
-h*(h + 3)*(h + 4)
Let a(q) be the second derivative of -7*q**6/45 - 13*q**5/15 - 13*q**4/18 + 2*q**3/3 - 122*q. Let a(p) = 0. What is p?
-3, -1, 0, 2/7
Let s(d) be the third derivative of d**6/160 - 7*d**4/32 - 3*d**3/4 + 75*d**2. Factor s(o).
3*(o - 3)*(o + 1)*(o + 2)/4
Let l(v) be the third derivative of v**5/120 + 13*v**4/48 - 7*v**3/6 - 16*v**2 + 10. Factor l(a).
(a - 1)*(a + 14)/2
Suppose -7*b = -4*b - 45. Let m be 24/9*b/50. Solve -m*u**2 + 0 + 2/5*u + 4/5*u**4 + 0*u**3 - 2/5*u**5 = 0.
-1, 0, 1
Let k be (-4)/90*(-35)/28. Let o(b) be the first derivative of 1/3*b + 10/9*b**3 - k*b**6 + 5 + 1/3*b**5 - 5/6*b**2 - 5/6*b**4. Determine j so that o(j) = 0.
1
Let a(p) = -76*p**4 - 98*p**3 - 12*p**2 + 11*p - 11. Let r(z) = 27*z**4 + 33*z**3 + 4*z**2 - 4*z + 4. Let o(y) = -4*a(y) - 11*r(y). Solve o(l) = 0 for l.
-4, -1/7, 0
Suppose -34*a = -41*a + 210. Factor 10*w + 3*w**4 - w**3 - 9*w**2 + 5*w - 2*w**3 + 24 - a.
3*(w - 1)**3*(w + 2)
Let b(j) = j**2 + 15*j + 31. Let d be b(-13). Let i(q) be the third derivative of -27/80*q**6 + 0*q + 0 - 3/10*q**5 + 0*q**3 - 1/12*q**4 - d*q**2. Factor i(y).
-y*(9*y + 2)**2/2
Let q(u) be the first derivative of 1/12*u**2 + 1/3*u + 1/12*u**6 - 1/6*u**4 - 1/3*u**3 + 2/15*u**5 - 13. Solve q(w) = 0.
-1, 2/3, 1
Suppose -38 = -4*r - 22. Find m such that 1 - 7*m**2 + 12*m**2 - 5*m**2 + 2*m**3 - m**r - 2*m = 0.
-1, 1
Let q(n) be the first derivative of -243*n**6/7 - 3888*n**5/35 - 1809*n**4/14 - 1420*n**3/21 - 124*n**2/7 - 16*n/7 - 50. Factor q(r).
-2*(r + 1)**2*(9*r + 2)**3/7
Factor -6*n**4 - 16*n**2 + 0*n + 1/2*n**5 + 18*n**3 + 0.
n**2*(n - 8)*(n - 2)**2/2
Let g(s) be the third derivative of 0 + 0*s + 16/3*s**3 + 15*s**2 + 1/30*s**5 - 2/3*s**4. Find x such that g(x) = 0.
4
Let a = -825 - -832. Let u(b) be the second derivative of 1/10*b**5 - 1/12*b**4 - a*b + 0 - 1/3*b**3 + 0*b**2 + 1/30*b**6. Determine p so that u(p) = 0.
-2, -1, 0, 1
Let r = 419/15 - 2843/105. Find d, given that -r*d**3 + 0 + 0*d + 4/7*d**2 = 0.
0, 2/3
Let 14/9*i**3 + 472/9*i - 104/9 - 382/9*i**2 = 0. What is i?
2/7, 1, 26
Let z(n) be the second derivative of n**8/40320 + n**7/3024 + 7*n**6/4320 + n**5/240 - n**4/3 + 4*n. Let b(f) be the third derivative of z(f). Factor b(o).
(o + 1)**2*(o + 3)/6
Let c(u) = -3*u + 84. Let q be c(28). Let t(v) be the third derivative of -2*v**3 - 2/15*v**5 - 6*v**2 - 7/6*v**4 + q + 0*v. Factor t(h).
-4*(h + 3)*(2*h + 1)
Let g(v) be the third derivative of 0 - 1/180*v**5 + 0*v**4 + 0*v + 4*v**2 + 0*v**3. Factor g(r).
-r**2/3
Let t(j) be the first derivative of -j**7/252 + j**6/45 - j**5/20 + j**4/18 - j**3/36 - 4*j - 13. Let q(s) be the first derivative of t(s). Factor q(k).
-k*(k - 1)**4/6
Let t(c) = 11*c**2 - 19*c + 20. Let h(a) = -9*a**2 + 18*a - 19. Let q(o) = 6*h(o) + 5*t(o). Factor q(v).
(v - 1)*(v + 14)
Let g(i) be the first derivative of i**3/6 + 15*i**2 + 59*i/2 + 62. Factor g(b).
(b + 1)*(b + 59)/2
Let b be (-3 - 26/(-10))*170. Let a be (-10)/(-12)*b/(-85). Suppose 2*o**3 + a*o**5 - 8/3*o**2 + 0 + 8/3*o**4 - 8/3*o = 0. What is o?
-2, -1, 0, 1
Let c = 23 - 17. Let d = c + -5. Let f(o) = o**3 + o - 1. Let b(m) = -7*m**3 + 4*m**2 - 7*m + 5. Let i(n) = d*b(n) + 5*f(n). Let i(g) = 0. Calculate g.
0, 1
Find a, given that 102/7*a**2 + 3/7*a**3 + 96/7 + 195/7*a = 0.
-32, -1
Let z be 0*(-1 + (-5)/(-10)). Let q = -742 - -746. Factor -1/4*i**q + 1/4*i**2 + z + 1/4*i**3 - 1/4*i.
-i*(i - 1)**2*(i + 1)/4
Let p(t) be the first derivative of t**6/48 + t**5/10 + t**4/8 + 102. Factor p(h).
h**3*(h + 2)**2/8
Factor -75*s**2 - 748*s - 664*s + 66*s + 338*s - 249*s**2 - 784.
-4*(9*s + 14)**2
Factor 6*s**2 + 21/4*s**3 + 3/4*s**4 - 12*s + 0.
3*s*(s - 1)*(s + 4)**2/4
Let a(g) be the second derivative of g**8/672 + g**7/280 - g**6/240 - 3*g**2/2 + 23*g. Let w(s) be the first derivative of a(s). Factor w(u).
u**3*(u + 2)*(2*u - 1)/4
Let b(j) = -j + 11. Let v be b(9). Suppose 5*m + 5*l - 5 = 0, 3*m + v*m = 4*l - 4. Factor -1/4*d**4 + 0*d + 1/4*d**2 + 0*d**3 + m.
-d**2*(d - 1)*(d + 1)/4
Let z be 2*((-270)/12)/(-15). Let y(s) be the first derivative of -18/7*s + 3/2*s**2 + 1 + 3/7*s**z. Factor y(x).
3*(x + 3)*(3*x - 2)/7
Let j be (2 + 12/(-8))*66. Let m = j + -29. Let 156*t**m - t**3 + 2*t**3 - 157*t**4 = 0. What is t?
0, 1
Let a(p) = -4*p - 1. Let m be a(-1). Let k be (1 + (-2)/(-3))/((-3)/(-9)). Factor -3*i**k + 3*i**4 + 0*i**3 - 3*i**3 + m*i**4 + 0*i**3.
-3*i**3*(i - 1)**2
Let g(d) = -7*d**3 + 64*d**2 - 164*d + 107. Let t(o) = -36*o**3 + 320*o**2 - 820*o + 536. Let l(n) = 16*g(n) - 3*t(n). Factor l(r).
-4*(r - 13)*(r - 2)*(r - 1)
Let i(t) be the second derivative of -t**5/180 - 5*t**4/72 + t**3/3 + 12*t**2 + 16*t. Let r(u) be the first derivative of i(u). Let r(c) = 0. Calculate c.
-6, 1
Let r(n) be the third derivative of -n**8/840 + n**7/1260 - 3*n**4/8 - 7*n**2. Let k(q) be the second derivative of r(q). Factor k(t).
-2*t**2*(4*t - 1)
Let c(j) be the first derivative of -j**3/12 - 3*j**2/4 + 4. Solve c(z) = 0.
-6, 0
Find n, given that 2/7*n**2 - 394/7 + 56*n = 0.
-197, 1
Let m = 229/700 - 27/350. Factor m*o**3 + 0*o**2 + 1/2*o**4 + 0 + 1/4*o**5 + 0*o.
o**3*(o + 1)**2/4
Let q(r) = -r**4 - 17*r**3 + 13*r**2 + 35*r - 10. Let b(i) = i**3 - 2*i**2 - 2*i + 1. Let t(j) = 30*b(j) + 3*q(j). Factor t(v).
-3*v*(v - 1)*(v + 3)*(v + 5)
Let l(s) be the second derivative of s**6/540 - s**5/108 + s**4/54 - s**3/54 + 5*s**2 + 15*s. Let u(j) be the first derivative of l(j). Factor u(r).
(r - 1)**2*(2*r - 1)/9
Let y = 10381/426 - -28/213. Determine x so that 1/2 + y*x**2 - 7*x = 0.
1/7
Let d(a) be the first derivative of a**4/36 - 7*a**3/9 - 328. Determine h, given that d(h) = 0.
0, 21
Let z(l) = -l**4 - 2*l + 1. Let o(y) = 15*y**4 - 3*y**3 + 36*y - 18. Let g(m) = o(m) + 18*z(m). Factor g(w).
-3*w**3*(w + 1)
Let p(w) be the third derivative of -w**10/100800 - w**9/13440 - w**8/6720 + w**5/60 - 4*w**2. Let x(j) be the third derivative of p(j). Factor x(s).
-3*s**2*(s + 1)*(s + 2)/2
Factor 76/7*z**3 - 256/7 - 48*z**2 - 6/7*z**4 + 576/7*z.
-2*(z - 4)**3*(3*z - 2)/7
