*2. Factor u(f).
-4*(f - 2)**2
Let c = 1 - 5. Let m(p) = p**3 + 4*p**2 - 2*p - 5. Let n be m(c). Find o such that 0*o - 2/5*o**n + 0 - 2/5*o**4 + 0*o**2 = 0.
-1, 0
Let z = -18 + 24. Factor 2*j**2 + 3*j**5 + 0*j**2 + 4*j**2 - 3*j - 3*j**4 + 6*j - 3 - z*j**3.
3*(j - 1)**3*(j + 1)**2
Factor -1 - 94*f + f**2 + 93*f + 5*f**3 - 4*f**3.
(f - 1)*(f + 1)**2
Let y(i) be the first derivative of 1/84*i**7 + 0*i**3 - 1/40*i**5 + 0*i**4 + 0*i**2 + 0*i**6 - 2*i + 2. Let w(u) be the first derivative of y(u). Factor w(q).
q**3*(q - 1)*(q + 1)/2
Let d(x) be the third derivative of x**5/210 - x**4/84 - 2*x**3/21 - 5*x**2. Factor d(o).
2*(o - 2)*(o + 1)/7
Let a = 58 - 288/5. Find u, given that -2/5*u**3 + 2/5 + a*u - 2/5*u**2 = 0.
-1, 1
Suppose b = 2*v + 2, 0*b - 15 = -5*b + 5*v. Let i(x) = -x**2 - 6*x - 3. Let d be i(-3). Determine n so that d*n + 2 - b + 2*n**2 - 4*n - 2*n**3 = 0.
-1, 1
Suppose 23 - 27 = -2*a. Factor 2/3*z**5 + 2/3*z**4 - 4/3*z**3 + 2/3*z + 2/3 - 4/3*z**a.
2*(z - 1)**2*(z + 1)**3/3
Let m(p) = p**4 - 2*p**3 - 1. Let a(v) = -4*v**4 + 64*v**3 + 192*v**2 + 256*v + 8. Let g(h) = -a(h) - 8*m(h). Find q, given that g(q) = 0.
-4, 0
Let v(d) = -d**2 + 7*d - 6. Let a be v(5). Let -u**3 + 2*u**4 + 0*u**a - u**3 = 0. Calculate u.
0, 1
Let b = 3538/7 + -505. Factor 1/7*j**3 + b*j**2 + 1/7 + 3/7*j.
(j + 1)**3/7
Let u be (-214)/10 - 15/25. Let i be 14/(-77) + (-4)/u. Solve 0 + 0*b + i*b**2 + 2/3*b**5 + 0*b**4 - 2/3*b**3 = 0.
-1, 0, 1
Let d(b) be the first derivative of -b**5/5 + 5*b**4/3 - 16*b**3/3 + 8*b**2 + 9*b - 7. Let c(p) be the first derivative of d(p). Factor c(q).
-4*(q - 2)**2*(q - 1)
Let w = -3128 - -14966/5. Let a = w - -136. Factor 4/5 + 2/5*q**2 + a*q.
2*(q + 1)*(q + 2)/5
Let w be ((-2)/3*3)/(-6 + 0). Determine u so that 0 + w*u + 4/3*u**2 + u**3 = 0.
-1, -1/3, 0
Let g be 18/3 - 4/2. Let o(j) be the second derivative of 3/10*j**5 + 0*j**2 + 1/42*j**7 - 2/15*j**6 + 0 + j - 1/3*j**g + 1/6*j**3. Find s such that o(s) = 0.
0, 1
Let g(c) = -c**2 - 5*c + 4. Let d be g(-7). Let j be (16/18)/(d/(-15)). Let 2/3 + j*b**3 - 4/3*b**2 - 2/3*b**5 - 2/3*b + 2/3*b**4 = 0. What is b?
-1, 1
Factor 0 - 2/7*m + 2/7*m**2.
2*m*(m - 1)/7
Let d be (-30)/(-9) + (-4)/2. Let t = -4/3 + 2. Solve t*w + 1/3 - 4/3*w**3 - w**2 + d*w**4 = 0 for w.
-1/2, 1
Let l be (2/(-3))/(2/16*-2). Find a, given that l*a + 2/3*a**3 + 8/3*a**2 + 0 = 0.
-2, 0
Suppose 51 = -8*s + 51. Factor -4/7*w**3 + 0 + 0*w**4 + 2/7*w**5 + s*w**2 + 2/7*w.
2*w*(w - 1)**2*(w + 1)**2/7
Determine f, given that 0*f**4 - f**4 + 1372*f - 588*f**2 + 84*f**3 - 3*f**4 = 0.
0, 7
Factor 14/9*t + 16/9*t**2 + 2/3*t**3 + 4/9.
2*(t + 1)**2*(3*t + 2)/9
Let h(y) be the first derivative of y**3/3 - y**2/2 - 2*y + 8. Let h(k) = 0. Calculate k.
-1, 2
Let o be ((-7)/14 + 2*1)*2. Factor 0*i**2 + 0 + 2/7*i**5 + 0*i**4 - 4/7*i**o + 2/7*i.
2*i*(i - 1)**2*(i + 1)**2/7
Let z(h) be the first derivative of 3*h**4/16 + h**3 + 15*h**2/8 + 3*h/2 - 7. Determine b so that z(b) = 0.
-2, -1
Let q be 543/(-12)*(-48)/357. Let o = q - 84/17. What is y in 2/7*y**2 + o*y + 8/7 = 0?
-2
Let i(p) be the first derivative of 8 + 1/12*p**2 - 1/3*p + 1/18*p**3. Factor i(t).
(t - 1)*(t + 2)/6
Let d(v) be the first derivative of -3 - 4/55*v**5 - 4/11*v**3 + 7/22*v**4 + 4/11*v - 1/11*v**2. Let d(o) = 0. Calculate o.
-1/2, 1, 2
Suppose 0 = -5*v + v + 52. Let s = -8 + v. Factor -2/7*o**4 + 0*o + 0 + 2/7*o**2 - 2/7*o**3 + 2/7*o**s.
2*o**2*(o - 1)**2*(o + 1)/7
Let m be (2/(-6))/((-11)/99). Let c(r) be the third derivative of 1/180*r**5 - 1/630*r**7 - 2*r**2 + 0*r**m + 0*r + 0*r**6 + 0 + 0*r**4. Solve c(f) = 0.
-1, 0, 1
Let c be (3/(-2))/(6/(-44)). Solve c*h**2 - 12*h**2 + h**3 + h**3 - h**3 = 0.
0, 1
Let u(r) be the third derivative of r**8/168 + r**7/35 + r**6/20 + r**5/30 - 3*r**2. Factor u(m).
2*m**2*(m + 1)**3
Let g(l) be the first derivative of 3*l**5 - 10*l**4 + 35*l**3/3 - 5*l**2 - 7. Let g(z) = 0. What is z?
0, 2/3, 1
Let x(k) be the second derivative of 0 - 5/12*k**4 - 7/20*k**5 - 2*k**2 - 4*k + 8/3*k**3. Determine q, given that x(q) = 0.
-2, 2/7, 1
Suppose -16 = -2*r - 0*r. Suppose -y + r = 5. Suppose -2/5*v**4 - 2/5*v + 0 + 2/5*v**y + 2/5*v**2 = 0. What is v?
-1, 0, 1
Let a be (-2)/4 + 3 + 15/(-6). Let v(l) be the first derivative of 1/6*l**6 - 2/5*l**5 + a*l**4 + 0*l - 1/2*l**2 - 2 + 2/3*l**3. Factor v(d).
d*(d - 1)**3*(d + 1)
Factor 2*o**2 - o + 3 - o**5 - 2*o**4 + 2*o**5 - 3.
o*(o - 1)**3*(o + 1)
Let g(i) = -6*i**2 + 16*i - 10. Let q(u) = -u**2 - 7*u + 6. Let h be q(-5). Let a(m) = -2*m**2 + 5*m - 3. Let d(k) = h*a(k) - 5*g(k). Let d(x) = 0. What is x?
-1, 1
Let o(n) be the third derivative of -n**8/1008 + n**7/210 - n**6/180 - n**5/90 + n**4/24 - n**3/18 + 7*n**2. Factor o(w).
-(w - 1)**4*(w + 1)/3
Let v be (-10)/(-24) + (-68)/(-16) + -4. Let t(f) be the first derivative of -v*f**3 + 3 + 1/2*f**4 + 2/5*f**5 - f**2 + 0*f. Factor t(g).
2*g*(g - 1)*(g + 1)**2
Let k(b) be the first derivative of -2*b**5/65 - 3*b**4/26 - 2*b**3/13 - b**2/13 - 10. Factor k(m).
-2*m*(m + 1)**3/13
Suppose -3*c = 4*j + 7, 0 = -4*c - 0*c - 4*j - 4. Let n = c - 3. Factor -1/5*y**5 + 2/5*y**3 - 1/5*y + 0*y**4 + 0 + n*y**2.
-y*(y - 1)**2*(y + 1)**2/5
Factor 6/7*n**3 - 3/7 + 10/7*n - 1/7*n**4 - 12/7*n**2.
-(n - 3)*(n - 1)**3/7
Let u(p) = 2*p**5 - 18*p**3 + 10*p**2 + 10*p - 6. Let v(s) = s**5 - 19*s**3 + 11*s**2 + 9*s - 5. Let h(o) = 3*u(o) - 2*v(o). Factor h(b).
4*(b - 1)**3*(b + 1)*(b + 2)
Let s(c) be the third derivative of -3*c**6/40 - 19*c**5/30 - 11*c**4/6 - 4*c**3/3 - 4*c**2. Find t such that s(t) = 0.
-2, -2/9
Suppose -2*p = -o + 10, 2*o + 2*p + 0 = -4. Suppose 2*s + 11*s**2 + 2*s**3 - 5*s**2 - 2*s**o = 0. What is s?
-1, 0
Let v(g) = -g**2 + 1. Let n be v(1). Suppose n = k + 2*k. Find s such that 2/7*s + 0*s**4 + 0*s**2 + k - 4/7*s**3 + 2/7*s**5 = 0.
-1, 0, 1
Let b(h) be the first derivative of 2*h**6/3 - 52*h**5/5 + 48*h**4 - 48*h**3 + 53. Determine w, given that b(w) = 0.
0, 1, 6
Let n = -159/1025 - -8/41. Let y(f) be the first derivative of 2/5*f**2 - 1/5*f - n*f**5 - 3 - 2/5*f**3 + 1/5*f**4. Suppose y(c) = 0. What is c?
1
Let l(m) be the second derivative of 0*m**5 + 1/15*m**3 + 1/15*m**4 + 0 - m - 1/105*m**7 + 0*m**2 - 2/75*m**6. Solve l(q) = 0 for q.
-1, 0, 1
Determine p so that -10/7*p + 2/7*p**5 - 4/7*p**2 + 8/7*p**4 - 4/7 + 8/7*p**3 = 0.
-2, -1, 1
Let t(a) = a**2 + 6*a + 8. Let p be t(-5). Suppose -p*c + 8*c = 0. Factor -2*v**3 + 8/3*v + c + 8/3*v**2.
-2*v*(v - 2)*(3*v + 2)/3
Let m(p) = 3*p**3 + p**2. Let w(s) = -6*s**3 - 3*s**2. Let j(l) = -9*m(l) - 4*w(l). Factor j(k).
-3*k**2*(k - 1)
Find h such that -1/5*h**3 + 0 + 0*h + 0*h**2 = 0.
0
Let q = 5 - 2. Suppose -2 = -w - 2*g - q, 0 = 2*w + 3*g - 1. Factor -l**w + 3*l**3 + 5*l**5 - 5*l**3 - 3*l**4 + l**3.
l**3*(l - 1)*(4*l + 1)
Suppose 2*r = 3*r. Suppose -3*a + v = r, -3*a + 5*v - v - 9 = 0. Factor -a + 1 + y**2.
y**2
Let f(p) be the third derivative of 3*p**6/8 - 2*p**5/5 + p**4/8 + 2*p**2. Factor f(c).
3*c*(3*c - 1)*(5*c - 1)
Let z = -115 - -117. Solve -24/5*c**5 + 2/5 + 8/5*c**z - 2*c**4 + 36/5*c**3 - 12/5*c = 0 for c.
-1, 1/4, 1/3, 1
Let a(j) = j + 6*j - 4*j + 13 - 4*j. Let m be a(13). Find k, given that 0 + m*k + 0*k**2 - 2/3*k**3 = 0.
0
Let j be 224/24 + -8 - 1. Factor -b - 2/3 - j*b**2.
-(b + 1)*(b + 2)/3
Let w(p) be the second derivative of -1/3*p**4 + 2*p**2 + 0 + 2/3*p**3 - 1/5*p**5 + 5*p. Factor w(z).
-4*(z - 1)*(z + 1)**2
Let j(z) be the first derivative of z**3/9 - z**2/6 - 2*z + 58. Factor j(r).
(r - 3)*(r + 2)/3
Let p(o) be the first derivative of -5/2*o**2 + 6 + 2/3*o**3 + 2*o. Factor p(c).
(c - 2)*(2*c - 1)
Let n be ((-24)/(-40))/(1/5). Let a(h) be the second derivative of 1/6*h**n - 1/18*h**4 + 1/3*h**2 - 1/15*h**5 + 0 + 1/126*h**7 + 3*h + 0*h**6. Factor a(s).
(s - 2)*(s - 1)*(s + 1)**3/3
Let i(u) be the second derivative of u**6/30 - u**5/10 - u**4/3 + u**3/3 + 3*u**2/2 + 14*u. Determine m so that i(m) = 0.
-1, 1, 3
Let u(j) = j**4 + j**3 + j**2 - 1. Let b(p) = -9*p**4 - 16*p**3 - 18*p**2 - 6*p + 5. Let z(r) = b(r) + 6*u(r). What is h in z(h) = 0?
-1, -1/3
Let i(q) be the first derivative of q**6/6 + 2*q**5/5 - 2*q**3/3 - q**2/2 + 8. Find y such that i(y) = 0.
-1, 0, 1
Let t = 3 + 0. Determine s, given that -22*s - 4*s**3 + 1 + t + 32*s**2 + 2*s**3 - 12*s**3 = 0.
2/7, 1
Let o(i) = -i + 13. L