 Let g(b) be the first derivative of i(b). Factor g(w).
-4*w*(w + 1)*(4*w + 1)
Let u(k) = -39*k**2 - 23*k + 5. Let d(v) = 1 - 3 + 5 - 12*v - 20*v**2. Let m(s) = -7*d(s) + 4*u(s). Factor m(t).
-(4*t + 1)**2
Let m(s) be the first derivative of -s**5/2 - 13*s**4/8 + 11*s**3/6 + 13*s**2/4 - 3*s - 5. Let m(a) = 0. What is a?
-3, -1, 2/5, 1
Let n(v) be the first derivative of 2*v**3/3 - 8*v**2/9 - 2*v/9 - 29. Determine p so that n(p) = 0.
-1/9, 1
Let w(k) be the first derivative of 0*k**4 + 0*k + 1/4*k**6 - 2 + 0*k**2 + 0*k**3 - 3/10*k**5. Determine g so that w(g) = 0.
0, 1
Let r(m) be the third derivative of 1/480*m**6 + 0*m + 0 + 1/1344*m**8 + 0*m**4 + 0*m**3 + 0*m**5 + 5*m**2 - 1/420*m**7. Factor r(b).
b**3*(b - 1)**2/4
Let x be (1/1)/(1/4). Suppose 20 = 3*r + 2. Suppose -m**4 + r*m**3 + 3*m**4 + x*m - 2*m + 6*m**2 = 0. What is m?
-1, 0
Suppose -4*n + 3 = -3*n. Factor 0*j**2 + 3*j**2 + 3*j + 0*j**2 - n*j**3 + 0*j**2 - 3*j**4.
-3*j*(j - 1)*(j + 1)**2
Suppose 0 - 6/13*b - 24/13*b**3 - 12/13*b**4 - 20/13*b**2 - 2/13*b**5 = 0. What is b?
-3, -1, 0
Let f(k) = 2*k**2 + 3*k. Let u be f(-2). Factor -50*m**2 + 52*m**u + 3*m + 2 + m.
2*(m + 1)**2
Suppose 14 = 2*k + 4*m, -m + 5*m + 21 = 3*k. Suppose -k*i + 30 = -3*i - 5*p, 2 = 2*i + 4*p. Factor 0*f**2 - 4/3*f**i + 0*f - 2/3*f**3 + 0 - 2*f**4.
-2*f**3*(f + 1)*(2*f + 1)/3
Let n(u) be the second derivative of u**9/3780 + u**8/2240 - u**7/504 - u**6/240 + u**5/120 - u**4/4 - u. Let y(r) be the third derivative of n(r). Factor y(d).
(d - 1)*(d + 1)**2*(4*d - 1)
Let -2/5*t - 8/15 + 2/15*t**2 = 0. Calculate t.
-1, 4
Let r(c) = -3*c**2 - 4*c. Let z(g) be the second derivative of -g**4/6 - g**3/2 - 3*g. Let x(t) = 3*r(t) - 4*z(t). Factor x(f).
-f**2
Let l(i) be the first derivative of -3/5*i**3 - 3/10*i**2 + 3 + 0*i - 3/25*i**5 - 9/20*i**4. Solve l(u) = 0 for u.
-1, 0
Let o = 1 + 0. Suppose 4*m + m = -3*l + o, 3*m + 5*l + 9 = 0. What is j in -4/3*j + 1/3*j**m + 4/3 = 0?
2
Let p(q) be the third derivative of -q**5/240 + q**4/32 - q**3/12 + 7*q**2. Factor p(d).
-(d - 2)*(d - 1)/4
Let a = 539/306 - 7/34. Let x(s) be the second derivative of 49/36*s**4 + a*s**3 + 2*s + 2/3*s**2 + 0. Factor x(m).
(7*m + 2)**2/3
Let c(j) be the first derivative of -2/33*j**3 - 1/44*j**4 + 0*j - 3 - 1/2*j**2 - 1/330*j**5. Let n(k) be the second derivative of c(k). Factor n(o).
-2*(o + 1)*(o + 2)/11
Let c(k) = -k**3 - 6*k**2 + 6*k - 5. Let b be c(-7). Suppose 7*a - b*a = 10. Factor -3*o + 3*o + 2*o**3 - 4*o**a.
2*o**2*(o - 2)
Suppose -2*z**2 + 1 + 108*z - 5 - 102*z = 0. What is z?
1, 2
Let b(d) be the first derivative of 5 + 1/3*d**6 + 0*d**3 - 2/5*d**5 + 0*d**2 + 0*d**4 + 0*d. Suppose b(o) = 0. Calculate o.
0, 1
Let o be ((-5)/(-2))/(3/2). Factor o*t**3 + 0 + 0*t - 4/3*t**4 - 1/3*t**2.
-t**2*(t - 1)*(4*t - 1)/3
Let q be (-40)/(-8) - (-6)/(-2). Factor -2/3 - 2/3*k**q - 4/3*k.
-2*(k + 1)**2/3
Let r(n) be the third derivative of 2*n**7/105 + 8*n**6/105 + 11*n**5/105 + n**4/21 - 35*n**2. Determine s, given that r(s) = 0.
-1, -2/7, 0
Let n be 14/(-4)*7/(-49). Let d(h) be the first derivative of 1/2*h**6 - n*h**2 + 4/5*h**5 + 0*h - 1/2*h**4 - 1 - 4/3*h**3. Determine y, given that d(y) = 0.
-1, -1/3, 0, 1
Let k(s) be the third derivative of -s**6/40 - s**5/5 - 5*s**4/8 - s**3 - 12*s**2. Find o, given that k(o) = 0.
-2, -1
Suppose 2 + 2 = n. Factor -6*l**3 + n*l**4 - 1 - 5*l**3 - l + 16*l**2 - 7*l**2.
(l - 1)**3*(4*l + 1)
Let s be (19 - 2) + -8 + 4/(-1). Let k(h) be the third derivative of -1/9*h**3 + 5/72*h**4 + 4*h**2 + 0 + 1/360*h**6 - 1/45*h**s + 0*h. Factor k(f).
(f - 2)*(f - 1)**2/3
Let w(k) = -k + 2*k**2 + 0*k**2 + 8*k + k - 13. Let t(s) = -9*s**2 - 32*s + 51. Let b(a) = 6*t(a) + 26*w(a). Factor b(y).
-2*(y - 4)**2
Let v = 55 + -52. Let g(n) be the first derivative of n**2 + 2/3*n**v + 0*n + 1. Solve g(j) = 0 for j.
-1, 0
Factor -16*r**2 + 97*r**2 - 20*r + 59*r**2 - 20*r - 150*r**3 + 45*r**4.
5*r*(r - 2)*(3*r - 2)**2
Let h(y) = -6*y**2 - 12*y - 12. Let u(b) = -b**2 - 1. Let d(j) = -h(j) + 3*u(j). Determine r so that d(r) = 0.
-3, -1
Let r(b) be the first derivative of -b**3/5 - 3*b**2/5 + 9*b/5 - 2. Factor r(i).
-3*(i - 1)*(i + 3)/5
Let b(s) be the third derivative of -s**8/144 - 8*s**7/315 - 11*s**6/360 - s**5/90 + 14*s**2. Suppose b(p) = 0. What is p?
-1, -2/7, 0
Determine l, given that 5*l**2 - 51 - 2*l**2 + 63 + 12*l = 0.
-2
Factor -3*m + 2 + 21*m**2 - 2 - 18*m**2 + 3*m**3 - 3*m**4.
-3*m*(m - 1)**2*(m + 1)
Let d(o) = -o**4 + o**3. Let p(j) = -2*j**4 + 2*j**3. Let l = 15 - 20. Let i(x) = l*p(x) + 6*d(x). Factor i(a).
4*a**3*(a - 1)
Solve 9/4*i**3 - 5/4*i**4 + 1/4*i**5 - 7/4*i**2 + 1/2*i + 0 = 0.
0, 1, 2
Suppose 0 = -q + 4*n - 6, 2*q - 3*q - 6 = 5*n. Let a = q + 10. Determine o so that -1/4 - 3/2*o - 9/4*o**a - 7/2*o**2 - 4*o**3 - 1/2*o**5 = 0.
-1, -1/2
Let f(g) be the first derivative of 0*g**2 + 0*g - 3/14*g**4 - 6/35*g**5 - 1/21*g**6 - 2/21*g**3 + 3. Factor f(q).
-2*q**2*(q + 1)**3/7
Suppose -2*g + 7*g - 21 = -c, g - 4*c = 0. Let d be 3 - 10*g/16. Factor 1/4*o**2 + d + 3/4*o.
(o + 1)*(o + 2)/4
Determine q, given that 0 + 1/2*q**4 + 9*q + 21/2*q**2 + 4*q**3 = 0.
-3, -2, 0
Let q(v) be the second derivative of -2*v**6/135 + 23*v**5/180 - 7*v**4/18 + 10*v**3/27 + 4*v**2/9 - 15*v. Factor q(w).
-(w - 2)**3*(4*w + 1)/9
Let b(w) be the third derivative of -w**6/360 - w**5/180 - 12*w**2. Factor b(v).
-v**2*(v + 1)/3
Let g(w) = 5*w**3 - w**2 + 2*w - 1. Let p be g(1). Find a such that 16*a**p - 5*a + a**3 - 15*a**5 + 5*a - 2*a**4 = 0.
0, 1
Let g(h) = -h**2 - 18*h - 29. Let f be g(-16). Let n = -3 + 3. Factor -1/4*q + n + 1/2*q**2 - 1/4*q**f.
-q*(q - 1)**2/4
Let s(i) be the second derivative of -i**8/6720 - i**7/1260 - i**4/12 - 3*i. Let v(l) be the third derivative of s(l). Determine u, given that v(u) = 0.
-2, 0
Let k = 19/60 - -1/60. Solve -v + v**2 + k - 1/3*v**3 = 0 for v.
1
Suppose -5*r = 6*r - 22. Factor 0*h - 2/9*h**r + 0.
-2*h**2/9
Let i be (324/(-25))/(3/10). Let c = i - -1964/45. Determine b so that -14/9*b + 14/3*b**2 + 230/9*b**3 + 40/3*b**5 + 298/9*b**4 - c = 0.
-1, -2/5, -1/3, 1/4
Let k(o) = -o**3 + 8*o**2 + 9*o + 12. Let q be k(9). Factor 12*d**4 + 12 + 0*d**3 - 9*d**2 - 9*d**4 - 6*d**3 + q*d.
3*(d - 2)**2*(d + 1)**2
Suppose -3*n = -4 + 1. Let r = n + 1. Factor s**2 + r*s + 2*s**2 - s**2.
2*s*(s + 1)
Let w(k) be the third derivative of k**5/36 - 7*k**4/72 + k**3/9 + 10*k**2. Factor w(a).
(a - 1)*(5*a - 2)/3
Factor -10*k**2 + 2*k**2 + 7*k**2 + k.
-k*(k - 1)
Let g = 157/4 - 39. What is s in -g - 1/4*s**2 - 1/2*s = 0?
-1
Let g(h) be the second derivative of -h**5/60 - h**4/36 + 2*h**3/9 + 2*h**2/3 + 6*h. Factor g(f).
-(f - 2)*(f + 1)*(f + 2)/3
What is w in 2/3*w**2 - 5/6*w + 1/3 - 1/6*w**3 = 0?
1, 2
Factor 2/5*o**2 + 0 - 4/5*o + 2/5*o**3.
2*o*(o - 1)*(o + 2)/5
Let x be 13 + -2 + -3 + -5. Find u such that -1/5*u**4 - 3/5*u**2 + u**x - 9/5*u + 0 = 0.
-1, 0, 3
Find n such that -108*n - 146*n**2 - 12 - 5*n**2 - 92*n**2 = 0.
-2/9
Let n(h) = h**3 - h**2 - 2*h + 2. Let v = -8 + 6. Let z(i) = -4*i**3 + 3*i**2 + 7*i - 7. Let l(s) = v*z(s) - 7*n(s). Factor l(t).
t**2*(t + 1)
Let d(b) be the third derivative of -b**5/60 + b**4/12 - b**3/6 - 5*b**2. Factor d(n).
-(n - 1)**2
Let h(y) be the second derivative of 4/5*y**3 + 1/50*y**5 - 5*y + 8/5*y**2 + 0 + 1/5*y**4. Solve h(c) = 0 for c.
-2
Let l(k) = -6*k**2 + k + 1. Suppose p - 1 = 2*p. Let z(q) = q**2 - q - 1. Let u(j) = p*l(j) - 5*z(j). Let u(n) = 0. What is n?
-2
Let s(i) = -8*i**5 - 3*i**4 + 4*i**3 - i**2 - 8*i - 4. Let z(g) = g**5 + g**2 + 2*g + 1. Let j(t) = -s(t) - 4*z(t). Factor j(c).
c**2*(c - 1)*(c + 1)*(4*c + 3)
Let t(h) = h**4 + h**3 - h**2 + h - 1. Let q(g) = -5*g**4 + 11*g**3 + 45*g**2 - 13*g - 39. Let v(s) = -q(s) - t(s). Find d such that v(d) = 0.
-2, -1, 1, 5
Let z be (3 - 8) + -1 + 0. Let y be (-35)/(-15) + (-4)/z. Factor -6*s**3 - 2*s**5 + 4*s**4 + s**y + 3*s**3.
-2*s**3*(s - 1)**2
Find l such that 1/3*l + 2/3 - 1/3*l**2 = 0.
-1, 2
Let f(k) be the first derivative of 2/3*k**3 + 6*k**2 + 3 + 18*k. Factor f(o).
2*(o + 3)**2
Let j(p) be the first derivative of -4*p**3/3 + 2*p**2 + 8*p - 13. Determine s, given that j(s) = 0.
-1, 2
Let u be 4/(-6) + (-20)/15. Let q be (u - 0)/(4/(-6)). Factor 2*y**3 - y**q + y**5 - 2*y**5.
-y**3*(y - 1)*(y + 1)
Let l(v) be the first derivative o