1)/(-2)). Determine s so that -1/2*s**2 + 1/2*s + l*s**4 + s**5 + 0 - 3/2*s**f = 0.
-1, 0, 1/2, 1
Let r(x) = -2*x**5 - 4*x**4 - 2*x**3. Let w = 6 - 2. Let v(t) = 2*t**5 + 0*t**3 - w*t**5 - 2*t**3 - 4*t**4. Let b(y) = 5*r(y) - 4*v(y). Factor b(o).
-2*o**3*(o + 1)**2
Suppose y = n, -n - 8 = -12. Factor 5/4*g**3 + 0 + g**2 + 1/4*g + 1/2*g**y.
g*(g + 1)**2*(2*g + 1)/4
Determine b, given that b**3 + 0*b + 0 + 3/2*b**2 - 1/2*b**4 = 0.
-1, 0, 3
Let x(f) be the first derivative of -f**6/50 - f**5/50 + f**4/20 + f**3/15 - 3*f + 3. Let w(n) be the first derivative of x(n). Factor w(y).
-y*(y - 1)*(y + 1)*(3*y + 2)/5
Let v(g) be the second derivative of 0*g**6 + 0*g**2 - 1/126*g**7 + 0*g**5 + 0*g**4 + 0 + 4*g + 0*g**3. Factor v(b).
-b**5/3
Let z be (-10)/105*(-12)/4. Factor -32/7*l - 512/7*l**3 + z + 512/7*l**4 + 192/7*l**2.
2*(4*l - 1)**4/7
Let y(a) be the second derivative of a**4/20 + a**3/5 - 9*a**2/10 + 3*a. Let y(p) = 0. What is p?
-3, 1
Let c(k) = k**3 + 3*k**2 - 11. Let d(g) = -2*g - 6. Let f be d(-4). Let n(i) = -2 - 3*i**2 + 6*i**f - 8 + i**3. Let j(s) = 6*c(s) - 7*n(s). Factor j(v).
-(v - 1)*(v + 2)**2
Let w(r) = 3*r - 3 + 2 + r**2 - 2*r. Let k(b) = 2 - 4 + 2 + b - 1. Let d(v) = k(v) - w(v). Factor d(i).
-i**2
Suppose 4*o + 8 = -2*z + o, z = -2*o - 6. Let v = 23/3 + -43/6. Factor v + d**z - 3/2*d.
(d - 1)*(2*d - 1)/2
Let -66/7*r**4 + 12*r**3 + 0 + 15/7*r**5 + 0*r - 24/7*r**2 = 0. Calculate r.
0, 2/5, 2
Factor -47*g - g**3 - 4*g**3 - 30*g**2 - 13*g - 40.
-5*(g + 2)**3
Suppose -3*w - 4 + 7 = 0. Let f be 1/((-2)/w + 4). Factor 1/2 + f*y**2 - y.
(y - 1)**2/2
Let z be -1*(0 + (-3)/(-3)). Let c = 2 + z. Factor -10*i + 4 + 8*i**2 - 1 - c.
2*(i - 1)*(4*i - 1)
Suppose 0*h = 4*h - 4. Let k be 1 + h - (-8)/(-6). Suppose -d**2 - k*d**3 + 0 - 1/3*d = 0. What is d?
-1, -1/2, 0
Let q(v) = 5*v**2 - v + 1. Let p be q(1). Let t(b) = 4*b**2 - 4. Let z(u) = -u + 1. Let a(r) = p*z(r) + t(r). Determine l so that a(l) = 0.
1/4, 1
Let z(x) be the third derivative of -x**6/300 + x**5/300 + x**4/120 - 10*x**2. Factor z(o).
-o*(o - 1)*(2*o + 1)/5
Let v = 65 - 65. Let m(p) be the third derivative of 0*p**3 + 0 + v*p**5 + 5/1344*p**8 + 0*p + 0*p**4 + 3*p**2 + 1/420*p**7 + 0*p**6. Find s such that m(s) = 0.
-2/5, 0
Let d = -47/56 + 9/8. Factor -2/7*q - 6/7*q**3 - d*q**4 + 0 - 6/7*q**2.
-2*q*(q + 1)**3/7
Let p(w) be the third derivative of -w**6/120 + w**5/15 - w**4/6 - 52*w**2. Solve p(r) = 0 for r.
0, 2
Let g(u) = 6*u**5 + 4*u**4 - 2*u**3 - 10*u**2 + 10*u + 10. Let n(q) = q**5 - q**3 - q**2 + q + 1. Let i(o) = -g(o) + 10*n(o). Factor i(d).
4*d**3*(d - 2)*(d + 1)
Factor 1/6*l**2 + 0 + 1/2*l.
l*(l + 3)/6
Factor 0 + 2/5*n**3 + 0*n**2 - 2/5*n.
2*n*(n - 1)*(n + 1)/5
Suppose -3 = -5*t + 2. What is u in u**2 + 5 - u + 5*u - t = 0?
-2
Suppose -4*m + 2 - 11 = -5*d, -4*m - 5*d = -41. Factor -3*x**2 + 8*x - 1 + 1 - 9*x**3 + m.
-(x - 1)*(3*x + 2)**2
Suppose 0 = -4*p + 12, 0 = 5*a - 3*a - 5*p + 11. Let c(z) be the first derivative of 3 + 0*z + 0*z**3 + z**a - 1/2*z**4. Factor c(i).
-2*i*(i - 1)*(i + 1)
Let m be 45/(-81)*6/(-5). Let p = 0 + 0. Factor p*i**2 - m - i + 1/3*i**3.
(i - 2)*(i + 1)**2/3
Let k(p) be the second derivative of -p**4/15 - 8*p**3/15 - 6*p**2/5 - 32*p. Factor k(m).
-4*(m + 1)*(m + 3)/5
Let s(y) = -2*y - 24. Let r be s(-12). Find b, given that 2/5*b + r + 2/5*b**2 - 2/5*b**3 - 2/5*b**4 = 0.
-1, 0, 1
Let a(y) be the second derivative of y**7/30 + 8*y**6/75 + 11*y**5/100 + y**4/30 + 4*y. Find s, given that a(s) = 0.
-1, -2/7, 0
Let y(v) be the second derivative of -11*v**6/135 - 7*v**5/18 - 13*v**4/18 - 17*v**3/27 - 2*v**2/9 - 7*v. Factor y(g).
-2*(g + 1)**3*(11*g + 2)/9
Suppose -6*h = -h + 575. Let p be h/(-35) - 4/14. Factor 0 + 2/5*c + 6/5*c**p - 8/5*c**2.
2*c*(c - 1)*(3*c - 1)/5
Let u(z) = 5*z**5 - 7*z**4 - 4*z**3 + 8*z**2 + 4*z + 4. Let h(f) = -6*f**5 + 8*f**4 + 5*f**3 - 9*f**2 - 5*f - 5. Let a(w) = -4*h(w) - 5*u(w). Factor a(t).
-t**2*(t - 2)**2*(t + 1)
Factor -12*a + 49*a**3 - 45*a**3 - 4*a.
4*a*(a - 2)*(a + 2)
Let -1/4*o**2 - 3/2 + 7/4*o = 0. What is o?
1, 6
Let c = 117 + -577/5. Factor 16/5 + 22/5*f**3 - 36/5*f**2 + c*f - 4/5*f**4.
-2*(f - 2)**3*(2*f + 1)/5
Let v be 3 - (12/(-30) + 1). Factor 2/5*d**4 - 8/5*d + 2/5 - 8/5*d**3 + v*d**2.
2*(d - 1)**4/5
Let i(n) = -n**2 - 5*n + 1. Let k be i(-5). Let f(x) be the first derivative of k - 1/2*x**2 + 1/4*x**4 + 1/3*x**3 - x. Factor f(c).
(c - 1)*(c + 1)**2
Let b = 124 + -118. Let f(i) be the second derivative of -1/60*i**b + 0*i**3 + 0*i**2 + 0 - i + 1/40*i**5 + 1/24*i**4 - 1/84*i**7. Factor f(s).
-s**2*(s - 1)*(s + 1)**2/2
Let p = -16 + 16. Let y(i) be the first derivative of 0*i**3 - 1 + 0*i**2 - 1/4*i**4 + p*i. Solve y(o) = 0.
0
Suppose -20*b**4 + 145*b**5 + 148*b**5 - 20*b**3 - 298*b**5 = 0. Calculate b.
-2, 0
Let o(u) = -8*u**5 - 11*u**4 - 8*u**3 + 9*u**2 + 9*u - 9. Let y(f) = f**5 + f**4 + f**3 - f**2 - f + 1. Let l(s) = -2*o(s) - 18*y(s). Factor l(n).
-2*n**3*(n - 1)**2
Let l = 1/798 - 1667/56658. Let p = 209/142 - l. Factor r**3 + r**2 - p*r**4 + 1/2 + 1/2*r**5 - 3/2*r.
(r - 1)**4*(r + 1)/2
Let c(k) be the first derivative of -4*k**5/5 + 4*k**4 - 8*k**3 + 8*k**2 - 4*k + 25. Factor c(z).
-4*(z - 1)**4
Let k = 6 - -2. Suppose k = 3*a + a. Factor -2*b**a - 2*b**3 - 2*b + 6*b + 0*b.
-2*b*(b - 1)*(b + 2)
Let y be -4 - 62/(-4)*-2. Let i = -139/4 - y. Factor 1/4*w + 0 - i*w**2.
-w*(w - 1)/4
Let 10*w**3 + 8*w**4 + 4*w**2 + 2*w**5 - 8*w**3 + 8*w**3 = 0. What is w?
-2, -1, 0
Factor p**5 + 3*p**4 + 2*p**3 - p**3 - 35*p**2 - 2*p + 32*p**2.
p*(p - 1)*(p + 1)**2*(p + 2)
Let f(z) be the second derivative of -z**6/60 - z**5/30 + z**4/6 + 3*z**2 + 6*z. Let c(h) be the first derivative of f(h). Factor c(m).
-2*m*(m - 1)*(m + 2)
Determine o, given that -12/17*o**3 - 2/17*o - 2/17*o**5 - 8/17*o**2 + 0 - 8/17*o**4 = 0.
-1, 0
Let f(m) = 3*m**3 - 33*m**2 + 54*m - 6. Let j(v) = 4*v**3 - 34*v**2 + 53*v - 7. Let c(a) = -5*f(a) + 6*j(a). Factor c(l).
3*(l - 2)**2*(3*l - 1)
Let j = 30 - 59/2. Let n(y) be the first derivative of 7/3*y**3 - 16/5*y**5 + j*y**2 + 0*y + 2*y**4 + 2. Suppose n(c) = 0. Calculate c.
-1/4, 0, 1
Let o(f) be the third derivative of 2*f**7/105 + 2*f**6/15 + 2*f**5/5 + 2*f**4/3 + 2*f**3/3 - 27*f**2. Determine x, given that o(x) = 0.
-1
Factor 17*z - 47*z - 40*z**3 + 65*z**2 - 3 + 5*z**4 + 3.
5*z*(z - 6)*(z - 1)**2
Suppose 112*g**2 - 62*g**2 + 16 + 0*g**3 + 4*g**3 - 62*g**2 = 0. Calculate g.
-1, 2
Let -2*p**4 - 3/2*p**5 + 0*p + 0 - 1/2*p**3 + 0*p**2 = 0. What is p?
-1, -1/3, 0
Let o be 6*(-3)/(-6) - 14/(-7). Let r(a) be the third derivative of -1/40*a**o + 1/8*a**4 + 1/480*a**6 + 0 - 1/3*a**3 + 0*a + 3*a**2. Factor r(w).
(w - 2)**3/4
Let h(r) = -4*r**2 - 2*r - 1. Let c be h(-2). Let o = 18 + c. Factor 0 + 3*d + 1 + d**2 - o*d.
(d - 1)**2
Let z(u) = u**3 + u**2 + u - 1. Let j be z(1). Suppose j*k - 34 = -4*g, g = k - 0*k + 1. Determine c so that 2*c**2 - 2 + 0*c**2 + g - 6*c = 0.
1, 2
Let m(u) be the second derivative of -2/15*u**3 - 1/30*u**4 - 7*u - 1/5*u**2 + 0. Suppose m(d) = 0. What is d?
-1
Let x = 7 - 4. Determine u, given that -5*u**x + 4*u**3 - 4*u**2 - 6*u**3 + u**3 = 0.
-2/3, 0
Find p, given that 2*p**3 + p**2 - 7*p**3 + 6*p**3 = 0.
-1, 0
Let t be (-3)/(1/(-1 - 0)). Find u such that -10 + t*u**2 + 4 + 3 = 0.
-1, 1
Let b(n) = n**2 + 2*n + 2. Let v be b(-2). Suppose 22*h = 19*h + 9. Factor -s**v + 5/4*s - 1/2 + 1/4*s**h.
(s - 2)*(s - 1)**2/4
Suppose 3*k = l + 6, 0 = -5*l + 2*l + 5*k - 6. Suppose -2*s - 4 = -l*s. Suppose -o + 2*o**s + 4*o - o - 2*o**3 - 2*o**2 = 0. What is o?
-1, 0, 1
Let f be (4/(-5))/((-4)/(-30)). Let p be (-8)/18*9/f. Factor p*a**3 + 1/3 - 1/3*a**4 - 2/3*a + 0*a**2.
-(a - 1)**3*(a + 1)/3
Let g(j) be the second derivative of -j**4/24 - 8*j. What is v in g(v) = 0?
0
Let y(o) be the first derivative of 0*o**2 - 6 + 1/18*o**3 + 0*o. Solve y(u) = 0 for u.
0
Let v(g) be the second derivative of -g**7/70 + 17*g**6/120 - g**5/2 + g**4/2 + 4*g**3/3 - g**2/2 - g. Let b(j) be the first derivative of v(j). Factor b(r).
-(r - 2)**3*(3*r + 1)
Let l(t) be the second derivative of 0*t**2 + 1/35*t**7 + 0 + 0*t**4 + 8/75*t**6 + 3/25*t**5 - 1/15*t**3 + 5*t. Find w, given that l(w) = 0.
-1, 0, 1/3
Find j, given that 4/9 + 2/9*j**2 + 2/3*j = 0.
-2, -1
Let g(a) be the first derivative of 1 - 3/20*a**4 - 8/5