*m**3/6 - 9*m**2. Let t(u) be the first derivative of v(u). Factor t(j).
-3*j*(j - 1)*(j + 1)**2/2
Let u(a) be the first derivative of -27/4*a**3 - 27/20*a**5 + 0*a + 0*a**2 - 1/8*a**6 + 1 - 81/16*a**4. Determine j so that u(j) = 0.
-3, 0
Let u = -36 - -36. Let t(r) be the first derivative of 1/2*r**4 - 1/3*r**3 + u*r**2 - 1/5*r**5 - 3 + 0*r. Factor t(p).
-p**2*(p - 1)**2
Let o(g) be the first derivative of g**6/3 - 3*g**4/2 - 4*g**3/3 + 15. Solve o(r) = 0.
-1, 0, 2
Let f(v) be the first derivative of -v**8/2520 + v**7/315 - v**6/90 + v**5/45 - v**4/36 + 2*v**3/3 + 3. Let l(c) be the third derivative of f(c). Factor l(r).
-2*(r - 1)**4/3
Let r(t) be the third derivative of -t**9/60480 + t**8/6720 - t**7/1680 + t**6/720 + t**5/30 + 3*t**2. Let g(d) be the third derivative of r(d). Factor g(u).
-(u - 1)**3
Let t = 909/10 - 181/2. Factor -4/5*m - 2/5 - t*m**2.
-2*(m + 1)**2/5
Let h(k) be the first derivative of -k**6/5 - k**5/5 + k**4/2 + 2*k**3/3 + 2*k - 1. Let c(o) be the first derivative of h(o). Factor c(z).
-2*z*(z - 1)*(z + 1)*(3*z + 2)
Suppose 2/11*s**5 - 4/11*s**3 + 0*s**2 + 0*s + 0 + 2/11*s**4 = 0. What is s?
-2, 0, 1
Factor 5*c - c**2 + 5*c**2 - 2*c**2 - 4 - 3*c.
2*(c - 1)*(c + 2)
Suppose 7 - 43 = -9*r. Let m = -2 + 2. Let 4/7*g**r - 6/7*g**3 + m*g + 2/7*g**2 + 0 = 0. What is g?
0, 1/2, 1
Let f(a) be the third derivative of 0 + 1/2*a**4 - 1/20*a**5 - 6*a**2 - 2*a**3 + 0*a. Factor f(q).
-3*(q - 2)**2
Let n be 1 - (-9)/(-36)*-4. Solve 1/7 - 3/7*g**5 - 2*g**3 - 6/7*g**n - 11/7*g**4 + 1/7*g = 0 for g.
-1, 1/3
Let j(k) be the second derivative of -1/54*k**4 + 3*k + 0*k**3 + 0*k**2 + 0. Let j(u) = 0. Calculate u.
0
Let w(o) be the third derivative of 0*o**3 + 1/30*o**5 + 0*o + 1/315*o**7 - 3*o**2 + 1/60*o**6 + 0 + 1/36*o**4. Determine u so that w(u) = 0.
-1, 0
Let x(y) be the third derivative of 1/6*y**4 - 1/15*y**7 - 4*y**2 + 4/15*y**6 + 0 + 0*y - 11/30*y**5 + 0*y**3. Find o such that x(o) = 0.
0, 2/7, 1
Find z, given that 0 + 8/11*z + 26/11*z**3 - 12/11*z**4 - 24/11*z**2 + 2/11*z**5 = 0.
0, 1, 2
Factor 18/5*j**3 + 14/5*j**2 + 2*j**4 + 4/5*j + 2/5*j**5 + 0.
2*j*(j + 1)**3*(j + 2)/5
Let i(t) = -t**4 + 3*t**3 - 7*t**2 - 3*t. Let m(u) = u**4 + u**2. Let b(a) = i(a) + 4*m(a). Factor b(f).
3*f*(f - 1)*(f + 1)**2
Let d be 1148/30 - (-2)/5. Let w = d - 38. Factor -13/3*f**2 + 0 + w*f + 20/3*f**3 - 3*f**4.
-f*(f - 1)**2*(9*f - 2)/3
Solve -4*n**4 - 9*n**3 + 4*n**5 - 5*n**3 + 6*n**3 = 0.
-1, 0, 2
Factor 4 + 10*v - 8*v**2 - 7 - 1 + 2*v**3.
2*(v - 2)*(v - 1)**2
Let x = 0 - -1. Suppose -6 = -2*z - 0. What is h in h**z - 1 + x - h**2 = 0?
0, 1
Let t(v) be the first derivative of 0*v**3 + 0*v - 2 - 1/5*v**5 - 1/2*v**4 + 0*v**2. Let t(a) = 0. Calculate a.
-2, 0
Let w(b) be the second derivative of -b**7/6 - 3*b**6/10 + b**5/4 + 3*b**4/4 + b**3/3 + 4*b. Let w(l) = 0. What is l?
-1, -2/7, 0, 1
Solve 2*v - 8/5*v**2 - 4/5 + 2/5*v**3 = 0.
1, 2
Factor 0*v**2 - 4/5*v + 1/5*v**3 + 0.
v*(v - 2)*(v + 2)/5
Let x(c) be the first derivative of -c**2 + 0*c**3 - 1/5*c**5 + 1/2*c**4 + 2 + c. Factor x(f).
-(f - 1)**3*(f + 1)
Let 3*q - 3/4*q**2 - 3 = 0. What is q?
2
Let b(d) be the first derivative of d**4/24 + 2*d**3/9 + d**2/4 + 6. Factor b(g).
g*(g + 1)*(g + 3)/6
Factor -8/3 - 4*m - 4/3*m**2.
-4*(m + 1)*(m + 2)/3
Let x be 0/17 + (6/(-5) - -2). Factor -2/5 - x*r**2 + 6/5*r.
-2*(r - 1)*(2*r - 1)/5
Find j such that 2/13*j - 4/13 + 2/13*j**2 = 0.
-2, 1
Let u be ((-24)/(-14))/(9/98). Suppose -3 = -a - 0. Solve -26/3*h + 26/3*h**2 + u*h**a + 4/3 = 0.
-1, 1/4, 2/7
Let v(x) = -x**3 + x**2 - x + 3. Let a(d) = -2*d**3 + 2*d**2 - d + 4. Let g(b) = 2*a(b) - 3*v(b). Determine h, given that g(h) = 0.
-1, 1
Let x be 6/(-9) - (-11)/3. Let k(m) be the first derivative of -1/4*m**2 + 0*m + 2 + 0*m**4 + 1/5*m**5 - 1/3*m**x + 1/12*m**6. Factor k(p).
p*(p - 1)*(p + 1)**3/2
Suppose -3*a + 5*k = -10, -2*a + 2*k + 2 = -2. Let q be (a/(-3))/(-1 - -2). Factor 2/7*r**3 + 0 - 2/7*r + q*r**2.
2*r*(r - 1)*(r + 1)/7
Let l(p) be the second derivative of p**6/6 - 3*p**5/2 + 5*p**4 - 20*p**3/3 - p - 24. Factor l(d).
5*d*(d - 2)**3
Let j be ((-3)/(-6))/((-3)/(-24)). Let u(q) = q**2 - 4*q + 3. Let v be u(j). Let -d + 3*d**v - 4*d + 2*d + 0*d = 0. Calculate d.
-1, 0, 1
Let r be (-2)/9 + 116/36. Factor r + 3*w**3 + 5 + 7*w**2 + 12*w + 4*w**2 - 4.
(w + 1)*(w + 2)*(3*w + 2)
Let u(n) be the third derivative of n**8/1680 - n**7/1050 - n**6/200 + n**5/60 - n**4/60 - n**2. Factor u(h).
h*(h - 1)**3*(h + 2)/5
Let w(y) be the second derivative of y**5/40 - y**4/8 + y**2 - y. Suppose w(u) = 0. What is u?
-1, 2
Let d(z) be the second derivative of -z**4/54 - z**3/27 + 2*z**2/9 - 9*z. Factor d(o).
-2*(o - 1)*(o + 2)/9
Let l(s) be the first derivative of 0*s**2 - 1/15*s**6 + 1/2*s**4 - 3*s + 2/3*s**3 + 0*s**5 - 4. Let n(p) be the first derivative of l(p). Factor n(t).
-2*t*(t - 2)*(t + 1)**2
Let h = 353 - 1762/5. Solve -h*b - 4/5*b**2 + 1/5 = 0 for b.
-1, 1/4
Let u = 7/15 - -1/5. Let o be 126/324*(2 - (-10)/(-7)). Determine x so that -4/9 + u*x - o*x**2 = 0.
1, 2
Let q = 7 - 9. Let i be (-7)/(-4) + q/4. Find o such that 0 + 9/4*o**2 + i*o**4 - 1/2*o - 3*o**3 = 0.
0, 2/5, 1
Let f be (9/12)/((-1)/128). Let r be ((-10)/(-6))/((-56)/f). Factor r*c**2 + 2/7 - 10/7*c + 10/7*c**4 - 2/7*c**5 - 20/7*c**3.
-2*(c - 1)**5/7
Let f(n) = -n**2 - n + 1. Let m(s) = 6*s**2 + 58*s - 154. Let y(u) = -10*f(u) - m(u). Factor y(t).
4*(t - 6)**2
Factor -2 - 8*l**3 - 6 + 8 + 4*l**2.
-4*l**2*(2*l - 1)
Suppose 8 = -17*w + 21*w. Let s(j) be the first derivative of -3/10*j**w - 2/5*j - 1/15*j**3 - 1. Factor s(z).
-(z + 1)*(z + 2)/5
Let p(s) be the third derivative of s**8/112 + s**7/70 - 8*s**2. Factor p(y).
3*y**4*(y + 1)
Let i(v) be the first derivative of -v**5/330 + v**4/66 - v**3/33 - v**2 + 3. Let g(u) be the second derivative of i(u). Solve g(r) = 0.
1
Let v be (10/18)/((-35)/(-42)). Determine r so that r - v - 1/3*r**2 = 0.
1, 2
Let l(m) be the first derivative of -m**3 + 3*m**2 + 24*m + 34. Factor l(b).
-3*(b - 4)*(b + 2)
Let 14/15*m + 6/5*m**3 + 2/15 + 2*m**2 = 0. What is m?
-1, -1/3
Suppose -4*r - 29 = -5*f, -9 = 5*r - 3*f + 11. Let x = r - -4/3. Factor 1/3*z - x*z**4 + 2/3*z**2 + 1/3*z**5 - 2/3*z**3 - 1/3.
(z - 1)**3*(z + 1)**2/3
Let o(c) = 13*c**3 - 11*c**2 + 24. Let l be 7/(-3*2/(-6)). Let d(t) = -9*t**3 + 7*t**2 - 16. Let v(p) = l*d(p) + 5*o(p). Factor v(m).
2*(m - 2)**2*(m + 1)
Let r = 167/10 + -33/2. Let z(i) be the first derivative of 0*i - r*i**2 + 1/10*i**4 - 2/15*i**3 - 1 + 2/25*i**5. Find l such that z(l) = 0.
-1, 0, 1
Let v be -1 - (2 - (2 + 0)). Let o be (v/5)/(6/(-10)). Factor -o*u**2 - 1/3 + 2/3*u.
-(u - 1)**2/3
Let u(g) be the second derivative of 0*g**3 - g + 1/6*g**4 + 1/5*g**6 + 1/21*g**7 + 0 + 3/10*g**5 + 0*g**2. Factor u(n).
2*n**2*(n + 1)**3
Let m = 9 - 5. Factor 2*d**4 - 4*d**4 + m*d + 4 + 6*d**3 - 2*d**2 - 10*d.
-2*(d - 2)*(d - 1)**2*(d + 1)
Let p = 343/795 - 5/159. Factor -2/5*g**5 - 4/5*g**3 + 6/5*g**4 + 6/5*g - 4/5*g**2 - p.
-2*(g - 1)**4*(g + 1)/5
Let g = 2494/5 + -497. Factor 3*q**2 + g*q**4 - 3/5*q - 21/5*q**3 + 0.
3*q*(q - 1)**2*(3*q - 1)/5
Suppose -3*z = -b - 14 + 4, -z = 3*b - 10. Factor -2/9*k**b - 2/9*k + 2/9*k**3 + 0 + 2/9*k**4.
2*k*(k - 1)*(k + 1)**2/9
Factor -12 - 16*t + 2*t**2 + 3*t**2 + 11*t**2 - 20*t**2.
-4*(t + 1)*(t + 3)
Let j = -17 + 20. Let d(i) be the third derivative of 2/3*i**3 + 0 + 1/60*i**5 - 1/6*i**4 + j*i**2 + 0*i. Find p such that d(p) = 0.
2
Factor -1/4*z + 1/4*z**3 - 1/4*z**4 + 0 + 1/4*z**2.
-z*(z - 1)**2*(z + 1)/4
Let k = 24 - 23. Suppose 6*l**2 + k - 3 + 3 - 10*l - 5 = 0. Calculate l.
-1/3, 2
Let v(w) be the third derivative of -w**6/60 - w**5/15 + 61*w**2. Factor v(j).
-2*j**2*(j + 2)
Let o be (5 - 1)/(2*1). Suppose -4 = -3*i + o. Factor 18*r**2 + 22*r - 1 + i + 3.
2*(r + 1)*(9*r + 2)
Suppose 5*u - 1 = 14. Let t(v) be the second derivative of 1/3*v**u + v**2 - 1/10*v**5 - 1/6*v**4 - 2*v + 0. Factor t(x).
-2*(x - 1)*(x + 1)**2
Let j(t) be the first derivative of -t**5/70 + t**4/14 - t**3/7 + t**2/7 - 2*t - 3. Let r(w) be the first derivative of j(w). Factor r(x).
-2*(x - 1)**3/7
Factor 12 - 10*t**2 - 10*t + 3*t**3 - 6*t**2 + 3*t**3.
2*(t - 3)*(t + 1)*(3*t - 2)
Factor -54 - 36*r**2 - 2/3*r**4 - 72*r - 8*r**3.
-2*(r + 3)**4/3
Factor -5/4*m**3 - 5/2 - 25/4*m - 5*m**2.
-5*(m + 1)*