 1)/3
Suppose 13 = 3*t + 2*s, 4*t + 3*s - 9 = 9. Suppose 3*j**t - 6*j**3 + 5*j**4 - 5*j**4 + 3*j**4 + 3*j - 3*j**2 = 0. What is j?
-1, 0, 1
Let i(w) = 4*w**3 - 8*w**2 + 9*w - 5. Let p(h) = -6*h**3 + 12*h**2 - 14*h + 8. Let r(k) = -8*i(k) - 5*p(k). Factor r(m).
-2*m*(m - 1)**2
Let s be 0 + 5 + 1 - 4. Let q(n) be the first derivative of n - 1/2*n**4 + 1 + n**s - 1/3*n**3. Factor q(i).
-(i - 1)*(i + 1)*(2*i + 1)
Let w(c) be the third derivative of 1/24*c**4 + 0*c + 0 + 3*c**2 - 1/12*c**3 - 1/120*c**5. Solve w(o) = 0.
1
Let t(g) be the first derivative of -g**3/15 + 4*g**2/5 + 33. Factor t(n).
-n*(n - 8)/5
Let w = 21719/5 + -4321. Factor 8/5 + 48/5*r + w*r**2 + 134/5*r**3 + 18/5*r**5 + 78/5*r**4.
2*(r + 1)**3*(3*r + 2)**2/5
Let z(f) be the first derivative of -2 + 2/11*f - 1/11*f**4 - 4/33*f**3 + 1/33*f**6 + 2/55*f**5 + 1/11*f**2. Factor z(t).
2*(t - 1)**2*(t + 1)**3/11
Suppose -14*s = -10*s - 20. Let n(a) be the first derivative of 1/9*a**3 + 0*a + 1/18*a**6 - 3 - 1/12*a**4 + 0*a**2 - 1/15*a**s. Factor n(m).
m**2*(m - 1)**2*(m + 1)/3
Solve 2*q**2 - 3*q**2 + 2*q**2 + 4*q + 3*q**2 = 0 for q.
-1, 0
Let r(p) be the first derivative of 2/3*p**3 + 1/5*p**5 + 0*p**2 + 0*p + 3/4*p**4 + 4. Let r(x) = 0. What is x?
-2, -1, 0
Let y(k) = k**2 - 2*k - 3. Let z be y(-2). Factor -z*u + 4*u - 2*u**2 - u.
-2*u*(u + 1)
Let s(p) = -13*p**2 - 16*p - 3. Let z(l) = -7*l**2 - 8*l - 1. Let h(q) = 3*s(q) - 5*z(q). Find k such that h(k) = 0.
-1
Let q = 19 + -14. Factor -13*c + 5*c**5 + 4 + 11*c**q + 28*c**4 - 32*c**2 - 8*c**3 + 5*c.
4*(c - 1)*(c + 1)**3*(4*c - 1)
Let y = -43 - -45. Let o(s) be the second derivative of 0*s**3 - 2*s - 1/30*s**4 + 0 + 0*s**y. Let o(u) = 0. Calculate u.
0
Let f(c) be the first derivative of -c**6/45 - c**5/30 + c**4/9 - 4*c - 8. Let i(l) be the first derivative of f(l). Factor i(z).
-2*z**2*(z - 1)*(z + 2)/3
Let w be (-7 - 371/(-49)) + 0. Find r such that -37/7*r**2 + 20/7*r - w + 30/7*r**3 - 9/7*r**4 = 0.
2/3, 1
Let n(m) be the third derivative of -1/24*m**4 + 0*m**3 + 0 - 1/60*m**5 - 6*m**2 + 0*m. Solve n(r) = 0 for r.
-1, 0
Factor 1/10*h**2 - 3/10 + 1/5*h.
(h - 1)*(h + 3)/10
Let i(v) = -v**5 - v**4 + v**3 - v - 1. Let u be (-3 - 3)*(-2)/(-2). Let b(a) = -4*a**5 - 2*a**4 + 8*a**3 - 6*a - 6. Let q(t) = u*i(t) + b(t). Factor q(k).
2*k**3*(k + 1)**2
Let n(r) be the first derivative of -7*r**4/24 - 5*r**3/3 - 29*r**2/12 - r + 15. Suppose n(m) = 0. Calculate m.
-3, -1, -2/7
Suppose 32 = -3*b + 8. Let u = b - -12. What is k in -k**4 + 8*k**3 - 2*k**4 + 12*k**2 + 8*k + 5*k**u + 2 = 0?
-1
Let w(k) = k**2 + 5*k - 48. Let o be w(5). Factor 4/9 - 14/3*b**o + 2/9*b.
-2*(3*b - 1)*(7*b + 2)/9
Factor f + 4*f**2 - 2*f**3 - 4*f**4 - 4*f**5 + 6*f**3 - f.
-4*f**2*(f - 1)*(f + 1)**2
Let z(g) be the first derivative of -g**4/6 + 2*g**3 - 9*g**2 - g - 1. Let n(j) be the first derivative of z(j). Factor n(p).
-2*(p - 3)**2
Let 2/9*q**3 + 0 + 2/9*q**4 + 0*q - 4/9*q**2 = 0. Calculate q.
-2, 0, 1
Factor -2/5*c**2 + 0 + 1/5*c + 1/5*c**3.
c*(c - 1)**2/5
Suppose 0*h + 4*l = -3*h + 11, 4*h + 2*l - 18 = 0. Let z = 2 + 0. Suppose 2*m**4 + m**3 - 4*m**h + 0*m**2 - 2*m**z + 3*m**3 = 0. What is m?
-1, 0, 1/2, 1
Let f = -2163/29 + 235627/3219. Let i = -2/37 - f. Factor -i*m + 4/3 + 1/3*m**2.
(m - 2)**2/3
Let x(k) be the second derivative of k**6/30 + k**5/10 + k**4/12 - 3*k. Suppose x(z) = 0. Calculate z.
-1, 0
Let m(f) be the third derivative of -f**7/210 + f**6/40 - f**4/6 + 10*f**2. Factor m(n).
-n*(n - 2)**2*(n + 1)
Let f(w) be the third derivative of -w**8/16800 + w**4/24 + 2*w**2. Let n(q) be the second derivative of f(q). Suppose n(d) = 0. What is d?
0
Let l be (6/(-44))/(-6 - 3/1). Let b(o) be the second derivative of l*o**4 - 1/110*o**5 + 2/33*o**3 + 3*o + 0*o**2 + 0. Determine g, given that b(g) = 0.
-1, 0, 2
Let a(w) be the third derivative of w**6/320 - w**5/80 - 7*w**4/64 - w**3/4 + 10*w**2. Factor a(g).
3*(g - 4)*(g + 1)**2/8
Factor -2/15*l**4 - 8/15*l**3 - 2/15 - 8/15*l - 4/5*l**2.
-2*(l + 1)**4/15
Let s(y) be the second derivative of 3*y**5/20 + y**4/4 - y**3 - 5*y. Suppose s(u) = 0. Calculate u.
-2, 0, 1
Let w(r) be the first derivative of -r**7/420 - r**6/80 - r**5/40 - r**4/48 - r**2/2 + 4. Let n(d) be the second derivative of w(d). Factor n(v).
-v*(v + 1)**3/2
Let g be ((-6)/6)/((-28)/16). Factor -g + 2*r**2 - 10/7*r.
2*(r - 1)*(7*r + 2)/7
Let i(z) be the second derivative of z**4/30 + 2*z**3/15 - 3*z**2/5 + 44*z. Factor i(g).
2*(g - 1)*(g + 3)/5
Let w(f) = 6*f**3 + 18*f**2 - 6*f - 9. Let p(m) = m**3 + m**2 - 1. Let j(l) = 9*p(l) - w(l). Find i, given that j(i) = 0.
0, 1, 2
Let k(j) be the second derivative of j**7/21 + j**6/9 - j**5/15 - j**4/3 - j**3/9 + j**2/3 - 6*j. Determine t so that k(t) = 0.
-1, 1/3, 1
Let l(g) be the third derivative of -23/630*g**7 + 2*g**2 + 0*g + 1/18*g**6 + 1/144*g**8 + 0 + 0*g**4 + 0*g**3 - 1/45*g**5. Suppose l(b) = 0. What is b?
0, 2/7, 1, 2
Let n be ((-63)/(-5) - 4) + -5 + 2. Factor 8/5 - 12/5*b - 48/5*b**2 - n*b**3.
-4*(b + 1)**2*(7*b - 2)/5
Suppose 5*t = -38 + 13, t - 30 = 5*a. Let g(y) = y**2 + 7*y + 3. Let l be g(a). Factor -23*d**4 + 6*d**2 - d**3 - 4*d - 16*d**5 + l*d - d**4.
-d*(d + 1)**2*(4*d - 1)**2
Let v(i) be the first derivative of i**3/4 - i**2/4 - i/4 + 12. Determine z so that v(z) = 0.
-1/3, 1
Let r = 11 + -11. Let j(f) = f**3 - f. Let d be j(1). Solve -6/5*u**4 + d + 2/5*u**2 + r*u - 4/5*u**3 = 0.
-1, 0, 1/3
Let c(w) be the third derivative of -w**4/24 + 5*w**3/2 - w**2. Let i be c(12). Factor 4*k**2 - 3*k**2 + k**2 + 2*k**i - 4*k**2.
2*k**2*(k - 1)
Let v(m) = 5 - m**2 - 4 + 2*m**2. Let f be v(1). Factor 1/4*q - 1/4*q**4 + 0 + 1/4*q**f - 1/4*q**3.
-q*(q - 1)*(q + 1)**2/4
Let g(a) be the third derivative of a**5/90 + 7*a**4/36 + 2*a**3/3 - 28*a**2. Factor g(n).
2*(n + 1)*(n + 6)/3
Suppose -4*o - 5*d + 18 = -0*d, o - 3*d = -4. Factor 1/2 + 1/2*f**o + f.
(f + 1)**2/2
Let o(r) be the second derivative of -r**5/80 + 11*r**4/48 - 19*r**3/24 + 9*r**2/8 - 33*r. Factor o(n).
-(n - 9)*(n - 1)**2/4
Find x such that 32/5*x**3 + 512/5*x - 512/5 - 2/5*x**4 - 192/5*x**2 = 0.
4
Let p(i) be the first derivative of i**5/10 - i**3/3 - 2*i - 1. Let y(s) be the first derivative of p(s). Suppose y(z) = 0. Calculate z.
-1, 0, 1
Let u(q) be the third derivative of -5*q**8/336 - q**7/42 + q**6/24 + q**5/12 - 21*q**2. Factor u(v).
-5*v**2*(v - 1)*(v + 1)**2
Let l(w) = w**2 + w + 1. Let y(a) = -4*a**2 - 9*a - 5. Let d(i) = -l(i) - y(i). Factor d(r).
(r + 2)*(3*r + 2)
Suppose 2/5*a**5 + 0 - 2/3*a**4 + 0*a + 4/15*a**3 + 0*a**2 = 0. Calculate a.
0, 2/3, 1
Suppose 8 = -2*u - 4*t, -5 = -2*u - 3*u - 5*t. Let i(f) = -4*f**3 + f. Let q(y) = -17*y**3 - y**2 + 5*y. Let r(b) = u*q(b) - 26*i(b). Factor r(n).
2*n*(n - 2)*(n - 1)
Let w(g) be the third derivative of -g**7/315 - g**6/45 - g**5/30 + g**4/9 + 4*g**3/9 - 4*g**2. Find a such that w(a) = 0.
-2, -1, 1
Let p(r) be the third derivative of -1/6*r**3 + 0 - 1/210*r**7 + 0*r + 2*r**2 + 0*r**4 + 1/30*r**5 + 0*r**6. Suppose p(u) = 0. Calculate u.
-1, 1
Let c(d) = -3*d**5 + 9*d**4 - 9*d**3 - 3*d**2 + 2*d + 9. Let n(v) = -v**5 + 4*v**4 - 4*v**3 - 2*v**2 + v + 4. Let t(a) = -2*c(a) + 5*n(a). Factor t(h).
(h - 1)**2*(h + 1)**2*(h + 2)
Let m(f) be the third derivative of f**8/6720 - f**7/420 + f**6/80 + 7*f**4/24 - 5*f**2. Let t(w) be the second derivative of m(w). Let t(k) = 0. Calculate k.
0, 3
Let m(l) be the second derivative of 1/42*l**4 - 1/105*l**6 + 0 + 0*l**2 + 1/42*l**3 - l + 0*l**5 - 1/294*l**7. Factor m(q).
-q*(q - 1)*(q + 1)**3/7
Suppose -6*g = -14 - 16. Let t**3 - 18*t + 12*t - 3 + g*t**3 + 3*t**4 = 0. What is t?
-1, 1
Let z be (-1)/(-1) - 21/35. Solve 4/5*v - 2/5 - z*v**2 = 0.
1
Let j(x) be the second derivative of x**6/40 - x**5/20 + x**4/24 - x**3/3 - 3*x. Let g(s) be the second derivative of j(s). Factor g(m).
(3*m - 1)**2
Suppose 18/5*y**3 - 8*y - 16/5 - 12/5*y**2 = 0. What is y?
-2/3, 2
Suppose 50*c - 52*c = 0. Factor 2/3*q**2 + 4/3*q - 2/3*q**4 - 4/3*q**3 + c.
-2*q*(q - 1)*(q + 1)*(q + 2)/3
Let q = 890/663 - 2/221. Let z be 2 - 28/33 - (-12)/66. Factor -q*j - j**2 + z.
-(j + 2)*(3*j - 2)/3
Suppose 2*f - 3*x - 16 = 0, -f - 4*f - x = -6. Factor t**f + 4*t - 4*t**2 - 2*t**2 + 6 + 3*t**2.
-2*(t - 3)*(t + 1)
Let y = 9 + -7. Suppose 0 = 5*s - 12 + y. Solve -2*m**s + 0 - m**2 + m**2 