(1). Suppose -2/3*a**2 + 2/3*a**4 - 2/3*a**y + 0*a + 2/3*a**5 + 0 = 0. Calculate a.
-1, 0, 1
Let n(v) be the first derivative of 2*v**6/3 - 2*v**4 + 2*v**2 - 6. Find m, given that n(m) = 0.
-1, 0, 1
Let p(u) be the third derivative of 4*u**2 + 0*u - 1/1260*u**7 - 1/360*u**6 + 0 + 1/360*u**5 + 0*u**3 + 1/72*u**4. Let p(v) = 0. What is v?
-2, -1, 0, 1
Let v(l) = 0*l**3 + 0*l**3 + l**2 - l**3 - 1. Let i(p) = 3*p**5 - 9*p**4 + 8*p**3 + 4*p**2 - 9*p + 5. Let h(u) = i(u) + 2*v(u). Determine w so that h(w) = 0.
-1, 1
Factor -3/2*p**2 + 0 + 0*p - 21/4*p**3.
-3*p**2*(7*p + 2)/4
Suppose -4*h + 0 = g - 8, 62 = 5*g - 2*h. Suppose 0 = -4*k - w + g, k + 4*k - 30 = -5*w. Factor 1/4*i**3 - 1/4*i**k + 0 + 0*i.
i**2*(i - 1)/4
Suppose -13 = -4*x - 5. Let d(m) be the second derivative of 0*m**x + 1/24*m**4 - 1/6*m**3 + 0 + 2*m. Find k, given that d(k) = 0.
0, 2
Let i(a) = -96*a - 12. Let g be i(3). Let o be (-2)/(-8)*g/(-125). Suppose 3/5*m**4 + 3/5 - 3/5*m + 6/5*m**3 - 6/5*m**2 - o*m**5 = 0. What is m?
-1, 1
Determine o, given that -1/4*o + 0 - 3/4*o**3 - 3/4*o**2 - 1/4*o**4 = 0.
-1, 0
Let c(f) = 14*f**3 + 28*f**2 + 8*f. Let u(y) = 12*y**3 + 29*y**2 + 9*y. Let q(j) = -4*c(j) + 3*u(j). Solve q(b) = 0.
-1, -1/4, 0
Suppose -1 + 30*g + 4*g**2 - 6*g + 37 = 0. Calculate g.
-3
Let f(l) = -l**2 + l - 1. Let d(s) = -30*s**2 + 25*s - 25. Let j(b) = d(b) - 25*f(b). Factor j(w).
-5*w**2
Let n = 2727/5 + -545. Factor -1/5*l**4 + 0*l**2 + n*l**3 + 0*l + 0.
-l**3*(l - 2)/5
Suppose d + 5*n - 8 = 3, 5 = 5*n. Determine f so that 58*f**3 - 4 + 3*f + 4 - 55*f**3 - d*f**2 = 0.
0, 1
Let r(g) be the third derivative of -g**8/504 + g**7/315 + g**6/180 - g**5/90 + 6*g**2. Solve r(p) = 0 for p.
-1, 0, 1
Let c = -154/115 - -40/23. Solve -c*u**4 + 7/5*u - 1/5*u**5 + 8/5*u**2 + 2/5 + 2/5*u**3 = 0.
-1, 2
Let i be (-1)/(-10)*(850/30)/17. Find l such that 1/6*l**2 - i*l - 1/3 = 0.
-1, 2
Let x(o) = 7*o**4 + 7*o**3 + 3*o**2 - 2*o - 5. Let p(u) = 0 + u**2 + 3*u - 2 + 3*u**4 - 4*u + 3*u**3. Let l(d) = -5*p(d) + 2*x(d). Factor l(r).
-r*(r - 1)*(r + 1)**2
Let v = 7 + -7. Suppose 5*n + v = s + 15, -2*n - 5*s = 21. Factor -f**2 + 3*f**2 - n*f**4 + 0*f**4.
-2*f**2*(f - 1)*(f + 1)
Let b(l) be the second derivative of l**6/75 - l**5/25 + 2*l**3/15 - l**2/5 + 17*l. Factor b(y).
2*(y - 1)**3*(y + 1)/5
Factor -1/4*s**3 + 0 - 5/4*s + 3/2*s**2.
-s*(s - 5)*(s - 1)/4
Let d = 2 + 0. Let v be (30/9)/(d/3). Factor -9/5*l**4 + 9/5*l + 3/5 + 6/5*l**2 - 3/5*l**v - 6/5*l**3.
-3*(l - 1)*(l + 1)**4/5
Let o(f) be the third derivative of f**9/15120 - f**7/2100 + f**5/600 - f**3/2 + 5*f**2. Let q(n) be the first derivative of o(n). Factor q(v).
v*(v - 1)**2*(v + 1)**2/5
Factor -6*r**4 + 2 + r - 5*r + 2*r**5 + 4*r + 4*r**3 - 6*r + 4*r**2.
2*(r - 1)**4*(r + 1)
Suppose -4 = -2*r - 0*r - 5*n, -r + 2 = -n. What is k in 2*k**r + 2*k**3 + k**5 - 3*k**5 - 6*k**4 + 4*k**4 = 0?
-1, 0, 1
Let s = -21 + 27. Let p(l) be the second derivative of 0 + 0*l**2 - 7/30*l**s - 3*l - 4/5*l**5 - 11/12*l**4 - 1/3*l**3. Solve p(b) = 0.
-1, -2/7, 0
Let d(n) be the third derivative of -n**8/504 + n**7/63 - n**6/20 + 7*n**5/90 - n**4/18 - 2*n**2. Suppose d(t) = 0. Calculate t.
0, 1, 2
Let h(g) be the second derivative of g**7/840 + g**6/120 + g**4/12 + 4*g. Let d(u) be the third derivative of h(u). Factor d(r).
3*r*(r + 2)
Let w(f) be the second derivative of -f**7/280 - f**6/20 - 3*f**5/10 - f**4 - 5*f**3/6 + 3*f. Let s(z) be the second derivative of w(z). Factor s(m).
-3*(m + 2)**3
Let u(h) be the second derivative of -h**4/9 + 4*h**3/3 - 6*h**2 + 9*h. Factor u(t).
-4*(t - 3)**2/3
Let k(h) = 3*h**2 - 6*h + 9. Let z(j) = -1. Let x(c) = -k(c) - 9*z(c). Factor x(s).
-3*s*(s - 2)
Let i be (-11)/(-198)*(-1)/(-10). Let c(x) be the third derivative of i*x**6 + 2/9*x**4 + 0 + x**2 + 0*x - 4/9*x**3 - 1/18*x**5. Factor c(g).
2*(g - 2)**2*(g - 1)/3
Let s(j) = j**3 - 3*j**2 + 2*j - 1. Let i be s(3). Suppose -5*b + i = g - 2*b, -2*g + 4*b = 0. Find w, given that -4*w**2 + 2*w**3 + 0*w**2 + 2*w**g = 0.
0, 1
Suppose -2*x + 12 = -i + x, -2*x - 20 = 4*i. Let a = i + 8. Let 2 + 5*u**2 - 5*u**a - 2*u**2 = 0. Calculate u.
-1, 1
Suppose 0 = -3*f + m + 18, 3*m - 37 = -4*f - 0*m. Let l = -4 + f. Factor -8*j - 5*j**2 + 3*j + 4 + l*j - 6*j.
-(j + 2)*(5*j - 2)
Let k = 0 + 4. Let w(z) be the first derivative of -3 + 0*z - 1/9*z**3 + 1/12*z**k + 0*z**2. Factor w(n).
n**2*(n - 1)/3
Let o be (2/(-5))/(18/(-190)) - 4. Solve 4/9*g + 0 + o*g**2 - 2/9*g**4 - 4/9*g**3 = 0.
-2, -1, 0, 1
Let i(v) be the second derivative of v**7/21 + 4*v**6/15 + 2*v**5/5 - v**4/3 - 5*v**3/3 - 2*v**2 - 29*v. Let i(j) = 0. Calculate j.
-2, -1, 1
Let j(s) = 4*s**5 + 9*s**4 - 5*s**3 - 3*s**2 - 5*s + 5. Let m(o) = -o**5 - o**4 + o**2 + o - 1. Let l(c) = -j(c) - 5*m(c). Factor l(h).
h**2*(h - 2)*(h - 1)**2
Let o(j) = -j**2 + 28*j + 167. Let h be o(33). Let 3/5*m**3 + 9/5*m**4 - 24/5*m**h + 0 + 12/5*m = 0. What is m?
-2, 0, 2/3, 1
Let w = 474 + -1409/3. Suppose w*j**2 - 2*j**3 - 4*j + 4/3 + 1/3*j**4 = 0. What is j?
1, 2
Let v(r) be the third derivative of 0 + r**4 - r**2 - 1/4*r**5 - 2*r**3 + 1/40*r**6 + 0*r. Find x, given that v(x) = 0.
1, 2
Let v be (-6)/12*(-4144)/(-10). Let u = v - -208. Factor 8/5*p**3 + 0*p + u*p**5 + 0 - 2/5*p**2 - 2*p**4.
2*p**2*(p - 1)**2*(2*p - 1)/5
Suppose 10 = -7*s + 24. Let p = -2 - -2. Factor p + 2/5*v**3 + 2/5*v**5 - 4/5*v**4 + 0*v + 0*v**s.
2*v**3*(v - 1)**2/5
Let p(x) = -x - 1. Let n = 5 - 10. Let g be p(n). Factor 2 - 2*i**5 - 3*i**2 - i**2 + 4*i**4 + g*i**3 - 2*i**4 - 2*i.
-2*(i - 1)**3*(i + 1)**2
Let y(v) be the third derivative of v**8/224 + 2*v**7/105 + 11*v**6/360 + v**5/45 + v**4/144 + 13*v**2. Factor y(b).
b*(b + 1)**2*(3*b + 1)**2/6
Let b(r) be the first derivative of 2 - 3*r**3 + 3/5*r**5 + 0*r**4 + 0*r - 3*r**2. Factor b(h).
3*h*(h - 2)*(h + 1)**2
Let d(c) be the second derivative of c**6/90 - c**5/20 + 2*c**3/9 + 14*c. Suppose d(q) = 0. What is q?
-1, 0, 2
Let u be ((-16)/(-10))/(10/25). Let c be ((-6)/9)/(u/(-18)). Factor -4/7*n**2 + 0 + 0*n**c - 2/7*n + 4/7*n**4 + 2/7*n**5.
2*n*(n - 1)*(n + 1)**3/7
Let m(n) be the first derivative of 24*n**5/25 - 9*n**4/10 - 3*n**3/5 + 3*n**2/10 + 14. Determine q so that m(q) = 0.
-1/2, 0, 1/4, 1
Let c(k) = 4*k**3 + 6*k**2 + 6*k + 6. Let l(h) = h**3 + h**2 + h + 1. Let w(y) = -c(y) + 6*l(y). Factor w(b).
2*b**3
Let d be -3*(0 - (3 - 2)). Suppose -c = -d*c + 8. What is b in b**2 + c*b + 1 - 2*b + 0*b**2 = 0?
-1
Let j = 195 + -192. Let b(g) be the second derivative of -2*g + 0*g**2 - 1/15*g**j - 1/30*g**4 + 0. Factor b(k).
-2*k*(k + 1)/5
Factor 0*m**2 + 0 + 2/5*m**3 - 2/5*m.
2*m*(m - 1)*(m + 1)/5
Let m(o) be the first derivative of o**4/24 + o**3/6 + o**2/4 + 5*o + 1. Let f(q) be the first derivative of m(q). Factor f(j).
(j + 1)**2/2
Let z(p) = 2*p**2 - 2. Let q be z(1). Let r(y) be the third derivative of -1/630*y**7 + 0*y**4 - 1/180*y**5 + 0 + 0*y - y**2 - 1/180*y**6 + q*y**3. Factor r(m).
-m**2*(m + 1)**2/3
Let a(t) = t**3 - t**2 + t + 2. Let c be a(0). Let q be (-80)/(-6) - (c - 0). Let 16*k + 98/3*k**5 - 146/3*k**3 + q*k**2 - 14*k**4 + 8/3 = 0. Calculate k.
-1, -2/7, 1
Factor 1/7*u**4 + 0 - 1/7*u**3 + 1/7*u - 1/7*u**2.
u*(u - 1)**2*(u + 1)/7
Factor -2/11*a**5 - 2/11*a**4 + 0*a**2 + 0*a + 0*a**3 + 0.
-2*a**4*(a + 1)/11
Let f(m) be the second derivative of -m**4/6 + 17*m**3/12 - m**2 + 5*m. Factor f(r).
-(r - 4)*(4*r - 1)/2
Let y(u) be the first derivative of 0*u**2 + 7 + 0*u + 0*u**3 + 0*u**4 + 2/3*u**6 - 4/5*u**5. Suppose y(g) = 0. What is g?
0, 1
Let l(d) be the second derivative of d**4/60 + d**3/30 - 11*d. Factor l(i).
i*(i + 1)/5
Suppose 0 = -2*x, -2*x - 12 = -6*w + 2*w. Suppose -c + y + 1 = -2, y = -2*c - w. Factor 0 + c*j**2 - 1/2*j**3 + 0*j**4 + 1/4*j**5 + 1/4*j.
j*(j - 1)**2*(j + 1)**2/4
Suppose 0*k = -5*k + 10. Let s be 1 + k + 8/(-8). Let -3/2*n**3 + 0 + 0*n + 0*n**s = 0. What is n?
0
Let v(i) be the first derivative of -i**3 - 18*i**2 - 108*i - 35. Factor v(w).
-3*(w + 6)**2
Let n(v) be the first derivative of -5*v**6/12 - 6*v**5/5 - v**4/2 + 5*v**3/3 + 9*v**2/4 + v - 6. Find d, given that n(d) = 0.
-1, -2/5, 1
Factor 4*r**3 + 26*r**4 - 4*r**5 - 24*r**4 + 2*r**5 + 0*r**3.
-2*r**3*(r - 2)*(r + 1)
Find m such that -1/5*m**2 + 1 - 4/5*m = 0.
-5, 1
Let n = 541/3 + -180. Let 0 - n*a**2 + 1/3*a = 0. What is a?
0, 1