 third derivative of r**8/840 + 4*r**7/525 + r**6/60 + r**5/75 - 4*r**2. Factor f(q).
2*q**2*(q + 1)**2*(q + 2)/5
Determine b, given that -4/3 + 2*b - 2/3*b**2 = 0.
1, 2
Let s(m) = 45*m**5 - 12*m**4 - 12*m**3 + 6. Let d(v) = -90*v**5 + 24*v**4 + 24*v**3 - 11. Let y = -4 + 15. Let c(j) = y*s(j) + 6*d(j). Factor c(a).
-3*a**3*(3*a - 2)*(5*a + 2)
Let z(v) = v**3 - 21*v**2 + 21*v - 18. Let j be z(20). Let d(h) be the second derivative of -4/5*h**3 - 1/50*h**5 - 8/5*h**j - 1/5*h**4 + 0 + h. Factor d(b).
-2*(b + 2)**3/5
Let n be ((-6)/(-33))/(8/4 - 1). Factor -8/11 + 8/11*f + n*f**2 - 2/11*f**3.
-2*(f - 2)*(f - 1)*(f + 2)/11
Let i(n) be the third derivative of n**6/600 + n**5/120 + n**4/60 - 5*n**3/6 - 4*n**2. Let l(a) be the first derivative of i(a). Factor l(y).
(y + 1)*(3*y + 2)/5
Let y(o) be the first derivative of 4*o**3/3 - 37. Determine r, given that y(r) = 0.
0
Solve 14/5*q - 12/5 - 2/5*q**3 + 0*q**2 = 0.
-3, 1, 2
Let d(u) be the third derivative of -u**7/7560 + u**6/540 - u**5/90 + u**4/12 - u**2. Let r(v) be the second derivative of d(v). What is y in r(y) = 0?
2
Let k(c) = c**3 - 6*c**2 + 5. Let l be k(6). Let i(x) = x**3 - x - 1. Let s(r) = 3*r**3 - 2*r**2 - 5*r - 5. Let g(t) = l*i(t) - s(t). Factor g(y).
2*y**2*(y + 1)
Let y(a) be the second derivative of 0 + 0*a**2 - 1/10*a**4 - 1/10*a**3 + 0*a**5 + 1/25*a**6 + 1/70*a**7 + 4*a. Determine f, given that y(f) = 0.
-1, 0, 1
Solve 1/5*j - 1/5*j**2 + 0 = 0 for j.
0, 1
Let g(a) be the first derivative of -a**7/3780 + a**6/270 - a**5/45 + 2*a**4/27 - a**3 + 3. Let t(q) be the third derivative of g(q). Let t(r) = 0. Calculate r.
2
Let r = 14 + -14. Let o(d) be the second derivative of 1/6*d**3 - 1/4*d**4 - d + 3/20*d**5 + r*d**2 - 1/30*d**6 + 0. Factor o(v).
-v*(v - 1)**3
Suppose -4*l + 15 = -5*r, -4*l - 5*r + 30 = l. What is j in j**3 + 3 + 2*j - j + 2*j**2 - l - 2*j**3 = 0?
-1, 1, 2
Find m, given that 2/13*m**5 + 0 - 4/13*m**3 + 0*m**4 + 2/13*m + 0*m**2 = 0.
-1, 0, 1
Let a be 3 - 4/(16/12). Suppose 2/9*y**5 + a - 8/9*y**2 - 8/9*y**4 + 2/9*y + 4/3*y**3 = 0. What is y?
0, 1
Let z be (2 - 14)*(-2)/(-2). Let d = -5 - z. Factor -2*u**2 - 3*u**2 + d*u**2.
2*u**2
Suppose -v = -3*g, -g + 14 - 1 = 4*v. Suppose -6 = v*l - 6*l. Let -1/3*s**l - 2/3 - s = 0. What is s?
-2, -1
Let s(c) be the first derivative of -56/15*c**3 + 1 - 8/5*c**2 + 0*c - 11/5*c**4 - 2/5*c**5. Factor s(h).
-2*h*(h + 2)**2*(5*h + 2)/5
Let x(r) be the first derivative of -r**6/18 - 2*r**5/15 - r**4/12 - 1. Solve x(o) = 0 for o.
-1, 0
Let j(a) = -2*a**2 - 2*a. Let s(w) be the second derivative of -w**4/12 - w**3/6 - 4*w. Let d(u) = 6*j(u) - 11*s(u). Solve d(f) = 0 for f.
-1, 0
Let c = -24 - -12. Let o = c - -14. Let 4/3*k + 0 + 2/3*k**2 - o*k**4 - 8/3*k**3 = 0. Calculate k.
-1, 0, 2/3
Suppose c = -3*i - 1, -i - 32 = 2*c - 5*i. Let r be c/(-3) - 4/(-6). Factor -r*f**2 - 24*f - 8 - 11*f**2 + f**3 - 4*f**3 - 4.
-3*(f + 1)*(f + 2)**2
Let b be 5/(-70)*(-2)/6. Let z(q) be the second derivative of 1/2*q**2 - b*q**7 + 0 + 1/10*q**5 - 1/6*q**4 - 1/6*q**3 + 1/30*q**6 + 2*q. Factor z(n).
-(n - 1)**3*(n + 1)**2
Let v = -37 - -40. Let f(x) be the first derivative of 1/2*x - 3/10*x**5 + 1/3*x**v - 1/2*x**4 - 2 + x**2. Find i such that f(i) = 0.
-1, -1/3, 1
Let u(s) be the first derivative of 0*s**2 - 1/1800*s**6 + 0*s + s**3 + 0*s**4 - 1/300*s**5 - 3. Let d(o) be the third derivative of u(o). Factor d(t).
-t*(t + 2)/5
Let h(n) be the second derivative of -1/20*n**4 + 1/15*n**3 + 2*n - 1/20*n**5 + 0*n**2 + 0. Let h(m) = 0. What is m?
-1, 0, 2/5
Let v(g) = -5*g**2 + 4*g + 1. Suppose 0*j - 5*j - 43 = 3*i, -4*i = 4*j + 44. Let y(t) = t**2 - t. Let c(o) = i*y(o) - v(o). Find r, given that c(r) = 0.
1
Let u be (18/(-45))/(2/(-10) + 0). Let n(m) be the third derivative of 3*m**u + 0 - 1/36*m**4 + 0*m**3 + 0*m + 1/36*m**5. Factor n(y).
y*(5*y - 2)/3
Suppose -1 = 6*d - 13. Suppose -9/4 + 3/2*k - 1/4*k**d = 0. What is k?
3
Let u(o) = o**3 + o**2 + 4. Let r be u(0). Let j be r/12*(5 + 1). Let -4*z**j + 2*z**2 + 2*z**3 + 0*z**2 = 0. Calculate z.
0, 1
Factor -1/3 + 1/3*d**3 - 1/3*d + 1/3*d**2.
(d - 1)*(d + 1)**2/3
Solve -q**3 - 8*q**5 + 14*q**5 - 3*q**3 - 2*q**5 = 0.
-1, 0, 1
Let t(m) be the first derivative of -m**4/10 - 2*m**3/15 + m**2/5 + 2*m/5 - 4. Factor t(v).
-2*(v - 1)*(v + 1)**2/5
Let s(o) = -8*o**2 - 5*o. Let x be 4/24*2*3. Let y(j) = 1 - j - j**2 - 1. Let z(p) = x*s(p) - 2*y(p). Factor z(d).
-3*d*(2*d + 1)
Let k(g) be the third derivative of -4*g**7/525 - 11*g**6/300 - 3*g**5/50 - g**4/60 + g**3/15 + 14*g**2. Factor k(m).
-2*(m + 1)**3*(4*m - 1)/5
Let x be (-60)/(-315)*((-21)/(-6) - 2). Factor 4/7*s - 2/7*s**3 + x*s**2 + 0.
-2*s*(s - 2)*(s + 1)/7
Let l(o) be the third derivative of o**6/160 - o**5/16 + 7*o**4/32 - 3*o**3/8 - 4*o**2. Let l(m) = 0. Calculate m.
1, 3
Let g = 16 - 10. Let r(v) be the third derivative of 4/35*v**5 - 1/15*v**7 + v**2 - 1/20*v**g + 0*v + 0 - 1/21*v**4 + 0*v**3. Factor r(n).
-2*n*(n + 1)*(7*n - 2)**2/7
Let b(l) be the second derivative of l**5/5 + l**4/3 - 2*l. Factor b(n).
4*n**2*(n + 1)
Let d be (-14)/21 + (-8)/(-3). Let o be 1/1 + -2 + 2. Factor 2*c**d + 1 - 4 - o + 2*c.
2*(c - 1)*(c + 2)
Let d(v) be the first derivative of 2*v**3 + 3. Let s(j) = 13*j**2. Let r(m) = -9*d(m) + 4*s(m). Solve r(y) = 0.
0
Factor 4*k**2 - 1 + 0 - 8*k - 1 + 6*k**2.
2*(k - 1)*(5*k + 1)
Factor 3993*g + 79*g**3 + 7*g**4 - 5*g**4 + 1089*g**2 + g**4 + 20*g**3.
3*g*(g + 11)**3
Let k(x) = -8*x**2 + 8*x - 2. Let c(g) = -8*g**2 + 8*g - 2. Let t(i) = -4*c(i) + 5*k(i). Factor t(s).
-2*(2*s - 1)**2
Let k(d) be the third derivative of d**8/13440 + d**4/6 + d**2. Let l(f) be the second derivative of k(f). Factor l(w).
w**3/2
What is k in 0 - 2/9*k**2 + 0*k = 0?
0
Suppose 5*n = -4*n. Factor 0*x**2 + 2/7*x**5 + 0 + 0*x - 2/7*x**3 + n*x**4.
2*x**3*(x - 1)*(x + 1)/7
Let r = -23 - -25. Suppose -5*x = -r*x - 6. Determine p so that -4/11*p**x - 2/11*p + 0 = 0.
-1/2, 0
Let u(w) be the second derivative of -w**6/6 - w**5/2 + 5*w**4/12 + 5*w**3/3 - 7*w. Factor u(t).
-5*t*(t - 1)*(t + 1)*(t + 2)
Let t(n) be the first derivative of -4*n**3/3 + 7. Find y, given that t(y) = 0.
0
Factor 8/13*q - 2/13*q**2 + 0.
-2*q*(q - 4)/13
Let k(a) = -5*a**4 + a - 3*a**2 - a**2 - 5*a**3 + 2*a**3 + 9*a**2. Let l(x) = 41*x**4 + 25*x**3 - 41*x**2 - 8*x. Let r(t) = 51*k(t) + 6*l(t). Factor r(d).
-3*d*(d - 1)*(d + 1)*(3*d + 1)
Let n = 11 - 9. Let i(f) = -4*f**2 + 4. Let q(p) = -17*p**2 - p + 16. Let k(a) = n*q(a) - 9*i(a). Factor k(v).
2*(v - 2)*(v + 1)
Let g = 152/441 + -6/49. Factor -g*z**2 - 2 + 4/3*z.
-2*(z - 3)**2/9
Let f = -2821/5 + 565. Factor -1/5*g**4 - f*g**2 + 4/5*g**3 + 0*g + 0.
-g**2*(g - 2)**2/5
Let g(q) = q - 7. Let a be g(9). Let k(d) be the second derivative of 0*d**3 + 2*d + 1/48*d**4 + 0 + 0*d**a. Factor k(h).
h**2/4
Let j = 8/101 - -1172/505. Suppose -7*i + 21 = -0. Factor -18/5*h + 32/5*h**2 - 28/5*h**i - 2/5*h**5 + 4/5 + j*h**4.
-2*(h - 2)*(h - 1)**4/5
Factor 22*o + o + 16 - 3*o + 4*o**2.
4*(o + 1)*(o + 4)
Suppose n = -0*n + 3. Suppose 0 = -t + 5 + n. Solve 3*m**3 + t*m**5 - 6*m**5 + 2*m**2 - 5*m**3 - 2*m**4 = 0 for m.
-1, 0, 1
Let i(z) be the second derivative of -z**6/20 - 3*z**5/20 + z**3/2 + 3*z**2/4 + 2*z. Factor i(u).
-3*(u - 1)*(u + 1)**3/2
Let w(a) = -6*a**2 + 3*a + 3. Let j(d) = d**3 - 5*d**2 + 2*d + 2. Let z(y) = -3*j(y) + 2*w(y). Factor z(g).
-3*g**2*(g - 1)
Let x(o) = o**3 + o**2 - 2*o. Let k(f) be the first derivative of -2*f**3 - 5/4*f**4 + 0*f + 11/2*f**2 + 3. Let y(g) = 4*k(g) + 22*x(g). What is a in y(a) = 0?
0, 1
Let j be (-6)/15 + 12/5. Factor 8*s**5 - 5*s**2 - 4*s + 4*s**j + 6*s**5 + 3*s**2 + 38*s**4 + 30*s**3.
2*s*(s + 1)**3*(7*s - 2)
Determine y so that 4*y - 12 - 1/3*y**2 = 0.
6
Let u be (1/(-6))/(60/(-9)). Let y(g) be the second derivative of -2*g + 0 - 1/24*g**4 - u*g**5 + 1/12*g**3 + 1/4*g**2. Solve y(k) = 0.
-1, 1
Let w be (2/4)/(15/60). What is l in 8/3*l - 8/3*l**3 - 2/3*l**w + 2/3 = 0?
-1, -1/4, 1
Factor 4/7*s**2 + 8/7 + 12/7*s.
4*(s + 1)*(s + 2)/7
Suppose -4*p - 2 - 2 = -2*q, -5*p = q + 5. Let c(r) = -r**2 + 2. Let w be c(q). Let -3*k**w + k + 1 - k**3 + 0*k + 2*k**2 + 0*k**2 = 0. What is k?
-1, 1
Factor 15*o + 8*o**2 - 11*o**2 - 30*o - 12.
-3*(o + 1)*(o + 4)
Let o(a) be the first derivative of 7*a**4/8 - 20*a**3/3 + 51*a**2/4 + 9*a -