et c(u) be the third derivative of -u**6/600 - u**5/75 + u**4/120 + 2*u**3/15 - 5*u**2. Factor c(a).
-(a - 1)*(a + 1)*(a + 4)/5
Let a(i) = i. Let t(q) = q**3 - 9*q**2 - 4*q - 10. Let o(j) = 5*a(j) - t(j). Let m be o(10). Factor 0 - 1/5*f**2 - 2/5*f**3 + m*f.
-f**2*(2*f + 1)/5
Let k be (-2)/6 - (-28)/21. Let g be (k + -1)/((-6)/3). Factor g + 2/3*f**2 + 2/3*f.
2*f*(f + 1)/3
Let h(o) be the first derivative of -o**8/1848 - o**7/1155 + o**6/660 + o**5/330 + o**2/2 + 1. Let f(k) be the second derivative of h(k). Factor f(n).
-2*n**2*(n - 1)*(n + 1)**2/11
Let y(a) = 6*a**2 + 4*a + 6. Let n(b) = 7*b**2 + 4*b + 7. Let f(p) = -4*n(p) + 5*y(p). Let f(w) = 0. Calculate w.
-1
Find h, given that 11*h**3 - 6*h**2 + 8*h**4 - h**3 + 0*h**4 - 10*h + 1 - 3 = 0.
-1, -1/4, 1
Let k(g) be the second derivative of g**6/90 - g**5/60 - 7*g. Factor k(a).
a**3*(a - 1)/3
Let b(m) be the first derivative of -1/6*m**6 + 0*m**4 + 2/3*m**3 + 0*m - 2/5*m**5 + 1/2*m**2 - 1. Factor b(g).
-g*(g - 1)*(g + 1)**3
Factor -18*v + 27 + 5*v**2 + v**2 + 2*v**2 - 5*v**2.
3*(v - 3)**2
Let x = -714 + 718. Factor 4/5 + 64/5*v**2 - 2*v**5 + 44/5*v**x - 26/5*v - 76/5*v**3.
-2*(v - 1)**4*(5*v - 2)/5
Let x(c) be the second derivative of -5*c**7/14 + 4*c**6/3 + 15*c**5/4 + 5*c**4/3 + 11*c. Find o, given that x(o) = 0.
-1, -1/3, 0, 4
Let m be 0/(0/2 - 1). Factor m + 2/5*r**3 - 2/5*r - 2/5*r**4 + 2/5*r**2.
-2*r*(r - 1)**2*(r + 1)/5
Let i = 574/3 - 191. Factor 1/3*f**5 + 0 + 1/3*f**4 - i*f**2 - 1/3*f**3 + 0*f.
f**2*(f - 1)*(f + 1)**2/3
Let i(z) be the second derivative of -1/6*z**4 + 0 - 4/3*z**3 - 4*z**2 - 7*z. Factor i(p).
-2*(p + 2)**2
Let s = 136 + -136. Factor 0*n + s*n**2 + 2/7*n**3 + 0 - 2/7*n**4 - 4/7*n**5.
-2*n**3*(n + 1)*(2*n - 1)/7
Let y = -133/3 + 45. Let r(x) be the second derivative of -1/18*x**4 + y*x**2 + x + 0 - 1/9*x**3. Factor r(l).
-2*(l - 1)*(l + 2)/3
Let t(k) be the third derivative of 0*k + 1/20*k**4 + 2/15*k**3 + 1/150*k**5 - 3*k**2 + 0. Factor t(b).
2*(b + 1)*(b + 2)/5
Let d(j) = j**3 - 23*j**2 + 42*j + 2. Let q be d(21). Factor -2/5*g - 1/5*g**q - 1/5.
-(g + 1)**2/5
Let u(k) = 14*k**3 + 8*k**2 - 14*k - 8. Let d be (3/4)/(2/8). Let c = -17 - -9. Let i(j) = 5*j**3 + 3*j**2 - 5*j - 3. Let s(p) = c*i(p) + d*u(p). Factor s(n).
2*n*(n - 1)*(n + 1)
Let t(m) = -17*m**3 + 13*m**2 - 9*m. Let i be 195/(-10)*4/3. Let u(s) = -4*s**3 + 3*s**2 - 2*s. Let w(c) = i*u(c) + 6*t(c). Factor w(n).
2*n*(n - 1)*(n + 1)
Let f(t) = -6*t**2 + t - 9. Let g(h) = -h**2 + h - 1. Let k(m) = -f(m) + 5*g(m). Factor k(z).
(z + 2)**2
Let m(f) be the second derivative of -f**6/90 - f**5/60 + 5*f**4/36 - f**3/6 - 16*f + 2. Factor m(t).
-t*(t - 1)**2*(t + 3)/3
Let v(d) be the first derivative of -d**4/16 - d**3/4 - 3*d**2/8 - d/4 + 1. Find q, given that v(q) = 0.
-1
Solve 0*h**2 - 2/3*h**5 - 2/3*h**4 + 0 + 0*h + 0*h**3 = 0 for h.
-1, 0
Suppose -3*b - 4 = -5*j - 13, 5*b = -5*j + 15. Factor 2/7*r**4 + 0*r**b + 0*r**2 + 0 + 0*r + 2/7*r**5.
2*r**4*(r + 1)/7
Factor 24*y**2 - y - 3*y**4 - 3*y + 8*y**4 - 7*y**3 - 14*y**3.
y*(y - 2)**2*(5*y - 1)
Suppose -3 = -f - d, d = -f + 2*f - 5. Let -15*t**2 + 3*t - 1 + f + 4*t**3 + 5*t**3 = 0. Calculate t.
-1/3, 1
Suppose 3*r = 4*r - 2. Factor -98*t + 4*t**r - 4*t**3 + 102*t - 16 + 12*t**2.
-4*(t - 4)*(t - 1)*(t + 1)
Let f(x) be the second derivative of x**5/240 + x**4/24 + x**3/6 - 5*x**2/2 - 5*x. Let q(n) be the first derivative of f(n). Determine a so that q(a) = 0.
-2
Suppose -3*j + 4*j - 7 = 0. Suppose x = j*x. Suppose x + 6/5*i**2 + 4/5*i**3 + 2/5*i = 0. Calculate i.
-1, -1/2, 0
Suppose 3*q = 3 + 9. Let l(v) be the second derivative of 0 + v + 5/12*v**q + 2*v**2 + 4/3*v**3 + 1/20*v**5. Determine s so that l(s) = 0.
-2, -1
Let w(n) be the third derivative of -n**5/120 + n**4/16 - 6*n**2. Let w(c) = 0. Calculate c.
0, 3
Let n(z) = 8*z**2 + 16*z - 4. Let c(w) = w**4 + 15*w**2 + 34*w - 9. Let b(l) = 4*c(l) - 9*n(l). What is m in b(m) = 0?
-1, 0, 2
Let x be ((-6)/8)/((-12)/(-48)). Let r be (x/60)/(2/(-8)). Factor 1/5*a**3 + 0 + 2/5*a**2 + r*a.
a*(a + 1)**2/5
Find y such that -18/5 - 12/5*y - 2/5*y**2 = 0.
-3
Let j(o) be the first derivative of -2 - 2*o**2 + 4*o**4 - 2/3*o**3 + 0*o - 2*o**5. Let j(n) = 0. Calculate n.
-2/5, 0, 1
Let w(t) be the third derivative of 0*t**3 + 1/20*t**5 + 0 + 0*t + 1/8*t**4 + t**2. Factor w(f).
3*f*(f + 1)
Let s(v) be the first derivative of 3/16*v**4 + 1/8*v**2 + 0*v + 1/20*v**5 - 3 + 1/4*v**3. Solve s(w) = 0.
-1, 0
Let s be ((-2)/(-20))/(31/124). Factor -s*x**4 + 2/5 - 4/5*x + 0*x**2 + 4/5*x**3.
-2*(x - 1)**3*(x + 1)/5
Let v(k) be the third derivative of k**6/120 + k**5/20 + k**4/8 + k**3/2 - 5*k**2. Let g(r) = -r**3 + r**2 - r - 1. Let x(b) = 6*g(b) + 2*v(b). Factor x(m).
-4*m**2*(m - 3)
Let s = -1806 + 12666/7. Factor -12/7*t**2 - 16/7 + s*t + 2/7*t**3.
2*(t - 2)**3/7
Suppose -2*r - 3*a = -15, -2*r + 0*a + a + 3 = 0. What is h in -1/4*h**5 - 1/4 - 1/2*h**r + 3/4*h + 3/4*h**4 - 1/2*h**2 = 0?
-1, 1
Let r = -729 + 729. Let 2/11*d**2 + 0*d + 0 + r*d**3 - 2/11*d**4 = 0. Calculate d.
-1, 0, 1
Let t(o) be the first derivative of -o**6/12 - o**5/10 + 10. Determine s, given that t(s) = 0.
-1, 0
Let v(b) be the second derivative of -b**6/15 - b**5/10 + b**4/12 + 3*b**2/2 - 3*b. Let u(x) be the first derivative of v(x). Factor u(d).
-2*d*(d + 1)*(4*d - 1)
Let v = -1363/7 + 195. Let w(x) be the first derivative of -2/7*x + v*x**2 - 2/21*x**3 - 3. Let w(f) = 0. What is f?
1
Let -1/4*z**4 - 5/2*z**3 + 0*z + 0 + 0*z**2 = 0. What is z?
-10, 0
Let a(k) be the first derivative of -2*k**5/45 - k**4/6 - 2*k**3/9 - k**2/9 - 6*k - 4. Let g(p) be the first derivative of a(p). Factor g(j).
-2*(j + 1)**2*(4*j + 1)/9
Suppose -4*l = -2*l - 7*l. Let z(y) be the third derivative of 2*y**2 + 1/132*y**4 - 1/660*y**6 + 0*y**5 + 0*y**3 + 0 + l*y. Factor z(q).
-2*q*(q - 1)*(q + 1)/11
Let r(w) = 2*w + 8. Let v(n) = n**3 + 8*n**2 + n + 4. Let p be v(-8). Let h be r(p). Let 0*o**2 + 0*o + h*o**4 + 1/2*o**5 + 0 - 1/2*o**3 = 0. What is o?
-1, 0, 1
Let p(c) be the second derivative of -c**4/8 + 3*c**2/4 - 14*c. Find a, given that p(a) = 0.
-1, 1
Let r(o) be the third derivative of o**8/210 - o**7/175 - o**6/300 + 2*o**2. Factor r(z).
2*z**3*(z - 1)*(4*z + 1)/5
Let a(x) be the second derivative of -x**6/120 + x**5/20 - x**4/8 + x**3/6 + x**2 + x. Let p(f) be the first derivative of a(f). What is q in p(q) = 0?
1
Let w = 2 - 3. Let l be (-2)/(-9)*6 + w. Factor 0 - 1/3*c**3 + 0*c - l*c**2.
-c**2*(c + 1)/3
Let n(u) be the third derivative of 5*u**2 - 1/70*u**7 + 0*u + 0*u**3 - 1/120*u**6 + 1/24*u**4 + 1/20*u**5 + 0. Factor n(m).
-m*(m - 1)*(m + 1)*(3*m + 1)
Let y(v) = -v**3 + 5*v**2 + v - 2. Let n be y(5). Suppose 3*a - 3*f - 6 = -f, -5*a = -n*f - 10. Determine b, given that -6*b**2 + 0*b - a*b - 2*b = 0.
-2/3, 0
Suppose 8/15*g**3 + 2/15 + 8/15*g + 2/15*g**4 + 4/5*g**2 = 0. Calculate g.
-1
Let j = 19 - 17. Suppose -6*x + 0*x**2 + x**j + x**2 = 0. What is x?
0, 3
Suppose -2*n + 9 = 5*k - 2, 21 = 5*k - 3*n. Factor -2*h**k + 1 + h**3 - 3*h**3 + 1 - 5*h**2 + 7*h.
-(h - 1)*(h + 2)*(4*h + 1)
Let a(r) be the second derivative of -r**5/4 - 5*r**4/12 + 5*r**3/6 + 5*r**2/2 + 6*r. Factor a(n).
-5*(n - 1)*(n + 1)**2
Let o(p) = -2*p**2 - 5*p + 7. Suppose 0*t = -3*t + 18. Let l(x) = x**2 + 5*x - 6. Let i(y) = t*l(y) + 5*o(y). Find k, given that i(k) = 0.
1/4, 1
Let n be (34/(-10) - -1)*-1. Let z = n + -26/15. Factor -4/3*p + 0 + z*p**2.
2*p*(p - 2)/3
Let h = 45 + -45. Let p(g) be the third derivative of 0*g**3 + 1/180*g**6 - 2*g**2 + 1/45*g**5 + h*g + 0 + 0*g**4. Factor p(u).
2*u**2*(u + 2)/3
Let r(o) be the first derivative of 14*o**5/25 + o**4/10 - 8. Let r(q) = 0. What is q?
-1/7, 0
Let f(j) = -j - 6. Let b be f(-7). Suppose 4*w = 2*w + 4*o - 6, 0 = -3*w + 2*o - b. Solve 0*k**2 - 3 - 2*k**2 - 6*k - w = 0 for k.
-2, -1
Suppose 2 = -0*p + p. Let l(h) be the first derivative of -2 - 1/2*h**p + 1/6*h**6 + 0*h**4 + 2/5*h**5 - 2/3*h**3 + 0*h. Factor l(n).
n*(n - 1)*(n + 1)**3
Suppose 0 = -0*h + 2*h - 6. Factor -3*j**2 - j**4 - 4*j**2 - 7*j**3 + 5*j**h + 6*j**2.
-j**2*(j + 1)**2
Let j(r) = 4*r. Let m(p) = -p - 3. Let v be m(-4). Let t be j(v). What is z in -z**t + 2 + 4*z**2 - 2*z**2 - 3 = 0?
-1, 1
Let f = 5 - 2. Let p be (-5)/(-2) - (3 - f). Let 0 - p*y**2 - y = 0. Calculate y.
-2/5, 0
Determine x, g