b(f) = 3*f + 5*f**2 + 14*f**3 + 10*f**2 + 0*f**3 - 2. Let g(u) = -15*u**3 - 15*u**2 - 3*u + 3. Let d(v) = -3*b(v) - 2*g(v). Factor d(m).
-3*m*(m + 1)*(4*m + 1)
Suppose -4/15*o**3 - 2/15*o**5 - 2/15 + 2/5*o + 2/5*o**4 - 4/15*o**2 = 0. What is o?
-1, 1
Let r(z) be the second derivative of 2*z**7/21 + 2*z**6/5 + 3*z**5/5 + z**4/3 - 9*z. Find g such that r(g) = 0.
-1, 0
Let i(l) be the second derivative of -1/3*l**3 + 0*l**2 + 0 + 1/10*l**5 - 1/30*l**6 + 1/12*l**4 - 3*l. Solve i(c) = 0.
-1, 0, 1, 2
Let w(o) = -8*o**2 - 15*o + 23. Let r(v) = 4*v**2 + 7*v - 11. Let n(h) = 7*r(h) + 3*w(h). Solve n(m) = 0.
-2, 1
Let q(t) be the first derivative of t**6/5 + 6*t**5/25 - 3*t**4/2 - 2*t**3/5 + 24*t**2/5 - 24*t/5 + 27. Factor q(x).
6*(x - 1)**3*(x + 2)**2/5
Suppose 0 = u + 2, -p = -0*p - 5*u - 14. Determine x, given that 24/5*x**3 + 14/5*x**p + 8/5 - 22/5*x**2 - 24/5*x = 0.
-2, -1, 2/7, 1
Suppose -4*h + h = -15. Suppose -h*j - 2*o + 5 = 0, -3*o + 7*o = -5*j - 5. Factor -2 - 8*l**2 + 10*l - 6*l**2 + 10*l**3 - 4*l**j.
2*(l - 1)**2*(3*l - 1)
Let j = 88 - 88. Let d be (-2)/6 - (-14)/6. What is c in 1/4*c**d + j - 1/4*c = 0?
0, 1
Factor 9 + 19*v**3 + 1 - 20*v**4 + 10*v**2 + v**3 - 54*v + 29*v + 5*v**5.
5*(v - 2)*(v - 1)**3*(v + 1)
Let w(g) be the second derivative of g**4/66 - 2*g**3/33 - 3*g**2/11 + 4*g. Factor w(z).
2*(z - 3)*(z + 1)/11
Let d = 1/7 + 2/35. Solve 0 + 0*c - d*c**2 + 2/5*c**3 - 1/5*c**4 = 0.
0, 1
Let y = 2 + 0. Let j(l) be the second derivative of -1/18*l**4 + 0*l**y - 1/9*l**3 + 0 - 2*l. Factor j(o).
-2*o*(o + 1)/3
Let x(y) be the third derivative of -y**8/13440 + y**7/3360 + y**5/15 + 4*y**2. Let v(d) be the third derivative of x(d). What is r in v(r) = 0?
0, 1
Let b(x) = 5*x**3 + 15*x**2 - 48*x + 23. Let h(k) = k**3 + 4*k**2 - 12*k + 6. Let f(r) = -2*b(r) + 9*h(r). Let f(i) = 0. What is i?
2
Let m(r) be the third derivative of -1/240*r**5 - 1/96*r**4 + 0 + 0*r + 1/12*r**3 - 3*r**2. What is c in m(c) = 0?
-2, 1
Let g(i) be the third derivative of 2*i**7/9 - 23*i**6/45 - i**5/5 + 8*i**4/9 + 8*i**3/9 - 31*i**2. Suppose g(f) = 0. What is f?
-2/5, -2/7, 1
Let f(p) be the second derivative of -p**8/5880 + p**7/2940 + p**6/1260 - p**5/420 + p**3/2 - 2*p. Let b(d) be the second derivative of f(d). Factor b(g).
-2*g*(g - 1)**2*(g + 1)/7
Let f(x) be the second derivative of x**8/112 - 3*x**6/40 - x**5/10 + 3*x**2/2 + x. Let o(t) be the first derivative of f(t). Suppose o(q) = 0. What is q?
-1, 0, 2
Factor -4/7*u**4 + 4/7*u**2 + 0 + 1/7*u**5 - 4/7*u + 3/7*u**3.
u*(u - 2)**2*(u - 1)*(u + 1)/7
Suppose -3*x + 5*v - 11 = 0, -3*x + 6*v - 7*v = -13. Let p = x + -1. Suppose 0*r**3 - 3*r**p + 3*r - 3*r**4 - 3*r**3 + 6*r**4 = 0. What is r?
-1, 0, 1
Let c = -1/823 - -9881/4115. Determine m so that -8/5*m**4 + 0 + 2/5*m + c*m**3 + 2/5*m**5 - 8/5*m**2 = 0.
0, 1
Suppose -3*v = -v + 10, -2*a + 3*v + 5 = 0. Let q(j) = -4*j**4 - 4*j**3 + 6*j**2 + j + 6. Let b(o) = -o**4 + o + 1. Let l(p) = a*b(p) + q(p). Factor l(t).
(t - 1)**4
Suppose 3*h + 5 - 11 = 0. Factor 12*a**2 + 8 - h + 0*a**3 + 3*a**3 + 15*a.
3*(a + 1)**2*(a + 2)
Let f(s) be the first derivative of -s**6/120 - s**5/120 + s**4/24 + s**3/12 + 3*s**2/2 - 3. Let j(o) be the second derivative of f(o). Factor j(v).
-(v - 1)*(v + 1)*(2*v + 1)/2
Let h be 27/12 - (-1)/(-4). Suppose 22 = 5*f + h. Solve 6*r**f + 2*r**2 + 3*r**3 + 2*r**3 + 2*r**5 + r**3 = 0.
-1, 0
Let t(a) = a**3 - 5*a**2 - a + 7. Let g be (-25)/(-20)*(1 - -3). Let c be t(g). Determine o, given that 2/7*o**4 + 0 + 0*o**c + 0*o**3 + 0*o = 0.
0
Let h(w) = -w**2 - 9*w - 6. Let f(x) = 2*x**2 + 19*x + 11. Let c = -18 + 11. Let k(b) = c*h(b) - 3*f(b). Factor k(r).
(r + 3)**2
Let n be (-4)/(-2) - 96/52. Factor -n*a**2 - 32/13 + 16/13*a.
-2*(a - 4)**2/13
Suppose w = -w + 4. Let q be ((-6)/(-4))/(15/20). Suppose r**5 + 0*r**5 + w + r**5 - 4*r**2 - 4*r**3 + q*r**4 + 2*r = 0. Calculate r.
-1, 1
Let i(f) be the first derivative of -8*f - 2/5*f**5 + 2 - 26/3*f**3 + 3*f**4 + 12*f**2. Factor i(g).
-2*(g - 2)**2*(g - 1)**2
Let z(k) be the first derivative of k**3/9 - k/3 + 3. Factor z(y).
(y - 1)*(y + 1)/3
Let g = -69 - -72. Let n(s) be the third derivative of 1/60*s**5 + 0 - 1/3*s**g - 4*s**2 + 0*s + 1/24*s**4. What is y in n(y) = 0?
-2, 1
Let h(v) be the first derivative of 4 + 2/5*v**5 + 0*v**2 + 1/2*v**4 + 0*v - 2/3*v**3 - 1/3*v**6. Factor h(i).
-2*i**2*(i - 1)**2*(i + 1)
Let k(u) = -u**3 + u + 1. Let r(b) = -4*b**4 + 2*b**3 + 16*b**2 - 2*b - 6. Let q(y) = -6*k(y) + r(y). Solve q(x) = 0.
-1, 1, 3
Suppose s = -4*h - 18, 4 + 0 = -3*s - 2*h. Suppose 6 = -s*o + 5*o. Factor 0 + 0*v - 8*v**4 - 2*v**3 + 4/3*v**o - 14/3*v**5.
-2*v**2*(v + 1)**2*(7*v - 2)/3
Let i(u) be the second derivative of -1/2*u**4 + 9/20*u**5 - 1/10*u**6 + 0*u**2 + 0*u**3 + 9*u + 0. Factor i(v).
-3*v**2*(v - 2)*(v - 1)
Let x(q) be the third derivative of q**5/30 + 2*q**4/3 + 16*q**3/3 - 4*q**2. What is d in x(d) = 0?
-4
Let p(w) = -9*w**2 + 91*w - 581. Let a(s) = -4*s**2 + 46*s - 290. Let k(m) = -5*a(m) + 2*p(m). Factor k(i).
2*(i - 12)**2
Let o(m) = 21*m**4 - 1 + m - 49*m**3 + 31*m**2 + 6 + 0 - 4. Let l(p) = 20*p**4 - 48*p**3 + 32*p**2. Let k(d) = 5*l(d) - 4*o(d). Solve k(u) = 0 for u.
-1/4, 1
Let p(x) be the second derivative of x**4/21 + x - 3. Determine g, given that p(g) = 0.
0
Factor 8*c**2 + 6*c - 22*c + 4*c**3 - 6*c**4 + 4*c**4.
-2*c*(c - 2)**2*(c + 2)
Suppose 3*k = 17 + 13. Suppose 5*r + k = 5*f, -3*f - f = 2*r - 20. Find h, given that 2/5*h**5 - 6/5*h**f + 6/5*h**3 + 0*h + 0 - 2/5*h**2 = 0.
0, 1
Let g(b) be the second derivative of 5*b**4/21 - 134*b**3/21 + 52*b**2/7 + 14*b. Factor g(a).
4*(a - 13)*(5*a - 2)/7
Let f(p) be the first derivative of 32*p**6/9 + 144*p**5/5 + 155*p**4/3 + 313*p**3/9 + 11*p**2 + 5*p/3 - 23. Factor f(u).
(u + 1)*(u + 5)*(4*u + 1)**3/3
Let y = -6 + 19/3. Factor 0*o**4 + 0*o**2 - 1/3*o**5 + 2/3*o**3 + 0 - y*o.
-o*(o - 1)**2*(o + 1)**2/3
Let t(w) be the first derivative of -2*w**3/3 - 4*w**2 - 6*w - 19. Let t(j) = 0. Calculate j.
-3, -1
Factor 0*q - 1/3 + 1/3*q**2.
(q - 1)*(q + 1)/3
Let d be (3 - 9)*7/(-21). Suppose -2/3*s - d*s**3 + 2*s**2 + 2/3*s**4 + 0 = 0. Calculate s.
0, 1
Let c(v) = 14*v**2 - 5 - 4*v + 1 + 2. Let m(i) be the first derivative of -5*i**3/3 + i**2/2 + i - 1. Let u(r) = 3*c(r) + 8*m(r). Factor u(j).
2*(j - 1)**2
Suppose -2*g = -7*g - 4*z - 4, 5 = -g - 5*z. Factor -3*p - 2 + 5*p + 2*p**2 + g*p**2 - 2.
2*(p - 1)*(p + 2)
Let q = 3421/20 - 171. Let p(z) be the third derivative of q*z**5 + 0 + 1/3*z**3 - 3*z**2 - 5/24*z**4 + 0*z. What is x in p(x) = 0?
2/3, 1
Let f(d) = 204*d**3 - 147*d**2 - 57*d - 15. Let y(m) = -29*m**3 + 21*m**2 + 8*m + 2. Let s(q) = 2*f(q) + 15*y(q). Factor s(r).
-3*r*(r - 1)*(9*r + 2)
Let j(o) be the third derivative of o**6/420 + o**5/210 - o**4/84 - o**3/21 - 5*o**2. Determine f so that j(f) = 0.
-1, 1
Let b(y) = -y**4 + y**3 + y**2 + y + 1. Let l(r) = 4*r**3 - 4*r**2 + 4*r + 8. Let f(s) = -4*b(s) + l(s). Factor f(u).
4*(u - 1)**2*(u + 1)**2
Let g = 14 - 12. Suppose -7*q = -g*q. Determine u, given that q - 4/7*u + 2/7*u**2 = 0.
0, 2
Let g = -335 + 339. Suppose -2/5*f**2 + 3/5*f**g + 2/5*f**3 + 1/5*f**5 - 1/5 - 3/5*f = 0. Calculate f.
-1, 1
Let y(f) = -f**3 - 3*f**2 - 3*f - 1. Let r be y(-2). Factor 6*b - 3*b**2 + r - 5 + 1.
-3*(b - 1)**2
Let c(t) be the second derivative of 0 + 2/27*t**4 - 2/45*t**5 + 0*t**2 - 1/27*t**3 + 6*t. Determine b, given that c(b) = 0.
0, 1/2
Let y be -9 - 3/6*-4. Let a be y/14 + (-14)/(-12). Factor 0 + 0*s - a*s**3 + 1/3*s**2 - 4/3*s**5 - 7/3*s**4.
-s**2*(s + 1)**2*(4*s - 1)/3
Suppose 0 = -a - 7*p + 4*p - 11, 0 = p + 4. Let h = 2 + a. Factor -x**2 + 4*x + x - 4*x - x**h + x**4.
x*(x - 1)**2*(x + 1)
Let p(f) be the second derivative of -f**4/42 - f**3/21 + 2*f**2/7 + 2*f. Factor p(w).
-2*(w - 1)*(w + 2)/7
Let l(y) be the second derivative of y**4/42 - y**2/7 - 3*y. Solve l(m) = 0 for m.
-1, 1
Let s be ((-1)/(-5))/((-12)/(-36)). Factor 12/5 + s*u**2 - 12/5*u.
3*(u - 2)**2/5
Let l(s) be the third derivative of -10*s**7/21 - 14*s**6/3 - 166*s**5/15 + 14*s**4 - 6*s**3 - 31*s**2. Factor l(h).
-4*(h + 3)**2*(5*h - 1)**2
Factor -5/7*t**3 + 0*t + 3/7*t**4 + 0 - 2/7*t**2.
t**2*(t - 2)*(3*t + 1)/7
Let i = 57 - 170/3. Suppose -2/3*a**2 + i*a**3 + 0 + 1/3*a = 0. Calculate a.
0, 1
Factor -1/2*n**2 - 1/2*n**3 + n + 0.