-6)*(f - 2). Factor x + 1/3*s + 1/3*s**2.
s*(s + 1)/3
Determine r, given that -2*r + 2*r**4 + 4*r**2 + 0*r**3 + r**2 - 6*r**3 + r**2 = 0.
0, 1
Let v(s) be the third derivative of s**7/735 + s**6/210 - s**5/70 - 6*s**2. Find a such that v(a) = 0.
-3, 0, 1
Suppose -151*z + 141*z + 30 = 0. Find o, given that 0*o + 0 - 2/9*o**2 + 2/9*o**z = 0.
0, 1
Let i be (-26)/39 + 2/3. Let v(p) be the first derivative of i*p + 2/21*p**3 - 1 + 1/7*p**2. Solve v(o) = 0.
-1, 0
Let v be -9*-2*(-1)/(-6). Factor 5*w**v - 4*w**3 + 3*w**3 - 2*w**3.
2*w**3
Let h(d) be the second derivative of -5*d**4/3 - 2*d**3 + 4*d**2 + 2*d - 11. Factor h(x).
-4*(x + 1)*(5*x - 2)
Let j be 1/5*20/16. Let y(z) be the first derivative of -3/2*z - 1 + j*z**3 - 3/8*z**2. What is l in y(l) = 0?
-1, 2
Let a = -49 - -53. Let r(z) be the first derivative of 1/3*z + 1 - 17/9*z**3 + 16/15*z**5 + 1/6*z**2 - 17/12*z**a + 8/9*z**6. Find i, given that r(i) = 0.
-1, -1/4, 1/4, 1
Let r(n) be the second derivative of -n**4/78 + 8*n**3/39 - 7*n**2/13 + 22*n. Factor r(u).
-2*(u - 7)*(u - 1)/13
Let f(q) = 5*q**2 - 25*q - 3. Let x(z) = z**2 - 6*z - 1. Let l be (5/((-10)/36))/1. Let y(g) = l*x(g) + 4*f(g). Factor y(h).
2*(h + 1)*(h + 3)
Let y(g) be the first derivative of -g**6/15 + 2*g**5/5 - 5*g**4/6 + 2*g**3/3 + 2*g + 6. Let b(w) be the first derivative of y(w). Solve b(v) = 0 for v.
0, 1, 2
Let z(r) be the first derivative of r**9/15120 - r**8/4200 + r**7/4200 - r**3 - 3. Let v(s) be the third derivative of z(s). Factor v(h).
h**3*(h - 1)**2/5
Let n be (-9)/6 + 1 - -1. Factor 0 - 1/2*s - n*s**3 - s**2.
-s*(s + 1)**2/2
Suppose 5*t + 3*f = -7 - 11, -f + 22 = -3*t. Let x = 10 + t. Solve -2*h**4 - 4*h**x - 11*h**3 + 6*h**2 + 3*h + 11*h**5 - h**3 - 2*h**5 = 0 for h.
-1, -1/3, 0, 1
Let y(u) be the first derivative of 1/20*u**5 + 1/2*u**2 - 6 + 1/4*u + 1/2*u**3 + 1/4*u**4. Factor y(p).
(p + 1)**4/4
Suppose 0 = 4*h - v + 3*v - 6, -h + 18 = -5*v. Let n(q) be the third derivative of -q**2 + 0 + 1/180*q**5 + 1/36*q**4 + 0*q + 1/18*q**h. Factor n(d).
(d + 1)**2/3
Let k(m) = m**3 - 5*m**2 - 7*m + 9. Let x be k(6). Find d, given that 12*d**3 + 2*d**4 + 0 - 4*d - 8*d**x - 2 = 0.
-1, 1
Suppose -4*c + 8 = 5*r - 8*c, -2*r - 4*c = 8. Let t = r + 2. Factor -2*n - 3*n**5 + 2*n**5 + 2*n**4 - n**4 + t*n**2 + 3*n**3 - 3*n**2.
-n*(n - 2)*(n - 1)*(n + 1)**2
Let o(m) be the first derivative of 3*m**4/16 + 5*m**3/12 - m**2/4 - 31. What is h in o(h) = 0?
-2, 0, 1/3
Let o(v) be the second derivative of 3/10*v**5 + 0*v**2 - 2/3*v**3 - 5/6*v**4 + 0 - 6*v. Suppose o(z) = 0. Calculate z.
-1/3, 0, 2
Let q(s) = -s - 4. Let x be q(-4). Let d(h) be the third derivative of x*h**3 + 0*h + 0*h**4 - 2*h**2 + 1/150*h**5 + 0. Factor d(l).
2*l**2/5
Let u = 523/2 - 257. Factor u*x**5 + 3*x**3 + 0 + 0*x**2 - 15/2*x**4 + 0*x.
3*x**3*(x - 1)*(3*x - 2)/2
Let q = 107/218 - -1/109. Let f(s) be the first derivative of 0*s**3 - 1/4*s**4 + 3 + 1/2*s - 1/10*s**5 + q*s**2. Suppose f(x) = 0. What is x?
-1, 1
Let i(v) be the third derivative of -v**6/200 + 3*v**5/25 - 6*v**4/5 + 32*v**3/5 - v**2. Factor i(p).
-3*(p - 4)**3/5
Factor 0 - 1/6*c**3 - 1/6*c + 1/3*c**2.
-c*(c - 1)**2/6
Let o(y) = y**3 + y**2 - 1. Let n(z) = -5*z**5 - 5*z**4 - 5*z**3 - 5*z**2 + 10. Let h(i) = -n(i) - 10*o(i). Factor h(x).
5*x**2*(x - 1)*(x + 1)**2
Let v(j) be the second derivative of 1/10*j**5 + 1/15*j**6 - 1/3*j**3 + 0 - 1/6*j**4 - 3*j + 0*j**2. Find c such that v(c) = 0.
-1, 0, 1
Let q be -1 + 0 + (-209)/(-133). Factor 4/7*i**2 + 0 + q*i.
4*i*(i + 1)/7
Let u(z) = -z**3 + z + z + 1 - 5*z**2 + 1 + 2*z**3. Let p be u(5). Let -1 + 8*j**4 + 3 + 13*j**2 + p*j + 24*j**3 + 13*j**2 = 0. What is j?
-1, -1/2
Let d = 2355/4 - 580. Let c = d - 73/12. Factor 2/3*l**5 + 2/3*l + 0 + 4*l**3 - c*l**2 - 8/3*l**4.
2*l*(l - 1)**4/3
Let v be 32/(-42) + 2 - (-8)/(-14). Let x be ((-2)/(-45))/(2/10). Suppose 2/3*l**2 - x*l**3 + 2/9 - v*l = 0. Calculate l.
1
Let s(h) be the first derivative of h**4/12 - h**3/12 - 3*h**2/8 - h/6 + 20. Factor s(w).
(w - 2)*(w + 1)*(4*w + 1)/12
Let i(j) = 3*j. Let f be i(-1). Let g = f - -6. Factor 10*m**2 + 2*m**g - 10*m**2.
2*m**3
Let k(g) be the first derivative of -g**2 - 1 + 5/3*g**3 - 7/6*g**4 + 3/10*g**5 + 3*g. Let z(i) be the first derivative of k(i). Suppose z(m) = 0. What is m?
1/3, 1
Suppose 2*c + 4*k = -k, -5*k = -2*c. Factor 0*f + 0 - 2/5*f**4 + 2/5*f**2 + c*f**3.
-2*f**2*(f - 1)*(f + 1)/5
Let j(k) be the second derivative of -k**5/50 + k**3/15 + 23*k. Determine u so that j(u) = 0.
-1, 0, 1
Let y(h) be the third derivative of h**6/80 + h**5/40 + h**4/64 - 24*h**2. Determine l so that y(l) = 0.
-1/2, 0
Let a(s) be the second derivative of -s**6/360 - s**2 - s. Let k(o) be the first derivative of a(o). Factor k(x).
-x**3/3
Let u(y) be the first derivative of 5*y**4/12 - 5*y**2/6 + 13. Find p such that u(p) = 0.
-1, 0, 1
Let f(x) = -39*x**4 - 2 - 6*x**3 + 6*x - 4*x**2 + 42*x**4 - 5. Let c(v) = 24*v**4 - 48*v**3 - 33*v**2 + 48*v - 57. Let l(d) = -4*c(d) + 33*f(d). Factor l(q).
3*(q - 1)**3*(q + 1)
Let n = 2 + -1. Let r be 3 - (n + 0/2). Determine f, given that -2*f**2 - f**3 - r*f**2 - f**3 + 6*f**4 = 0.
-2/3, 0, 1
Let c be 12/10*60/84. Let q = 73 + -509/7. Find f, given that -8/7*f**2 + q + c*f = 0.
-1/4, 1
Suppose -2*z - 3*r = 4, -4*z + 3*r + 7 = -21. Factor n - 3*n + z*n**2 + n**2 - 3*n**2.
2*n*(n - 1)
Factor 0 + 2/9*i**3 - 2/3*i**2 + 4/9*i.
2*i*(i - 2)*(i - 1)/9
Let g(p) be the first derivative of 4*p**5/5 - 8*p**4 - 4*p**3/3 + 16*p**2 + 46. What is a in g(a) = 0?
-1, 0, 1, 8
Suppose 0*n - 9 = -3*n. Let r be (-2)/(-14) - 205/(-574). Factor 0 + c**2 + 1/2*c**n + r*c.
c*(c + 1)**2/2
Let x(s) = -s**3 - s**2 + s + 4. Let z(b) = 2*b**3 + 2*b**2 - 2*b - 7. Let c(y) = 5*x(y) + 3*z(y). Factor c(k).
(k - 1)*(k + 1)**2
Factor -1/2*i + 1/2*i**2 + 0.
i*(i - 1)/2
Suppose 0*o = -o + 2. Suppose -o*y + 1 = -3. Factor -y*u + 4*u + 0*u - 6*u**2.
-2*u*(3*u - 1)
Let u be 24/(-32)*(-24)/2655. Let m = u - -877/1180. Factor -m*t**2 + 3/4*t + 3/2.
-3*(t - 2)*(t + 1)/4
Suppose 3 = -5*q + 13. Factor l**4 - 9*l - l**q + l + 8*l.
l**2*(l - 1)*(l + 1)
Let x = -15 + 19. Let t(c) be the third derivative of 0*c + 0 + 1/24*c**x + 1/30*c**5 + 1/120*c**6 - 2*c**2 + 0*c**3. Let t(l) = 0. What is l?
-1, 0
Let s(u) = 10*u**4 - 24*u**3 + 4*u**2 + 24*u - 12. Let c(q) = q**5 - q**4 - q. Let f(l) = -2*c(l) - s(l). Factor f(y).
-2*(y - 1)**3*(y + 1)*(y + 6)
Suppose o + 3*u - 2 = 2*u, -5*o + 2*u = -10. Find z, given that 4*z**3 + 1 - 3*z**3 + 3*z - 3*z**2 - o = 0.
1
Suppose -w = -4*b - 0*w + 13, -2*b + 5 = w. Let d(v) be the first derivative of 8*v - 1 + 4*v**2 + 2/3*v**b. Suppose d(i) = 0. Calculate i.
-2
Let d(m) be the first derivative of -3*m**4 + 20*m**3/3 - 2*m**2 - 4*m + 40. Factor d(t).
-4*(t - 1)**2*(3*t + 1)
Suppose -r = 4*a - 42, -5*a - 5*r + 60 = -0*r. Suppose a = 2*n + 2. Determine c, given that 1/5 - 1/5*c**n + 0*c**2 - 2/5*c + 2/5*c**3 = 0.
-1, 1
Let z = -21 - -151. Let x = z - 1428/11. Suppose 0 - 4/11*d**2 + x*d + 2/11*d**3 = 0. What is d?
0, 1
Let i be ((-2)/(-27))/(6/9). Let v(s) be the first derivative of 0*s + i*s**3 + 0*s**2 + 2. Solve v(o) = 0.
0
Let z = -12 - -16. Factor -4*c**2 - 11*c**3 + 12*c**3 - 7*c**3 - 2*c**z.
-2*c**2*(c + 1)*(c + 2)
Let q(k) be the third derivative of 0*k**4 + 0*k + 3/20*k**6 - 1/15*k**5 + 0*k**3 - 3*k**2 + 0 - 1/15*k**7. Find j such that q(j) = 0.
0, 2/7, 1
Let c = -25/9 - -28/9. Let r(m) be the first derivative of 0*m + 3 - c*m**2 + 2/9*m**3. Find z such that r(z) = 0.
0, 1
Let o(p) be the first derivative of -p**5/240 + p**3/6 - p**2/2 - 4. Let x(t) be the second derivative of o(t). What is z in x(z) = 0?
-2, 2
Let i(c) be the first derivative of c**6/10 - 3*c**5/10 + c**4/4 - 3*c - 2. Let k(w) be the first derivative of i(w). Solve k(d) = 0 for d.
0, 1
Suppose o + 10*o = 0. Solve o*r + 0 - 1/4*r**2 = 0.
0
Let x(t) be the third derivative of t**8/168 - t**6/30 + t**4/12 - 4*t**2. Factor x(d).
2*d*(d - 1)**2*(d + 1)**2
Let q(i) be the second derivative of i**7/63 - 2*i**6/15 + 7*i**5/15 - 8*i**4/9 + i**3 - 2*i**2/3 - 14*i. What is g in q(g) = 0?
1, 2
Let y(l) = 6*l**4 + 3*l**3 - 3. Let p(d) = -11*d**4 - 5*d**3 + d**2 + 5. Let g(f) = -3*p(f) - 5*y(f). Solve g(w) = 0 for w.
-1, 0, 1
Let w = -2 + 4. Solve 8*l**2 - w*l - 4*l**2 + 4*l**3 - 6*l**3 = 0 for l.