 - 8. Factor m(o).
-(7*o + 4)**2/4
Let m(z) be the third derivative of -1/20*z**5 + 0*z + 0 - 1/120*z**6 + 0*z**3 + z**2 - 1/12*z**4. Factor m(n).
-n*(n + 1)*(n + 2)
Let l be (-2)/(-4)*76/95. Factor l*h**2 - 2/5*h**3 + 0 + 4/5*h.
-2*h*(h - 2)*(h + 1)/5
Let k(b) be the third derivative of 4*b**2 - 1/30*b**5 + 0*b**4 + 0 - 1/105*b**7 + 0*b**3 - 1/30*b**6 + 0*b. Factor k(v).
-2*v**2*(v + 1)**2
Let j be ((-115)/(-276))/((-1)/(-8)). Let 30*f**4 + j*f**2 - 38*f**3 - 4/3 + 6*f = 0. What is f?
-2/5, 1/3, 1
Let s = 91/76 + 20/19. Let m be (2/12)/((-3)/(-27)). Factor s*w**2 + 1/4 + m*w.
(3*w + 1)**2/4
Let w(o) be the second derivative of -o**5/60 + o**3/6 - 2*o**2 - 3*o. Let s(j) be the first derivative of w(j). Determine t, given that s(t) = 0.
-1, 1
Let z(g) be the first derivative of -g**3/6 + 3*g**2/2 - 1. Suppose z(l) = 0. What is l?
0, 6
Suppose -4 + 1 = -q. Solve 5*s**4 + 0*s**5 - s**4 + s**q + 3*s**5 = 0.
-1, -1/3, 0
Let k(h) be the first derivative of h**9/12096 - h**8/2240 + h**7/1120 - h**6/1440 - 4*h**3/3 + 4. Let x(f) be the third derivative of k(f). Factor x(d).
d**2*(d - 1)**3/4
Let d = -17 + 21. Let v(t) be the second derivative of -1/168*t**7 - 1/120*t**6 + 1/24*t**d - t + 1/40*t**5 - 1/8*t**2 + 0 - 1/24*t**3. Solve v(l) = 0 for l.
-1, 1
Let x(k) be the second derivative of -k**3/6 + 3*k**2 + 7*k. Let r be x(4). Determine o, given that -2/3*o**r + 0*o + 0 = 0.
0
Let -1/6*y + 1/6*y**2 + 1/6*y**3 - 1/6*y**4 + 0 = 0. What is y?
-1, 0, 1
Let p(d) = d**2 + 5*d + 2. Let x be p(-5). Factor -x*f**2 - 2*f**3 + f + 0*f + f**5 + 2*f**2.
f*(f - 1)**2*(f + 1)**2
Let h(x) = 11*x + 99. Let p be h(-9). Determine b, given that p + 2*b**2 + 4/3*b = 0.
-2/3, 0
Let x(s) = 3*s**4 - 4*s**3 + 6*s**2 - 2. Let y(p) = -16*p**4 + 20*p**3 - 31*p**2 + 11. Let a(f) = -33*x(f) - 6*y(f). Factor a(g).
-3*g**2*(g - 2)**2
Let c(l) be the first derivative of -2*l**3/21 + 6*l**2/7 - 18*l/7 - 3. Suppose c(v) = 0. Calculate v.
3
Let k be (2 + -3)*27/9 + 5. Determine j, given that j**k + 4/3*j + 1/3 = 0.
-1, -1/3
Let k be -9*(-1)/3 - -1. Let r(m) be the third derivative of 0 - 1/3*m**3 - 1/24*m**k + 0*m + 2*m**2 + 1/60*m**5. Let r(d) = 0. Calculate d.
-1, 2
Let r(z) be the first derivative of z**5/5 - z**4 + 5*z**3/3 - z**2 + 2. Let r(w) = 0. Calculate w.
0, 1, 2
Suppose 0 = -2*t + 6. Let m be (t/(-18))/(3/(-9)). Solve 0 - m*z + 3/2*z**2 = 0.
0, 1/3
Let b = -68 - -72. Let 2 - 8/3*r**5 - 8/3*r + 16/3*r**3 - b*r**2 + 2*r**4 = 0. Calculate r.
-1, 3/4, 1
Let u(s) be the first derivative of -s**4/32 + 3*s**3/8 - 27*s**2/16 + 27*s/8 - 12. Factor u(i).
-(i - 3)**3/8
Let j be 2 + (1/3 - (-2028)/(-900)). Let a(g) be the first derivative of j*g**5 + 0*g**3 + 0*g - 1 + 1/10*g**4 + 0*g**2. Factor a(h).
2*h**3*(h + 1)/5
Let c(z) = z**4 + z**3 + z**2. Let y(r) = -5*r**5 - r**4 + 14*r**3 + 14*r**2 - 5*r - 5. Let s(k) = 4*c(k) - y(k). Solve s(f) = 0.
-1, 1
Let s = 7 - 1. Factor 4*l**3 + 0*l + l**3 - 3*l + s - 6*l**2 - 2*l**3.
3*(l - 2)*(l - 1)*(l + 1)
Let x(f) be the first derivative of f**4/20 + 2*f**3/15 + f**2/10 + 6. Factor x(r).
r*(r + 1)**2/5
Let p = 15 - 15. Let h(y) be the second derivative of -1/54*y**4 + 1/45*y**5 + 0*y**2 + p*y**3 - 1/135*y**6 - y + 0. Factor h(g).
-2*g**2*(g - 1)**2/9
Let o(m) be the first derivative of m**4/4 - 3*m**2/2 + 2*m + 4. Suppose o(z) = 0. Calculate z.
-2, 1
Let o be 1 + 34/15 - 17/(-51). Let g be (2/20)/(2/32). Factor o*p**3 + 0 + 2/5*p + 12/5*p**2 + g*p**4.
2*p*(p + 1)**2*(4*p + 1)/5
Let o(r) be the first derivative of -6*r**5/5 + 7*r**4 - 34*r**3/3 + 6*r**2 - 39. Let o(i) = 0. What is i?
0, 2/3, 1, 3
Let f be (63/(-28))/((-1)/2). Factor -21/2*w**2 - 8*w - f*w**3 - 2.
-(w + 1)*(3*w + 2)**2/2
Suppose 2*i = 4*i - 4. Factor -d - d**2 + d - i*d + 0*d.
-d*(d + 2)
Factor 1/4*t**4 + 1 - 3/4*t**2 - t + 1/2*t**3.
(t - 1)**2*(t + 2)**2/4
Suppose 5*o - 2*o = 6. Suppose 0*k = -k + o. Let -5*l + 3*l + l + 0*l - l**k = 0. Calculate l.
-1, 0
Suppose 0 = g - 4*l - 3, -6 - 9 = -5*g + 4*l. Factor 3/5*m + 3/5*m**g + 0 - 6/5*m**2.
3*m*(m - 1)**2/5
Let r(q) = 4*q**3 + 4*q**2 - 16*q - 16. Let z(u) = -u**3 - u**2 + 5*u + 5. Let o(h) = 5*r(h) + 16*z(h). Factor o(l).
4*l**2*(l + 1)
Let p(l) be the third derivative of -l**8/1120 - l**7/630 + l**6/360 - l**4/24 - 3*l**2. Let f(w) be the second derivative of p(w). Factor f(y).
-2*y*(y + 1)*(3*y - 1)
Let y(v) = v**4 + 4*v**3 - 7*v**2 + 8*v. Let j(n) = 2*n**4 + 9*n**3 - 15*n**2 + 17*n. Let o(p) = -6*j(p) + 13*y(p). Factor o(g).
g*(g - 2)*(g - 1)*(g + 1)
Let x(q) be the second derivative of q + 0*q**4 + 1/15*q**5 + 0*q**2 + 0 + 0*q**3 + 1/63*q**7 + 1/15*q**6. Factor x(s).
2*s**3*(s + 1)*(s + 2)/3
Let y(o) be the third derivative of -o**5/15 - o**4/2 - o**2. Let y(q) = 0. Calculate q.
-3, 0
Let m = 141 - 141. Let 2/3*p**3 + 0*p + 0*p**2 + m = 0. What is p?
0
Let g(h) be the first derivative of -5*h**3/18 + 10*h/3 + 13. Determine f so that g(f) = 0.
-2, 2
Suppose -4 + 12 = 4*s. Suppose 0 = -o - 2*h - 4, -s*h + 10 - 2 = 4*o. What is b in -4*b**3 - b**3 + b + o*b**3 - 2*b**2 - 2*b = 0?
-1, 0
Let c(d) = -2*d**2 + 3*d. Let o(v) = -v**2 + v. Let n(r) = c(r) - o(r). Factor n(s).
-s*(s - 2)
Let i(n) = -4*n**3 + 4*n**2 + 3*n + 3. Let d(s) = 12*s**2 + 5*s + 3*s + 8 - 11*s**3 - s**2. Let z(q) = 3*d(q) - 8*i(q). Solve z(p) = 0 for p.
0, 1
Suppose k + 8 = 3*z + 2*k, -4*k = -z - 6. Suppose 5*g - 2*a - 4 - z = 0, -2*g = -2*a - 6. What is r in 2/3*r**2 - 4/3*r + g = 0?
0, 2
Let m(c) be the first derivative of 0*c**2 - 1/10*c**4 - 2 + 0*c - 2/15*c**3. Factor m(a).
-2*a**2*(a + 1)/5
Let h be 112/18 - (7 + 488/(-72)). Find o such that -2/3*o - h*o**5 - 2/3 + 20/3*o**3 - 6*o**4 + 20/3*o**2 = 0.
-1, -1/3, 1/3, 1
Let h(c) be the third derivative of 1/210*c**7 + 0*c + 0 + 0*c**4 + 0*c**3 + 1/40*c**6 + 1/30*c**5 - 2*c**2. Let h(u) = 0. What is u?
-2, -1, 0
Factor -29 + 0*u**3 - 12*u**2 + 48*u - 11 + u**3 - 24.
(u - 4)**3
Let q(s) = -s**3 - 7*s**2 - 6*s + 6. Let p be q(-5). Let m be p + 14 - (-2)/4. Factor -m*i**3 + 1/2*i + 1/2 - 1/2*i**2.
-(i - 1)*(i + 1)**2/2
Let d(m) be the third derivative of -3*m**2 + 1/20*m**5 + 0*m**4 - 1/40*m**6 + 0*m**3 + 0 - 1/70*m**7 + 1/112*m**8 + 0*m. Factor d(q).
3*q**2*(q - 1)**2*(q + 1)
Suppose 2*f + f = 66. Let x(c) = -c**2 - 9*c - 19. Let m(p) = 2*p + 4. Let h(q) = f*m(q) + 4*x(q). Factor h(a).
-4*(a - 3)*(a + 1)
Suppose 5 = -9*u + 10*u. Factor -2*k**2 + k**4 + k**2 + k**3 + 4*k**5 - 5*k**u.
-k**2*(k - 1)**2*(k + 1)
Let g(n) be the third derivative of -n**7/1890 - n**6/540 - n**5/540 + 13*n**2. Factor g(r).
-r**2*(r + 1)**2/9
Let g(s) be the second derivative of s**4/3 - 8*s**3 + 72*s**2 - 10*s. Factor g(m).
4*(m - 6)**2
Let f(a) be the third derivative of -a**7/140 - a**6/80 + 3*a**5/40 + 5*a**4/16 + a**3/2 + 14*a**2. Determine j, given that f(j) = 0.
-1, 2
Let c(y) = -2*y - 33. Let r be c(-19). Factor -2/9*w**3 + 0*w**2 + 0 - 2/9*w**r - 4/9*w**4 + 0*w.
-2*w**3*(w + 1)**2/9
Let i(y) be the second derivative of 1/24*y**3 + 1/12*y**4 + 3/80*y**5 + 3*y + 0*y**2 + 0. Factor i(c).
c*(c + 1)*(3*c + 1)/4
Suppose 57*c**2 - 9*c**5 - 63*c**2 - 14*c**4 - 54 + 117*c + 74*c**4 - 108*c**3 = 0. What is c?
-1, 2/3, 1, 3
Let t(l) be the third derivative of -l**6/480 + l**5/120 - l**2 - 4. Suppose t(y) = 0. Calculate y.
0, 2
Let v(b) = b**2 + b. Let d(t) = -4*t**2 - 4*t. Let l(o) = -d(o) - 8*v(o). Factor l(j).
-4*j*(j + 1)
Let b(g) be the third derivative of g**6/30 + 2*g**5/15 - g**4/6 - 4*g**3/3 - 4*g**2. Determine w so that b(w) = 0.
-2, -1, 1
Let q = 9 - 3. Suppose 0 = -q*d + d. Determine i, given that 2/3*i - 1/3*i**3 - i**4 + i**2 - 1/3*i**5 + d = 0.
-2, -1, 0, 1
Let x(m) be the first derivative of -7*m**3/12 - 37*m**2/8 - 5*m/2 + 5. Factor x(v).
-(v + 5)*(7*v + 2)/4
Let -2/3*n**4 - 4/3*n + 8/3*n**2 - n**3 + 1/3*n**5 + 0 = 0. Calculate n.
-2, 0, 1, 2
Suppose -8 + 2228*g - 2*g**2 - 2232*g + 6*g**2 = 0. Calculate g.
-1, 2
Let v = 127 - 125. Let 0 - 2/5*l**v - 4/5*l = 0. What is l?
-2, 0
Let l(w) be the third derivative of w**6/840 + w**5/70 + w**4/14 + 4*w**3/21 + 31*w**2. Factor l(i).
(i + 2)**3/7
Let a be ((-12)/(-20))/((-4)/(-10)). Solve -3/4*y**3 + 3/4*y**2 + 0 + a*y = 0 for y.
-1, 0, 2
Let m(a) be the second derivative of a**4/12 - a**2/2 - 6*a. Factor m(z).
(z - 1)*(z + 1)
Let a be (-7)/21*0*1. What is f in a + 0*f**2 + 3/2*