, 2
Let l(f) be the second derivative of f**4/28 + 5*f**3/7 + 9*f**2/2 + 95*f. Factor l(n).
3*(n + 3)*(n + 7)/7
Let r(c) = -c - 1. Suppose 21 = -7*i - 7. Let o be r(i). Factor -8*v**3 - 10*v**2 + 10 + 5*v + 2*v**3 + v**o.
-5*(v - 1)*(v + 1)*(v + 2)
Let 14/3*j**5 - 10/3*j**3 - 6*j**4 + 6*j**2 - 4/3*j + 0 = 0. Calculate j.
-1, 0, 2/7, 1
Let w(u) be the third derivative of u**9/4032 + u**8/840 - 19*u**7/1680 + u**6/40 + 5*u**5/12 - 2*u**2. Let q(j) be the third derivative of w(j). Factor q(p).
3*(p - 1)*(p + 3)*(5*p - 2)
Let r(a) = -a**2 + 1. Suppose 4*u + 2 = 2*u. Let p(s) = 13*s - 4*s + 7*s + 20*s**2. Let m(o) = u*p(o) - 16*r(o). Let m(q) = 0. What is q?
-2
Factor 1 - 664*u**2 - 2*u + 0 + 655*u**2 - 5*u**3 - u.
-(u + 1)**2*(5*u - 1)
Let -165/8*v**3 + 13/4*v**4 - 1/8*v**5 - 13*v**2 + 0 + 169/2*v = 0. What is v?
-2, 0, 2, 13
Let f = -1537 - -13835/9. Factor -2/9*a**3 + 2/9*a + f - 2/9*a**2.
-2*(a - 1)*(a + 1)**2/9
Let f(r) be the first derivative of r**3/3 - 17*r**2 + 289*r - 70. Solve f(i) = 0 for i.
17
Factor -156/7*w - 2/7*w**2 - 3042/7.
-2*(w + 39)**2/7
Let m(j) = -j**3 - 12*j**2 - 15*j + 8. Let f be m(-11). Let a = 52 - f. Factor -14/11*l**4 + 0*l + 4/11*l**3 + 0*l**2 + a.
-2*l**3*(7*l - 2)/11
Let v(d) = -10*d**3 - 68*d**2 - 30*d. Let a(z) = 130*z**3 + 885*z**2 + 390*z. Let f(w) = 3*a(w) + 40*v(w). Factor f(u).
-5*u*(u + 6)*(2*u + 1)
Let z = -224 + 226. Let j(i) be the first derivative of 1/9*i**3 + 0*i - 8 + 1/12*i**4 - 1/3*i**z. Solve j(q) = 0 for q.
-2, 0, 1
Suppose 3*l = 3*p - 6, 4*p + 41 = 2*l + 45. Let b(d) be the third derivative of -1/120*d**5 + p*d - 1/4*d**3 + 0 - 14*d**2 - 1/12*d**4. Solve b(m) = 0.
-3, -1
Suppose 4*n = -2*l - 0*n - 2, 2*n + 6 = 0. Let o(u) = 4*u**2 - 4. Let s(h) = -5*h**2 + 5. Let c(i) = l*s(i) + 6*o(i). Determine k, given that c(k) = 0.
-1, 1
Let g(n) be the first derivative of -4*n**3/3 - 2*n**2 + 80*n - 1. Factor g(s).
-4*(s - 4)*(s + 5)
Let i be (-16)/24 - (-32)/30. Let z be 4/(-16)*352/(-110). Factor -z*o + i*o**2 + 2/5.
2*(o - 1)**2/5
Let o = 15329 + -45985/3. Factor -o*w**5 + 0 + 4/3*w**4 + 8/3*w**2 + 14/3*w**3 + 0*w.
-2*w**2*(w - 4)*(w + 1)**2/3
Let q(p) be the first derivative of -5*p**6/6 + 24*p**5/35 + 139*p**4/7 - 128*p**3/7 + 32*p**2/7 + 501. Solve q(n) = 0.
-4, 0, 2/7, 2/5, 4
Let i(n) be the second derivative of -3*n**5/40 + n**4/4 - n**3/4 + 3*n. Find p, given that i(p) = 0.
0, 1
Let p(n) be the first derivative of 5*n**3 + 1 + 7*n - 7/2*n**2 + 3/4*n**4. Let h(m) = 2*m**3 + 8*m**2 - 4*m + 4. Let k(g) = 7*h(g) - 4*p(g). Factor k(z).
2*z**2*(z - 2)
Let z be ((-15)/12)/(2 - (-18)/(-8)). Suppose -4*b - 2*i + 2 = 0, b = 5*b - 5*i - 37. Factor t**2 + 10*t**3 - 3 + b*t**4 + 3 - t**z - 13*t**3.
-t**2*(t - 1)**3
Let l = 181 - 265. Let d be -2 + (l/35)/(-1). Suppose 0 + 2/5*n**3 + 4/5*n**2 - d*n**4 + 0*n = 0. Calculate n.
-1, 0, 2
Let a(m) be the first derivative of 27/10*m**2 + 6/5*m + 4/5*m**3 - 2. Factor a(g).
3*(g + 2)*(4*g + 1)/5
Solve -80*u + 40*u**3 + 2*u**5 - 96*u**4 - 7*u**5 - 60*u**2 + 111*u**4 = 0.
-2, -1, 0, 2, 4
Let w(b) = b**5 + 30*b**4 + 2*b**3 - 56*b**2 + 5*b + 2. Let k(p) = -10*p**4 - p**3 + 19*p**2 - 2*p. Let g(y) = 8*k(y) + 3*w(y). What is n in g(n) = 0?
-3, -1, 2/3, 1
Let -9/4 - 3/4*d**2 + 3*d = 0. Calculate d.
1, 3
Let j(g) be the first derivative of g**5/5 - 3*g**4/4 - 268. Factor j(n).
n**3*(n - 3)
Find o, given that -4/7*o**4 - 40/7*o - 48/7*o**2 - 24/7*o**3 - 12/7 = 0.
-3, -1
Let b(u) = -2*u - 2. Let m be b(-2). Suppose -n = -0*n - m. Let -3*j - 2*j + 3*j**3 + 0*j**3 + n*j = 0. Calculate j.
-1, 0, 1
Let b(k) = -k**2 - 3*k. Let v(i) = 3*i**4 + 69*i**3 + 588*i**2 + 2250*i + 3240. Let c(z) = -6*b(z) + v(z). Factor c(o).
3*(o + 5)*(o + 6)**3
Let z(v) be the third derivative of -v**6/12 - 53*v**5/30 - 17*v**4/3 + 12*v**3 + 31*v**2. Factor z(b).
-2*(b + 2)*(b + 9)*(5*b - 2)
Let o(d) = 2*d**2 - 6*d + 13. Let v(k) = -3*k**2 + 3*k - 12. Let g(m) = 4*o(m) + 3*v(m). Factor g(h).
-(h - 1)*(h + 16)
Factor 1/2*x**4 + 4*x - 7/2 + 3*x**2 - 4*x**3.
(x - 7)*(x - 1)**2*(x + 1)/2
Let i(p) = p**2 - 15*p + 17. Let v be i(11). Let w be (0 + 1)/((-36)/v). Find m, given that -w*m**5 + 0 + 0*m**2 + 3/2*m**3 - 3/4*m + 0*m**4 = 0.
-1, 0, 1
Factor 8 + 5*c**2 + 11*c + 33*c + 30 + 6*c + 82.
5*(c + 4)*(c + 6)
Factor -380*g**3 - 2888/3*g**2 + 0 - 4/3*g**5 + 48*g**4 + 0*g.
-4*g**2*(g - 19)**2*(g + 2)/3
Let y(p) be the third derivative of p**8/336 - p**7/21 + 37*p**6/120 - p**5 + 3*p**4/2 - 2*p**2 + 2. Let y(u) = 0. Calculate u.
0, 2, 3
Let q(s) be the second derivative of -s**4/4 - 25*s**3/2 - 16*s. Solve q(z) = 0.
-25, 0
Find f, given that -2/9*f**3 + 6*f - 12 + 0*f**2 = 0.
-6, 3
Let a(i) be the third derivative of 1/180*i**5 + 0 + 11*i**2 + 0*i + 1/36*i**4 + 1/18*i**3. Factor a(w).
(w + 1)**2/3
Let z(l) be the first derivative of -l**8/2520 + l**7/630 + l**6/180 - 5*l**3/3 - 20. Let h(q) be the third derivative of z(q). Factor h(k).
-2*k**2*(k - 3)*(k + 1)/3
Let o(c) be the first derivative of 7*c**3 - 867*c**2/2 + 246*c + 168. Factor o(j).
3*(j - 41)*(7*j - 2)
Let f = 724 - 420. Let i = -1516/5 + f. Factor 0 - 2/5*z**2 + i*z.
-2*z*(z - 2)/5
Let k(f) = -9*f**3 - 27*f**2 + 53*f - 47. Let v(p) = 5*p**3 + 14*p**2 - 27*p + 24. Let c(n) = 6*k(n) + 11*v(n). Suppose c(h) = 0. Calculate h.
2, 3
Solve 88/9*q + 8/9 + 28*q**3 - 106/3*q**2 = 0 for q.
-1/14, 2/3
Let n(b) be the second derivative of -b**7/3150 + b**6/225 - b**5/50 + b**4/6 + 3*b. Let v(p) be the third derivative of n(p). Suppose v(s) = 0. What is s?
1, 3
Let r be (-300)/(-18) + 2/(-3). Suppose -5*j - 2*l = -r, -2*j + 7*l - 2*l = 11. Solve -q**j + 0*q**2 - 8*q + 1 + 8*q = 0.
-1, 1
Let v(i) = i**2 + i - 1. Let d be (-15)/(-45) + (-6)/(-9). Let w(y) = 6*y**2 - 6*y + 3. Let m = 2 - 5. Let s(n) = d*w(n) + m*v(n). Find z, given that s(z) = 0.
1, 2
Let r(w) be the third derivative of -w**7/5040 + w**6/240 - 3*w**5/80 - 11*w**4/24 - 2*w**2. Let m(u) be the second derivative of r(u). Factor m(c).
-(c - 3)**2/2
Let p(z) be the third derivative of z**8/8960 - z**7/840 + z**6/240 + 5*z**4/12 + 17*z**2. Let k(m) be the second derivative of p(m). Solve k(q) = 0.
0, 2
Let y(n) be the third derivative of n**9/12096 + n**8/2240 - n**6/360 + 3*n**3 + 20*n**2. Let b(l) be the first derivative of y(l). Factor b(s).
s**2*(s - 1)*(s + 2)**2/4
Let l(o) = -16*o**5 + 2*o**4 - 10*o**3 - 20*o**2. Let n(u) = 5*u**5 - u**4 + 3*u**3 + 6*u**2. Let r(x) = -3*l(x) - 10*n(x). Find g such that r(g) = 0.
0, 2
Factor -46/7 - 2/7*a**2 + 48/7*a.
-2*(a - 23)*(a - 1)/7
Let x = 54 + -52. Let m = -5/4 + x. Let 0*t**2 - 1/4*t**3 + 1/2 + m*t = 0. Calculate t.
-1, 2
Let h be (52/(-65))/((-102)/30 - -3). Factor 10/3*o**h + 0*o - 5/6*o**5 - 5/2*o**4 + 0*o**3 + 0.
-5*o**2*(o - 1)*(o + 2)**2/6
Let g be ((-1)/(-5))/1 - (-3880)/(-25). Let v = 311/2 + g. Factor 1/4*y**3 + v*y**2 + 0 + 1/4*y.
y*(y + 1)**2/4
Suppose -i + 0*i = 4*a - 14, -4*i + 14 = 2*a. Let n = 60 - 60. Determine v, given that 8 + 4 + 11*v**i + n*v**3 - 3*v**3 - 20*v**2 = 0.
-2, 1
Let a(z) = -z**2 + 18*z - 12. Let q be a(17). Suppose -q*h + 2*o = -h - 52, -15 = -h + o. Solve h*n**2 + 14*n**2 + 7*n**2 - 4 + 2 = 0 for n.
-1/4, 1/4
Let d(t) be the third derivative of t**10/529200 - t**9/211680 + t**5/12 - 6*t**2. Let k(b) be the third derivative of d(b). Factor k(a).
2*a**3*(a - 1)/7
Let c(u) be the second derivative of u**4/28 - 5*u**3/14 + 9*u**2/7 + 130*u. Factor c(m).
3*(m - 3)*(m - 2)/7
Let u(f) = -8*f**4 + 21*f**2 + 5*f - 8. Let a(r) = -4*r**4 + 10*r**2 + 2*r - 4. Let y be 1*(2 - (1 - 1)). Let q(x) = y*u(x) - 5*a(x). Factor q(o).
4*(o - 1)**2*(o + 1)**2
Let m(b) be the second derivative of 0*b**2 + 0 - 1/21*b**4 + 0*b**3 - 4/105*b**6 + 22*b - 1/14*b**5 - 1/147*b**7. Factor m(h).
-2*h**2*(h + 1)**2*(h + 2)/7
Let b = 1051/70 + -15. Let l(z) be the second derivative of 3*z + 0*z**2 + 0 + 1/21*z**3 - 1/21*z**4 + b*z**5. Find d, given that l(d) = 0.
0, 1
Let l(d) be the third derivative of -1/84*d**8 + 0*d + 2/35*d**7 + 0*d**3 + 13*d**2 + 0*d**4 - 1/10*d**6 + 1/15*d**5 + 0. Factor l(o).
-4*o**2*(o - 1)**3
Let s(k) = -k**5 - k**4 - k**3 + k**2 - 2. Let j(t) = -t**5 + 10*t**4 + 7*t**3 - 6*t**2 + 10. Let c(f) = 3*j(f) + 15*s(f). Suppose c(n) = 0. What is n?
-1/2, 0, 1/3, 1
Let i(b) be the third derivative of b**8/42 + b**7/35 - 17*b**6/60 - 2*b**5/5