t k be (-6 + 12/3 - -2)/(-1). Suppose 8*m**3 + 0 - 98*m**5 + k*m - 16/7*m**2 + 28*m**4 = 0. Calculate m.
-2/7, 0, 2/7
Let m(s) be the first derivative of 9*s**5/5 - 15*s**4/4 + 13*s**3/12 + 5*s**2/4 + s/4 - 1. Factor m(w).
(w - 1)**2*(6*w + 1)**2/4
Let q(o) = o**2 + 4*o + 3. Let h be q(-5). Let k = h - 3. Factor 1/2*n**k + 0*n**4 + 0*n**2 - 1/2*n**3 + 0 + 0*n.
n**3*(n - 1)*(n + 1)/2
Let s be (125/(-15) - -5)*(-2)/5. Factor -l**3 + 10/3*l**2 - s*l - 8/3.
-(l - 2)**2*(3*l + 2)/3
Let z(a) = -4*a**3 - 4*a**2 + 7*a + 4. Let r(i) = 3*i**3 + 3*i**2 - 6*i - 4. Let n(p) = -3*r(p) - 2*z(p). Find x, given that n(x) = 0.
-2, -1, 2
Let h(f) = f**3 - 4*f**2 + 6*f - 2. Let x be h(2). Factor 2/9*c**x + 8/9*c + 8/9.
2*(c + 2)**2/9
Let z be 14/6 + 4/6. Factor -t**z + 0*t + 3*t + 5 - 3.
-(t - 2)*(t + 1)**2
Let f(b) = -b**3 + b**2 - b + 1. Let g be f(1). Factor -7*p**2 + 2*p**5 + 9*p**2 - 3*p**4 + g*p**5 + p**4 - 2*p**3.
2*p**2*(p - 1)**2*(p + 1)
Let j(s) be the third derivative of s**7/1260 + s**6/120 + s**5/30 + s**4/24 - 3*s**2. Let o(c) be the second derivative of j(c). Find q, given that o(q) = 0.
-2, -1
Let y(z) be the first derivative of z**6/105 + 2*z**5/35 + 5*z**4/42 + 2*z**3/21 - 7*z + 4. Let j(h) be the first derivative of y(h). Factor j(v).
2*v*(v + 1)**2*(v + 2)/7
Suppose 2/7*t**5 + 0 + 6/7*t**3 - 2/7*t**2 + 0*t - 6/7*t**4 = 0. Calculate t.
0, 1
Let z = -152 + 158. Let u(m) be the third derivative of 0*m + 4*m**2 - 1/66*m**4 + 0 + 0*m**3 + 2/165*m**z + 1/330*m**5 + 1/231*m**7. Factor u(t).
2*t*(t + 1)**2*(5*t - 2)/11
Let q = -104/3 + 35. Determine t so that -q*t**2 + 0*t + 0 = 0.
0
Let s = 4 - 7. Let n be 16/18*s/(-4). Factor -v + n + 1/3*v**2.
(v - 2)*(v - 1)/3
Let l(c) be the first derivative of -5 + 1/6*c**3 + 1/8*c**2 - 1/20*c**5 - 1/4*c - 1/8*c**4 + 1/24*c**6. Factor l(w).
(w - 1)**3*(w + 1)**2/4
Let g be (-9 - -5)*(-3 - -1). Let d(p) = p - 4. Let i be d(g). Factor i + 10*u + 0 + 2*u**3 + 3*u**2 + 5*u**2.
2*(u + 1)**2*(u + 2)
Find u, given that 2*u**2 + 92 - 180 + 86 = 0.
-1, 1
Suppose -2 = 3*n - 4*n. Determine x so that 2*x**n + 0*x**4 - 15*x**3 - 2*x**4 + 12*x**3 = 0.
-2, 0, 1/2
Let x(i) be the third derivative of i**8/30240 - i**7/7560 + i**5/20 + i**2. Let t(r) be the third derivative of x(r). Factor t(d).
2*d*(d - 1)/3
Let i be 6*24/(-9)*2/(-16). Factor 0*u**3 + 0 - 1/2*u**5 - u**4 + u**i + 1/2*u.
-u*(u - 1)*(u + 1)**3/2
Let f(a) be the first derivative of 1/8*a**4 + 1/2*a**3 - 5 + 1/2*a**2 + 0*a. What is o in f(o) = 0?
-2, -1, 0
Let r be (36/(-330))/(0 + 9/(-30)). Find k such that 0 + r*k - 2/11*k**2 = 0.
0, 2
Let o(z) be the second derivative of -z**5/60 - z**4/36 + z**3/18 + z**2/6 + 4*z. Suppose o(c) = 0. Calculate c.
-1, 1
Let x be (-3*11)/(-3)*-10. Let k be 8/11 - (-20)/x. Factor 2/11*v - 4/11 + k*v**2.
2*(v + 1)*(3*v - 2)/11
Let u be (-1 + 0)/(11 - 13). Factor -q - u*q**2 - 1/2.
-(q + 1)**2/2
Determine o so that -2/3*o**3 + 0 + 2/3*o**4 - 4/3*o**2 + 0*o = 0.
-1, 0, 2
Suppose 5*z - 44 + 2 = 4*f, -12 = 4*f. Let d be ((-3)/z)/((-1)/6). Factor 0 - 1/4*o**5 + 0*o + 1/4*o**4 - 1/4*o**2 + 1/4*o**d.
-o**2*(o - 1)**2*(o + 1)/4
Let m(a) be the third derivative of -a**5/330 - 8*a**2. Factor m(l).
-2*l**2/11
Suppose 0 = -5*s - 3*g, 0 = 2*g - 7*g. Suppose 8*y**3 - 21/2*y**4 - 2*y**2 + 0 + s*y + 9/2*y**5 = 0. Calculate y.
0, 2/3, 1
Let 5*z**2 + 50 - 479*z - 3*z**2 + 459*z = 0. What is z?
5
Let m(z) be the second derivative of 1/24*z**4 + 0*z**2 + 2*z + 0*z**3 + 0. Find n, given that m(n) = 0.
0
Let 6/7*y - 2/7*y**3 + 0*y**2 + 4/7 = 0. What is y?
-1, 2
Let w be 182/39 - 6/9. Factor -1/2*v**w - 3*v**2 + 2*v**3 + 2*v - 1/2.
-(v - 1)**4/2
Let g(v) = -2*v**2 + 32*v - 110. Let h be g(11). Find m such that 8/9 - 2/9*m**2 + h*m = 0.
-2, 2
Suppose 4*k - 13 = -1. Let r(n) be the second derivative of 0 - n + 1/6*n**2 + 1/9*n**k + 1/36*n**4. Suppose r(m) = 0. Calculate m.
-1
Let y be 18/(-105) + (-20)/(-35). Determine i, given that y - 2/5*i**2 + 2/5*i - 2/5*i**3 = 0.
-1, 1
Let d = -5 - -8. Suppose 4*y - 8 = d*y + b, -b + 10 = 5*y. Solve 6*l**2 + 2 + 6*l + 2*l**y + 2 - 2 = 0 for l.
-1
Find y such that 7*y**5 - 4*y**3 - 8*y**2 - 4*y**4 + 12*y**2 - 4*y**5 + y**5 = 0.
-1, 0, 1
Let x(c) = -11*c**3 + 15*c**2 - 4*c - 9. Suppose -4*v + 4 = 40. Let i(r) = 5*r**3 - 7*r**2 + 2*r + 4. Let z(q) = v*i(q) - 4*x(q). Factor z(o).
-o*(o - 2)*(o - 1)
Factor 2/9*f**2 + 0 + 0*f - 1/9*f**3 - 1/9*f**4.
-f**2*(f - 1)*(f + 2)/9
Suppose o - 18 = -15. Let 0 - 2/11*n + 0*n**2 + 0*n**4 - 2/11*n**5 + 4/11*n**o = 0. Calculate n.
-1, 0, 1
Let y(z) = 4*z**2 + z. Suppose 0*a = -4*a - 12. Let j(q) = 0 + 0 - q. Let f(d) = a*j(d) - y(d). Factor f(k).
-2*k*(2*k - 1)
Let x = 7797/5 - 1557. Determine y, given that 28/5*y**3 + 18/5*y + 2/5*y**5 - 4/5 - x*y**4 - 32/5*y**2 = 0.
1, 2
Suppose d = 2*d - 22. Suppose -5*v + 62 - d = 0. Factor 0*y**4 + v*y**3 + y - 12*y**2 - 2 - 2*y**4 + 7*y.
-2*(y - 1)**4
Let l(d) = -2*d - 4. Suppose -2*p - p = 9. Let c be l(p). Factor -y**4 - 4*y**2 + 2*y**3 + 2*y**c + y**2.
-y**2*(y - 1)**2
Let y(w) be the first derivative of -w**5/5 + 5*w**4/4 - 8*w**3/3 + 2*w**2 + 8. Let y(i) = 0. Calculate i.
0, 1, 2
Let j(r) be the third derivative of 0*r**5 + 3*r**2 + 1/210*r**6 - 1/21*r**3 + 0*r + 1/735*r**7 - 1/42*r**4 + 0. Factor j(y).
2*(y - 1)*(y + 1)**3/7
Suppose -4*b = -7*b - 6, 0 = -w + 5*b + 18. Suppose w - 20 = -4*a. Factor 22*i**2 - 32*i**a + 22*i**4 - 8*i**4 + 0*i - 4*i.
2*i*(i - 1)**2*(7*i - 2)
Let r(s) be the first derivative of 3 - 1/10*s**4 + 0*s - 4/15*s**3 + 0*s**2. Factor r(d).
-2*d**2*(d + 2)/5
Let v(w) be the second derivative of -w**5/110 + 5*w**4/66 + 13*w**3/33 + 7*w**2/11 + w - 26. Factor v(c).
-2*(c - 7)*(c + 1)**2/11
Let m(b) be the third derivative of -5*b**8/2016 + b**7/36 - 5*b**6/48 + b**5/8 - 12*b**2. Factor m(l).
-5*l**2*(l - 3)**2*(l - 1)/6
Suppose 4*p = -6 + 14. Let r(g) be the first derivative of 1/9*g**2 + 0*g - 1/27*g**6 - 4/45*g**5 - p + 0*g**4 + 4/27*g**3. Find u such that r(u) = 0.
-1, 0, 1
Let u(b) be the second derivative of -73/75*b**6 + 2*b - 1/30*b**4 + 2/5*b**2 - 3/5*b**3 + 51/50*b**5 + 0 + 2/7*b**7. Let u(f) = 0. Calculate f.
-2/5, 1/3, 1/2, 1
Let o be -1*(-3)/(2 - -1)*2. Factor -2/3*t + 0 - 2/3*t**o.
-2*t*(t + 1)/3
Factor 2/3*i**2 - 1/3*i**4 + 0 - 1/3*i**3 + 0*i.
-i**2*(i - 1)*(i + 2)/3
Suppose -9*n + 4*n = -10. Suppose -l - 3 = a, -n*l = -3*l - 2*a - 6. Factor -1/2*b**2 + l + 1/2*b**3 + b**4 + 0*b.
b**2*(b + 1)*(2*b - 1)/2
Factor 9*v**2 - 2*v**3 - 4 + 0*v**3 + 2*v - 3*v**2 - 5*v**4 + 3*v**4.
-2*(v - 1)**2*(v + 1)*(v + 2)
Let b(y) be the first derivative of -y**3/15 - y**2/5 + 7. Factor b(w).
-w*(w + 2)/5
Suppose -4*n = -c - 6*n - 6, 3*n = -12. Determine b so that 0 + 1/4*b**c - 1/4*b = 0.
0, 1
Let j(g) = g**3 + 3*g**2 - 2*g - 2. Let z be j(2). Determine s, given that -3 - 1 + 5*s - z*s - 2 + 3*s**3 = 0.
-1, 2
Let p(a) be the first derivative of 0*a - 2/3*a**3 - a**2 + 4. Factor p(d).
-2*d*(d + 1)
Let y(j) be the second derivative of j**9/15120 - j**8/2880 + j**7/1512 - j**6/2160 + 3*j**4/4 + j. Let b(u) be the third derivative of y(u). Factor b(n).
n*(n - 1)**2*(3*n - 1)/3
Let u(h) be the second derivative of 0*h**3 - 1/12*h**4 + 1/2*h**2 + 2*h + 0. Factor u(x).
-(x - 1)*(x + 1)
Let i(h) be the first derivative of -4/13*h + 1 - 7/13*h**2 + 1/39*h**6 - 16/39*h**3 + 4/65*h**5 - 1/13*h**4. Factor i(r).
2*(r - 2)*(r + 1)**4/13
Factor -12*p**3 + 1 - 1 + 8*p**2 + 0 + 4*p**5.
4*p**2*(p - 1)**2*(p + 2)
Suppose 2/7*w**2 - 2/7*w - 4/7 = 0. What is w?
-1, 2
Let b(w) = 5*w**3 - 28*w**2 - 60*w - 52. Let f(s) = -13*s**3 + 83*s**2 + 180*s + 155. Let n(c) = -11*b(c) - 4*f(c). Find j such that n(j) = 0.
-4, -2
Let t(r) = -r**2 + 2. Let k be t(0). Factor 2*x - 3*x**k - 4*x**3 + 7*x**2 + x**2 - 3*x**3.
-x*(x - 1)*(7*x + 2)
Let l be 2*-1*(-1)/(8/6). Suppose 3 = -3*t + 12. Find c such that l*c**3 + 0 - 3/2*c**2 - t*c = 0.
-1, 0, 2
Let c = -56 - -1009/18. Let w(m) be the first derivative of -2/27*m**3 - 2/9*m**2 + 0*m - 4 + c*m**4. Determine h so that w(h) = 0.
-1, 0, 2
Let c(z) = 3*z**2 + 4*z - 18. Let y(j) = -j**2 - j + 6. Let g(x) = -6*c(x) - 21*y(x). Factor g(t).
3*(t - 3)*(t + 2)
Let j = -13 - -14. Let f(n) = 5*n**4 + 4*n**3 - n**2 + 4*n + 4. Let o(z) = -z**4 - z**3 - z - 1. Let k(r) = j*f(r) + 4*o(r). Factor k(s).
s**2*(s - 1)*(s + 1)
Let k(l