g**3 + 21*g**2 + 20*g + 4. Let m be w(-20). Factor 6*p**3 + 17*p**2 - 3*p - 3*p**4 + p**3 - 18 + 4*p**4 - m*p**2.
(p - 1)*(p + 2)*(p + 3)**2
Suppose y - 4*y = -9. Factor 3*l - 3*l + l**5 - 5*l**4 + l + 5*l**2 + 3*l**y - 5*l.
l*(l - 4)*(l - 1)**2*(l + 1)
Let p be 105/(-28) + (-1)/4. Let o be (-8)/(1*(p - -2)). Determine f, given that 15*f**4 + 3*f**2 + 28*f**3 + f - o*f**3 - 7*f = 0.
-1, 0, 2/5
Let d(w) = 8*w - 25. Let x be d(-7). Let l be -5 + x/(-15) - (-34)/15. Factor f**2 + 2/3*f**3 - l*f + 4/3 - 1/3*f**4.
-(f - 2)*(f - 1)**2*(f + 2)/3
Let d(n) be the first derivative of n**3/30 - 7*n**2/20 - 84. Factor d(m).
m*(m - 7)/10
Let u(o) be the third derivative of -o**7/210 + o**6/480 + o**5/80 + o**2 - 5. Factor u(c).
-c**2*(c - 1)*(4*c + 3)/4
Let s = 5203 - 5201. Factor -3*v - 5 - 1/5*v**3 + 9/5*v**s.
-(v - 5)**2*(v + 1)/5
Factor -3/4*m + 0 - 3/8*m**2 + 3/8*m**3.
3*m*(m - 2)*(m + 1)/8
Let y(w) be the second derivative of -w**6/6 - w**5/2 + 5*w**4/4 - 366*w + 1. Factor y(k).
-5*k**2*(k - 1)*(k + 3)
Let b(n) be the second derivative of -n**6/255 - 4*n**5/85 + 11*n**4/102 + 6*n**3/17 + 23*n + 3. Find l such that b(l) = 0.
-9, -1, 0, 2
Let h = 636539/222796 - -3/31828. What is v in 6/7*v + 2/7*v**2 - h = 0?
-5, 2
Let t be 1/((-3)/27*-3). Find w such that -18 + 4 + 1 + 7 + 9*w - t*w**2 = 0.
1, 2
Let j(o) be the second derivative of -o**6/195 + o**5/130 + o**4/26 - 5*o**3/39 + 2*o**2/13 + 13*o - 4. Solve j(y) = 0.
-2, 1
Suppose -882/11 - 2/11*q**2 - 84/11*q = 0. What is q?
-21
Factor -8 - 8/3*s**3 + 52/3*s**2 - 20/3*s.
-4*(s - 6)*(s - 1)*(2*s + 1)/3
Let l be -1 + 1 + 1*(3 + -1). Suppose l*r + 4*c + 4 = 0, -5*c = 5*r - 0*r. Solve 1/5*q**3 + 0 + 0*q**r + 0*q + 3/5*q**4 = 0.
-1/3, 0
Let a(s) = 4*s**2 + 10*s + 2. Let g(h) = 3*h**2 + 11*h + 2. Let f(i) = -5*i + 22. Let w be f(5). Let c(x) = w*a(x) + 2*g(x). Let c(p) = 0. What is p?
-1, -1/3
Suppose -3 = -m, 22*m - 19*m = -2*a + 13. Factor -16/11*p + 4/11*p**a + 2/11*p**3 + 0.
2*p*(p - 2)*(p + 4)/11
Let k(v) be the third derivative of -v**5/90 + 5*v**4/36 - 208*v**2. Factor k(i).
-2*i*(i - 5)/3
Let t(x) be the second derivative of -27*x**5/100 - x**4 - 2*x**3/5 - 2*x - 37. Solve t(l) = 0 for l.
-2, -2/9, 0
Suppose -8*c + 40*c = 160. Let s(n) be the first derivative of 0*n - 3/2*n**2 - 3/4*n**4 + 2*n**3 + c. Factor s(h).
-3*h*(h - 1)**2
Let g = 48/655 + 2188/5895. Factor -2/3*j**3 - g*j**4 + 0*j + 2/9*j**5 + 0*j**2 + 0.
2*j**3*(j - 3)*(j + 1)/9
Let q(a) = a**3 - 15*a**2 + 42*a + 19. Let b be q(11). Let i be (3 - 5) + (-1 - b). Factor 1/2*d**5 + 0*d - 1/2*d**3 - d**2 + d**4 + i.
d**2*(d - 1)*(d + 1)*(d + 2)/2
Suppose -4 = -4*g + 4. Factor 4*c - 11*c - 3*c**3 + 4*c + 0*c**2 + 2 - 8*c**g.
-(c + 1)*(c + 2)*(3*c - 1)
Let x(a) be the first derivative of 3*a**4 + 12 - 6*a**2 - 4/5*a**5 + 8*a - 4/3*a**3. Factor x(k).
-4*(k - 2)*(k - 1)**2*(k + 1)
Let m = 1158 - 8131/7. Let l = m - -131/21. Let 10*t**3 - 7/3*t**4 + l*t + 0 - 12*t**2 = 0. Calculate t.
0, 2/7, 2
Let x be 12/2*((-12)/(-3) + -3). Suppose -4*v**4 + 11*v**4 - x*v**4 - v**2 - 4*v**3 + 4*v**5 = 0. What is v?
-1, -1/4, 0, 1
Let j(q) be the second derivative of q**4/3 - 16*q**3/3 - 18*q**2 + q - 2. Find m such that j(m) = 0.
-1, 9
Factor 2/17*x**2 - 40/17*x - 42/17.
2*(x - 21)*(x + 1)/17
Let y be (-6780)/(-570) + (-4)/(-38) - 6. Let l(d) be the first derivative of -23/16*d**4 + 0*d + 5/3*d**3 - 1/2*d**2 + 7/20*d**5 - y. Factor l(q).
q*(q - 2)*(q - 1)*(7*q - 2)/4
Let a(l) be the second derivative of l**6/120 + 69*l**5/80 + 1289*l**4/48 + 1133*l**3/8 + 1089*l**2/4 + 541*l. Factor a(r).
(r + 1)*(r + 2)*(r + 33)**2/4
Let i = -159 - -163. Let z(d) be the second derivative of 0*d**2 + 2*d + 0 - 1/36*d**i + 0*d**3. Factor z(m).
-m**2/3
Let u(z) be the second derivative of -z**5/10 + 7*z**4/6 + 4*z - 13. Factor u(f).
-2*f**2*(f - 7)
Suppose m + 5 = 11. Suppose 5*l - 3*j + m = 22, 0 = -2*l + j + 6. Factor 1/5*y**3 + 12/5*y - 8/5 - 6/5*y**l.
(y - 2)**3/5
Let y(r) be the first derivative of -1/2*r**2 + 1/2*r**4 - 1/6*r**6 - 2/3*r**3 + 1/5*r**5 + 11 + r. Factor y(s).
-(s - 1)**3*(s + 1)**2
Let n = 41 + -32. Let v = n - 6. Factor -45 + 5*j**4 + 23*j**3 - 5*j**v - 30*j + 12*j**3 + 40*j**2.
5*(j - 1)*(j + 1)*(j + 3)**2
Let p(u) be the second derivative of -u**2 + 1/75*u**5 + 0 - 10*u + 0*u**3 + 1/300*u**6 + 1/60*u**4. Let c(m) be the first derivative of p(m). Factor c(b).
2*b*(b + 1)**2/5
Let s(t) = -t**2 + 23*t + 30. Let f be s(24). Suppose -3 = -f*r + 5*r. Factor 0*a + 0 + 0*a**2 + 3/2*a**r - 3/4*a**4.
-3*a**3*(a - 2)/4
Factor 0 - 2/9*n**2 + 2/9*n**4 + 0*n**3 + 0*n.
2*n**2*(n - 1)*(n + 1)/9
Let r(n) be the second derivative of 0 + 0*n**2 - 1/30*n**4 + 0*n**3 + 19*n. Factor r(g).
-2*g**2/5
Suppose -222*t = 369*t. Factor 1/3*g**2 + 0 + 1/6*g**5 - 1/3*g**4 - 1/6*g + t*g**3.
g*(g - 1)**3*(g + 1)/6
Let j = 84 - 37. Let v = -23 + j. Solve -2*w**3 - 4*w**5 + v*w**4 + 5*w**5 - 23*w**4 = 0 for w.
-2, 0, 1
Let j(c) = 6*c**2 + 60*c + 142. Let v(g) = 2*g + 7. Let a be v(-2). Let b(h) = 2*h**2 + 20*h + 47. Let p(m) = a*j(m) - 8*b(m). Factor p(s).
2*(s + 5)**2
Let u(c) = -c**3 + 8*c**2 - 13*c - 2. Let t be u(4). Find d, given that t*d**3 - 5*d - 9*d**3 - 5 - d**2 + 2 = 0.
-1, 3
Let b(r) = r**2 - 4*r + 3. Let q be (-18 - -6)*(-2)/6. Let f be b(q). Factor -4*s**3 - 2*s**f + 3*s**2 + 3*s + 3*s**3 - 3.
-3*(s - 1)**2*(s + 1)
Let f(b) be the first derivative of -4/5*b**5 - 24*b**2 + 14 + 2*b**4 + 44/3*b**3 - 144*b. Factor f(k).
-4*(k - 3)**2*(k + 2)**2
Let b = -67461/2 + 34931. Factor -49*i**3 + 16807/10 + 7/2*i**4 - 1/10*i**5 - b*i + 343*i**2.
-(i - 7)**5/10
Let d(f) be the first derivative of 16*f**3/9 - 74*f**2/3 - 40*f - 50. Let d(w) = 0. What is w?
-3/4, 10
Let i(y) be the first derivative of -2*y**6/3 - 8*y**5/5 + 4*y**4 + 32*y**3/3 - 95. Let i(m) = 0. What is m?
-2, 0, 2
Factor -10/3*a - 34*a**3 + 0 + 62/3*a**2 + 6*a**4.
2*a*(a - 5)*(3*a - 1)**2/3
Factor 3*b**2 - 99/8*b + 3/8*b**3 + 0.
3*b*(b - 3)*(b + 11)/8
Let p(j) be the first derivative of 5*j**3/3 + 30*j**2 + 160*j + 6. Factor p(q).
5*(q + 4)*(q + 8)
Suppose -1/3*y**3 + 0 - 13/3*y**2 + 14/3*y = 0. What is y?
-14, 0, 1
Factor 3 + 3*c**2 + 1/2*c**3 + 11/2*c.
(c + 1)*(c + 2)*(c + 3)/2
Let r = -6149 - -6151. Factor 7/2*d + 3 + 1/2*d**r.
(d + 1)*(d + 6)/2
Let y(u) = -3*u - 15. Let q be y(-6). Factor -13*o + q*o**2 + 4*o + o + o**2.
4*o*(o - 2)
Let l(d) = -d**3 - d**2 - 1. Let a(n) = 9*n**4 + 43*n**3 + 58*n**2 + 24*n + 4. Let q(z) = -a(z) - 4*l(z). Factor q(t).
-3*t*(t + 1)*(t + 2)*(3*t + 4)
Let s(o) be the first derivative of 3/25*o**5 - 3/5*o**3 - 3/10*o**2 + 3/20*o**4 - 17 + 6/5*o. Factor s(r).
3*(r - 1)**2*(r + 1)*(r + 2)/5
Let r(k) = 4*k**3 + 3*k**2 - 38. Let x(v) = 15*v**3 + 13*v**2 - 150. Let s(b) = 22*r(b) - 6*x(b). Let s(p) = 0. What is p?
-4, 2
Suppose 5*w = 2*c - 29, w - 5*w = 5*c + 10. Let r(m) be the second derivative of 0*m**c + m - 1/18*m**4 + 1/45*m**6 + 0 + 1/30*m**5 - 1/9*m**3. Factor r(a).
2*a*(a - 1)*(a + 1)**2/3
Let l(g) = -g**2 + 17*g - 3. Let d(v) = 2*v**2 - 18*v + 2. Let t be ((-7)/14)/(1/(-6)). Let b(m) = t*d(m) + 2*l(m). Suppose b(z) = 0. Calculate z.
0, 5
Let z be (6/8 - 1)/((-3)/2). Let u(q) be the first derivative of 1/9*q**3 + 0*q - 6 + z*q**2. Find t such that u(t) = 0.
-1, 0
Let b(s) be the first derivative of -s**4/42 + s**3/7 - 2*s**2/7 - 13*s - 7. Let v(p) be the first derivative of b(p). Solve v(g) = 0.
1, 2
Let w = 55/8 + -49/8. Let m(r) be the second derivative of -12*r - 1/24*r**4 + 0 + 1/6*r**3 + w*r**2. Solve m(a) = 0 for a.
-1, 3
Let h(w) be the first derivative of -5*w**4 - 204*w**3 + 444*w**2 - 256*w - 309. Factor h(a).
-4*(a - 1)*(a + 32)*(5*a - 2)
Suppose -3*t = -5*n + 117, t + 49 = 2*n + 2*t. Suppose 0*v = -4*v + n. Factor 4 - 3*h**2 - h**3 - 3*h - v + 1.
-(h + 1)**3
Let q = 29 - 30. Let s(d) = -d**2 + 7*d + 6. Let p(t) = -t**2 - t. Let r(n) = q*s(n) + 4*p(n). Suppose r(k) = 0. What is k?
-3, -2/3
Suppose -2*v + 130 = 8*k - 6*k, -v - 325 = -5*k. Let -67*d**2 - k*d**2 + 135*d**2 = 0. Calculate d.
0
Let x(b) = 972*b**3 - 16100*b**2 - 7304*b - 808. Let c(f) = 648*f**3 - 10733*f**2 - 4869*f - 539. Let m(u) = -8*c(u) + 5*x(u). Find w, given that m(w) = 0.
-2/9, 17
Let 16*k**3 - 48*k - 29*k**3 + 17*k**3 + 44*k**2 = 0. What is k?
-12, 0, 1
Let u = -46 + 49. Suppose -60*n = -42*n. Factor n*w**