1)
Solve 2/3*q - 4/3*q**2 - 2/3*q**3 + 4/3 = 0.
-2, -1, 1
Let w(p) be the second derivative of 0*p**3 + 0 + 1/45*p**6 + 0*p**2 + 1/18*p**4 - 2*p + 1/15*p**5. Suppose w(l) = 0. Calculate l.
-1, 0
Let j be (-3 + 2)/((-1)/25). Suppose 0 = -4*c - 1 + j. Factor -2*w**3 + 0*w**2 + 0*w**2 - c*w**2 + 2*w**4 + 2*w**5 + 4*w**2.
2*w**2*(w - 1)*(w + 1)**2
Let t = 28 + -26. Suppose 0 = -t*k - 0*k + 8. Factor 0 - k*d**3 - 5/3*d**4 - 3*d**2 - 2/3*d.
-d*(d + 1)**2*(5*d + 2)/3
Let j(x) be the second derivative of x**6/30 + x**5/20 - x**4/4 - 5*x**3/6 - x**2 + x. Determine g, given that j(g) = 0.
-1, 2
Factor -20*k**2 - k + 0*k**4 + 2*k**4 + 18*k**2 + k**5.
k*(k - 1)*(k + 1)**3
What is x in 4/3*x**3 + 4*x**2 - 16/3 + 0*x = 0?
-2, 1
Factor 0 - 22/3*y**2 + 1/3*y**3 + 121/3*y.
y*(y - 11)**2/3
Let u(s) be the second derivative of -s**8/3360 - s**7/630 - s**6/360 - s**4/4 - 2*s. Let i(t) be the third derivative of u(t). Suppose i(b) = 0. Calculate b.
-1, 0
Let a(v) be the first derivative of 3/5*v**3 - 9/25*v**5 - 2 + 0*v - 3/20*v**4 - 1/10*v**6 + 3/5*v**2. Let a(o) = 0. Calculate o.
-2, -1, 0, 1
Factor 0 + 0*z**2 + 1/6*z**3 - 1/6*z.
z*(z - 1)*(z + 1)/6
Let p(z) = 2*z**4 + 3*z**3 - 6*z**2 - z + 3. Let g(b) = 8*b**4 + 13*b**3 - 24*b**2 - 3*b + 13. Let m(u) = 6*g(u) - 26*p(u). Factor m(c).
-4*c*(c - 2)*(c + 1)**2
Factor -10*q**2 - 3 + 9*q + 7*q**2 + 3.
-3*q*(q - 3)
Let x(o) be the third derivative of -o**7/7140 + o**6/1020 - o**5/340 + o**4/204 + 5*o**3/6 + 2*o**2. Let y(l) be the first derivative of x(l). Factor y(a).
-2*(a - 1)**3/17
Determine a so that 2/7*a + 0 + 12/7*a**3 + 8/7*a**2 + 2/7*a**5 + 8/7*a**4 = 0.
-1, 0
Suppose -o = -1 - 1. Factor -a**o - 2*a - 6*a + 2*a + 4*a.
-a*(a + 2)
Let x be (72/8 - 6)*2/3. Suppose 1/2*t + 1/2*t**3 + 0 + t**x = 0. Calculate t.
-1, 0
Let p(r) = r**2 + 10*r - 52. Let g be p(4). Suppose 5/2*x**g + 1/2*x**5 + 5*x**2 + 5/2*x + 1/2 + 5*x**3 = 0. Calculate x.
-1
Let j(x) be the second derivative of -9*x + 0 + 1/2*x**4 + 0*x**3 + 3/20*x**5 + 0*x**2. Factor j(q).
3*q**2*(q + 2)
Let v(j) be the third derivative of -j**6/30 + j**5/5 - j**4/3 - 2*j**2. Factor v(z).
-4*z*(z - 2)*(z - 1)
Let x be 0/(-1*(-2)/(-1)). Let x*a**3 + 2*a - 2*a**5 + 4*a**5 - 4*a**3 = 0. What is a?
-1, 0, 1
Let i(w) be the third derivative of -1/105*w**7 - 1/30*w**6 - 2*w**2 + 0*w**3 + 0 - 1/30*w**5 + 0*w + 0*w**4. Factor i(k).
-2*k**2*(k + 1)**2
Let j(n) be the first derivative of 0*n + 0*n**2 + 1 - 3/10*n**5 - n**3 - 9/8*n**4. Let j(x) = 0. What is x?
-2, -1, 0
Let x(j) be the first derivative of -j**8/2520 - j**7/1260 + j**3/3 + 1. Let f(m) be the third derivative of x(m). Suppose f(r) = 0. Calculate r.
-1, 0
Factor 25*s**3 - s**4 + 4*s**4 - 7 + 9*s - 34*s**3 + 1 + 3*s**2.
3*(s - 2)*(s - 1)**2*(s + 1)
Let p(v) be the third derivative of v**6/360 + v**5/90 + v**4/72 - 5*v**2. Factor p(x).
x*(x + 1)**2/3
Suppose 3*v - 4*b - 28 = 0, 2*v + 3*b = -2*v + 29. Factor v*y - 5*y - 3*y**2 - 6 + 6*y**2.
3*(y - 1)*(y + 2)
Suppose 6 = 4*z + n + n, 4*n - 6 = -5*z. Determine s, given that 0 - 5/2*s**4 + 17/2*s**3 + z*s - 8*s**2 = 0.
0, 2/5, 1, 2
Suppose 2*s = -3*s. Let 2/5*o**3 - 3/5*o**4 + s - 2/5*o + 3/5*o**2 = 0. Calculate o.
-1, 0, 2/3, 1
Let g be (2/(-98))/(21/(-147)). Factor 0*l**2 + 3/7*l - g*l**3 - 2/7.
-(l - 1)**2*(l + 2)/7
Let w be 10/4*(-18)/15. Let q be w/(-10) - (-4)/20. Find t such that 1/2 + 1/2*t**3 - 1/2*t - q*t**2 = 0.
-1, 1
Factor 8/3*u**2 + 4/3 - 2/3*u**3 - 10/3*u.
-2*(u - 2)*(u - 1)**2/3
Let p(f) be the second derivative of -1/72*f**4 - 2/9*f**3 - 8*f - 1/3*f**2 + 1/40*f**5 + 0. Find h such that p(h) = 0.
-1, -2/3, 2
Suppose 4*p + 3*y = -4, -4*p + 7*p + 3 = -2*y. Let u be 1 - (p + (-1 - -1)). Factor 2*m**2 - u*m**2 - m - m**2.
-m*(m + 1)
Let y(s) be the third derivative of 0 + 1/24*s**3 - 1/48*s**4 + 0*s + 1/240*s**5 + 4*s**2. Factor y(o).
(o - 1)**2/4
Let c(p) be the first derivative of p**4/2 - 6*p**3/7 - 12*p**2/7 + 8*p/7 - 5. Determine u so that c(u) = 0.
-1, 2/7, 2
Let b(n) be the third derivative of -n**11/498960 - n**10/56700 - n**9/22680 - n**5/20 - 4*n**2. Let k(z) be the third derivative of b(z). Factor k(q).
-2*q**3*(q + 2)**2/3
Factor -2/5*y**5 + 16/5 - 10*y**3 + 76/5*y**2 - 56/5*y + 16/5*y**4.
-2*(y - 2)**3*(y - 1)**2/5
Let h(w) = -3*w**3 + 2*w**2 - 4*w + 4. Let q(b) = 8*b**3 - 6*b**2 + 11*b - 11. Let v(s) = -11*h(s) - 4*q(s). Factor v(i).
i**2*(i + 2)
Let v(u) be the first derivative of -u**5 + 5*u**3 + 5*u**2 + 13. Factor v(z).
-5*z*(z - 2)*(z + 1)**2
Suppose -3*m + 141 = -4*r, 2*r = -3*m - 0*r + 141. Let z = m - 139/3. Factor -4/3*o + z*o**2 + 2/3.
2*(o - 1)**2/3
Suppose -5*p + 20 = -0*p. Let h = -4 + p. Factor -1/4*f**2 + 0*f + h.
-f**2/4
Let v(q) be the first derivative of 1/60*q**6 - 1/2*q**2 - 2 - 1/4*q**4 - 2/3*q**3 + 0*q**5 + 0*q. Let k(z) be the second derivative of v(z). Factor k(h).
2*(h - 2)*(h + 1)**2
Let j(p) be the second derivative of 0 - 1/7*p**3 + 0*p**6 + 2*p + 2/35*p**5 - 2/7*p**2 + 1/21*p**4 - 1/147*p**7. Determine y, given that j(y) = 0.
-1, 1, 2
Let p(q) be the second derivative of 9*q**6/40 - 81*q**5/80 + 15*q**4/8 - 11*q**3/6 + q**2 + 9*q. Solve p(x) = 0 for x.
2/3, 1
Let l(z) be the third derivative of -2*z**7/105 + 2*z**6/15 - z**5/3 + z**4/3 + 4*z**2. Factor l(j).
-4*j*(j - 2)*(j - 1)**2
Suppose 2*g = g + 56. Let a = -164/3 + g. What is x in -1/3*x**2 - a + 4/3*x = 0?
2
Let q(u) = -u**2 - 7*u + 3. Let y be q(-7). Suppose y*k - 8 = -k. Solve 0*w + 2/5 - 2/5*w**k = 0 for w.
-1, 1
Let u = -4 + 14. Suppose 5*j = -0*j + u. Factor -6*t**2 - 3*t - 4 + 0*t**4 + 2*t**4 - j*t**3 + 13*t.
2*(t - 1)**3*(t + 2)
Let d be 2/1 - (-1 + 0). Factor 2*u**3 - 5*u + d*u + 2*u.
2*u**3
Let n(l) = -4*l**2 + 22*l - 16. Let f(z) = z**2 - 11*z + 18. Let g be f(8). Let k(j) = 4*j**2 - 21*j + 16. Let i(h) = g*k(h) - 5*n(h). Solve i(v) = 0 for v.
2
Determine p, given that 4/7*p**5 - 16/7*p**3 - 8/7 + 8/7*p**2 + 12/7*p + 0*p**4 = 0.
-2, -1, 1
Factor -3/7*d + 3/7 - 3/7*d**2 + 3/7*d**3.
3*(d - 1)**2*(d + 1)/7
Find g such that 0*g + 2/3*g**2 - 2/3*g**3 + 0 + 2/3*g**5 - 2/3*g**4 = 0.
-1, 0, 1
Let v = 11 - 7. Suppose -4*c = l - 10, -v*c = -2*l - 7 + 3. Factor 1/4*z**l - 1/2*z**3 + 0 + 1/4*z**4 + 0*z.
z**2*(z - 1)**2/4
Let l(k) be the third derivative of -1/120*k**6 - 11/240*k**5 + 0 + 2*k**2 + 0*k - 5/96*k**4 + 1/12*k**3. Factor l(f).
-(f + 1)*(f + 2)*(4*f - 1)/4
Let d(c) = -c**4 + 1. Let o(k) = 18*k**5 + 49*k**4 + 44*k**3 + 3*k**2 - 12*k - 2. Let p(q) = 2*d(q) - o(q). Let p(a) = 0. What is a?
-1, -2/3, 1/2
Let c(x) be the second derivative of x**5/240 + x**4/96 - x**3/12 - 4*x**2 - 3*x. Let g(a) be the first derivative of c(a). Factor g(k).
(k - 1)*(k + 2)/4
Let s(r) be the first derivative of -r**6/36 + r**5/15 - r**4/24 - 3. Factor s(u).
-u**3*(u - 1)**2/6
Let h = 29 - -18. Let z = h + -140/3. Factor -1/3*s - z + 1/3*s**3 + 1/3*s**2.
(s - 1)*(s + 1)**2/3
Let j(a) = -3*a**2 + 8*a + 5. Let k be j(-5). Let o = 552/5 + k. Factor 2/5*y**3 - 2/5*y**2 + o*y**4 + 0*y - 2/5*y**5 + 0.
-2*y**2*(y - 1)**2*(y + 1)/5
Let b(j) be the second derivative of -j**6/30 + j**5/15 + 3*j**2/2 - 8*j. Let q(v) be the first derivative of b(v). Factor q(y).
-4*y**2*(y - 1)
Let k be (0 + 2)/(1 - 0). Let h be 22/6*(588/(-154) - -4). Factor 1/3*l**k + h*l + 1/3.
(l + 1)**2/3
Suppose 54*n - 184*n**2 + 49*n**3 - 4*n**4 + 186*n - n**3 - 100 = 0. What is n?
1, 5
Determine m, given that 2/3*m - 1/3*m**3 - m**4 + 0 - 1/3*m**5 + m**2 = 0.
-2, -1, 0, 1
Let m(q) be the third derivative of 0 + 1/96*q**4 + 4*q**2 - 1/240*q**5 + 0*q + 0*q**3. Let m(c) = 0. Calculate c.
0, 1
Let a(u) be the second derivative of u**6/180 + u**5/12 + 11*u**4/24 + 10*u**3/9 + 4*u**2/3 - 19*u. Factor a(t).
(t + 1)**2*(t + 4)**2/6
Let u = -70 + 73. Let k(f) be the second derivative of -1/66*f**4 + f + 1/33*f**u + 0 + 0*f**2. Let k(o) = 0. What is o?
0, 1
Suppose -2*q - 3*s + 15 = 2*q, 0 = q + 5*s + 9. Let n(c) be the first derivative of 0*c**2 - 1/21*c**q - 1/14*c**4 + 0*c**3 + 0*c - 2 - 4/35*c**5. Factor n(w).
-2*w**3*(w + 1)**2/7
Determine t, given that 8/9*t**3 + 8/9*t**2 + 4/9 + 4/9*t**5 - 4/3*t - 4/3*t**4 = 0.
-1, 1
Factor -2/11*k**2 - 2/11*k + 2/11 + 2/11*k**3.
2*(k - 1)**2*(k + 1)/11
Let d = 73/21 + -61/21. Factor 2/7*m + 2/7*m**2 - d.
2*(m - 1)*(m + 2)/7
Let p(v) be the third derivative of v**8/1512 + v**