0*a**5. Factor k(n).
n**3*(n - 1)*(n + 1)/4
Let t(f) be the third derivative of -f**5/720 + f**4/72 + 17*f**2. Solve t(k) = 0 for k.
0, 4
Let i(x) = -4*x**2 + 12*x**3 - x**2 - 5*x**3 - 8*x. Let p(m) = -6*m**3 + 4*m**2 + 7*m. Let j(y) = -5*i(y) - 6*p(y). Let j(h) = 0. What is h?
-2, 0, 1
Let t(o) be the third derivative of 1/20*o**5 + 0*o - o**2 + 0*o**3 - 1/40*o**6 + 1/4*o**4 + 0. Factor t(m).
-3*m*(m - 2)*(m + 1)
Determine p, given that -6/7*p**3 + 6/7*p**4 - 12/7 + 30/7*p - 18/7*p**2 = 0.
-2, 1
Suppose 0 = 3*h + 5*o + 14, -h = -0*o - 3*o - 14. Suppose h*x - 4*x + 4*f = 10, 0 = -3*x + 2*f + 1. Find u, given that 2/3*u**2 + 0*u - 2/3*u**x + 0 = 0.
0, 1
Let m(n) = -n**2 + 19*n - 14. Let v be m(18). Let w(f) be the first derivative of -1/2*f**v + 0*f + 0*f**2 - 1/3*f**3 - 1/5*f**5 + 3. Solve w(b) = 0.
-1, 0
Let h(a) = -13*a**3 + 11*a**2 - 7*a - 3. Let x(b) = 66*b**3 - 54*b**2 + 36*b + 16. Let d = 24 + -8. Let z(k) = d*h(k) + 3*x(k). Suppose z(t) = 0. What is t?
0, 2/5, 1
Let g = 22 + -17. Let l(v) be the second derivative of -7/80*v**g + 0 + 0*v**3 + 2*v + 1/24*v**7 - 1/60*v**6 + 0*v**2 + 1/24*v**4. Find k, given that l(k) = 0.
-1, 0, 2/7, 1
Let i = 936/119 + -56/17. Let 2*n**3 + 4/7 + 22/7*n + i*n**2 = 0. What is n?
-1, -2/7
Let z be -3 - (-4 + (-5)/(-25)). Factor 2/5*k + 4/5*k**2 - 2/5*k**3 - z.
-2*(k - 2)*(k - 1)*(k + 1)/5
Determine f so that -4/3 + 2*f - 2/3*f**2 = 0.
1, 2
Let o(z) be the first derivative of -z**6/51 + 4*z**5/85 + z**4/17 - 16*z**3/51 + 7*z**2/17 - 4*z/17 - 5. Factor o(h).
-2*(h - 1)**4*(h + 2)/17
Let l(h) be the third derivative of h**6/300 + h**5/50 + h**4/30 - 3*h**2. Determine f so that l(f) = 0.
-2, -1, 0
Let u(d) = d**2 + d + 1. Let o(r) = -4*r**2 - 25*r - 4. Let c(t) = -o(t) + 5*u(t). What is z in c(z) = 0?
-3, -1/3
Let c(w) be the second derivative of w**4/36 - w**3/6 + w**2/3 - 30*w. Factor c(s).
(s - 2)*(s - 1)/3
Let p(s) = 3*s**2 - 3*s - 5. Let g(h) = -2*h**2 + h + 2. Let f(q) = -5*g(q) - 2*p(q). Let m(b) = 6*b**2 + 2*b. Let n(t) = -8*f(t) + 5*m(t). Factor n(y).
-2*y*(y - 1)
Let m(x) be the third derivative of x**8/1008 + x**7/210 + x**6/360 - x**5/60 - x**4/36 + 19*x**2 - 1. Factor m(p).
p*(p - 1)*(p + 1)**2*(p + 2)/3
Let a(h) = -15*h**3 - 15*h**2 - 3*h + 11. Let c(l) = -14*l**3 - 16*l**2 - 4*l + 10. Let v(u) = 6*a(u) - 7*c(u). What is k in v(k) = 0?
-2, -1, 1/4
Let z(s) be the first derivative of s**4/2 + 6*s**3 + 27*s**2 + 54*s + 1. Suppose z(q) = 0. Calculate q.
-3
Let n = -107/4 - -27. Suppose 0*c - 1/4*c**5 + 0*c**2 + 0 + 0*c**4 + n*c**3 = 0. Calculate c.
-1, 0, 1
Let r(d) = -d + 5. Let b be r(3). Let w(v) be the second derivative of 0 + 0*v**b + 1/30*v**4 + 1/15*v**3 + v. Determine c so that w(c) = 0.
-1, 0
Determine f, given that 78*f**2 + 75 + 11*f + 19*f - 75*f**2 = 0.
-5
Let i(d) be the first derivative of -d**2 - 3*d + 1. Let g be i(-3). Factor -g*l + 3*l**3 + l - l.
3*l*(l - 1)*(l + 1)
Let m = -42605/54 - -789. Let x(u) be the second derivative of 2*u + 0 - 1/9*u**2 + 0*u**3 + m*u**4. Factor x(n).
2*(n - 1)*(n + 1)/9
Let i(n) be the first derivative of n**6/24 - 2*n**5/5 + 13*n**4/16 - n**3/2 + 7. Factor i(t).
t**2*(t - 6)*(t - 1)**2/4
Factor -10/9*o**3 - 8/9*o**4 - 4/9*o**2 + 0 - 2/9*o**5 + 0*o.
-2*o**2*(o + 1)**2*(o + 2)/9
Let j(g) be the second derivative of g**5/5 - g**4/3 - g. Factor j(h).
4*h**2*(h - 1)
Let z = -46/21 + 20/7. Let a(f) be the first derivative of 2/9*f**3 + 2/3*f + z*f**2 - 2. Factor a(w).
2*(w + 1)**2/3
Let m(b) be the second derivative of b**7/70 - b**6/50 - 3*b**5/20 - 3*b**4/20 + 6*b. Suppose m(d) = 0. Calculate d.
-1, 0, 3
Let m(g) be the third derivative of 1/12*g**4 + 1/42*g**7 - 1/60*g**6 - g**2 - 1/12*g**5 + 0 + 0*g**3 + 0*g. Suppose m(r) = 0. What is r?
-1, 0, 2/5, 1
Factor -1/3*d**2 + 4*d + 13/3.
-(d - 13)*(d + 1)/3
Suppose 8/7*z - 2/7*z**2 + 0 = 0. What is z?
0, 4
Let v(p) be the third derivative of -p**6/300 + p**5/30 - 2*p**4/15 + 4*p**3/15 - 7*p**2. Factor v(l).
-2*(l - 2)**2*(l - 1)/5
Let j be 1/2 - (-147)/(-14). Let g be (30/25)/((-9)/j). Factor -2/3*f**2 - g*f + 0.
-2*f*(f + 2)/3
Suppose 0 = 5*t - 3 - 7. Let j(x) be the first derivative of 0*x + 1/3*x**3 - t - 1/2*x**2. Find l such that j(l) = 0.
0, 1
Let p be 0/(-3*8/12). Let w(n) be the third derivative of -1/12*n**5 + 0*n**3 + 0*n - 5/96*n**6 + p - 1/24*n**4 - 2*n**2. Solve w(g) = 0 for g.
-2/5, 0
Let t = 459 - 2414/5. Let q = 25 + t. Factor -6/5*i**2 + 0 - q*i**3 - 2/5*i - 2/5*i**4.
-2*i*(i + 1)**3/5
Suppose 4*b + 12 + 4 = 0, 0 = -5*a - 3*b - 2. Factor 6 + 2*l**a - 9*l + 0*l**2 + l**2.
3*(l - 2)*(l - 1)
Suppose 3*y - 10 = 2*x, 1 = -y - 0*y + 5*x. Solve 0*g**4 - 3*g**y - 5*g**2 - 2*g**3 + 6*g**2 + 2 + 5*g - 3*g**3 = 0.
-1, -2/3, 1
Suppose 5*u - 1 = j + 1, -2*j + 14 = -u. Solve 2*q**5 + 3*q**5 - 12*q**3 + 12*q**4 - j*q**5 = 0 for q.
0, 2
Let q(n) = -8*n**2 - 6*n - 16. Let j(r) = -7*r**2 - 6*r - 15. Let t(x) = 7*j(x) - 6*q(x). Let t(v) = 0. Calculate v.
-3
Let u(g) be the second derivative of 9*g**5/40 - g**4/4 - g**3/4 + 16*g. Factor u(q).
3*q*(q - 1)*(3*q + 1)/2
Let g be 0 + (-12)/8 + 11/6. Let j be (-9)/(-4) - (-2)/(-8). Factor -g*k**j - 1/3 - 2/3*k.
-(k + 1)**2/3
Let n(b) be the second derivative of 0 + 8*b - 9/10*b**2 + 1/20*b**4 - 1/5*b**3. Let n(c) = 0. What is c?
-1, 3
Let l(n) = n**3 + 4*n**2 - n - 1. Let t be l(-4). Let v = 5 - t. Factor -3 + 3 + a**4 + a**v - 2*a**3.
a**2*(a - 1)**2
Let n be 7*30/63*(-6)/(-5). Factor 0*u + 0*u**3 - 1/4*u**5 - 1/4*u**n + 0 + 0*u**2.
-u**4*(u + 1)/4
Suppose -2*x + 6*x = 0. Let w(n) be the first derivative of 1/6*n**6 + 1/4*n**4 + x*n**2 - 1 + 0*n**3 + 2/5*n**5 + 0*n. Determine u so that w(u) = 0.
-1, 0
Let c(o) = 26*o**3 - 65*o**2 + 4*o - 1. Let x(d) = -3*d**2 + 2*d**2 + d**3 - 4 + 5. Let m(u) = 2*c(u) + 18*x(u). Factor m(f).
2*(f - 2)*(5*f - 2)*(7*f + 2)
Suppose 0 + 2/9*m**2 + 2/9*m = 0. Calculate m.
-1, 0
Let y(w) = -w - 1. Let t be y(0). Let c = t - -6. Factor 0*x + 0*x**2 + 0 + 1/3*x**c - 1/3*x**3 + 0*x**4.
x**3*(x - 1)*(x + 1)/3
Let o = -1108 + 1112. Determine d so that 9/4*d - 9/4*d**3 - 3/2 + 3/4*d**o + 3/4*d**2 = 0.
-1, 1, 2
Let m be 3 - (-1 - (-1 + 1)). Suppose -5*b - 9*f + 4*f + 35 = 0, -5*f + 23 = b. Factor -3*w**4 - b*w**3 + 2*w**m + 2*w**3.
-w**3*(w + 1)
Let l(b) be the first derivative of -2*b**5/5 + 2*b**4 - 2*b**3 - 4*b**2 + 8*b + 3. Suppose l(h) = 0. Calculate h.
-1, 1, 2
Let k(d) be the first derivative of -5/4*d**3 + 2*d**2 + 2 - d. Factor k(g).
-(3*g - 2)*(5*g - 2)/4
Let r(v) be the first derivative of -2*v**6/3 + 16*v**5/5 - 2*v**4 - 16*v**3/3 + 6*v**2 + 16. Suppose r(j) = 0. Calculate j.
-1, 0, 1, 3
Let s(x) be the second derivative of -x**7/6300 + x**6/600 + 5*x**4/12 - 6*x. Let f(j) be the third derivative of s(j). Factor f(t).
-2*t*(t - 3)/5
Let m(i) be the second derivative of -i**6/180 + i**5/20 - i**4/6 - i**3/2 - i. Let h(t) be the second derivative of m(t). Factor h(k).
-2*(k - 2)*(k - 1)
Let x(j) be the second derivative of 0 + 4/5*j**2 + 4/15*j**3 + 1/30*j**4 + 8*j. Factor x(y).
2*(y + 2)**2/5
Let i(d) be the third derivative of 5*d**6/16 - 7*d**5/8 + 11*d**4/16 - d**3/4 + 12*d**2. Factor i(s).
3*(s - 1)*(5*s - 1)**2/2
Let q(s) = -s**2 + 8*s - 4. Let u be q(7). Solve 7 - 2*f**u - 12*f**2 + 4 - 27 - 24*f = 0.
-2
Let j be 4*(-1 + 0) + 0. Let p(y) = -y**3 - 4*y**2 - y - 2. Let g be p(j). Factor -1 - 1 - 5*w + 7*w**g - 4*w**2 + 4.
(w - 1)*(3*w - 2)
Determine h so that 6/7 - 4/7*h**2 - 2/7*h**5 - 10/7*h + 12/7*h**3 - 2/7*h**4 = 0.
-3, -1, 1
Let z(a) = a + 1. Let y(w) = -w**2 + w + 4. Let n(l) = 3*y(l) - 12*z(l). Factor n(o).
-3*o*(o + 3)
Suppose 2*k - a = 5*k - 11, 4*k = a + 10. Let d(h) be the first derivative of 2/15*h**k - 1 - 2/5*h + 0*h**2. Solve d(l) = 0 for l.
-1, 1
Let l(z) be the third derivative of -z**6/24 - 5*z**5/4 - 105*z**4/8 - 245*z**3/6 + 9*z**2. Factor l(n).
-5*(n + 1)*(n + 7)**2
Let q = -30839/18 + 1714. Let x = q + -2/9. Determine v, given that -1/2*v + 1 - x*v**2 = 0.
-2, 1
Let l(h) be the third derivative of h**8/84 + 2*h**7/21 + 7*h**6/30 - h**5/15 - 4*h**4/3 - 8*h**3/3 - 6*h**2. Suppose l(g) = 0. Calculate g.
-2, -1, 1
Suppose -5*r = -29 + 4. Suppose 27 = 5*c - o, c = r*o - 2 + 17. Factor -j**5 - 4*j**4 + 2*j**5 + 3*j**2 - 2*j**2 + j + 6*j**3 - c*j**2.
j*(j - 1)**4
Let f = 732 + -5120/7. Factor -f*m**2 + 0 - 4/7*m.