lculate j.
-1, -2/5, 0
Factor 8/5 + 4/5*d**2 + 12/5*d.
4*(d + 1)*(d + 2)/5
Suppose 4*f + 4 = n, 5*f + 2 + 3 = -n. Let s(l) be the second derivative of 0*l**5 + 1/30*l**6 + 2*l + 0*l**3 - 1/6*l**4 + n + 1/2*l**2. Factor s(y).
(y - 1)**2*(y + 1)**2
Solve -1/5*w + 1/5*w**4 + 1/5*w**3 - 1/5*w**2 + 0 = 0.
-1, 0, 1
Let u = -5/9 + 61/45. Suppose -8 = d - 5*d. Factor -2/5*g**d - 2/5 - u*g.
-2*(g + 1)**2/5
Let d(c) = -9*c**2 + 63*c - 21. Let g(u) = 2*u**2 - 16*u + 5. Let j(r) = -5*d(r) - 21*g(r). Factor j(v).
3*v*(v + 7)
Let g(d) = -4*d**2 - 25*d - 3. Let y be g(-6). Factor 7/5*l**4 + 0*l + 1/5*l**2 + l**y + 0 + 3/5*l**5.
l**2*(l + 1)**2*(3*l + 1)/5
Let r(a) be the first derivative of 5 - 7*a**2 - 4*a - 16/3*a**3 - 3/2*a**4. Factor r(m).
-2*(m + 1)**2*(3*m + 2)
Let l be 2 + 0 + 128/(-66). Let u(t) be the first derivative of 1 - 1/11*t**4 + l*t**3 + 0*t + 0*t**2 + 2/55*t**5. Factor u(v).
2*v**2*(v - 1)**2/11
Suppose h = -4*p + 13, -4*p - h = -6*h - 31. Find f such that 8*f - 4*f + p*f**2 + 5*f**3 - 4*f**3 = 0.
-2, 0
Let x(k) be the second derivative of 0 + 1/18*k**4 + 3*k + k**2 - 4/9*k**3. Factor x(r).
2*(r - 3)*(r - 1)/3
Let z(s) be the first derivative of s**6/60 - s**4/12 - s**2 - 3. Let w(g) be the second derivative of z(g). Solve w(u) = 0 for u.
-1, 0, 1
Let u be (-48)/(-21) + -3 - -1. Factor -2/7 - 2/7*h**4 - 4/7*h**3 + 4/7*h**2 + 2/7*h + u*h**5.
2*(h - 1)**3*(h + 1)**2/7
Let d = 1 + 2. Suppose -3 = 2*f - d*f. Determine r, given that 2*r**3 + r**3 - 2*r**f - 4*r**4 = 0.
0, 1/4
Let q(z) be the second derivative of z**4/4 - z**3 + 3*z**2/2 + 5*z + 3. Factor q(i).
3*(i - 1)**2
Let q(r) = r**2 - r - 2. Suppose 8 = -f - 3*f. Let i(o) = -o**2 + 0 - 3 + 0 + 4. Let u(x) = f*q(x) - 4*i(x). Factor u(w).
2*w*(w + 1)
Let v be (-20)/15 + 10/3. Solve -25/4*b**3 - 1 + 4*b - 5/4*b**v = 0 for b.
-1, 2/5
Let x(n) = -3*n - 12. Let w be x(-4). Find k, given that w + 0*k**3 + 4/9*k**2 - 2/9*k + 2/9*k**5 - 4/9*k**4 = 0.
-1, 0, 1
Let h(m) be the third derivative of m**8/10080 + m**7/2520 - m**6/180 - m**5/30 - 3*m**2. Let t(k) be the third derivative of h(k). Find z such that t(z) = 0.
-2, 1
Let a(n) be the second derivative of -1/60*n**6 + 4*n + 0 + 1/24*n**4 + 0*n**2 + 1/40*n**5 - 1/12*n**3. Determine z so that a(z) = 0.
-1, 0, 1
Suppose 4*x - 4*z = 24, -3*x + 0*z = -2*z - 15. Suppose -x*k + 6*k = 6. What is d in -4*d**3 + d - 2*d**k + 6*d**4 - d - 8*d**4 = 0?
-1, 0
Let r = -21 - -23. Suppose r = -2*a + 6. Solve 0 + 0*m**4 - 2/5*m - 2/5*m**5 + 0*m**a + 4/5*m**3 = 0 for m.
-1, 0, 1
Let t(o) be the third derivative of o**7/490 - o**5/28 + 2*o**3/7 - 30*o**2. Determine b, given that t(b) = 0.
-2, -1, 1, 2
Let i(l) = -9*l**2 - 3*l. Let w(o) = -19*o**2 - 6*o - 1. Let v(x) = 13*i(x) - 6*w(x). Let v(h) = 0. What is h?
-2, 1
Suppose 3*s - 7 + 4 = 0. Solve s - 2*i**2 + 2*i + 3*i**2 + 3 - 3*i**2 = 0 for i.
-1, 2
Suppose -4*r - 2 = -3*o + 2, 5*o = -2*r + 50. Suppose 20*d = 16*d + o. Find q, given that 0 - 1/2*q**d + 1/2*q = 0.
0, 1
Factor 3*y - 2*y - 36 - 4*y**2 + 8*y + 15*y.
-4*(y - 3)**2
Determine t, given that 20*t - 1 - 21*t - 1 + t**2 = 0.
-1, 2
Let s(w) be the third derivative of 0*w - 2*w**2 + 1/5*w**5 + 1/70*w**7 - 1/10*w**6 + 0 + 0*w**3 + 0*w**4. Determine h so that s(h) = 0.
0, 2
Let a(g) be the third derivative of -2*g**2 - 1/24*g**4 - 1/120*g**6 + 0*g**3 + 1/30*g**5 + 0 + 0*g. Factor a(f).
-f*(f - 1)**2
Let t(q) be the first derivative of q**3/12 + q**2/4 - 51. Factor t(p).
p*(p + 2)/4
Let h(m) = m**2 - 4*m + 7. Suppose 0 = z + u - 4, 2 = -u + 3*u. Let x be h(z). Factor 8/7*a + 6/7*a**2 - 8/7*a**3 + 2/7*a**x - 8/7.
2*(a - 2)**2*(a - 1)*(a + 1)/7
Let v = 14596/105 - 139. Let b(h) be the third derivative of 0*h**3 + 1/210*h**6 + 2*h**2 + 0*h**4 + 0 + 0*h + 0*h**5 - v*h**7. Factor b(t).
-2*t**3*(7*t - 2)/7
Let v(b) be the second derivative of 0*b**3 - 3/2*b**2 - 4*b + 1/4*b**4 + 0. Find f such that v(f) = 0.
-1, 1
Factor 3*j**3 + 4*j**3 - j**2 - 6*j**3.
j**2*(j - 1)
Let b = -2333/5 + 467. Factor -4/5 - 2*x - b*x**3 - 8/5*x**2.
-2*(x + 1)**2*(x + 2)/5
Factor 0*p - 1/2*p**3 + 3*p**2 - 16.
-(p - 4)**2*(p + 2)/2
Suppose 4 = -2*p + 4*c, 0 = -11*p + 16*p - 5*c. Let 1/8*i**p + 0 - 1/4*i = 0. What is i?
0, 2
Let n(k) be the second derivative of 2*k**6/15 + k**5/4 - 7*k**4/12 - k**3/3 + 12*k. Factor n(o).
o*(o - 1)*(o + 2)*(4*o + 1)
Let w(k) = k - 11. Let a be w(6). Let y = a + 8. Let -4/5*o**y + 0*o**4 + 0 + 2/5*o**5 + 0*o**2 + 2/5*o = 0. What is o?
-1, 0, 1
Solve -1/3 + 0*b + 1/3*b**2 = 0.
-1, 1
Let u(c) be the third derivative of c**6/1020 + c**5/255 - 2*c**2. Solve u(l) = 0.
-2, 0
Let s(y) be the first derivative of -y**2 + 0*y - 2 + 1/3*y**3. Factor s(z).
z*(z - 2)
Suppose -3*b = -37 - 71. Let -2*p**3 + 0*p**4 + 53*p**4 - 4 - 13*p**4 + 24*p**5 - 22*p - b*p**2 = 0. Calculate p.
-1, -2/3, -1/2, 1
Let g(c) be the third derivative of c**6/480 + c**5/240 - 4*c**2. Suppose g(z) = 0. What is z?
-1, 0
Solve 2*l**3 - 12*l**2 - 1 + 3*l + 1 - 17*l = 0 for l.
-1, 0, 7
Let b(w) be the third derivative of w**6/200 - w**5/60 - w**4/30 + 2*w**3/15 - 7*w**2. Factor b(p).
(p - 2)*(p + 1)*(3*p - 2)/5
Suppose -36 = 2*o - 2*j + 14, 4*j - 122 = 5*o. Let f = 45/2 + o. Find h such that 0 + 0*h - f*h**2 + 3/4*h**3 - 1/4*h**4 = 0.
0, 1, 2
Let -4/5*i**4 - 48/5*i - 24/5*i**3 - 16/5 - 52/5*i**2 = 0. What is i?
-2, -1
Let n be 3 - 1/(-1 - -2). Suppose 0 = -n*q + 3*q - 2. Let 3*x + 2 + 1/4*x**3 + 3/2*x**q = 0. What is x?
-2
Let f(n) be the third derivative of n**7/840 + n**6/480 - n**5/80 - 5*n**4/96 - n**3/12 + 4*n**2. Find m, given that f(m) = 0.
-1, 2
Let q(x) = -x**3 - x**2 + 3*x - 3. Let w be -5 + (-1 - -1 - -2). Let z be q(w). Solve -19*c - 18*c**2 - 14 + z - 5*c = 0 for c.
-2/3
Let j(h) = h**3 - 4*h**2 - 2*h - 4. Let l be j(5). Factor x**2 + x - 5*x + 18*x - 4 - l*x**2.
-2*(x - 1)*(5*x - 2)
Find a such that 6 + 32*a**2 - 9*a**2 + a**3 + 11*a - 17*a**2 = 0.
-3, -2, -1
Let a be 14/4*((-8)/(-14))/4. Find r such that a + 3/2*r**2 - 1/2*r**3 - 3/2*r = 0.
1
Suppose 5*h = 4*n + 25, 3*n - h + 5 = -0. Find q such that 4 - 3*q + 2 + n*q - 3*q**2 = 0.
-2, 1
Factor -1 + 0 + 3*p**2 - 142*p**3 + 143*p**3 - 2 - p.
(p - 1)*(p + 1)*(p + 3)
Let l = -4843/15 - -323. Let o(a) be the first derivative of 0*a - 2 + l*a**3 - 1/10*a**2 - 1/20*a**4. Suppose o(n) = 0. What is n?
0, 1
Let p(k) be the second derivative of 0 - 1/28*k**7 + 3/4*k**2 - 3/20*k**5 - 3/20*k**6 + 1/4*k**4 - 3*k + 3/4*k**3. Factor p(y).
-3*(y - 1)*(y + 1)**4/2
Factor 14/15*s**5 + 0 + 0*s + 0*s**2 + 4/15*s**3 - 6/5*s**4.
2*s**3*(s - 1)*(7*s - 2)/15
Factor -26*h**3 - h**4 + 120*h**2 - 5*h**4 - 96*h + 10*h**3 + 3*h**5 - 20*h**3.
3*h*(h - 2)**3*(h + 4)
Let p(n) be the first derivative of -2*n**3/9 + n**2/3 + 3. Factor p(f).
-2*f*(f - 1)/3
Let o(y) = -7*y - 11. Let a be o(-2). Factor -2*x**a + 0 + 2/3*x**2 - 2/3*x**5 + 2*x**4 + 0*x.
-2*x**2*(x - 1)**3/3
Let m be (-1)/2*-6*1. Let i = m + -1. Factor -o - 2*o**i + 3 - o + 3*o**2 - 2.
(o - 1)**2
Factor -11/9*l - 2/3 - 1/9*l**3 - 2/3*l**2.
-(l + 1)*(l + 2)*(l + 3)/9
Let q(d) = -3*d - 31*d**3 + 3 + 30*d**3 - 4 + 5*d**2. Let s be q(4). Factor 12/7*o**2 + 2/7 + 2/7*o**4 - 8/7*o - 8/7*o**s.
2*(o - 1)**4/7
Let u(l) be the third derivative of -l**5/5 + 2*l**4/3 - 3*l**2. Factor u(z).
-4*z*(3*z - 4)
Suppose 3*i - 13 = -2*u + u, 0 = 2*u + 10. Suppose -13 = 4*m + 5*j, -j - i = -2*m + 5. Factor -4 + m*h**2 + 4 - 3 + 0*h**2.
3*(h - 1)*(h + 1)
Suppose 3*y**2 + 7*y - 6*y**2 + 7*y - 5*y = 0. Calculate y.
0, 3
Let r(w) = -w**3 - 7*w**2 + 4. Let x be r(-7). Let u be (-2)/(-5) - 2/(-20). Factor -3/4*o**x + 0 + 0*o + 1/4*o**3 + u*o**2.
-o**2*(o - 1)*(3*o + 2)/4
Suppose q - 5*f + 16 = 0, 0 = 4*q - 6*q - f + 12. Suppose r + 4*t = 4*r - 22, -3*t = 5*r + 2. Suppose q - m - m**r - 4 = 0. What is m?
-1, 0
Let o = 19/31 + 5/93. Determine s, given that -4/9 - 2/9*s**3 + o*s + 0*s**2 = 0.
-2, 1
Let r(n) be the second derivative of -n**5/30 + n**3/9 - n. Solve r(o) = 0.
-1, 0, 1
Let l(y) be the first derivative of -5*y**6/21 - 6*y**5/35 + y**4/7 + 30. Factor l(f).
-2*f**3*(f + 1)*(5*f - 2)/7
Let d(c) be the first derivative of c**4/10 - 4*c**3/5 + 9*c**2/5 - 8*c/5 - 4. Factor d(m).
2*(m - 4)*(m - 1)**2/5
Let i = 199/315 - 28/45. Let c(b) be the second derivative of 1/42*b**4 + 1/35*b**5 - b + 0*b**2 + i*b**6 + 0*b**3 + 0. Factor c(o