- 4. Let s be o(12). Let b(v) = -12*v**3 - 44*v**2 - 8*v + 56. Let h(k) = s*q(k) + 3*b(k). Factor h(g).
-4*(g - 1)*(g + 2)**2
Let f(v) be the third derivative of v**5/20 + 25*v**4/32 + 3*v**3/4 - 21*v**2. Solve f(p) = 0.
-6, -1/4
Let y be ((-15)/(-6))/5 + (-9)/18. Factor -4/7*i**3 + 0 + 0*i**4 + y*i**2 + 2/7*i**5 + 2/7*i.
2*i*(i - 1)**2*(i + 1)**2/7
Factor 6*p**4 - 8*p**2 + 5*p**4 - 7*p**4 + 4*p**2.
4*p**2*(p - 1)*(p + 1)
Let u(n) = n**4 + 3*n**3 - 4*n**2 + 4*n. Let l(c) = -3*c**4 - 8*c**3 + 11*c**2 - 11*c. Let t(d) = 4*l(d) + 11*u(d). Determine p so that t(p) = 0.
0, 1
Let u(g) be the third derivative of g**9/37800 - g**7/2100 - g**6/900 + g**4/3 + 7*g**2. Let o(r) be the second derivative of u(r). Let o(x) = 0. Calculate x.
-1, 0, 2
Let d(c) be the first derivative of c**4/26 + 2*c**3/13 + 15. Solve d(r) = 0.
-3, 0
Let b = 2/457 + 2732/2285. Suppose -21/5*g**2 - 21/5*g - b - 6/5*g**3 = 0. Calculate g.
-2, -1, -1/2
Let i(b) be the first derivative of -7*b**5/80 + b**4/4 - b**3/8 - b**2/4 + b + 2. Let m(j) be the first derivative of i(j). Factor m(g).
-(g - 1)**2*(7*g + 2)/4
Let p(x) be the second derivative of -5*x**4/12 - 5*x**3 - 20*x**2 + 20*x. Factor p(v).
-5*(v + 2)*(v + 4)
Let i(x) = -3*x**4 + 307*x**3 - 2537*x**2 + 4193*x - 1960. Let t(k) = 2*k**4 - 153*k**3 + 1268*k**2 - 2097*k + 980. Let s(r) = -3*i(r) - 7*t(r). Factor s(f).
-5*(f - 14)**2*(f - 1)**2
Let c(g) be the third derivative of -g**9/30240 - g**8/3360 + g**6/90 + g**5/20 - g**2. Let n(d) be the third derivative of c(d). Factor n(l).
-2*(l - 1)*(l + 2)**2
Let y = 312 + -310. Factor -2/7*g**y + 2/7*g**4 - 4/7*g + 0 + 4/7*g**3.
2*g*(g - 1)*(g + 1)*(g + 2)/7
Let z(q) be the third derivative of -1/12*q**4 + 1/9*q**3 + 1/30*q**5 + 0 - q**2 - 1/180*q**6 + 0*q. Factor z(s).
-2*(s - 1)**3/3
Let f(m) be the first derivative of -4*m**5/5 + 2*m**4 - 4*m**3/3 + 7. Determine z so that f(z) = 0.
0, 1
Let a(f) be the second derivative of -3/4*f**2 - 7*f + 0 + 1/16*f**4 - 1/8*f**3. Factor a(i).
3*(i - 2)*(i + 1)/4
Let k(m) be the first derivative of 1/6*m**3 + 0*m**2 - 1/2*m + 7. Suppose k(t) = 0. Calculate t.
-1, 1
Let g = 5 - -7. Suppose g = -0*v + 4*v. Suppose 2/9 + 2/9*x - 2/9*x**v - 2/9*x**2 = 0. What is x?
-1, 1
Suppose 4*f = 27 - 11. Suppose 3*q - 5*b = -25, -20 = -f*q - b - 3*b. Solve 2/3*p**4 + q*p + 0 - 4/3*p**3 - 2/3*p**2 + 4/3*p**5 = 0.
-1, -1/2, 0, 1
Let x(p) be the third derivative of -p**7/280 - p**6/60 - p**5/40 + p**3/3 + 2*p**2. Let j(b) be the first derivative of x(b). Factor j(t).
-3*t*(t + 1)**2
Let i(j) = -7*j - 2*j + 2 - 6 - j**3 + 4*j - 5*j**2. Let f be i(-4). Let 0*s - 1/2*s**2 + 0 + f*s**3 + 1/2*s**4 = 0. What is s?
-1, 0, 1
Let x = 2192/7623 + -2/1089. Determine z so that x*z**4 + 6/7*z**5 + 2/7 + 6/7*z - 4/7*z**2 - 12/7*z**3 = 0.
-1, -1/3, 1
Let f(x) = 7*x**4 - 4*x**3 - x**2 + x + 3. Let m(s) = 6*s**4 - 4*s**3 - 2*s**2 + 2*s + 2. Let i(n) = 2*f(n) - 3*m(n). Factor i(y).
-4*y*(y - 1)**2*(y + 1)
Suppose 0 = h + v - 8, 33*h - 4 = 36*h - 4*v. Factor 39/2*o**3 + 0 + 2/3*o + 20/3*o**2 + 27/2*o**h.
o*(o + 1)*(9*o + 2)**2/6
Suppose d + 4 = -4*z, 0*z - 5*z + 16 = -4*d. What is h in 4*h**4 + 8/3*h**3 - 28/3*h**2 + 8/3*h + z = 0?
-2, 0, 1/3, 1
Let i be 3/(-9) + 8/(-12). Let x be i/(0 - 3)*3. Find a such that -x - 4*a - 1 - a**2 + a + 0 = 0.
-2, -1
Find l such that 4/13*l + 0*l**2 + 2/13*l**4 - 4/13*l**3 - 2/13 = 0.
-1, 1
Let a = -388 - -1184/3. Let r(c) be the first derivative of -4*c**2 + 16*c - 3/2*c**4 - a*c**3 + 1. Solve r(b) = 0 for b.
-2, 2/3
Let b = -113566/3 + 38214. Let x = 362 - b. Solve 2*z - 2*z**3 + 4/3 - 14/3*z**2 + x*z**4 = 0.
-1, -2/5, 1
Factor -102*p - 12*p**5 + 17*p**4 - 162*p**3 + 45*p + 132*p**2 + 33*p + 58*p**4.
-3*p*(p - 2)**3*(4*p - 1)
Suppose -7*w + 2*w = -10. Suppose 0 = -0*v + v - 3. Let c**5 - 2*c**4 + 0*c**2 + 2*c**w + v*c - 4*c = 0. Calculate c.
-1, 0, 1
Let u = 23 + -20. Suppose 5*j - 2*c - c - 7 = 0, -u*j + 2*c + 4 = 0. Factor -6/5*g**j + 2/5*g**4 + 0*g**3 - 4/5*g + 0.
2*g*(g - 2)*(g + 1)**2/5
Let r(h) be the first derivative of -1/60*h**5 - 1 - 2*h + 0*h**3 + 0*h**2 - 1/36*h**4. Let c(s) be the first derivative of r(s). Factor c(y).
-y**2*(y + 1)/3
Let g be 0*-3*(-1)/6. Let u(f) be the first derivative of -1/4*f**2 - 1/6*f**3 + g*f - 2. Factor u(z).
-z*(z + 1)/2
Let l(r) = -r**2 - 1. Let f(v) = -2*v**2 + 2*v - 3. Suppose k = 4*k + 3. Let q(t) = k*f(t) + 3*l(t). What is g in q(g) = 0?
-2, 0
Let c(g) be the first derivative of -g**5/70 - 5*g**4/42 - 8*g**3/21 - 4*g**2/7 + 2*g - 3. Let k(q) be the first derivative of c(q). Factor k(s).
-2*(s + 1)*(s + 2)**2/7
Solve -4/3*a - 1/3*a**4 + 0 + 1/3*a**3 + 4/3*a**2 = 0 for a.
-2, 0, 1, 2
Suppose a = 7*a - 18. Factor 0*y**a - 2*y**3 + 5*y**3.
3*y**3
Let u(b) = -b**4 - 6*b**3 + 7*b**2 + 3*b - 3. Let m(o) = 6*o**3 - 6*o**2 - 2*o + 2. Let i(v) = 3*m(v) + 2*u(v). Factor i(x).
-2*x**2*(x - 2)*(x - 1)
Let a be (2 - -1) + (-12 - -11). Factor 0*x + 6/7*x**a - 8/7 + 2/7*x**3.
2*(x - 1)*(x + 2)**2/7
Let h be 22/28 + (-845)/91 + 9. Suppose -27/2*u - h*u**3 - 27/2 - 9/2*u**2 = 0. Calculate u.
-3
Suppose 6*f + 8 = 10*f. Let y(u) be the second derivative of 0 - 1/24*u**4 + 1/80*u**5 + 1/24*u**3 + 0*u**f - 3*u. Factor y(i).
i*(i - 1)**2/4
Factor 9/7*s**4 + 3/7 + 18/7*s + 36/7*s**2 + 30/7*s**3.
3*(s + 1)**3*(3*s + 1)/7
Let i be 6/(-14) - 832/(-1680). Let k(c) be the second derivative of 0*c**4 + 2*c + 0 + 1/50*c**5 - i*c**3 + 0*c**2. Let k(n) = 0. What is n?
-1, 0, 1
Let z(t) be the first derivative of 5*t**6/3 - 6*t**5/5 - 17*t**4/2 + 38*t**3/3 - 8*t + 1. Factor z(r).
2*(r - 1)**3*(r + 2)*(5*r + 2)
Let c = -80 - -114. Suppose 4*j**4 - 2*j**2 + 18*j**5 - c*j**4 + 14*j**3 + 0*j**2 = 0. What is j?
0, 1/3, 1
Let w(c) be the third derivative of c**8/60480 - c**7/3780 + c**6/540 - c**5/60 - c**2. Let g(p) be the third derivative of w(p). Let g(l) = 0. Calculate l.
2
Let z(o) = o**3 + 11*o**2 - o - 7. Let y be z(-11). Let i be (y/(-18))/(4/(-48)). Factor 0 + 8*h**2 - 6*h**3 - i*h.
-2*h*(3*h - 2)**2/3
Let i be (0/((-4 + 8)/(-2)))/(-1). Factor 0*z**2 + i - 2/3*z**5 + 0*z**4 - 2/3*z + 4/3*z**3.
-2*z*(z - 1)**2*(z + 1)**2/3
Let 0 + 2/5*g**4 + 2/5*g**2 + 0*g + 4/5*g**3 = 0. Calculate g.
-1, 0
Let q(o) be the second derivative of 125*o**4/12 + 50*o**3 + 90*o**2 + 11*o. Determine t so that q(t) = 0.
-6/5
Let x(v) be the first derivative of 15/4*v**4 - 3 - 12/5*v**5 + 7*v**3 - 3*v**2 + 0*v. Factor x(h).
-3*h*(h - 2)*(h + 1)*(4*h - 1)
Let f = -18 - -21. Factor -f*q + q**2 + 4*q**2 + 18*q + 6 + 4*q**2.
3*(q + 1)*(3*q + 2)
Let h(y) be the first derivative of 5*y**4/8 - 2*y**3 + y**2 + 2. Factor h(g).
g*(g - 2)*(5*g - 2)/2
Let r(v) be the first derivative of 12*v**5/25 - 2*v**4 + 13*v**3/5 - 9*v**2/10 + 5. Find h such that r(h) = 0.
0, 1/3, 3/2
Let u(j) be the third derivative of -j**6/780 - j**5/130 + j**4/156 + j**3/13 + 5*j**2. Factor u(y).
-2*(y - 1)*(y + 1)*(y + 3)/13
Let h(m) = 6 + 0 + 1 - 4 + 14*m + 11*m**2. Let v(x) = -4*x**2 - 5*x - 1. Let k(a) = -3*h(a) - 8*v(a). Find q such that k(q) = 0.
-1
Let s(g) be the third derivative of g**11/665280 + g**10/302400 - g**5/20 + 2*g**2. Let y(z) be the third derivative of s(z). Factor y(i).
i**4*(i + 1)/2
Factor 1/11*y**3 - 4/11*y - 8/11 + 2/11*y**2.
(y - 2)*(y + 2)**2/11
Let r(w) be the second derivative of 0 - 14/5*w**5 - 16/3*w**3 - 49/120*w**6 - 13/2*w**4 - 2*w**2 + 2*w. Find x such that r(x) = 0.
-2, -2/7
Let s(k) be the first derivative of 7/18*k**3 - 7 + 5/4*k**2 + 3/2*k + 1/24*k**4. Factor s(u).
(u + 1)*(u + 3)**2/6
Let n(y) be the third derivative of -y**7/420 - y**6/240 + y**5/40 + y**4/48 - y**3/6 + 4*y**2. Let n(a) = 0. What is a?
-2, -1, 1
Let t = -6 + 2. Let v(s) = -2*s - 6. Let i be v(t). Factor -h**3 - 3*h**3 + 2*h**3 + h**5 - 9*h**2 + h - 1 + 11*h**i - h**4.
(h - 1)**3*(h + 1)**2
Let t = -571/4 - -13705/96. Let y(z) be the third derivative of -1/24*z**3 - t*z**4 + 1/240*z**5 + 0 + 3*z**2 + 0*z + 1/480*z**6. Determine f so that y(f) = 0.
-1, 1
Let x(b) = -13*b**3 + 25*b**2 - 24*b - 3. Let w = 2 - -3. Let u(n) = 7*n**3 - 12*n**2 + 12*n + 1. Let p(o) = w*u(o) + 3*x(o). Determine d so that p(d) = 0.
-1/4, 2
Let w(d) = 10*d**4 + 30*d**3 - 21*d**2 - 41*d - 11. Let q(x) = 2*x**4 + 6*x**3 - 4*x**2 - 8*x - 2. Let l(t) = -22*q(t) + 4*w(t). Factor l(m).
-4*m*(m - 1)*(m + 1)*(m + 