 i(m) be the first derivative of -1/15*m**6 - 9 + 2/25*m**5 + 2/5*m + 1/5*m**4 - 4/15*m**3 - 1/5*m**2. Factor i(u).
-2*(u - 1)**3*(u + 1)**2/5
Let c(m) be the first derivative of -2*m**3/27 - m**2 - 16*m/9 - 29. Factor c(q).
-2*(q + 1)*(q + 8)/9
Solve 123*h**3 + 16*h - 31*h**3 + 88*h**2 - 8*h**2 + 8*h**3 = 0 for h.
-2/5, 0
Factor -62*o**4 + 8*o**3 - 2*o**2 + 31*o**4 - 14*o**2 + 30*o**4.
-o**2*(o - 4)**2
Suppose 0*x - 4*x + 7 = t, 3*x = -4*t - 11. Let y = -10 - -14. Factor -6*r**5 - x*r**y + 7*r**5 + 8*r**3 + 3*r**4 + 4*r**2 + 5*r**4.
r**2*(r + 1)*(r + 2)**2
Let t(w) be the third derivative of -w**6/24 + 5*w**4/8 - 5*w**3/3 + 8*w**2. Factor t(o).
-5*(o - 1)**2*(o + 2)
Suppose 0 = 3*s - 12, -4*w - 4*s + 15 = -1. Let v(j) be the second derivative of 0*j**2 + w - j - 2/27*j**3 - 1/54*j**4. Factor v(z).
-2*z*(z + 2)/9
Find o, given that -1/4*o**3 + 1/4*o + 3/4*o**2 - 3/4*o**4 + 0 = 0.
-1, -1/3, 0, 1
Let g(p) be the first derivative of p**9/112 - p**7/28 + p**5/40 + p**3 + 1. Let n(h) be the third derivative of g(h). Determine c, given that n(c) = 0.
-1, -1/3, 0, 1/3, 1
Let y(n) be the third derivative of n**6/120 + n**5/15 + n**4/6 + n**3/3 - 2*n**2. Let d be y(-2). Factor -2/5*b**d - 8/5 - 8/5*b.
-2*(b + 2)**2/5
Let c(q) = q + 1. Let f = 3 + 0. Let y(v) = -f + 1 + 5 + 2*v - v**2 + 0*v. Let m(r) = -4*c(r) + y(r). Factor m(a).
-(a + 1)**2
Let l(j) be the second derivative of -j**8/6720 - j**7/2520 + j**4/4 - 3*j. Let i(g) be the third derivative of l(g). Suppose i(f) = 0. What is f?
-1, 0
Let o(x) be the first derivative of -x**5/12 - x**4/8 + x**3/3 - 5*x**2/2 - 5. Let j(y) be the second derivative of o(y). What is k in j(k) = 0?
-1, 2/5
Let k(v) be the second derivative of -v**6/6 + 5*v**5/4 - 10*v**4/3 + 10*v**3/3 + 34*v. Find t such that k(t) = 0.
0, 1, 2
Let i(c) be the second derivative of c**6/30 - c**5/20 - 5*c**4/12 - c**3/2 + 14*c + 3. Let i(v) = 0. What is v?
-1, 0, 3
Let p(f) be the second derivative of -f**7/210 + f**6/60 - 3*f**2/2 - f. Let s(n) be the first derivative of p(n). Factor s(h).
-h**3*(h - 2)
Let j(a) be the first derivative of a**4/4 + 2*a**3/3 - 2*a**2 + a + 2. Let l(d) be the first derivative of j(d). Factor l(p).
(p + 2)*(3*p - 2)
Factor 1/2 + 1/4*k**2 - 3/4*k.
(k - 2)*(k - 1)/4
Let r(z) be the first derivative of 0*z**3 + 1/7*z**4 + 0*z**2 - 1/21*z**6 + 3 + 0*z - 2/35*z**5. Factor r(k).
-2*k**3*(k - 1)*(k + 2)/7
Suppose -224 = -15*l - 41*l. Factor 6*d**3 - 1/2*d**l - 27*d**2 - 81/2 + 54*d.
-(d - 3)**4/2
Let s(r) be the first derivative of r**6/60 - r**5/40 - r**4/12 + r - 3. Let k(i) be the first derivative of s(i). Factor k(y).
y**2*(y - 2)*(y + 1)/2
Let y(w) = -w**2. Let d(s) = -32*s**2 - 4*s. Let g(j) = d(j) - 12*y(j). Factor g(a).
-4*a*(5*a + 1)
Let k(i) be the first derivative of 128*i**3/63 - 16*i**2/21 + 2*i/21 - 14. Factor k(y).
2*(8*y - 1)**2/21
Let d(b) = -b**5 - b**3 - b**2 - b + 1. Let q(h) = -5*h**5 + 4*h**4 - 8*h**3 - 6*h**2 + h + 2. Let n(t) = -4*d(t) + q(t). Find a, given that n(a) = 0.
-1, 1, 2
Let s(m) = -m**2 + 10*m + 144. Let n be s(-8). Factor 1/3*g**2 + n - g.
g*(g - 3)/3
Suppose 0 = 3*g - 2*g - 3. Determine k, given that 4*k**3 + 8*k - 20*k**g - k**2 - 7*k**2 + 8*k**5 + 4 + 4*k**4 = 0.
-1, -1/2, 1
Suppose 10 + 20 = 10*c. Solve -6/7*b**2 - 2/7 + 2/7*b**c + 6/7*b = 0.
1
Solve 3 + 154*l**2 + 196*l**3 - 1418*l + 1450*l - 1 = 0 for l.
-1/2, -1/7
Let u(a) = -a**3 + 10*a**2 - 10*a + 11. Let w be u(9). Factor 6*d + 2*d - 4*d**2 + d**w - 5*d.
-3*d*(d - 1)
Factor 0 + 3/7*j - 12/7*j**3 + 9/7*j**2.
-3*j*(j - 1)*(4*j + 1)/7
Let h = 7 - 5. Suppose -4*f - 24 = -h*n, -f = 5*n - 4*n. Factor -y**n + 3*y - y**5 + y**2 + 2*y**3 - 4*y - 1 + y**2.
-(y - 1)**2*(y + 1)**3
Let h be -8 + 5 + 5 + 11/(-7). Let -3/7*i**3 + h*i - 3/7 + 3/7*i**2 = 0. Calculate i.
-1, 1
Let c(y) = 2*y**3 - y**2 - 4*y + 5. Let b be c(1). Factor 2/3*k**b + 2/3 + 4/3*k.
2*(k + 1)**2/3
Let z(u) be the first derivative of -1/4*u**2 + 1/8*u**4 + 2 + 1/2*u - 1/6*u**3. Determine n so that z(n) = 0.
-1, 1
Let h(m) be the first derivative of -m**4/10 - 2*m**3/15 + m**2/5 + 2*m/5 + 1. Find c such that h(c) = 0.
-1, 1
Let p = -11 - -29. Find u such that 3 - p*u**4 + 46*u**2 - 26*u + 0 - 6*u**3 + 1 = 0.
-2, 1/3, 1
Let r = 75 - 70. Let a(j) be the first derivative of 1/5*j**r - 1 + 3/4*j**4 - 2*j - 3/2*j**2 + 1/3*j**3. Find w such that a(w) = 0.
-2, -1, 1
Let k(o) be the third derivative of 1/120*o**5 + 1/420*o**7 + 0*o**4 + 0*o**3 + 0*o - 1/120*o**6 + 2*o**2 + 0. Find u such that k(u) = 0.
0, 1
Let u(b) be the first derivative of -1/3*b**4 + 2/3*b + b**2 - 1/9*b**6 - 2/5*b**5 - 1 + 4/9*b**3. Factor u(x).
-2*(x - 1)*(x + 1)**4/3
Factor 3/4 - 1/4*r**2 - 1/2*r.
-(r - 1)*(r + 3)/4
Let j(l) be the third derivative of l**8/560 - l**7/175 + l**5/50 - l**4/40 + 3*l**2. Factor j(d).
3*d*(d - 1)**3*(d + 1)/5
Suppose 3*g + 6 = 0, 5*g + 19 = 3*m + 3. Factor 2 + 12*j**3 + 1 - 3 + 8*j**4 + 2*j + 8*j**2 + m*j**5.
2*j*(j + 1)**4
Suppose 3*j = d + 2*j - 56, -4*d + 5*j + 224 = 0. Let y be 2 + (d/9)/(-4). Suppose 2/9*m + 0*m**2 + 2/9*m**5 + 0*m**4 - y*m**3 + 0 = 0. What is m?
-1, 0, 1
What is z in 0*z + 2 - 1/2*z**3 - 3/2*z**2 = 0?
-2, 1
Let -5*a**2 - 24 + 6*a - 3*a**4 + 23*a**2 - 3*a**3 + 6*a = 0. What is a?
-2, 1, 2
Factor -26*m + 21*m**2 + 6 + 0*m**3 - 6*m**3 + 5*m.
-3*(m - 2)*(m - 1)*(2*m - 1)
Factor 0*g**2 + 132 - g**2 - 132 + g.
-g*(g - 1)
Let l = 10 - 4. Suppose k = -k + l. Factor -g**2 + 7/2*g**k - 1/2*g + 0 - 2*g**4.
-g*(g - 1)**2*(4*g + 1)/2
Let w = 437/441 + -5/49. Let f be -2*(-2)/(-54)*-3. Determine r, given that 0 - 2/9*r**5 + w*r**4 - 4/3*r**3 - f*r + 8/9*r**2 = 0.
0, 1
Let s(z) = 7*z**4 - 63*z**3 + 51*z**2 + 94*z - 22. Let k(x) = x**4 + x - 1. Let d(v) = 5*k(v) + s(v). Factor d(h).
3*(h - 3)**2*(h + 1)*(4*h - 1)
Let t(h) be the second derivative of 0*h**2 + 2/21*h**3 + 37/105*h**6 - 1/6*h**4 - 20/147*h**7 - 2*h + 0 - 6/35*h**5. Solve t(o) = 0 for o.
-2/5, 0, 1/4, 1
Let k(c) be the first derivative of 3*c**4/20 + c**3/5 - 3*c**2/10 - 3*c/5 + 6. Factor k(v).
3*(v - 1)*(v + 1)**2/5
Let d(g) be the third derivative of -g**5/210 + g**4/21 - g**3/7 + g**2 - 11. Factor d(x).
-2*(x - 3)*(x - 1)/7
Let t(p) be the third derivative of p**6/1440 - p**5/480 - p**4/48 - p**3/6 - p**2. Let j(f) be the first derivative of t(f). Solve j(s) = 0 for s.
-1, 2
Let f(x) be the third derivative of -x**6/780 - 7*x**5/130 - 49*x**4/52 - 343*x**3/39 + 10*x**2. Find n such that f(n) = 0.
-7
Let n = -69/4 + 18. Factor 27/4*k - 9/2*k**2 + n*k**3 + 0.
3*k*(k - 3)**2/4
Let m = -44 + 44. Find y such that -2/7*y**3 + 0 + m*y**2 + 0*y - 2/7*y**4 = 0.
-1, 0
Determine q, given that 0*q**3 - 162*q**5 - 5*q**3 - 10*q**4 + 83*q**5 + 74*q**5 = 0.
-1, 0
Let s(k) be the third derivative of k**8/616 - k**7/231 - k**6/165 + 2*k**5/165 - 20*k**2. Determine f, given that s(f) = 0.
-1, 0, 2/3, 2
Factor -1/7*f**4 + 0 + 4/7*f**2 - 4/7*f + 1/7*f**3.
-f*(f - 2)*(f - 1)*(f + 2)/7
Let i = 85/3 - 28. Let o = 22 + -17. Suppose 0*y**3 + 0*y**2 + 1/3*y**4 - i*y**o + 0 + 0*y = 0. Calculate y.
0, 1
Suppose 37 = 5*n + 17. Factor -14*b**2 - 2*b**3 + 20*b**3 + 99*b + 2*b**5 - 10*b**n - 95*b.
2*b*(b - 2)*(b - 1)**3
Let j(q) be the first derivative of 2*q**4/13 + 2*q**3/39 - 9. Factor j(y).
2*y**2*(4*y + 1)/13
Let w be (12/4 - 0)/1. Suppose 6*k = w*k. Solve k - 3/5*a**2 - 3/5*a**4 + 0*a - 6/5*a**3 = 0.
-1, 0
Determine p, given that -1/10*p**2 + 3/10 + 1/5*p = 0.
-1, 3
Let u(s) be the third derivative of 3*s**8/224 - 3*s**7/140 - 5*s**6/48 + 3*s**5/8 - s**4/2 + s**3/3 - 25*s**2. Solve u(b) = 0.
-2, 1/3, 2/3, 1
Let w(u) be the second derivative of -1/3*u**3 + 1/10*u**5 + 0*u**4 + 0 + 0*u**2 + 2*u. Factor w(p).
2*p*(p - 1)*(p + 1)
Let j(a) be the second derivative of a**5/12 + 5*a**4/36 - 12*a. Factor j(t).
5*t**2*(t + 1)/3
Let m(d) = d**2 + 2*d - 8. Let p be m(-4). Let w(i) be the third derivative of -1/3*i**3 + p - 1/10*i**5 - 1/4*i**4 + 0*i - 3*i**2 - 1/60*i**6. Factor w(l).
-2*(l + 1)**3
Let j = 23/2 + -67/6. Let h(r) be the third derivative of 0 + r**2 + 1/12*r**4 - 1/60*r**6 + 0*r + 1/30*r**5 - j*r**3. Factor h(o).
-2*(o - 1)**2*(o + 1)
Let z(s) be the first derivative of 2/3*s**3 + s**2 + 1 - 7/6*s**4 + 13/12*s**5 - 5/12*s**6 + 0*s. Let p(l) be the second derivative of z(l). Factor p(x).
-(2*x - 1)*(5*x - 2)**2
Le