 -57. Let p(j) be the second derivative of 0 + 1/5*j**2 - j + 1/10*j**4 - q*j**3 - 1/50*j**5. Factor p(f).
-2*(f - 1)**3/5
Let z(h) = h**2. Let v be z(-2). Let s be 3/12 - (-1)/v. Determine l, given that -l**2 - 1/4*l**3 - s - 5/4*l = 0.
-2, -1
Let u(t) be the first derivative of -3 + 0*t + 2/3*t**3 + 1/20*t**5 - 5/16*t**4 - 1/2*t**2. Factor u(v).
v*(v - 2)**2*(v - 1)/4
Find n such that 0 + 0*n - 1/8*n**2 - 1/8*n**4 + 1/4*n**3 = 0.
0, 1
Let o(v) be the third derivative of -v**8/336 + v**7/35 - 3*v**6/40 + 2*v**2. Let o(d) = 0. What is d?
0, 3
Factor 0*f + 0 + 8/5*f**2 - 2/5*f**3.
-2*f**2*(f - 4)/5
Suppose 5*j - 5*w + 3 = 8, 3*j - 5*w = -1. Factor -1/5*q**4 - 3/5*q**2 + 1/5*q + 3/5*q**j + 0.
-q*(q - 1)**3/5
Let y(b) = -1. Let z(k) = -k**2 - 8*k - 13. Let t(v) = -6*y(v) - 2*z(v). Factor t(n).
2*(n + 4)**2
Let h be ((-12)/(-9))/((-6)/(-18)). Factor 0*o**2 + o**2 - 5*o**h + 9*o**4 - 5*o**2 - 4*o + 4*o**3.
4*o*(o - 1)*(o + 1)**2
Let o be (-2)/7 - 130/35. Let h be o + 3 + 2 + -1. Factor -4/5*r**2 + h*r + 2/5 + 2/5*r**4 + 0*r**3.
2*(r - 1)**2*(r + 1)**2/5
Suppose 29*s - 6 = 27*s. Factor 1/3 - 1/6*l**s + 1/2*l + 0*l**2.
-(l - 2)*(l + 1)**2/6
Let h = 349/1197 - 1/171. Suppose 0*z + 2/7*z**2 - h*z**4 + 0*z**3 + 0 = 0. Calculate z.
-1, 0, 1
Let i(o) be the second derivative of o**5/110 + 2*o**4/33 + 4*o**3/33 + 5*o. Factor i(n).
2*n*(n + 2)**2/11
Let m = 6 + -3. Let -m*p + p + p**3 - 3*p**3 + 4*p + 2*p**2 - 2 = 0. Calculate p.
-1, 1
Let d(v) = 4*v**2 - 11*v - 5. Let o(f) = -2*f**2 + 6*f + 2. Let a(g) = -6*d(g) - 11*o(g). What is w in a(w) = 0?
-2, 2
Let l(v) = -v + 4. Let d be l(0). Find g such that 5*g - 4*g**3 - 2*g**2 - 2*g**4 + d*g**4 - g = 0.
-1, 0, 1, 2
Let n(i) = -11*i**3 - i**2 + 11*i + 1. Let l(z) = -5*z**3 - z**2 + 5*z + 1. Let y be (-11)/(-1) - 4 - 2. Let t(s) = y*l(s) - 2*n(s). Solve t(w) = 0.
-1, 1
Suppose -39*z + 132 = 5*z. Find r such that -4/5 - 82/5*r**z + 22/5*r + 0*r**2 - 56/5*r**4 = 0.
-1, 1/4, 2/7
Let v(r) = -36*r**5 + 21*r**4 + 36*r**3 - 6*r**2 - 15*r. Let u(b) = 5*b**5 - 3*b**4 - 5*b**3 + b**2 + 2*b. Let w(g) = 15*u(g) + 2*v(g). Factor w(h).
3*h**2*(h - 1)**2*(h + 1)
Factor -2/9*v**2 + 0 - 4/9*v.
-2*v*(v + 2)/9
Factor 196/3*b**5 - 16/3*b**3 + 0*b + 0*b**4 + 0 + 0*b**2.
4*b**3*(7*b - 2)*(7*b + 2)/3
Let r(f) be the second derivative of -f**7/9 + 4*f**6/45 + f**5/3 - 2*f**4/9 - f**3/3 + 28*f. Find i, given that r(i) = 0.
-1, -3/7, 0, 1
Let c(i) = -i**3 + 13*i**2 - 23*i + 13. Let w be c(11). Solve -23/2*n**2 - 9/4*n**3 - w + 27/2*n**4 + 9*n - 27/4*n**5 = 0 for n.
-1, 2/3, 1
Factor 8*h**2 + 10*h - 5*h**3 + 2*h**2 - 5*h**2.
-5*h*(h - 2)*(h + 1)
Suppose w = 5*l - 0*l - 17, 3*w = -2*l. Let q be (-3)/9 + 16/l. Factor -q + 5 - 2*j**3.
-2*j**3
Let a(z) = z - 2. Let l be a(4). Let v = l - 4/3. Factor -2/9*d - 8/9*d**2 - v*d**3 + 0.
-2*d*(d + 1)*(3*d + 1)/9
Let 1/5*w**2 - 6/5 + 1/5*w = 0. Calculate w.
-3, 2
Let c(i) be the first derivative of 3*i**5/20 + 3*i**4/4 + 3*i**3/4 - 2. Factor c(w).
3*w**2*(w + 1)*(w + 3)/4
Factor -12/13 - 2/13*g**2 + 10/13*g.
-2*(g - 3)*(g - 2)/13
Let x be (0 + -2)*(-2 - -1). Let r be 5/(-18)*(-8)/10. Solve -2/9*y**3 + 2/9*y**4 - 2/9*y**x + 0 + r*y = 0 for y.
-1, 0, 1
Let s be 0*(0 - (-3 - -4)). Let c(q) be the first derivative of -q**2 - q**2 + 4*q + 1 - 4*q**3 + s + 3*q**3. Solve c(k) = 0.
-2, 2/3
Factor 8*u**2 - 4*u**4 - 728*u + 4*u**3 + 728*u.
-4*u**2*(u - 2)*(u + 1)
Let l(d) = d**5 - 5*d**4 + 3*d**3 - 3*d**2 + 2*d. Let m(p) = -3*p**5 + 16*p**4 - 9*p**3 + 10*p**2 - 7*p. Let f(j) = -21*l(j) - 6*m(j). What is z in f(z) = 0?
0, 1
Let c(s) = 5*s**5 + 6*s**4 - 4*s**3 + 6*s**2 + 5*s - 6. Let o(n) = 11*n**5 + 13*n**4 - 9*n**3 + 13*n**2 + 11*n - 13. Let q(b) = -13*c(b) + 6*o(b). Factor q(l).
l*(l - 1)**2*(l + 1)**2
Let u(b) = -2*b**3 + 8*b**2 - 4*b + 2. Let j(m) = -2*m**3 + 9*m**2 - 4*m + 3. Let v(a) = 4*j(a) - 6*u(a). Factor v(i).
4*i*(i - 2)*(i - 1)
Let p be (-3)/7 + 177/21. Factor -3*f**3 + p*f**4 - 2*f - 8*f**3 + 12*f**2 - 7*f**3.
2*f*(f - 1)**2*(4*f - 1)
Suppose 0 = 4*w - 8*w - 24. Let u be -1 - (w - (-3 - -1)). Find x, given that -2/5*x**u - 2/5*x**2 + 2/5*x + 2/5 = 0.
-1, 1
Factor -3*i**2 + 3 + 79*i - 79*i.
-3*(i - 1)*(i + 1)
Let v(i) be the third derivative of 0*i + 1/6*i**3 + 1/12*i**4 + 0 - 1/210*i**7 - 1/60*i**6 + 0*i**5 - 3*i**2. Let v(l) = 0. What is l?
-1, 1
Let x(m) be the second derivative of 3*m**5/20 - m**4/4 - m**3/2 + 3*m**2/2 - 8*m. Find c, given that x(c) = 0.
-1, 1
Let u(o) = o**3 - o + 1. Let z(d) = 2*d**4 - 10*d**3 + 42*d**2 - 50*d + 22. Let h(g) = 6*u(g) - z(g). Find c such that h(c) = 0.
1, 2, 4
Let u be (22/(-330))/(3/(-18)). Factor 0 - 2/5*y + u*y**2.
2*y*(y - 1)/5
Let t(s) = -s**2 - 3*s + 1. Let z be t(-5). Let a be (z/6)/((-2)/4). Suppose 5*l**3 + l**3 - 2*l**2 + 2 - 4*l**a - 2*l = 0. What is l?
-1, 1
Let k = 141 + -139. Factor 0 + 0*i + 2/9*i**k + 2/3*i**4 - 2/9*i**5 - 2/3*i**3.
-2*i**2*(i - 1)**3/9
Let q(g) be the first derivative of -1/2*g**4 + 0*g + 5 - g**2 + 4/3*g**3. Let q(a) = 0. Calculate a.
0, 1
Let d(a) be the first derivative of 5*a**6/18 + 2*a**5/3 - 10*a**3/9 - 5*a**2/6 + 5. Factor d(b).
5*b*(b - 1)*(b + 1)**3/3
Let d(c) be the first derivative of -c**6/60 - c**5/20 - c**4/24 - 3*c + 6. Let p(q) be the first derivative of d(q). Factor p(x).
-x**2*(x + 1)**2/2
Factor 3/5*y**2 + 78/5*y + 507/5.
3*(y + 13)**2/5
Let x(u) be the third derivative of u**7/1260 - u**5/360 - 4*u**2. Suppose x(q) = 0. What is q?
-1, 0, 1
Let v(t) be the second derivative of t**4/4 + t**3/3 + t**2/6 + 19*t. Factor v(z).
(3*z + 1)**2/3
Let r(w) be the third derivative of w**5/300 + w**4/15 + 8*w**3/15 + w**2. Factor r(y).
(y + 4)**2/5
Let y(n) be the third derivative of n**6/300 - 2*n**5/25 + 4*n**4/5 - 64*n**3/15 + 6*n**2. Determine o, given that y(o) = 0.
4
Let m(v) be the third derivative of 0 + 1/84*v**4 + 0*v**3 + 2/147*v**7 + 1/35*v**6 + 0*v + 1/35*v**5 + 1/392*v**8 - 2*v**2. Factor m(i).
2*i*(i + 1)**3*(3*i + 1)/7
Factor -2/3*r**2 - 6 - 4*r.
-2*(r + 3)**2/3
Suppose 4*o = 3 + 13. Let h(a) be the second derivative of 1/10*a**5 - 2*a - 1/3*a**3 + 0*a**o + 0 + 1/2*a**2 - 1/30*a**6. Factor h(v).
-(v - 1)**3*(v + 1)
Let d(h) = -2*h**4 + 8*h**3 + 4*h**2 - 8*h - 2. Let n(p) = -p**4 + 7*p**3 + 3*p**2 - 7*p - 2. Let r(w) = -3*d(w) + 4*n(w). Find c such that r(c) = 0.
-1, 1
Suppose 3*i = 3*k - 12, k - 5*i - 1 = 7. Factor -5 + j**2 - 2*j + 3 + k.
(j - 1)**2
Factor -8/13*j + 2/13*j**3 - 4/13*j**2 + 16/13.
2*(j - 2)**2*(j + 2)/13
Suppose -5*d = 3*j + 11, 7*d + 10 = -2*j + 3*d. Let t(l) = l**2 - 4*l + 3. Let s be t(j). Factor 0*b + s*b**3 + 3/2 - 3*b**2 + 3/2*b**4.
3*(b - 1)**2*(b + 1)**2/2
Let u(g) be the third derivative of -2/5*g**3 + 0*g - 6*g**2 + 1/100*g**5 + 0 + 0*g**4. Solve u(j) = 0.
-2, 2
Find z, given that -56/5*z**2 + 0 - 2/5*z**3 - 392/5*z = 0.
-14, 0
Let a be (-1 + 1)*1/(-2). Let v(z) = -z**2 + 2. Let y be v(a). Suppose 2 - y - k**4 + k**3 = 0. What is k?
0, 1
Let b = 3 - -5. Let l be (-6)/15*(-10)/b. Solve l + 2*h + 3/2*h**2 = 0 for h.
-1, -1/3
Let b be 56/18 + 1/(-9). Let x = 1057/422 + -1/211. Factor 1 - 1/2*d - 9/2*d**2 - x*d**4 + 13/2*d**b.
-(d - 1)**3*(5*d + 2)/2
Let c be 254/7 - 4/14. Let l be (c/(-15))/((-2)/10). Factor -l*v**3 - 18*v**2 - 3 - 12*v - 3*v**4 - 8*v**2 + 8*v**2.
-3*(v + 1)**4
Let n be 55/15 + (-6)/9. Suppose -2*p - 2*r - 5 + 13 = 0, 0 = n*p - r - 8. Factor 0 + v**2 + 1/3*v**4 - v**p - 1/3*v.
v*(v - 1)**3/3
Solve 0*w**2 + 4/17 - 2/17*w**3 + 6/17*w = 0 for w.
-1, 2
Let v(m) be the third derivative of 2*m**7/105 + m**6/15 - m**5/5 - 4*m**4/3 - 8*m**3/3 + 15*m**2. Factor v(l).
4*(l - 2)*(l + 1)**2*(l + 2)
Factor -3*u + 2/5*u**2 - 8/5.
(u - 8)*(2*u + 1)/5
Let a = 42 + -39. Let i(w) be the first derivative of a + 1/6*w**2 + 0*w - 2/9*w**3 + 1/12*w**4. Determine j, given that i(j) = 0.
0, 1
Let p(v) = -5 + 1 - v + 1. Let n be p(-5). Let -2*c**3 - 2*c**2 - 2*c**2 + n*c**2 = 0. What is c?
-1, 0
Let q(d) be the second derivative of d**2 + 0 + 2/3*d**3 + 1/6*d**4 + 5*d. Let q(u) = 0. Calculate u.
-1
Let l(p) be the second derivative of 11/9*p**3 - p + 17/30*p**5 + 0 + 7/6*p**4 + 2/3*p**2 + 1/9*p**6. Factor l(q).
2*(q + 1)**3*(5*q + 2)/3
Let n(w) be the second derivative of w**6/12 + 9*w**5/20 + 17*w**4/24 - w**2 + 4*w. Suppose n(m) = 0. What is m?
-2, -1, 2/5
Find w, given that 9/2*w*