*t**4 - 2/21*t**3. Let o(a) be the first derivative of r(a). Solve o(y) = 0.
0, 2
Let g(w) be the first derivative of 3*w**8/224 - w**6/24 + w**4/48 - 2*w**2 + 6. Let n(p) be the second derivative of g(p). What is c in n(c) = 0?
-1, -1/3, 0, 1/3, 1
Suppose 78*n - 150*n + 5*n**2 + 67*n = 0. Calculate n.
0, 1
Factor 0*m**2 + 4/7 - 2/7*m**3 + 6/7*m.
-2*(m - 2)*(m + 1)**2/7
Factor -5*i**3 - 3*i + 7*i**2 - 4*i**2 + 12*i - i**3.
-3*i*(i + 1)*(2*i - 3)
Let u(l) be the first derivative of l**6/12 + l**5/5 - l**3/3 - l**2/4 + 7. Solve u(s) = 0 for s.
-1, 0, 1
Let q(a) be the second derivative of -a**9/15120 - a**8/3360 - a**7/2520 - a**4/6 - 3*a. Let i(x) be the third derivative of q(x). Solve i(t) = 0 for t.
-1, 0
Suppose -5*p - 2*x = x, 5*x = -2*p. Suppose -6*t + 11 + 13 = p. Factor -s**2 - 1/3*s**3 + 1/3*s + 1/3*s**t + 2/3.
(s - 2)*(s - 1)*(s + 1)**2/3
Suppose -4*y**3 + 4*y**5 - 804 - 12*y**4 + 12*y**2 + 804 = 0. What is y?
-1, 0, 1, 3
Suppose -19 + 31 = 6*l. Factor -l + 12*s + 25/2*s**3 - 45/2*s**2.
(s - 1)*(5*s - 2)**2/2
Let o be -3*(-16)/(-9)*3. Let a be 4/(-9)*24/o. Suppose 0 - a*i + 2/9*i**2 = 0. Calculate i.
0, 3
Let u(m) = -4*m. Suppose 6*p = p - 5. Let r be u(p). Factor -2*v**4 - 4*v**r + 7*v**4.
v**4
Suppose 3*y - 2 - 20 = 5*f, 0 = -y - 2*f. What is v in -1/2*v**2 + 1/4*v**3 + 0 + 1/4*v**y + 0*v = 0?
-2, 0, 1
Let b(w) be the first derivative of w**5 + 5*w**4/2 - 5*w**2 - 5*w - 9. Factor b(p).
5*(p - 1)*(p + 1)**3
Let v = 48 - 48. Let w(l) be the first derivative of v*l + 0*l**2 + 2/3*l**3 - 2. Find f, given that w(f) = 0.
0
Let s(b) = 6*b - 2. Let u be s(1). Let j(w) be the third derivative of 1/30*w**5 + 0*w + 0 + w**2 + 0*w**u + 0*w**3. What is q in j(q) = 0?
0
Let c(a) be the first derivative of -a**6/4 - 3*a**5/5 + 9*a**4/8 + 2*a**3 - 3*a**2 + 31. Determine u so that c(u) = 0.
-2, 0, 1
Let s = 16 - 14. Let l(w) be the second derivative of 1/135*w**6 + 0*w**4 + 1/45*w**5 - s*w + 0 - 1/9*w**2 - 2/27*w**3. What is h in l(h) = 0?
-1, 1
Let j be 312/(-18)*(-10)/368. Let s = 2/69 + j. Solve -3/2*f**2 + 0 - f - s*f**3 = 0 for f.
-2, -1, 0
Let w(g) be the first derivative of 4*g**3/3 + 8*g**2 + 16*g - 3. Factor w(l).
4*(l + 2)**2
Let n = 14 + -11. Let -r**3 + 3*r - 2*r**n - r**4 + 2*r**4 + 3*r**2 - 4*r**4 = 0. What is r?
-1, 0, 1
Suppose 5*b = 2*n + 15, b + 0*b = 5*n - 20. Suppose 4*l - r = 16, 4*l - b*r - 16 = -r. What is p in p**l + p**2 - 2*p**3 - 24 + 24 = 0?
0, 1
Let z(y) = -y**3 - 18*y**2 + 18*y - 15. Let b be z(-19). Factor -4/7*w**3 + 0 + 2/7*w**b + 0*w + 2/7*w**2.
2*w**2*(w - 1)**2/7
Let d(m) be the first derivative of m**6/20 - 3*m**5/20 + m**3/2 - 3*m**2/4 + 2*m - 2. Let a(j) be the first derivative of d(j). Factor a(w).
3*(w - 1)**3*(w + 1)/2
Let p be (1/1)/(5/(-30)). Let t be -3*(-2 + (-8)/p). Factor -1/2*f**t - 1/4*f + 0.
-f*(2*f + 1)/4
Let d(c) be the third derivative of -c**6/420 - c**5/105 + 6*c**2. Determine f, given that d(f) = 0.
-2, 0
Let m(l) = -5*l**2 + 4. Let d(v) = 10*v**2 + 8*v - 12. Let b(g) = -7*g**2 - 5*g + 8. Let s(w) = -8*b(w) - 5*d(w). Let t(q) = -5*m(q) - 4*s(q). Factor t(k).
(k - 2)*(k + 2)
Let u(v) = v**3 + 25*v**2 - 25*v + 26. Let o be u(-26). Suppose o + 3/2*l - 3*l**2 + 3/2*l**3 = 0. What is l?
0, 1
Let s(z) = 9*z**2 - 51*z. Let b(y) = -y**2 + 5*y. Let w be (8 - 22)/(4/(-6)). Let k(g) = w*b(g) + 2*s(g). Factor k(u).
-3*u*(u - 1)
Let l = 25 + 2. Let k be -1 + l/6 + -2. Factor -1/2 - k*w**2 + 1/2*w**3 + 3/2*w.
(w - 1)**3/2
Let d(x) be the second derivative of -1/48*x**4 + 0 - 1/6*x**3 - 3*x - 1/2*x**2. Factor d(p).
-(p + 2)**2/4
Factor 9*u**3 + 2*u + 13*u**3 - 23*u**3 - 2*u**2 - 3*u.
-u*(u + 1)**2
Let f(w) be the third derivative of 0 - 1/210*w**5 - 3*w**2 + 0*w - 1/42*w**4 - 1/21*w**3. Factor f(g).
-2*(g + 1)**2/7
Let z = -9 - -15. Suppose 4*c - 5*b + z = 13, 4*b = 5*c - 11. Factor -3/2*k**5 - 3/2*k - 3/2*k**4 + 3*k**2 - 3/2 + 3*k**c.
-3*(k - 1)**2*(k + 1)**3/2
Let r be 8/14 + (-16664)/56. Let b = -2075/7 - r. Factor 0 + 0*z**2 + 0*z - b*z**3 - 6/7*z**5 + 10/7*z**4.
-2*z**3*(z - 1)*(3*z - 2)/7
Solve -2/3 - m - 1/3*m**2 = 0 for m.
-2, -1
Let l(r) = r**3 - r**2 - r + 1. Let g(h) = -5*h**3 + 8*h**2 - h - 2. Let d(t) = g(t) + 2*l(t). Suppose d(z) = 0. Calculate z.
0, 1
Let q(g) be the second derivative of g**6/15 - g**5/5 + 2*g**3/3 - g**2 + 8*g. Find u, given that q(u) = 0.
-1, 1
Let o(i) = 2*i**3 + 2*i**2 + i - 1. Let a be o(2). Let x = a - 12. Factor -3 - 2*q**3 - 2*q**5 + 20*q**2 - x + 8*q - 8*q**4 + 0*q**5.
-2*(q - 1)**2*(q + 2)**3
Factor -56*z**2 + 30*z**4 + 5*z**5 - 65*z**4 + 20*z + 75*z**3 - 9*z**2.
5*z*(z - 4)*(z - 1)**3
Let o(u) be the second derivative of u**7/6300 + u**6/1800 - u**4/4 + 3*u. Let j(a) be the third derivative of o(a). Let j(n) = 0. What is n?
-1, 0
Let k(w) be the first derivative of 0*w - 2/15*w**6 + 0*w**2 - 2/25*w**5 + 0*w**3 + 3 + 1/10*w**4. Let k(d) = 0. What is d?
-1, 0, 1/2
Let x = -7 - -7. Solve -10*l**4 + 3*l**3 + x*l - 2*l + 3*l**2 + 6*l**3 = 0 for l.
-1/2, 0, 2/5, 1
Let s be 7 - 6*(-1)/(-2). Let o be s*2/8*2. Let 0*y**o - y**3 - 1/2 + 1/2*y**4 + y = 0. What is y?
-1, 1
Let a(k) be the second derivative of k**7/273 + k**6/195 - 4*k**5/65 - 4*k**4/39 + 16*k**3/39 + 16*k**2/13 + 12*k. Let a(s) = 0. Calculate s.
-2, -1, 2
Determine z so that -3*z**4 - 12*z - 19*z**3 + 37*z**3 - 9*z**3 = 0.
-1, 0, 2
Let d(z) = -z**2 - z + 2. Let c be d(0). Let w = c - 1. Suppose -w - 3/2*o - 1/2*o**2 = 0. What is o?
-2, -1
Let v(f) = 2*f**2 + 2*f - 2. Let d be v(1). Factor -z**2 + 4*z**2 - 2 + z - 2*z**d.
(z - 1)*(z + 2)
Let s(y) = -y**3 - 15*y**2 + 100*y + 2. Let o be s(-20). Find d such that -9/2*d**o + 3/4*d**3 + 9*d - 6 = 0.
2
Let n = 1211/2 + -630. Let i = 25 + n. Factor 0*k + 1/2*k**3 - i*k**5 + 0*k**4 + 0*k**2 + 0.
-k**3*(k - 1)*(k + 1)/2
Suppose -4*j + 69 - 57 = 0. Let l(i) be the first derivative of 0*i - i**j + 3/2*i**2 + 4. What is x in l(x) = 0?
0, 1
Let o be 2/4 + (-5)/(-2). Let x = o + -1. Determine l so that -2*l**3 - 6*l**x + 2 - 2*l + 1 - 4*l - 5 = 0.
-1
Let -16 - 2*h**2 - 2*h**2 - 765*h + 749*h = 0. Calculate h.
-2
Let g = 3/59 + 50/177. Factor -10/3*a**2 + 8/3 - 4/3*a + 1/3*a**3 + 4/3*a**4 + g*a**5.
(a - 1)**2*(a + 2)**3/3
Let h(z) be the first derivative of z**6/9 - z**4/3 + z**2/3 - 5. Factor h(g).
2*g*(g - 1)**2*(g + 1)**2/3
Let b be ((-10)/4 - 5)*(-4)/6. Factor -2/3*m**2 + 8/3*m**b - 22/3*m**4 + 6*m**3 + 0 - 2/3*m.
2*m*(m - 1)**3*(4*m + 1)/3
Let v be -1 - (-2)/(4 + -2). Suppose 3*q = 5*u - 4, 7*u - 2*u - 2*q - 6 = v. Find f such that -2*f - 10 - u*f**5 + 10 + 4*f**3 = 0.
-1, 0, 1
Let v(q) = -7*q**2 - 6*q + 7. Suppose 0 = -5*o - 6 + 41. Let r(p) = -8*p**2 - 7*p + 8. Let s(j) = o*v(j) - 6*r(j). Factor s(u).
-(u - 1)*(u + 1)
Let g = 18 - 13. Let s(j) be the third derivative of -1/6*j**3 - 1/8*j**4 + 0 + 0*j + 1/40*j**6 - 2*j**2 + 1/60*j**g. Factor s(i).
(i - 1)*(i + 1)*(3*i + 1)
Let w(j) be the third derivative of 2*j**7/315 - j**6/180 - j**5/90 - 3*j**2. Factor w(a).
2*a**2*(a - 1)*(2*a + 1)/3
Let u(p) be the second derivative of p**8/168 + p**7/105 + 2*p**2 - 3*p. Let c(l) be the first derivative of u(l). Factor c(h).
2*h**4*(h + 1)
Suppose 4/5*r**2 + 0 - 1/2*r**3 + 1/10*r**4 - 2/5*r = 0. Calculate r.
0, 1, 2
Solve -4*t**2 + 62 - 8*t - 34 - 32 = 0.
-1
Let r(x) be the third derivative of -x**8/336 - x**7/70 - x**6/60 + x**5/30 + x**4/8 + x**3/6 + 4*x**2. Let r(u) = 0. What is u?
-1, 1
Let u be (-3)/6 - 427/(-840). Let x(s) be the third derivative of 1/60*s**5 + 0 + 0*s**4 + 0*s + 0*s**3 - u*s**6 - s**2. Suppose x(y) = 0. What is y?
0, 1
Let b be 16/15 - 4/4. Let f(l) be the second derivative of 0*l**4 + 0*l**3 - 1/20*l**5 + 0*l**2 + 2*l - 1/42*l**7 - b*l**6 + 0. Factor f(k).
-k**3*(k + 1)**2
Factor 0 + 2/5*i**4 - 2/5*i**5 + 0*i - 2/5*i**2 + 2/5*i**3.
-2*i**2*(i - 1)**2*(i + 1)/5
Let s = 12 + -8. Let y be s/(-14) - (-160)/70. Factor 1/3*t + 0*t**y - 1/3*t**3 + 1/6 - 1/6*t**4.
-(t - 1)*(t + 1)**3/6
Let k(f) be the third derivative of 0*f**5 + 0*f**3 + 0*f**7 - 8*f**2 + 0 + 0*f - 1/84*f**8 + 1/15*f**6 - 1/6*f**4. Determine l, given that k(l) = 0.
-1, 0, 1
Let f(x) be the second derivative of x**6/30 - 3*x**5/20 + x**4/4 - x**3/6 - 7*x. Suppose f(s) = 0. What is s?
0, 1
Let k(i) = i**2 + 4*i - 55. Let t be k(-10). Suppose -864/7*f**3 + 32/7 + 624/7*f**2 - 162/7*f**t - 32*f +