 8. Let c be (-44)/(-7) + (10 - 16). Suppose 2/7*m**v - c*m + 0 = 0. Calculate m.
0, 1
Let j = -2 + -5. Let y(o) = o**3 - 11*o**2 - 25*o - 13. Let r(i) = -i**3 + 7*i**2 + 17*i + 9. Let s(t) = j*r(t) - 5*y(t). Find x such that s(x) = 0.
-1
Factor 2 + 0*n - 1/2*n**2.
-(n - 2)*(n + 2)/2
Factor z**2 + z**3 + 0*z**2 - 2*z - 2*z**2.
z*(z - 2)*(z + 1)
Let p(s) = -s - 10. Let y be p(-10). Factor 0 + 3*v**2 - 2*v**2 + y.
v**2
Find y, given that -4/11*y**3 + 8/11 + 8/11*y + 2/11*y**4 - 6/11*y**2 = 0.
-1, 2
Let t(m) be the third derivative of -3*m**2 + 0*m**3 + 1/60*m**5 - 1/210*m**7 - 1/12*m**4 - 1/336*m**8 + 1/40*m**6 + 0 + 0*m. Let t(x) = 0. Calculate x.
-2, -1, 0, 1
Suppose 2*f - 3*f + 13 = 2*o, -f + o - 2 = 0. Let a be (-16)/f*21/(-98). Determine m, given that -a*m**4 + 0*m**3 + 6/7*m**2 + 0 - 2/7*m = 0.
-1, 0, 1/2
Suppose 4*f - 16 = 4*g - g, 5*f = -4*g + 20. Suppose 4*m = 5*q + 8, -2*m - 3*q + 3 + 1 = g. Factor 2*b**3 - 2*b**4 - b**4 - 2*b - b**m + 4*b**4 + 0*b**2.
b*(b - 1)*(b + 1)*(b + 2)
Let c(g) = -19*g - 2. Let o be c(-1). Factor -7 + 24*f + 3*f**3 - o*f**2 - 1 + 2*f**2 - 4.
3*(f - 2)**2*(f - 1)
Let a(y) be the third derivative of -y**6/720 - y**5/80 - y**4/24 + 5*y**3/6 + 5*y**2. Let o(b) be the first derivative of a(b). Factor o(l).
-(l + 1)*(l + 2)/2
Let g be (0 - 0)*(-4)/(-8). Let 8*q**2 - 7*q**5 + g*q - 3*q - 8*q**4 + 3*q**5 + 7*q = 0. Calculate q.
-1, 0, 1
Factor -77 - 12*p**2 + 4*p**5 - 20*p**4 + 77 + 28*p**3.
4*p**2*(p - 3)*(p - 1)**2
Let f = -115668/79 + 80567326/54905. Let v = f + -6/139. Factor 2/5*h - v*h**2 + 32/5*h**3 + 0.
2*h*(4*h - 1)**2/5
Let j(h) be the third derivative of -h**5/210 - h**4/42 + h**3/7 + 6*h**2. Find r such that j(r) = 0.
-3, 1
Let w(v) be the second derivative of v**5/60 + 3*v**2/2 + v. Let g(m) be the first derivative of w(m). Determine j so that g(j) = 0.
0
Let n(x) be the second derivative of x**4/6 + 3*x**3/2 - 5*x**2/2 + x + 9. Suppose n(l) = 0. Calculate l.
-5, 1/2
Let f(c) be the third derivative of 1/90*c**5 + 0*c + 1/540*c**6 + 0 + 1/54*c**4 - c**2 + 0*c**3. Solve f(u) = 0.
-2, -1, 0
Let u(y) = y**2 + 10*y + 12. Let q be (0 + 0 + -3)*3. Let k be u(q). Solve 2/5*h**k + 2*h**2 + 8/5 + 16/5*h = 0 for h.
-2, -1
Let d(v) be the first derivative of v**4/6 - 2*v**3/27 - v**2/3 + 2*v/9 + 5. What is h in d(h) = 0?
-1, 1/3, 1
Let z(j) be the second derivative of -j**5/70 - j**4/42 + 2*j**3/7 - 13*j + 1. Factor z(k).
-2*k*(k - 2)*(k + 3)/7
Let s(f) = f**3 - 7*f**2 - 7*f - 5. Let o be s(8). Find z such that -2*z**4 + 2*z**2 - 10*z**o + 10*z**3 = 0.
-1, 0, 1
Let w(c) be the first derivative of -3 - 4/3*c**3 + 2/5*c**5 + 0*c**4 + 2*c + 0*c**2. Factor w(g).
2*(g - 1)**2*(g + 1)**2
Let o(g) = -4*g - 3. Let y be o(-2). Suppose 5 = 5*u - y. Factor 1/2 + 3/4*v + 1/4*v**u.
(v + 1)*(v + 2)/4
Let j(c) be the second derivative of -c**8/1680 + c**7/315 - c**6/180 + 11*c**4/12 - 4*c. Let f(p) be the third derivative of j(p). Factor f(w).
-4*w*(w - 1)**2
Let d(m) be the second derivative of 5/18*m**4 - 1/63*m**7 + 0*m**2 + 0 - 6*m + 2/9*m**3 + 1/10*m**5 - 1/45*m**6. Solve d(v) = 0 for v.
-1, 0, 2
Let v(g) be the second derivative of -g**5/5 + 8*g**3/3 - 12*g. Determine f so that v(f) = 0.
-2, 0, 2
Factor -2/3 - r**3 - 8/3*r**2 - 7/3*r.
-(r + 1)**2*(3*r + 2)/3
Let 16*j + 18*j - 30*j**2 - 9 + 5 = 0. What is j?
2/15, 1
Let n = -835 + 5861/7. Factor 162/7*y**4 + 0 + 54/7*y**5 + 180/7*y**3 + n*y + 88/7*y**2.
2*y*(y + 1)*(3*y + 2)**3/7
Let v = -66 - -69. Factor 1/5*t**2 + 0 + 1/5*t**v - 2/5*t.
t*(t - 1)*(t + 2)/5
Let g(p) be the third derivative of p**7/1470 - p**6/168 + p**5/60 - p**4/56 - 6*p**2. Factor g(x).
x*(x - 3)*(x - 1)**2/7
Suppose -4*f - r + 3 = 0, -13*f + 17*f - 4*r + 12 = 0. Factor -2/13*u + f + 2/13*u**2.
2*u*(u - 1)/13
Let -30 - c - 4*c**3 + 6 + 29*c = 0. Calculate c.
-3, 1, 2
Let l = -466/5 - -94. Factor -2/5*f**3 + l*f**2 + 2/5*f - 4/5.
-2*(f - 2)*(f - 1)*(f + 1)/5
Suppose -4*t = 2*y + 14, t + 2*y + 10 = -2*t. Let s be t/(-14) - (-214)/35. Factor 4/5 + 14/5*k**3 + s*k**2 + 22/5*k.
2*(k + 1)**2*(7*k + 2)/5
Let c = -29 + 29. Let o(n) be the second derivative of n + 1/3*n**3 + c + 0*n**2 + 1/6*n**4. Suppose o(t) = 0. What is t?
-1, 0
Let g(x) be the second derivative of 1/15*x**6 - 1/10*x**5 - 1/3*x**4 + 0*x**3 + 0 + 0*x**2 - 2*x. Determine h so that g(h) = 0.
-1, 0, 2
Let s be (-3)/1 + 58/18. Suppose 4*c = -c + 10. Factor s*j + 2/9*j**c - 4/9.
2*(j - 1)*(j + 2)/9
Let j(i) be the second derivative of 2*i + 0*i**2 + 0*i**3 + 0 - 1/54*i**4. Let j(n) = 0. Calculate n.
0
Let u(s) be the second derivative of -s**6/6 - s**5/2 + 5*s**4/12 + 5*s**3/3 - 5*s. Factor u(a).
-5*a*(a - 1)*(a + 1)*(a + 2)
Let y(h) = 2*h + 16. Let t be y(-7). Suppose 2/5*f**t + 2/5 - 4/5*f = 0. What is f?
1
Let k(g) = 2*g**2 - 11*g + 2. Let x(y) = -2*y**2 + 12*y - 3. Let a(n) = -4*k(n) - 3*x(n). Let t(q) = q**2 - 4*q. Let h(f) = -4*a(f) - 9*t(f). Solve h(w) = 0.
2
Let y(t) be the first derivative of t**6/15 - t**4/6 - 3*t + 3. Let s(u) be the first derivative of y(u). Let s(h) = 0. What is h?
-1, 0, 1
Let y = -8 + 13. Let u = 2/173 - -1378/519. Let 14/3*b + 4/3 - 2*b**y - 16/3*b**4 + 4*b**2 - u*b**3 = 0. Calculate b.
-1, -2/3, 1
Factor -2/11*o**4 + 0 - 2/11*o**3 + 2/11*o + 2/11*o**2.
-2*o*(o - 1)*(o + 1)**2/11
Let h(w) = -2*w**2 - 4. Let t(v) = v**2 + v + 3. Let d(s) = -3*h(s) - 4*t(s). Let d(c) = 0. What is c?
0, 2
Let f(s) = s**2 + 4. Let w be f(0). Let x = w - 2. Solve -1 - x*b + 1 + 2*b**3 = 0 for b.
-1, 0, 1
Factor -380 + 380 + t**3 - t.
t*(t - 1)*(t + 1)
Let p(l) be the second derivative of -l**5/100 + 2*l**3/15 - 9*l. Suppose p(j) = 0. What is j?
-2, 0, 2
Factor 4*n**4 - n**2 - 2*n**3 - 3*n**4 + 3*n**3 - n.
n*(n - 1)*(n + 1)**2
Determine f, given that 1/2*f - 1/2*f**3 + 0*f**2 + 0 = 0.
-1, 0, 1
Let k = 21527/4179 - 5/597. Factor -2*t + 12/7 - 10/7*t**3 - k*t**2.
-2*(t + 1)*(t + 3)*(5*t - 2)/7
Let u(n) be the second derivative of 1/12*n**3 - 1/42*n**7 + 1/8*n**4 + 1/40*n**5 + 0 + 2*n + 0*n**2 - 1/20*n**6. What is f in u(f) = 0?
-1, -1/2, 0, 1
Let m(u) be the third derivative of -1/40*u**6 - 7/180*u**5 - 1/36*u**4 + 0 + 0*u**3 + 0*u - 1/126*u**7 - 1/1008*u**8 - 2*u**2. Solve m(b) = 0 for b.
-2, -1, 0
Let y = 2/553 + 549/1106. Determine k so that -3/4*k - y - 1/4*k**2 = 0.
-2, -1
Let m(l) = 2*l + 34. Let u be m(-16). Let o(y) be the third derivative of -3*y**u + 1/120*y**6 + 1/2*y**4 + 1/10*y**5 + 0*y + 4/3*y**3 + 0. Factor o(b).
(b + 2)**3
Let r(w) = -9*w + 1. Let c be r(1). Let d be (-6)/4*c/6. Factor 4/9*a**2 - d*a**3 + 8/3*a**4 - 10/9*a**5 + 0*a + 0.
-2*a**2*(a - 1)**2*(5*a - 2)/9
Let b(r) = 2*r + 1. Let l be b(7). Suppose -2*f + 5*q - l = 0, -3 = f + 2*q - 9. Factor 1/3*n**4 + 1/3*n**2 + 0*n + f + 2/3*n**3.
n**2*(n + 1)**2/3
Determine k, given that -36*k**2 + 21*k**3 - 23*k + 35*k - 6*k**3 = 0.
0, 2/5, 2
Determine h, given that 6/7*h + 2/7*h**3 + 0 - 8/7*h**2 = 0.
0, 1, 3
Let m be (1 - -1)*(9 - 7). Let q(j) be the second derivative of 1/3*j**4 + m*j - 1/4*j**2 + 0 - 7/60*j**6 + 3/80*j**5 - 1/8*j**3. Suppose q(g) = 0. Calculate g.
-1, -2/7, 1/2, 1
Let z(o) be the second derivative of -o**6/10 + o**4/4 - 3*o. Solve z(j) = 0.
-1, 0, 1
Let k(j) be the first derivative of j**4 - 4*j**3/3 - 10*j**2 - 12*j - 13. Factor k(a).
4*(a - 3)*(a + 1)**2
Let u(c) be the first derivative of -c**4/18 - 2*c**3/27 - 7. Determine i, given that u(i) = 0.
-1, 0
Suppose -4*y + 4 = 2*n, -4 = n + n - 4*y. Solve n + 0*j - 1/3*j**2 + 2/3*j**3 - 1/3*j**4 = 0.
0, 1
Let t(w) be the third derivative of 0*w + 1/30*w**3 + 0*w**4 - 1/150*w**5 + 3*w**2 + 0*w**6 + 0 + 1/1050*w**7. Factor t(z).
(z - 1)**2*(z + 1)**2/5
Let u(m) be the third derivative of -1/330*m**6 + 1/330*m**5 + 0*m**4 + 0*m**3 + 1/1155*m**7 + 0 - 2*m**2 + 0*m. Factor u(f).
2*f**2*(f - 1)**2/11
Let t be (-1)/((-10)/4 + 2). What is l in 2*l**t + 6*l + 0*l**2 - 3*l**2 - 3 - 2*l**2 = 0?
1
Let j(r) = 2*r**4 - 8*r**3 + 8*r**2 - 12*r - 2. Let i(o) = o**2 + o + 1. Let g(f) = 4*i(f) + j(f). Factor g(m).
2*(m - 1)**4
Let v = 55 + -39. Suppose v = -m + 9*m. What is f in 2/11 - 18/11*f + 50/11*f**3 + 30/11*f**m = 0?
-1, 1/5
Suppose -3*d + 10 = 2*d, -2*h = -2*d. Factor h*s**4 + 0*s**4 + s**4 - 4*s**2 + s**5.
s**2*(s - 1)*(s + 2)**2
Let t(c) = -8*c**2 - c + 4. Let n(y) = -y**2 + y - 1. Let l(z) = -5*n(z) + t(z). Factor