m(o) = 2*o**2 - 10*o - 12. Let q(z) be the second derivative of -z**4/12 + 2*z**3/3 + 5*z**2/2 + z. Let s(f) = 5*m(f) + 12*q(f). Factor s(b).
-2*b*(b + 1)
Let c(i) = -7*i**3 + 17*i**2 - 48*i + 36. Let f(p) = -48*p**3 + 120*p**2 - 336*p + 252. Let k(z) = -27*c(z) + 4*f(z). Suppose k(t) = 0. What is t?
2, 3
Let r(w) = -80*w - 6. Let z be r(-4). Let x = -2822/9 + z. Let 2/9*m**5 + 0 + 0*m**3 - 2/9*m + x*m**4 - 4/9*m**2 = 0. What is m?
-1, 0, 1
Factor -12*b**3 - 8*b**2 - 3*b**3 + 7*b**3 - 4*b**3.
-4*b**2*(3*b + 2)
Let o(y) be the second derivative of y**6/100 - y**5/150 + 2*y**2 + 4*y. Let l(i) be the first derivative of o(i). Solve l(q) = 0.
0, 1/3
Let l be 3/(-5) + 28/30. Let -1/3*h**4 + l*h + 0 - 1/3*h**3 + 1/3*h**2 = 0. Calculate h.
-1, 0, 1
Let u(z) be the first derivative of -z**7/147 + z**5/70 + 3*z - 3. Let d(m) be the first derivative of u(m). Factor d(c).
-2*c**3*(c - 1)*(c + 1)/7
Suppose -3*h = -3*c + 3, 5*h - 2 = 2*c - 1. Let a(u) be the third derivative of 1/24*u**4 + 0 + 1/60*u**5 + 0*u - 2*u**c + 0*u**3. Factor a(r).
r*(r + 1)
Suppose 5*s + 34 = 4*m, -s + 6*s - 14 = -4*m. Suppose 7*x**2 - 3*x**2 - m*x**2 = 0. What is x?
0
Suppose -3*z + 36 - 6 = 0. Let j = -8 + z. Factor 0*b - 2/5*b**j + 2/5.
-2*(b - 1)*(b + 1)/5
Let a(t) be the first derivative of -7*t**6/180 + t**5/30 + t**3 + 5. Let k(w) be the third derivative of a(w). Determine y, given that k(y) = 0.
0, 2/7
Suppose x = 7*n - 3*n + 10, 4*n + 28 = 4*x. Let m = 8 - x. Factor -3*y - y + y**m - 2 + 5*y.
(y - 1)*(y + 2)
Let y(s) be the second derivative of 0*s**2 + 1/40*s**6 - 3/40*s**5 + 0*s**3 + 1/16*s**4 + 0 - 4*s. Find o such that y(o) = 0.
0, 1
Let 2*c**4 + 4*c**3 + 4*c**4 - 5*c**4 + 3*c**4 = 0. What is c?
-1, 0
Let f(b) = -8*b + 3. Let w(k) = -7*k + 2. Let c(p) = 4*f(p) - 5*w(p). Let m be c(6). Suppose 2*v**3 + m*v**4 - 4*v**3 - 19*v**4 = 0. Calculate v.
0, 2
Let b(i) be the third derivative of -i**8/42 - 4*i**7/105 + 11*i**6/60 + 2*i**5/3 + 11*i**4/12 + 2*i**3/3 - 5*i**2. Determine a so that b(a) = 0.
-1, -1/2, 2
Suppose -6 = -2*p + p. Let h(f) be the third derivative of -f**2 + 0*f**3 + 0 - 1/105*f**7 + 0*f**4 - 1/42*f**8 + 0*f + 0*f**p + 0*f**5. Factor h(s).
-2*s**4*(4*s + 1)
Let d = -15 + 18. Let c(m) be the first derivative of 0*m - 1 + 1/15*m**d + 1/10*m**2. Factor c(f).
f*(f + 1)/5
Let a be (12/9)/(1/3). Factor -a*c + 4 - 2 + 0*c**2 + 2*c**2.
2*(c - 1)**2
Let k(d) be the third derivative of -d**8/336 - d**7/105 + d**6/60 + d**5/15 - d**4/24 - d**3/3 - 6*d**2. Factor k(n).
-(n - 1)**2*(n + 1)**2*(n + 2)
Let r(c) be the third derivative of -1/120*c**5 + 0*c - 1/12*c**4 + 0 - 8*c**2 - 1/4*c**3. Factor r(k).
-(k + 1)*(k + 3)/2
Let h(a) = a**2 - 2*a - 5. Let j = 25 + -21. Let f be h(j). Determine i so that 0*i**2 + f - 3/2*i**3 + 9/2*i = 0.
-1, 2
Let k be -2 + -2 - -1*(8 + -2). Factor 1/2*g - 1/2*g**k - 1/2*g**3 + 0 + 1/2*g**4.
g*(g - 1)**2*(g + 1)/2
Let m = 206 - 1027/5. Factor 0*i + 0 + 3/5*i**3 + m*i**2.
3*i**2*(i + 1)/5
Suppose -5 = -5*v + 15. Let y be 18/v + 4/(-8). Solve -2*j**2 - 3*j + y*j + j = 0.
0, 1
Let q(j) be the third derivative of -j**6/840 - j**5/210 - j**4/168 - 3*j**2. Let q(u) = 0. Calculate u.
-1, 0
Factor -2/5*w**3 - 1/5*w**5 - 1/5 + 3/5*w**4 - 2/5*w**2 + 3/5*w.
-(w - 1)**4*(w + 1)/5
Suppose -3*m = p - 20, -p + 0*m = -2*m + 5. Let r be (-1)/(-1)*(-3)/(-1). Let 0 - 4*f**3 - r*f**4 + p*f**4 - 2 + 4*f = 0. Calculate f.
-1, 1
Let z = 0 - -2. Let x be (-24)/15 - (0 + -2). Find a, given that x*a**z + 0 + 4/5*a = 0.
-2, 0
Let l(j) = -8*j**3 + 28*j**2 - 12*j - 42. Let t(s) = 15*s**3 - 55*s**2 + 25*s + 85. Let f(c) = -5*l(c) - 3*t(c). Factor f(k).
-5*(k - 3)**2*(k + 1)
Let l = -146 + 148. Let b be 20/72 + (-2)/(-9). Factor i + b*i**l + 0.
i*(i + 2)/2
Suppose 4*c = -40 + 56. Let m(w) be the first derivative of 0*w**2 - 2/3*w**3 + 1/6*w**6 + 0*w + 2/5*w**5 - 3 - 1/4*w**c. Factor m(n).
n**2*(n - 1)*(n + 1)*(n + 2)
Let g be 35/20 + (-2)/(-8). Suppose 0 = -2*u - m + g, 0*m + 14 = 4*u - 3*m. Let -3 + 2 + 2*b + b**u - 2*b**2 = 0. Calculate b.
1
Let k(b) be the third derivative of -b**11/997920 + b**10/226800 - b**9/181440 + b**5/20 + b**2. Let h(o) be the third derivative of k(o). Factor h(g).
-g**3*(g - 1)**2/3
Suppose z - 4*w = 16, 3*w = 3*z + w - 8. Let r(a) be the third derivative of 0*a + z*a**3 + 1/420*a**6 - 1/42*a**4 - 2*a**2 + 1/210*a**5 + 0. Factor r(t).
2*t*(t - 1)*(t + 2)/7
Find s, given that -9/7*s**3 - 2/7 - 13/7*s - 24/7*s**2 = 0.
-2, -1/3
Factor 45*h**3 - 27*h**3 + 8*h**2 + 13*h - 17*h**3 + 6.
(h + 1)**2*(h + 6)
Let w(m) = -36*m**4 + 120*m**3 - 97*m**2 + 19. Let z(j) = 72*j**4 - 240*j**3 + 195*j**2 - 37. Let h(i) = 5*w(i) + 3*z(i). Determine t so that h(t) = 0.
-1/3, 2/3, 1, 2
Let j be (-155)/6 - (-16)/(-24). Let v = -26 - j. Factor -1/4 - v*b - 1/4*b**2.
-(b + 1)**2/4
Let f(n) be the second derivative of -n**4/3 + 16*n**3/3 - 32*n**2 + 7*n. Factor f(o).
-4*(o - 4)**2
Let b(j) = -j**3 + 5*j**2 - 2*j - 4. Let h be b(4). Let t(u) be the second derivative of -u + u**2 - 1/6*u**h + 1/3*u**3 + 0 - 1/10*u**5. Factor t(f).
-2*(f - 1)*(f + 1)**2
Let h(b) be the second derivative of -1/18*b**4 + 0 + 0*b**2 + 0*b**3 + 1/90*b**5 + 8*b. Find m such that h(m) = 0.
0, 3
Let f(m) be the third derivative of -m**5/30 + m**4/48 - 42*m**2. Suppose f(n) = 0. What is n?
0, 1/4
Let c(r) = -r**2 + 2*r + 3. Let j(y) = -1. Suppose -6 = -3*o, 1 = 3*t - o + 6. Let d(v) = t*c(v) - 3*j(v). Factor d(h).
h*(h - 2)
Let x(k) be the third derivative of k**5/90 + k**4/6 + 5*k**3/9 + 37*k**2. Suppose x(i) = 0. What is i?
-5, -1
Let b = 2102/7 - 300. Factor -2/7*j**2 + 6/7*j**3 + b*j**5 - 6/7*j**4 + 0 + 0*j.
2*j**2*(j - 1)**3/7
Suppose 7 = -x + 2. Let b(v) = -v**2 - 5*v + 4. Let f be b(x). Factor 6*u**3 + 4*u**3 + 8*u**4 + f*u**2 - 3*u**5 + 5*u**5.
2*u**2*(u + 1)**2*(u + 2)
Suppose -9 + 21 = 3*m. Factor 3*i**3 - i**3 + i**m + 5*i - 5*i.
i**3*(i + 2)
Let d(b) be the first derivative of b**6/9 + 4*b**5/15 - b**4/6 - 4*b**3/9 + 8. Find z, given that d(z) = 0.
-2, -1, 0, 1
Suppose 7 - 4 = c. Suppose y - 20 = -4*d, -c*d + 0*d + 3*y = 0. Factor 0 + 0*r - 1/2*r**d + 0*r**2 - 1/2*r**3.
-r**3*(r + 1)/2
Let r(p) be the first derivative of -2*p**6/3 - 16*p**5/5 - 6*p**4 - 16*p**3/3 - 2*p**2 + 1. Factor r(y).
-4*y*(y + 1)**4
Let t = 3 + -1. Factor -10*y - 3 + 4*y - t*y**2 - y**2.
-3*(y + 1)**2
Let r be (-4)/(-10) - (-3058)/30. Let a = -101 + r. Solve 0 - 10/3*h**3 - 2/3*h**2 + a*h + 2/3*h**4 + 2*h**5 = 0 for h.
-1, 0, 2/3, 1
Suppose -14 = -4*u + 3*k, -u - 5*k + 2*k = -11. Solve -4*v**4 - 3*v**3 - 4*v - 4*v**3 + 6*v**3 + 4*v**2 + u*v**3 = 0 for v.
-1, 0, 1
Let r(s) be the first derivative of 1/7*s**2 + 0*s - 1 + 0*s**5 + 0*s**3 - 1/7*s**4 + 1/21*s**6. Determine c, given that r(c) = 0.
-1, 0, 1
Let j = 1009/5489 - 1/499. Solve 0*w + j*w**3 + 2/11*w**2 + 0 - 4/11*w**4 = 0 for w.
-1/2, 0, 1
Let o(u) = -3*u**2 + 27*u + 11. Let x(s) = -s**2 + 7*s + 3. Let q(m) = -6*o(m) + 22*x(m). Factor q(y).
-4*y*(y + 2)
Let a(d) = 8*d**4 - 12*d**3 + 8*d**2 - 4*d. Let c(z) = z**5 + 8*z**4 - 12*z**3 + 8*z**2 - 5*z. Let x(n) = -3*a(n) + 2*c(n). Factor x(w).
2*w*(w - 1)**4
Let m be 0 - -6 - -1 - 3. Find k such that 2*k + 5*k + m + 0*k - k - 2*k**3 = 0.
-1, 2
Let k(w) be the first derivative of -w**3/3 - 4*w**2 - 16*w - 7. Determine l, given that k(l) = 0.
-4
Factor -6*l**5 - 4*l**3 + 0*l**5 + l**5 - 3*l**5 - 12*l**4.
-4*l**3*(l + 1)*(2*l + 1)
What is b in -1 - 3/2*b**3 + 3/2*b + 1/2*b**2 + 1/2*b**4 = 0?
-1, 1, 2
Let r(h) = -h**2 + 8*h + 14. Let o be r(10). Let p be (-7)/(-2) + 9/o. Factor 7*l**2 - 4*l**p - 3*l**2 + l**3 - l**2.
l**2*(l - 1)
Let h = -69225 - -3115366/45. Let z = h - 5/9. Find u, given that 18/5*u**2 + 0 + 4/5*u + z*u**3 + 2*u**4 = 0.
-1, -2/5, 0
Let p be (-1 + 2)/(-1)*-2. Factor -7*i - i**p + 7*i.
-i**2
Suppose 11*u - 15 = 6*u. Factor -u*k**2 - 3*k**4 + 3*k + 6*k**2 - 3*k**3 + 0*k**4.
-3*k*(k - 1)*(k + 1)**2
Let n(r) be the second derivative of -r**7/56 + 2*r. Factor n(b).
-3*b**5/4
Factor 0*i + 0*i**3 + 1/5*i**2 + 0 - 1/5*i**4.
-i**2*(i - 1)*(i + 1)/5
Let i(j) = 81*j**4 + 48*j**3 - 81*j**2 - 15*j - 33. Let w(z) = -5*z**4 - 3*z**3 + 5*z**2 + z + 2. Let k(m) = -2*i(m) - 33*w(m). Factor k(l).
3*l*(l - 1)*(l + 1)**2
Let a(q) be the second derivative of -3*q**6/5 + 6*q**5/5 + q**4/3 - 4*q**3/3 - q**2 + 5*q. F