 18*p**3 - 7*p**i - 12*p**2 + 0*p + 3*p**5 + 3*p - 5*p**4 = 0. Calculate p.
0, 1
Factor -2/3*u**3 + 7/6*u**2 + 17/3*u + 4/3.
-(u - 4)*(u + 2)*(4*u + 1)/6
Let i be (-25618)/(-45) - (-6)/(-15). Let h = i + -568. Determine m so that 2/9*m**2 + h - 8/9*m = 0.
2
Factor 0*o + 3/7*o**2 + 0.
3*o**2/7
Suppose -8*i + 12*i = 0. Factor -1/4*g**2 + i - 1/4*g.
-g*(g + 1)/4
Let a(f) be the third derivative of f**7/273 - 11*f**6/390 + 11*f**5/130 - 5*f**4/39 + 4*f**3/39 + 8*f**2. Find b such that a(b) = 0.
2/5, 1, 2
Let d be (6/(-12))/(3/(-18)). Factor 0*x - 1/2*x**2 + 0 + 0*x**d + 1/2*x**4.
x**2*(x - 1)*(x + 1)/2
Let l(k) be the third derivative of -1/60*k**6 + 0*k**5 - 1/210*k**7 + 0*k + 0*k**3 + 2*k**2 + 0*k**4 + 0. Factor l(u).
-u**3*(u + 2)
Let x(i) be the first derivative of 2*i**5/25 - i**4/5 - 8*i**3/15 + 2*i**2/5 + 6*i/5 + 17. Suppose x(p) = 0. What is p?
-1, 1, 3
Let r(z) be the first derivative of -z**8/9240 + z**7/4620 + z**6/1980 - z**5/660 - z**3/3 + 1. Let p(f) be the third derivative of r(f). Factor p(c).
-2*c*(c - 1)**2*(c + 1)/11
Let r = -7 - 1. Let i be 27/12 + 2/r. Factor 1 + 2*v**i + 0*v + 1 + 4*v.
2*(v + 1)**2
Let a(h) be the third derivative of 0*h**3 - 3*h**2 + 0*h**4 + 0 - 1/60*h**5 + 0*h. Suppose a(l) = 0. What is l?
0
Let y(f) be the first derivative of -f**4 - 16*f**3/3 + 2*f**2 + 16*f + 22. Solve y(z) = 0.
-4, -1, 1
Let o(a) be the third derivative of -2*a**2 + 0*a + 1/36*a**4 + 0*a**3 - 1/180*a**6 - 1/315*a**7 + 0 + 1/90*a**5. Suppose o(t) = 0. Calculate t.
-1, 0, 1
Let x be (8/(-6))/(4/(-6)). Let d be (-5)/10*x*-2. Factor -f**2 - 2*f**3 + 2*f**5 + 0*f**2 + d*f**4 - f**2.
2*f**2*(f - 1)*(f + 1)**2
Let k(u) be the second derivative of u**7/21 - 2*u**6/15 - 3*u**5/10 + 2*u**4/3 + 4*u**3/3 - 3*u. Factor k(i).
2*i*(i - 2)**2*(i + 1)**2
Let q(k) = -k**2 - 11*k - 16. Let s be q(-9). Factor -3/5*v**s + 6/5 + 3/5*v.
-3*(v - 2)*(v + 1)/5
Let k(g) be the third derivative of -1/30*g**5 + 1/60*g**6 - 1/315*g**7 + 0 + 0*g + 0*g**3 + 3*g**2 + 1/36*g**4. Factor k(a).
-2*a*(a - 1)**3/3
Let t(q) be the second derivative of -2/3*q**3 + 1/2*q**4 + 0*q**2 + 0 - 3*q - 1/10*q**5. Factor t(l).
-2*l*(l - 2)*(l - 1)
Let r(k) be the second derivative of k**8/33600 - k**7/12600 - k**6/3600 + k**5/600 - 5*k**4/12 + k. Let a(w) be the third derivative of r(w). Factor a(l).
(l - 1)**2*(l + 1)/5
Let s(z) be the second derivative of 0*z**4 + 0*z**2 - 3*z + 1/40*z**5 + 0 - 1/12*z**3. Factor s(t).
t*(t - 1)*(t + 1)/2
Let l(m) = -m**2 - 10*m - 7. Let s be l(-8). Determine v, given that s*v**2 - 2 + 2 - 6*v**2 + 3*v = 0.
-1, 0
Suppose 3*w - 4 = 2*w. Let o(t) = 2*t + 0*t**2 - t**2 + 8 - 5*t**2 + 0. Let m(j) = 2*j**2 - j - 3. Let s(b) = w*o(b) + 11*m(b). Factor s(q).
-(q + 1)*(2*q + 1)
Suppose 3/2*g**2 + 0 + 21/4*g**3 + 0*g = 0. What is g?
-2/7, 0
Let s = -4/417 + 445/2919. What is z in 0 - 1/7*z**4 + 1/7*z**3 - s*z + 1/7*z**2 = 0?
-1, 0, 1
Let v(o) be the second derivative of o**6/900 + o**3/3 - o. Let n(l) be the second derivative of v(l). Let n(k) = 0. Calculate k.
0
Let z(d) = -3 + 4 + 3 + 5 + d. Let f be z(-7). Factor 0*x**f - 1/3*x + 1/3*x**3 + 0.
x*(x - 1)*(x + 1)/3
Let d(x) be the third derivative of 1/48*x**4 - 10*x**2 - 1/24*x**3 + 0*x - 1/240*x**5 + 0. Suppose d(u) = 0. What is u?
1
Let u(g) be the first derivative of -6/5*g**2 - 1/5*g**3 - 12/5*g - 1. Factor u(p).
-3*(p + 2)**2/5
Let m(o) be the first derivative of 3*o**5/5 + 15*o**4 + 118*o**3 + 270*o**2 + 243*o + 40. Factor m(b).
3*(b + 1)**2*(b + 9)**2
Factor -1 + 4/5*y + 1/5*y**2.
(y - 1)*(y + 5)/5
Let 6/11 - 14/11*h + 10/11*h**2 - 2/11*h**3 = 0. What is h?
1, 3
Let f(o) = 14*o**2 + 12*o + 17. Let k(s) = -5*s**2 - 4*s - 6. Let m(b) = 6*f(b) + 17*k(b). Factor m(a).
-a*(a - 4)
Let f(n) be the first derivative of n**4/12 - n**3/3 + 9*n + 6. Let i(l) be the first derivative of f(l). Factor i(x).
x*(x - 2)
Suppose 4*j - 9 = 15. Let t(a) = 6*a**3 - 2*a**2 - 4*a + 5. Let k(i) = 7*i**3 - 2*i**2 - 5*i + 6. Let l(n) = j*t(n) - 5*k(n). Factor l(q).
q*(q - 1)**2
Let v(t) = t**3 - 7*t**2 - 7*t + 1. Let g be v(8). Let l = -5 + g. Solve -6*d + 6*d + d**l - d**5 = 0.
0, 1
Suppose -o = -3*o + 5*k - 13, -5*k + 49 = 4*o. Determine p, given that p**4 - 6*p**3 + 3 + 6*p + 0*p**4 - o*p**4 + 2*p**4 = 0.
-1, 1
Let i(f) be the second derivative of 11/3*f**3 + 2*f**2 + 7/10*f**5 + 8/3*f**4 - f + 0. Factor i(c).
2*(c + 1)**2*(7*c + 2)
Let l be (6 + -2 - -17) + -1. Factor l + 8*k + k**3 - 8*k**2 - 5*k**2 - 4 + 6*k**2.
(k - 4)**2*(k + 1)
Let i(q) be the third derivative of -1/240*q**6 + 0*q**3 + 0*q**4 + 0*q**5 + 0*q + 0 + 1/840*q**7 - 3*q**2. Suppose i(y) = 0. What is y?
0, 2
Let z = 0 - -7. Factor 21*s**3 + 0*s**2 - s - 6 - s + 9*s**4 + 9*s**2 - z*s.
3*(s + 1)**3*(3*s - 2)
Let o(i) = 5*i + 8*i**2 + 11*i**2 + 17 + 11*i + 13*i. Let s(f) = -6*f**2 - 10*f - 6. Let v(j) = 2*o(j) + 7*s(j). Factor v(k).
-4*(k + 1)*(k + 2)
Let t = 388/1407 + 2/201. Let s = 1525/7 - 217. Let s*z**2 - t*z**3 - 6/7*z**4 + 2/7*z + 0 = 0. What is z?
-1, -1/3, 0, 1
Factor 4 + 3*z**2 - z**3 - 4 - 18*z + 16*z.
-z*(z - 2)*(z - 1)
Let d(a) = 12*a**4 - 41*a**3 + 72*a**2 - 55*a + 19. Let j(t) = -4*t**4 + 14*t**3 - 24*t**2 + 18*t - 6. Let w(q) = -2*d(q) - 7*j(q). Let w(i) = 0. What is i?
1
Let c(o) = 5*o**3 - 34*o**2 + 41*o - 16. Let t(y) = -5*y**3 + 35*y**2 - 40*y + 15. Let q(h) = -5*c(h) - 4*t(h). Factor q(d).
-5*(d - 4)*(d - 1)**2
Let k be (-14)/(-10) - (-21)/(-15). Determine v so that 0 + 2/15*v**5 + k*v**3 + 4/15*v**4 - 2/15*v - 4/15*v**2 = 0.
-1, 0, 1
Let n(h) be the first derivative of 1/3*h**3 + 1/2*h**2 + 1/3*h + 7 + 1/12*h**4. Factor n(z).
(z + 1)**3/3
Suppose 2*c - 2 = 4*c. Let x be 21/(-98) - c/2. Find d, given that -x*d**2 + 2/7*d**4 + 6/7*d**3 - 2/7*d**5 - 4/7*d + 0 = 0.
-1, 0, 1, 2
Suppose -4*l + 34 = -6. Solve -30*g**3 - l*g**5 - 3*g - 2*g - 13*g**2 - 29*g**4 + 3*g = 0 for g.
-1, -1/2, -2/5, 0
Factor -1/2 + 1/2*l - 1/2*l**3 + 1/2*l**2.
-(l - 1)**2*(l + 1)/2
Let i = 247/2958 - 5/102. Let f = i + 55/87. Determine r, given that 5/3*r**2 - f + r = 0.
-1, 2/5
Let h(o) be the second derivative of 2*o**6/15 - 4*o**5/5 + 2*o**4 - 8*o**3/3 + 2*o**2 - 25*o. Let h(v) = 0. Calculate v.
1
Let f(z) be the first derivative of -z**7/105 + z**6/30 - z**5/30 - z**2 - 2. Let r(d) be the second derivative of f(d). Factor r(g).
-2*g**2*(g - 1)**2
Factor -2/7*i**5 + 4/7*i**2 - 2/7*i**4 - 2/7*i - 2/7 + 4/7*i**3.
-2*(i - 1)**2*(i + 1)**3/7
Let j(s) be the second derivative of s**5/20 + s**4/4 + s**3/3 + 8*s. Factor j(c).
c*(c + 1)*(c + 2)
Let p(y) be the third derivative of -y**9/25704 - y**8/14280 + y**7/3570 - 4*y**3/3 + 4*y**2. Let q(i) be the first derivative of p(i). Factor q(z).
-2*z**3*(z - 1)*(z + 2)/17
Let b(g) be the third derivative of g**7/20160 + g**6/5760 - g**5/480 - 5*g**4/24 + 3*g**2. Let l(x) be the second derivative of b(x). Factor l(w).
(w - 1)*(w + 2)/8
Factor -93*s - s**2 - s**3 + 93*s.
-s**2*(s + 1)
Let w(l) be the first derivative of -5*l**4/4 + 55*l**3/3 - 60*l**2 - 180*l + 16. Factor w(m).
-5*(m - 6)**2*(m + 1)
Factor -3/2*y**4 - 6 - 9*y**3 - 39/2*y**2 - 18*y.
-3*(y + 1)**2*(y + 2)**2/2
Let s(c) = -5*c**2 + 7*c - 7. Suppose 3*i + 6 = -4*p, 3*p = -2*i + 6*i - 17. Let n(t) = 2*t**2 - 3*t + 3. Let o(z) = p*s(z) - 7*n(z). Factor o(l).
l**2
Let q = -95/2 - -48. Let z**2 + 0 + q*z = 0. What is z?
-1/2, 0
Determine h so that -14/9*h**3 - 32/9*h**2 - 2/9*h**4 + 0 - 8/3*h = 0.
-3, -2, 0
Factor -16/3*a + 4*a**2 + 2*a**3 - 2/3*a**4 + 0.
-2*a*(a - 4)*(a - 1)*(a + 2)/3
Let p(z) be the second derivative of 0*z**3 + 4*z - 1/3*z**2 + 1/18*z**4 + 0. Determine g, given that p(g) = 0.
-1, 1
Let h(g) be the first derivative of -2*g**5/65 - g**4/26 + 2*g**3/39 + g**2/13 - 1. Find m, given that h(m) = 0.
-1, 0, 1
Factor 2/3 + 4/3*k + 2/3*k**2.
2*(k + 1)**2/3
Suppose -2*v = 2*v. Let u(r) be the third derivative of -21/40*r**6 + 3*r**2 + 0*r - 1/6*r**4 + 0 + 8/15*r**5 + v*r**3. Factor u(n).
-n*(7*n - 2)*(9*n - 2)
Let y(h) = -h**3 - 10*h**2 - h - 8. Let u be 16/(-20)*50/4. Let z be y(u). Factor 0*p + 4/3*p**3 + 0 + 2/3*p**4 + 2/3*p**z.
2*p**2*(p + 1)**2/3
Let g = 71/68 + -5/17. Determine l so that -3/2*l**3 + 0 + 0*l**2 - g*l**4 + 0*l + 3/4*l**5 = 0.
-1, 0, 2
Let w(d) = 43*d**5 + 28*d**4 + 10*d**3 - 6*d. Let f(a) = -a**5 + a**3 - a. Let h(k) = -6*f(k) + w(k). What is