 + m*y + 2*y**2 + 3.
2*y*(y + 2)
Let j(r) be the first derivative of 4/5*r**5 + 32/3*r**3 - 5 + 0*r + 5*r**4 + 8*r**2. Factor j(y).
4*y*(y + 1)*(y + 2)**2
Let g(q) = -q**4. Let u(t) = -2*t**4 - 4*t**3 - 4*t**2 + 4*t. Let f(i) = 6*g(i) - u(i). Find o, given that f(o) = 0.
-1, 0, 1
Let n = 38381/4605 - 2/1535. Let a = n - 23/3. Find y such that -4*y**3 + 2*y - a*y**4 + 2*y**5 + 4/3*y**2 - 2/3 = 0.
-1, 1/3, 1
Let m(d) be the third derivative of -d**8/1440 - 19*d**7/3780 - d**6/135 + d**5/45 - d**4/12 - 2*d**2. Let o(a) be the second derivative of m(a). Factor o(i).
-2*(i + 1)*(i + 2)*(7*i - 2)/3
Let v(n) = -3*n**2 + 6*n + 5. Let c(j) = 2*j**2 - 5*j - 4. Let b(f) = 4*c(f) + 3*v(f). Let b(k) = 0. Calculate k.
-1
Let u = 39 - 39. Factor -2/7*f**4 + 12/7*f**3 + 16/7*f - 24/7*f**2 + u.
-2*f*(f - 2)**3/7
Let b(u) = -u**3 - 4*u**2 + u. Let r(l) = 2*l**3 + 11*l**2 - 2*l. Let z(y) = 11*b(y) + 4*r(y). Factor z(w).
-3*w*(w - 1)*(w + 1)
Factor -6/19*n + 2/19*n**2 + 4/19.
2*(n - 2)*(n - 1)/19
Suppose -20/9*t**2 - 10/9*t**5 - 8/9*t**3 + 2*t - 4/9 + 8/3*t**4 = 0. What is t?
-1, 2/5, 1
Suppose 2*m - 8 = 3*u, 0 = -2*m - 0*u + u. Let w be 3/(-2)*4/m. Factor 1/4*r**w + 0 + 1/2*r - 3/4*r**2.
r*(r - 2)*(r - 1)/4
Let x(t) be the second derivative of -t**7/1960 + t**6/420 - t**5/280 + t**3/3 + 4*t. Let c(r) be the second derivative of x(r). Factor c(q).
-3*q*(q - 1)**2/7
Let g(t) be the first derivative of t**7/4620 + t**6/990 + t**5/660 + 2*t**3/3 - 5. Let n(w) be the third derivative of g(w). What is a in n(a) = 0?
-1, 0
Suppose -2*t = -81 + 27. Suppose 5*x = -0*x + a + t, -x - 5*a = 5. What is c in -4*c + 9*c**3 - 3*c**3 - 6*c**2 + 22*c**4 - 8*c**4 + 6*c**x = 0?
-1, 0, 2/3
Let d(k) be the third derivative of 5*k**8/336 - k**7/21 + k**5/6 - 5*k**4/24 + 16*k**2. Let d(p) = 0. Calculate p.
-1, 0, 1
Factor 0*l + 6*l - 4*l - l**2.
-l*(l - 2)
Factor 6/7 - 33/7*q + 27/7*q**2.
3*(q - 1)*(9*q - 2)/7
Let t(q) be the second derivative of q**7/7 + 29*q**6/15 + 89*q**5/10 + 29*q**4/2 + 8*q**3/3 - 16*q**2 - 8*q - 1. Solve t(w) = 0 for w.
-4, -1, 1/3
Let a(o) be the second derivative of 1/2*o**2 - 1/2*o**3 + 1/10*o**5 + 1/6*o**4 - 5*o - 1/10*o**6 + 1/42*o**7 + 0. What is c in a(c) = 0?
-1, 1
Let l(z) be the first derivative of -2/3*z**2 - 4 - 2/9*z**3 + 0*z + 1/6*z**4. Factor l(t).
2*t*(t - 2)*(t + 1)/3
Let x(g) be the first derivative of -g**5/5 - g**4/4 - g**3/12 - 5. Suppose x(z) = 0. What is z?
-1/2, 0
Let f(b) be the second derivative of b**10/120960 + b**9/60480 - b**8/26880 - b**7/10080 - b**4/12 - b. Let y(q) be the third derivative of f(q). Factor y(c).
c**2*(c - 1)*(c + 1)**2/4
Suppose -3*x = -v + 13, 19 - 3 = -4*x. Suppose 4*b + 6 = 18. Find u such that v - b*u**3 - 4*u**2 - 1 - u = 0.
-1, -1/3, 0
Let y(b) = -9*b**3 + 28*b**2 - 69*b + 53. Let t(d) = 10*d**3 - 28*d**2 + 70*d - 54. Let m(n) = 5*t(n) + 6*y(n). Solve m(g) = 0 for g.
2, 3
Let a(w) be the second derivative of -1/300*w**6 - 1/300*w**5 + 1/30*w**4 + 2*w + 0 + 1/3*w**3 + 0*w**2. Let h(m) be the second derivative of a(m). Factor h(c).
-2*(c + 1)*(3*c - 2)/5
Factor 1/2*i**2 + 1/6*i**5 - 1/2*i**4 + 0 + 1/6*i**3 - 1/3*i.
i*(i - 2)*(i - 1)**2*(i + 1)/6
Factor 0*r + 2/19*r**4 - 4/19*r**3 + 0 + 2/19*r**2.
2*r**2*(r - 1)**2/19
Let d = -3 + -4. Let c be 16/28 - 10/d. Factor 4/7*i**3 + 0*i**c - 2/7*i**4 + 2/7 - 4/7*i.
-2*(i - 1)**3*(i + 1)/7
Let o be -1*0*(2 + -1). Let a(n) be the second derivative of -2*n + 0 + o*n**3 + 1/8*n**2 - 1/48*n**4. Factor a(y).
-(y - 1)*(y + 1)/4
Factor 4/7*v**3 + 0*v**2 + 6/7*v**5 + 0*v + 10/7*v**4 + 0.
2*v**3*(v + 1)*(3*v + 2)/7
Let j(b) be the third derivative of b**7/42 + b**6/24 - b**5/12 - 5*b**4/24 + 2*b**2. Find y, given that j(y) = 0.
-1, 0, 1
Let z be (16/(-12))/((-4)/6). Let x(t) be the second derivative of 0 + 8/3*t**3 - 4*t**2 - 1/2*t**4 + z*t. Factor x(r).
-2*(r - 2)*(3*r - 2)
Let m(f) be the second derivative of -1/90*f**5 + f + 0 - 4/9*f**3 + f**2 + 1/9*f**4. Let k(o) be the first derivative of m(o). Suppose k(v) = 0. Calculate v.
2
Let j(y) be the third derivative of -y**6/210 + y**5/35 - y**4/14 + 2*y**3/21 + 3*y**2. Factor j(i).
-4*(i - 1)**3/7
Factor 7/2*b - b**2 - 3*b**3 + 5/2*b**4 - 3/2 - 1/2*b**5.
-(b - 3)*(b - 1)**3*(b + 1)/2
Let y = 137/21 + -16433/2520. Let c(i) be the third derivative of 0*i + y*i**6 - 1/60*i**5 + 1/36*i**4 + 0*i**3 - i**2 + 0. Factor c(x).
x*(x - 2)*(x - 1)/3
Let i(a) be the first derivative of -a**6/35 + a**5/14 - a**4/21 - 6*a - 1. Let t(w) be the first derivative of i(w). Factor t(k).
-2*k**2*(k - 1)*(3*k - 2)/7
Factor 2/11*f**3 - 2/11*f + 2/11*f**2 - 2/11.
2*(f - 1)*(f + 1)**2/11
Let q = -31 + 1. Let p = q + 63/2. Factor -3/2*z**4 - 1/2*z + 0 + 1/2*z**3 + p*z**2.
-z*(z - 1)*(z + 1)*(3*z - 1)/2
Let b = -909 - -4547/5. Suppose -4/5*c**2 + 6/5*c**4 - 4/5*c**3 + 6/5*c - b - 2/5*c**5 = 0. Calculate c.
-1, 1
Let y(a) be the second derivative of -a**3 - 3*a - 3/2*a**2 + 0 - 1/4*a**4. Factor y(i).
-3*(i + 1)**2
Let t(m) be the first derivative of 49*m**5/30 + 7*m**4/3 + 4*m**3/3 + 2*m**2 - 1. Let o(x) be the second derivative of t(x). Factor o(r).
2*(7*r + 2)**2
Let i(y) = -y**2 - 11*y + 2. Let d be i(-7). Let g be 36/(-63) + d/28. Factor p**2 + 0 - g*p.
p*(2*p - 1)/2
Let g(m) be the third derivative of m**7/210 + m**6/180 - 7*m**5/480 + m**4/96 - m**3/6 + m**2. Let k(c) be the first derivative of g(c). Factor k(o).
(o + 1)*(4*o - 1)**2/4
Let m(a) be the first derivative of -a**4/28 - a**3/21 + 43. What is w in m(w) = 0?
-1, 0
Let j be (14/21)/(2/6). Let l(x) be the first derivative of 11/3*x**3 + 5*x**4 - 2/5*x**j - 4/5*x - 1. Factor l(v).
(4*v - 1)*(5*v + 2)**2/5
Let j be (-243)/66 - 6/(-4). Let t = -50/33 - j. Suppose 0 - t*o + 5/3*o**4 - 5/3*o**2 + 2/3*o**3 = 0. Calculate o.
-1, -2/5, 0, 1
Let p(n) = -3*n**2 - 3*n. Let m(o) = 4*o**2 + 4*o. Let y(d) = -d**2 + 7*d + 2. Let t be y(8). Let u be (-30)/(-9)*t/5. Let i(r) = u*m(r) - 5*p(r). Factor i(b).
-b*(b + 1)
Let x = 2/477 - -2852/2385. Let g be 4/5 + (2 - (1 - -1)). Solve x*u**4 + 0 - 6/5*u**2 - 2/5*u**3 + g*u**5 - 2/5*u = 0 for u.
-1, -1/2, 0, 1
Let r(f) be the second derivative of f**8/6720 - f**7/630 + f**6/144 - f**5/60 + f**4/6 + 2*f. Let s(b) be the third derivative of r(b). Factor s(x).
(x - 2)*(x - 1)**2
Let r(z) = 5*z**4 - 6*z**3 - 13*z**2 + 5*z. Let d(b) = b**4 - b**2 + b. Let l(i) = -14*d(i) + 2*r(i). Let l(f) = 0. What is f?
-1, 0
Factor 0 - 3/4*v - 3/2*v**3 + 3/8*v**4 + 15/8*v**2.
3*v*(v - 2)*(v - 1)**2/8
Let s(a) be the first derivative of -2*a**3/33 + a**2/11 + 40. Factor s(j).
-2*j*(j - 1)/11
Let d = 6 + -9. Let i be (d/(-15))/(4/10). Factor 0*a - 1/2*a**3 + 0 - i*a**4 + 1/2*a**5 + 1/2*a**2.
a**2*(a - 1)**2*(a + 1)/2
Let l(c) be the first derivative of c**6/540 - c**5/90 + c**3/3 - 1. Let n(p) be the third derivative of l(p). Determine m so that n(m) = 0.
0, 2
Let c(j) be the first derivative of -2 + 0*j - 2/3*j**3 - 2/5*j**5 + j**4 + 0*j**2. Factor c(y).
-2*y**2*(y - 1)**2
Let d(n) = -5*n**3 - n**2 + n - 3. Suppose 2*i + 3*r = 0, -2*i + 4*i + 2*r - 4 = 0. Let w(t) = -4*t**3 - 2*t**2 - 2. Let z(m) = i*w(m) - 4*d(m). Factor z(l).
-4*l*(l + 1)**2
Let p(j) = -j**2 + 1. Let a be p(1). Factor 0 + a*t**2 + 2*t - t**2 - 6*t - 4.
-(t + 2)**2
Suppose 0 = 2*a - t + 5, -4*a - a - 2*t = 17. Let u be (-20)/12 - 9/a. Find m such that -u + m**4 + 4/3*m + 7/3*m**2 - 10/3*m**3 = 0.
-2/3, 1, 2
Let h be 10/6 + (-48)/72 - 1. Let b(t) be the first derivative of -1/18*t**6 - 2/15*t**5 - 1 + 0*t**3 + 0*t**2 - 1/12*t**4 + h*t. Factor b(m).
-m**3*(m + 1)**2/3
Suppose 3*c - 5*c = -6. Let z(j) = -j - 1. Let o(m) = m**2 - 8*m. Let i(l) = c*o(l) - 12*z(l). Factor i(q).
3*(q - 2)**2
Suppose -2/3*i**3 + 7/6*i - 1/3 - 2/3*i**2 = 0. What is i?
-2, 1/2
Let j(a) be the third derivative of -a**5/20 - 2*a**4 - 32*a**3 - 11*a**2. Suppose j(b) = 0. What is b?
-8
Let l(a) = a**3 - 10*a**2 + a - 7. Let j be l(10). Suppose 0 = 2*p + 5*b - 4, -b + 6*b + 8 = 4*p. What is o in 0*o + p*o**5 - 4*o**j - o + 3*o = 0?
-1, 0, 1
Let h = 11 - 9. Let n(q) = 2*q**2 + 2*q - 1. Let g be n(-2). Factor -2*o - h*o**g + 2*o + 4*o**4.
2*o**3*(2*o - 1)
Factor 4/5 + 2/5*s**4 - 2*s**3 + 18/5*s**2 - 14/5*s.
2*(s - 2)*(s - 1)**3/5
Let v(p) = -6*p**2 - 5*p. Let q be -1*(1 + (-21)/3). Let l(w) = -7*w**2 - 6*w. Let u(o) = q*v(o) - 5*l(o). Find d suc