**3/5
Let f(v) be the first derivative of -2*v**5/5 + 3*v**4 - 6*v**3 - 40. Factor f(y).
-2*y**2*(y - 3)**2
Let u = -3350/9 - -11393/36. Let c = u - -56. Factor -1/2*k**2 - c*k**3 + 0 - 1/4*k.
-k*(k + 1)**2/4
Let m(s) be the third derivative of -s**8/112 + s**7/35 + s**6/20 - s**5/5 - s**4/8 + s**3 - 16*s**2. Determine q so that m(q) = 0.
-1, 1, 2
What is w in -8/3*w**2 - 52/3*w**3 + 52/3*w + 8/3 = 0?
-1, -2/13, 1
Factor 1875 + 1744*m + 27*m**3 - 244*m - 6*m**3 + 450*m**2 + 3*m**4 + 39*m**3.
3*(m + 5)**4
Let o(r) be the third derivative of 5*r**8/84 - 44*r**7/105 + 19*r**6/15 - 32*r**5/15 + 13*r**4/6 - 4*r**3/3 + 2*r**2. Let o(b) = 0. What is b?
2/5, 1
Let z(h) = -245*h**3 - 626*h**2 - 304*h - 44. Let q(r) = -2695*r**3 - 6885*r**2 - 3345*r - 485. Let y(n) = 4*q(n) - 45*z(n). What is m in y(m) = 0?
-2, -2/7
Let o(n) be the third derivative of 2*n**7/105 + n**6/15 - n**5/5 - 4*n**4/3 - 8*n**3/3 + 29*n**2. Factor o(c).
4*(c - 2)*(c + 1)**2*(c + 2)
Suppose -5*v = -2*v - 6. Factor 37 + k**v - 5*k**2 - 21.
-4*(k - 2)*(k + 2)
Solve 2/3 - 5/6*g**2 + 4/3*g = 0.
-2/5, 2
Let f be 6/9 + 49/(-84). Let x(a) be the third derivative of 1/20*a**6 + 1/105*a**7 + f*a**4 - 2*a**2 + 0 + 0*a + 1/10*a**5 + 0*a**3. Let x(y) = 0. Calculate y.
-1, 0
Let x(z) be the first derivative of 0*z + 5 + 1/6*z**2 - 1/9*z**3 + 1/15*z**5 - 1/12*z**4. Factor x(l).
l*(l - 1)**2*(l + 1)/3
Let k(v) be the second derivative of v**7/105 - v**5/10 + 4*v**3/15 + v + 2. Solve k(j) = 0 for j.
-2, -1, 0, 1, 2
Let k be (-4)/(-14) - 234/(-63). Factor -s**4 - s + 0*s**k - s**3 + s**2 + 2*s**3.
-s*(s - 1)**2*(s + 1)
Suppose -2*v - 2*v + 12 = 0. Let f be 2*6*1/v. Factor -q**2 - 2*q**3 - f*q + 0*q**3 + 7*q**2.
-2*q*(q - 2)*(q - 1)
Let k(l) be the second derivative of 4/15*l**6 + 0 + 3*l + 0*l**3 + 1/6*l**4 - 7/20*l**5 + 0*l**2 - 1/14*l**7. Factor k(p).
-p**2*(p - 1)**2*(3*p - 2)
Let c = -58 + 62. Let g(w) be the second derivative of 1/6*w**c + 0*w**2 + 0 + 4*w + 1/10*w**5 + 0*w**3. Suppose g(t) = 0. What is t?
-1, 0
Factor 3*g**2 - 5 - 3*g**3 + 5.
-3*g**2*(g - 1)
Solve 28/5*g**3 + 16/5 + 81/5*g**2 + 3/5*g**4 + 72/5*g = 0.
-4, -1, -1/3
Let z(t) = 4*t - 7. Let j be z(3). Let r(s) = s - 3. Let h be r(j). Suppose 0 + 2/7*k**4 - 2/7*k**3 + 2/7*k - 2/7*k**h = 0. What is k?
-1, 0, 1
Let 33/2*a**3 + 0*a + 6*a**5 - 39/2*a**4 - 3*a**2 + 0 = 0. What is a?
0, 1/4, 1, 2
Suppose 7*y + 20 = 3*y. Let m = y + 5. Suppose -2/7*a**5 + m*a**3 + 0*a**2 + 0*a + 0 + 2/7*a**4 = 0. What is a?
0, 1
Let s(q) be the second derivative of -1/4*q**4 + q + 0 + 3*q**2 - 1/2*q**3. Factor s(y).
-3*(y - 1)*(y + 2)
Let m(o) be the third derivative of -o**6/1980 + o**5/165 - o**4/33 + o**3/3 - 4*o**2. Let y(g) be the first derivative of m(g). Find f such that y(f) = 0.
2
Let s(z) be the second derivative of -z**5/180 + z**4/72 + z**2/2 - 5*z. Let l(a) be the first derivative of s(a). Suppose l(v) = 0. Calculate v.
0, 1
Let o(v) be the first derivative of v**6/6 - v**5/4 - 3*v**4/8 + 37. Let o(l) = 0. What is l?
-3/4, 0, 2
Let z be 4/24*0*4/(-8). Factor -1/4*f**3 + z*f + 0*f**2 + 0*f**4 + 1/4*f**5 + 0.
f**3*(f - 1)*(f + 1)/4
Factor 0*y + 0 - 1/10*y**4 + 4/5*y**2 - 1/5*y**3.
-y**2*(y - 2)*(y + 4)/10
Let a = -27 + 31. Let s(t) be the second derivative of 2/3*t**a + 0 - 2*t + 5/3*t**3 + t**2. Factor s(q).
2*(q + 1)*(4*q + 1)
Let g(j) = 4*j**4 - 3*j**3 - 5*j - 5. Let b(f) = -2*f**4 + 2*f**3 + 2*f + 2. Let h(u) = 5*b(u) + 2*g(u). Suppose h(k) = 0. Calculate k.
0, 2
Let k(f) be the second derivative of -f**4/6 + 2*f**3/3 - 27*f. Suppose k(g) = 0. Calculate g.
0, 2
Let h = 45 + -45. Find d such that 0 + 2/7*d**5 + h*d**4 + 0*d**3 + 0*d**2 + 0*d = 0.
0
Find u such that 10/9*u - 4/9 - 8/9*u**2 + 2/9*u**3 = 0.
1, 2
Let z be 92/99 - 2/(-11). Let i = -7/9 + z. Factor 4/3*t**3 + 2*t**2 + 1/3*t**4 + 4/3*t + i.
(t + 1)**4/3
Let y(m) = -m**3 + m**2 + m - 1. Let c(j) = 5*j**3 - 9*j**2 + 3*j + 1. Let w(t) = -2*c(t) - 6*y(t). Find h, given that w(h) = 0.
1
Let o be (2/(-98))/((-4)/14). Let l(v) be the first derivative of 0*v - 4/21*v**3 - 2 + 1/7*v**2 + o*v**4. Suppose l(k) = 0. What is k?
0, 1
Let d = 97/5 - 659/35. Let t = 316 - 313. Factor 2/7*o - d*o**2 + 0 + 2/7*o**t.
2*o*(o - 1)**2/7
Suppose -4*a + h + 1 - 3 = 0, 3*h = -2*a + 6. Determine j so that a*j**4 - 2/3*j**5 + 0*j**2 + 0 + 4/3*j**3 - 2/3*j = 0.
-1, 0, 1
Let y(m) be the third derivative of m**8/1680 - m**6/60 + m**5/15 - m**4/8 - 4*m**2. Let h(n) be the second derivative of y(n). Factor h(a).
4*(a - 1)**2*(a + 2)
Let 21*b - 14*b - 7*b - 18*b + 21*b**2 - 3*b**3 = 0. What is b?
0, 1, 6
Let m(t) be the third derivative of t**8/336 + t**7/70 + t**6/40 + t**5/60 + 4*t**2. Factor m(v).
v**2*(v + 1)**3
Suppose -14 = -5*r + 1. Let c(i) be the third derivative of 0 + 0*i**r + 0*i**4 + 1/60*i**5 + 3*i**2 + 0*i. Factor c(t).
t**2
Let l(a) = 3*a**5 + 3*a**4 + 3*a**3 - 6*a**2 - 6*a + 3. Let v(y) = 6*y**5 + 5*y**4 + 7*y**3 - 12*y**2 - 13*y + 7. Let q(k) = 7*l(k) - 3*v(k). Factor q(p).
3*p*(p - 1)*(p + 1)**3
Solve -18*k**3 + 12*k**2 + 6*k**4 + 6*k**3 + 0*k**4 - 2*k**4 - 4*k = 0.
0, 1
Let d be 27/(-6)*(-105)/135. Factor -2 - d*x**2 + 8*x.
-(x - 2)*(7*x - 2)/2
Let r(l) be the third derivative of l**5/20 + l**4/8 - l**3 + 3*l**2. Factor r(f).
3*(f - 1)*(f + 2)
Let z(g) = 5*g**3 + 4*g**2 - 5*g + 4. Let o(u) = -5*u**3 - 3*u**2 + 5*u - 3. Let b(h) = -4*o(h) - 3*z(h). Factor b(d).
5*d*(d - 1)*(d + 1)
Solve -3/4*z**5 + 3/2*z**2 + 0 + 3/4*z - 3/2*z**4 + 0*z**3 = 0.
-1, 0, 1
Let h(y) be the first derivative of -y**4/10 + 2*y**3/15 + y**2/5 - 2*y/5 - 48. Let h(f) = 0. Calculate f.
-1, 1
Let p(d) be the third derivative of -d**6/300 - d**5/150 + d**4/15 + 4*d**3/15 - 4*d**2. Let p(k) = 0. Calculate k.
-2, -1, 2
Suppose z = 3*z - 6. Suppose a = -z*a. Factor 0 + a*l - 1/3*l**2.
-l**2/3
Let l = 18 - 14. Determine u, given that 1/4*u**l + 1/2*u**2 + 3/4*u**3 + 0 + 0*u = 0.
-2, -1, 0
Let v(o) be the first derivative of -o**6/3 + 16*o**5/15 - 7*o**4/6 + 4*o**3/9 + 4. Determine y, given that v(y) = 0.
0, 2/3, 1
Suppose -3*o - 24 = -4*f, -f + 4*f + 3*o = -3. Determine t so that 4*t**4 - 5*t**f + t - 4 + 4*t**3 + 3*t**2 + 2 - 5*t**4 = 0.
-2, -1, 1
Suppose -n - 2*r - 25 = 0, 4*r - 8*r = -n - 37. Let q = n - -147/5. Factor q*p**2 + 0 - 8/5*p**4 + 6/5*p**3 + 0*p.
-2*p**2*(p - 1)*(4*p + 1)/5
Suppose 2*s + m = 9, -s = s + 3*m - 11. Suppose -s*w - 6 = -7*w. Factor 3*k**5 - 5*k**4 + 6*k**w - 2*k - k - k**4.
3*k*(k - 1)**3*(k + 1)
Let v(a) be the third derivative of -1/80*a**6 - 3/40*a**5 + 0 + 0*a**3 + 2*a**2 - 1/8*a**4 + 0*a. Factor v(f).
-3*f*(f + 1)*(f + 2)/2
Let k(n) = -2*n**3 + n**2 + 5*n - 5. Let r(j) = -3*j**3 + j**2 + 6*j - 6. Suppose 0 = -4*w + 5*w + 6. Let l(a) = w*k(a) + 5*r(a). Determine p so that l(p) = 0.
-1/3, 0
Solve 3/5*y**3 - 4/5*y + 0*y**2 + 0 - 1/5*y**4 = 0 for y.
-1, 0, 2
Let z(k) be the second derivative of k**5/70 + k**4/14 + 2*k**3/21 + 5*k. Let z(g) = 0. What is g?
-2, -1, 0
Let z(b) = -b + 6. Let p be z(6). Find v such that 3*v**2 - 5*v**3 - v + 3*v**2 - 2 + p*v**3 + 2*v**2 = 0.
-2/5, 1
Let v(d) = -d**4 + 17*d**3 - 17*d**2 + d. Let f(k) = 4*k**3 - 4*k**2. Let j(a) = -9*f(a) + 2*v(a). Factor j(p).
-2*p*(p - 1)*(p + 1)**2
Let w(v) be the third derivative of -1/72*v**4 + 0*v**5 + 0 + 0*v + 1/360*v**6 + 0*v**3 + v**2. Factor w(r).
r*(r - 1)*(r + 1)/3
Factor 8*x + 2 - 3 - 7 - 2*x**2.
-2*(x - 2)**2
Let p be 8/(-20) - (-268)/20. Let d = -13 + p. Factor -1/2*s + d + 1/2*s**2.
s*(s - 1)/2
Let c(u) be the first derivative of 2*u**5/5 + 20*u**4/7 + 48*u**3/7 + 32*u**2/7 - 32*u/7 - 10. Factor c(k).
2*(k + 2)**3*(7*k - 2)/7
Suppose -3 = -x - 0. Determine o so that -4*o**2 - 12 - 12*o + o**2 + x + 0*o**2 = 0.
-3, -1
Suppose 4*u - 11 = 3*t, -3*u + 1 + 8 = -2*t. Solve -2 + 2*y**2 - u*y + 4*y + y = 0 for y.
-1, 1
Determine k, given that 5*k**2 - k**2 + 6 - 9*k + 4*k**2 - 5*k**2 = 0.
1, 2
Let p(i) be the first derivative of -2*i**6/15 - 16*i**5/25 + 11*i**4/5 - 8*i**3/5 + 7. Suppose p(m) = 0. Calculate m.
-6, 0, 1
Suppose -2*n + 1 = 5*i, -i - 16 = -8*n + 3*n. Let f = 7 - n. Factor 1/3*b**f - 2/3*b**3 + 1/3*b + 1/3 - 2/3*b**2 + 1/3*b**5.
(b - 1)**2*(b + 1)**3/3
Let c(t) be the second derivative of t**6/120 - t**5/30 + t**4/24 + t**2 + 3*t. Let j(i) be the first derivative of c(i). Factor j(o).
o*(o - 1)**2
Let y(t) be the 