1
Let n(i) = -79*i**2. Let d be n(-3). Let w = -4961/7 - d. Find o, given that 6/7*o**4 + 34/7*o**3 - w*o - 2*o**2 - 18/7*o**5 + 8/7 = 0.
-1, 2/3, 1
Let a(o) be the second derivative of o**4/22 + 5*o**3/33 - 2*o**2/11 - 14*o. Factor a(m).
2*(m + 2)*(3*m - 1)/11
Let a = 1/326 + 161/652. Solve -1/4*i**4 + 0 + 1/4*i**3 + 0*i - a*i**5 + 1/4*i**2 = 0 for i.
-1, 0, 1
Let -47*b**2 + 122*b**2 + 5*b**3 - 5*b**4 + 10 - 60*b**2 - 25*b = 0. Calculate b.
-2, 1
Let k = -60 + 60. Let -2/11*b**3 + 0 + k*b**2 + 0*b = 0. What is b?
0
Let w(x) be the first derivative of x**6/2 - 3*x**5/5 + 25. Factor w(r).
3*r**4*(r - 1)
Factor -2/3*s**2 + 4/3*s - 2/3.
-2*(s - 1)**2/3
Let l(d) = 8*d**2 - 5*d + 3. Let f(c) be the second derivative of -7*c**4/12 + 5*c**3/6 - c**2 + 3*c. Let m(v) = 5*f(v) + 4*l(v). Suppose m(u) = 0. What is u?
-1/3, 2
Factor -8 + 8*s**2 - 4*s**3 + 0*s + 3*s - s + 2*s.
-4*(s - 2)*(s - 1)*(s + 1)
Let u(n) = 2*n**2 + 4*n - 1. Let v be u(-3). Let g(c) = c**3 + 4*c**2 - 4*c - 13. Let f be g(-4). Factor 1/3*y**v + 1/3*y + 0*y**4 + 0 - 2/3*y**f + 0*y**2.
y*(y - 1)**2*(y + 1)**2/3
Let z(p) = p**2 - 17*p + 32. Let y be z(15). Let u(n) be the first derivative of -1/4*n**4 + 0*n**2 - y - 1/9*n**3 + 0*n. Factor u(t).
-t**2*(3*t + 1)/3
Suppose 0 = 5*d + 3*f - 27, 22 = 4*d + 2*f + 2. Let c(i) be the first derivative of -1/6*i**d - 1/4*i**2 - 3 + 0*i. Factor c(a).
-a*(a + 1)/2
Factor 3*d**4 - 7*d - 5*d - 28*d**2 - 7*d**4 - 20*d**3.
-4*d*(d + 1)**2*(d + 3)
Let o(i) be the third derivative of i**5/30 + i**4/12 + 7*i**2. Let o(p) = 0. Calculate p.
-1, 0
Let q be (-4)/6 - 56/(-12). Factor -5*x**3 + x**4 + 5*x**q + 2*x**3.
3*x**3*(2*x - 1)
Let r(b) be the first derivative of 2*b**3/27 + 2*b**2/9 - 2. Determine p so that r(p) = 0.
-2, 0
Let w = -42 + 1261/30. Let a(v) be the third derivative of 0 - 1/18*v**4 + 0*v + w*v**5 + 1/630*v**7 + 2*v**2 - 1/90*v**6 + 1/18*v**3. Factor a(d).
(d - 1)**4/3
Suppose 0 = -4*b + 5*b. Determine f so that 6*f**4 + b*f**3 + 2*f**4 - 2*f**3 - 6*f**5 = 0.
0, 1/3, 1
Let t(n) be the second derivative of 9*n**7/14 + n**6/5 - 81*n**5/20 - 6*n**4 - 2*n**3 - 10*n. Solve t(m) = 0.
-1, -2/9, 0, 2
Let d(y) be the first derivative of 0*y**2 + 3/10*y**5 + 1/6*y**3 - 7 + 3/8*y**4 + 1/12*y**6 + 0*y. Factor d(l).
l**2*(l + 1)**3/2
Let g(s) = -s**2 - 4*s - 5. Let c = -1 + 6. Let m(y) = -3*y**2 + 4 - 5*y - 2 - 8 + 2*y**2. Let r(d) = c*m(d) - 6*g(d). Suppose r(a) = 0. Calculate a.
0, 1
Suppose 35*w - 58 - 12 = 0. Determine u, given that -5/2*u + 1 - 1/2*u**3 + w*u**2 = 0.
1, 2
Let i(w) = 3*w**4 - 2*w**3 - 3*w**2 + 4*w + 2. Let k(v) = 13*v**4 - 9*v**3 - 12*v**2 + 17*v + 9. Let n(p) = -9*i(p) + 2*k(p). Determine t so that n(t) = 0.
-2, 0, 1
Suppose -5*g + g = 864. Let d = -640/3 - g. Factor -20/3*f - 6*f**2 - 1/3*f**4 - d - 7/3*f**3.
-(f + 1)*(f + 2)**3/3
Let f(m) = -8*m**2 + 21*m - 13. Let p(w) = 4*w**2 - 10*w + 6. Let s(k) = 2*f(k) + 5*p(k). Let s(h) = 0. What is h?
1
Let l(k) be the third derivative of k**6/8 + k**5/10 - 15*k**2. Factor l(m).
3*m**2*(5*m + 2)
Let y(x) be the first derivative of -x**6/1440 + x**5/120 - x**4/24 + 4*x**3/3 - 7. Let t(l) be the third derivative of y(l). Find q, given that t(q) = 0.
2
Suppose 4*n + 3 - 55 = 0. Let b = -8 + n. Factor 2/5*g**b + 0*g**2 + 0*g**4 - 2/5*g**3 + 0 + 0*g.
2*g**3*(g - 1)*(g + 1)/5
Let p(x) = -4*x**2 + 3*x + 5. Let k be p(6). Let t = -477/4 - k. Factor 1/2 + 5/4*u**2 - t*u.
(u - 1)*(5*u - 2)/4
Suppose -3*x = x. Suppose x = 3*l - 6*l. Suppose 1/2*s**2 + l + 3/4*s**3 + 1/4*s**4 + 0*s = 0. What is s?
-2, -1, 0
Determine s so that 8*s**4 + 0 + 2*s**3 + 2*s - 20/3*s**2 - 8/3*s**5 = 0.
-1, 0, 1/2, 3
Let k(f) be the first derivative of -1/18*f**4 - 3*f**2 + 2/3*f**3 + 6*f + 6. Solve k(j) = 0 for j.
3
Let k be (2/(-3))/((-2)/4). Suppose 0 = -4*f - 3*f + 28. Factor k*j + 0 - 10/3*j**f - 2/3*j**2 - 16/3*j**3.
-2*j*(j + 1)**2*(5*j - 2)/3
Suppose s = 4*g - 1, -22 = 5*s - 17. What is i in i - 2/3 + g*i**2 - 1/3*i**3 = 0?
-2, 1
Let l(o) = -o**3 + 12*o**2 + 5. Let u be l(12). Let s(x) be the third derivative of 1/30*x**u - 1/6*x**4 + 0 + 0*x + 1/3*x**3 - 2*x**2. Factor s(g).
2*(g - 1)**2
Let l be 90/375*(-20)/(-12). Factor 0 + 2/5*u**2 - l*u**3 + 0*u.
-2*u**2*(u - 1)/5
Let d(u) be the third derivative of u**7/840 - u**6/96 + 7*u**5/240 - u**4/32 - 14*u**2. Let d(z) = 0. What is z?
0, 1, 3
Let f(q) be the first derivative of -q**4/22 + 4*q**3/33 - q**2/11 + 6. Factor f(n).
-2*n*(n - 1)**2/11
Let o(c) be the second derivative of -3*c**5/20 + c**4/4 + c**3/2 - 3*c**2/2 + 4*c. Factor o(s).
-3*(s - 1)**2*(s + 1)
Factor 25 + 1/4*o**2 - 5*o.
(o - 10)**2/4
Find p such that -2*p**4 + p**5 - 6*p**5 + 5*p**4 + 2*p**5 = 0.
0, 1
Let t(g) be the second derivative of -g**7/63 + 2*g**6/45 + g**5/15 - 4*g**4/9 + 7*g**3/9 - 2*g**2/3 - 5*g. Factor t(p).
-2*(p - 1)**4*(p + 2)/3
Let x(d) = 1 + 7*d + 2*d - 8*d. Let h(f) = f**2 + 6*f + 15. Let z(v) = 4*h(v) - 44*x(v). Let z(k) = 0. What is k?
1, 4
Let l(j) = 2*j**2 + 11*j + 7. Let a be l(-5). Suppose 1/3*x**a + 0 - 2/3*x = 0. What is x?
0, 2
Let f be (((-4)/(-2))/4)/((-7)/(-42)). Let x(p) be the third derivative of -3*p**2 + 1/180*p**5 + 1/72*p**4 + 0 + 0*p - 1/9*p**f. Find h, given that x(h) = 0.
-2, 1
Let g(u) = 3*u**2 - 7*u. Suppose -3*l + 11 = -13. Let z(s) = 5*s**2 - 11*s. Let p(k) = l*g(k) - 5*z(k). Let p(w) = 0. What is w?
-1, 0
Let -2/7*c**2 + 2/7*c + 4/7 = 0. What is c?
-1, 2
Let r(h) be the third derivative of 7*h**6/120 + h**5/30 - 7*h**4/24 - h**3/3 - h**2. Factor r(v).
(v - 1)*(v + 1)*(7*v + 2)
Suppose 2*d = -0*d - 2*u, 4*d + u = 12. Suppose -b = -d*b. Factor 0 + b*a - 2/7*a**4 - 4/7*a**3 - 2/7*a**2.
-2*a**2*(a + 1)**2/7
Let s = 715 + -6427/9. Solve -s*z - 2/9*z**3 + 0 - 8/9*z**2 = 0 for z.
-2, 0
Let z(r) be the first derivative of -3*r**7/980 - r**6/84 - r**5/60 - r**4/84 + 2*r**3/3 + 2. Let g(j) be the third derivative of z(j). Factor g(l).
-2*(l + 1)*(3*l + 1)**2/7
Suppose 0 = 3*g + 3*k, 0 = 4*g + 2*k - 0*k - 4. Factor -2*h**2 + 0*h + g - 5*h + 5*h.
-2*(h - 1)*(h + 1)
Let t(a) be the second derivative of -a**5/25 + a**4/20 + 5*a**3/6 + 3*a**2/5 + a + 3. Factor t(g).
-(g - 3)*(g + 2)*(4*g + 1)/5
Let m(r) be the first derivative of r**9/4032 - 3*r**7/1120 + r**6/240 - 4*r**3/3 + 2. Let j(p) be the third derivative of m(p). Let j(q) = 0. Calculate q.
-2, 0, 1
Let h(i) be the first derivative of 9/2*i**4 + 0*i - 1 + 4/9*i**2 - 8/3*i**3. Let h(q) = 0. What is q?
0, 2/9
Let w(v) be the second derivative of v**5/100 + v**4/60 - v**3/15 - 7*v. Solve w(h) = 0 for h.
-2, 0, 1
Let v be (-96)/(-10) + (-18)/(-45). Factor -7*x**4 + x + 3*x**3 + v*x**4 - x.
3*x**3*(x + 1)
Let n(v) be the second derivative of -3*v - 4/11*v**2 - 1/165*v**6 - 1/55*v**5 + 0 + 4/33*v**3 + 1/22*v**4. Solve n(g) = 0.
-2, 1
Suppose -3 = -2*m - i, -3*m + 5*m - 4 = -2*i. Let k = m + 1. Find t such that -2*t**k + 3*t**2 - 2*t**3 - 2*t + 3*t = 0.
-1/2, 0, 1
Let u(i) be the third derivative of -i**8/420 - 2*i**7/105 - i**6/15 - 2*i**5/15 - i**4/6 - 2*i**3/15 + 38*i**2. Factor u(r).
-4*(r + 1)**5/5
Let d be 1 + (2 - (2 + -2)). Factor b**2 - b + d*b**2 - 4*b + 2 - b**3.
-(b - 2)*(b - 1)**2
Let h(b) be the first derivative of -5*b**6/3 - 46*b**5/5 - 35*b**4/2 - 34*b**3/3 + 4*b**2 + 8*b + 3. What is k in h(k) = 0?
-2, -1, 2/5
Let z be 20/6 - 12/(-18). Let t(b) be the second derivative of 0 + 2/7*b**2 + 1/7*b**3 - b + 1/42*b**z. Solve t(k) = 0.
-2, -1
Suppose 5*b = 3*r + 2*r - 40, -4*r = 4*b - 48. Let l be (-63)/(-15) - 2/r. Factor t**3 + l - 6*t - 3*t**3 + 4*t**3.
2*(t - 1)**2*(t + 2)
Suppose w + 27 = 6*w + 2*y, 0 = -3*w - 3*y + 9. Let p(a) = a - 5. Let n be p(w). Factor -7*q + 4*q + 4*q**2 - 18*q**n - q.
-2*q*(7*q + 2)
Let q(d) be the third derivative of 5*d**2 - 3/200*d**6 + 0 + 0*d + 1/40*d**4 - 1/5*d**3 + 1/25*d**5. Factor q(a).
-3*(a - 1)**2*(3*a + 2)/5
Factor 0 - 2/3*a**4 + 2*a**3 + 2/3*a - 2*a**2.
-2*a*(a - 1)**3/3
Let q(g) be the first derivative of g**6/60 + g**5/20 - g**3/6 - g**2/4 - 2*g + 5. Let b(j) be the first derivative of q(j). Determine n so that b(n) = 0.
-1, 1
Let q(s) be the third derivative of -s**5/20 + 3*s**4/8 - s**3 + 9*s**2. Solve q(p) = 0 for p.
1, 2
Let c(p) = -p + 1. Let z be c(-2). Suppose -2*y + 19 = z*m, -y = m - 3*m + 1. Factor -2*r + 3 + 0 - m*r**2 + 2*r.
-3*(r - 1)*(r + 1)
Let q(c) 