 - 2)*(r - 1)*(r + 1)
Let j(d) be the second derivative of -5/12*d**4 + 20*d**2 + 36*d + 0 - 5/3*d**3. Factor j(t).
-5*(t - 2)*(t + 4)
Let x = 33 + -48. Let c = x + 18. Factor -3*i**2 + 1 - 2*i**4 + 3*i**2 + c*i**4 - 2*i**2.
(i - 1)**2*(i + 1)**2
Suppose -18*g + 78 - 6 = 0. Let o(m) be the first derivative of -3/22*m**g + 2 + 0*m - 2/55*m**5 + 0*m**2 - 4/33*m**3. Factor o(y).
-2*y**2*(y + 1)*(y + 2)/11
Let x = -5881 - -5881. Factor 0 - 1/2*j**2 + x*j.
-j**2/2
Factor -3 - 1/2*n**5 + 13/2*n + 4*n**4 - 6*n**3 - n**2.
-(n - 6)*(n - 1)**3*(n + 1)/2
Suppose 4*x = 20, -24*x = 2*g - 29*x + 25. Let n(t) be the second derivative of t - 1/6*t**4 + 0 - t**3 + g*t**2. Determine q, given that n(q) = 0.
-3, 0
Let o(d) be the third derivative of d**7/1890 - d**6/540 + d**5/540 - 2*d**2 + 295. Factor o(u).
u**2*(u - 1)**2/9
Let x = 1074 - 1072. Let u(j) be the first derivative of -6/13*j**x - 2/39*j**3 - 18/13*j - 1. What is b in u(b) = 0?
-3
Let f be (-8 + 0)/(-4) - 1. Suppose 4*r = p + 10, 5*p + 0*p = 3*r + f. Factor -p - 3*t + t**4 - 1 + t**2 + 3*t**3 + 1.
(t - 1)*(t + 1)**2*(t + 2)
Solve -33*h**2 + 162 + 0*h**3 - 9*h**3 - 3*h**3 - 15*h - 156 = 0 for h.
-2, -1, 1/4
Let p(m) be the second derivative of 1/6*m**4 + 1/10*m**5 + 12*m + 1/45*m**6 + 1/9*m**3 + 0*m**2 + 0. Solve p(n) = 0 for n.
-1, 0
Let j(i) = 4*i**2 + 63*i + 61. Let o be j(-1). Factor -1/2 - 1/6*m**o - 2/3*m.
-(m + 1)*(m + 3)/6
Let j(h) be the third derivative of h**6/80 + 23*h**5/120 - 5*h**4/6 - 3*h**3 - h**2 + 43. Factor j(q).
(q - 2)*(q + 9)*(3*q + 2)/2
Let g(d) be the second derivative of -3/4*d**4 - 11*d + 9/2*d**2 + 0 + 3/20*d**5 - 1/2*d**3. Factor g(y).
3*(y - 3)*(y - 1)*(y + 1)
Suppose -4*h + 12 = -20. Determine s so that -4*s**5 - 3*s - h*s**2 + 3*s**4 + 10*s + 5*s**4 - 3*s = 0.
-1, 0, 1
Solve -10/19 + 12/19*g - 2/19*g**2 = 0 for g.
1, 5
Suppose -169*a - 4 + 4 = 761*a. Factor -5/4*b + 1/4*b**2 + a.
b*(b - 5)/4
Let k(c) be the first derivative of 9*c**3/2 - 105*c**2/2 - 24*c + 107. Factor k(j).
3*(j - 8)*(9*j + 2)/2
Let w(o) be the third derivative of -o**6/24 + o**5/2 - 5*o**4/2 + 20*o**3/3 - 9*o**2 - 2. Factor w(l).
-5*(l - 2)**3
Let r = 83 - 81. Suppose -r*s = s + 5*s. Factor 0 - 3/4*a**4 + s*a - 3*a**3 - 3*a**2.
-3*a**2*(a + 2)**2/4
Let b(h) be the first derivative of -3/4*h**2 + 3/8*h**4 + 10 - 6*h + 2*h**3. Factor b(v).
3*(v - 1)*(v + 1)*(v + 4)/2
Let h(r) be the third derivative of r**5/90 + 7*r**4/36 - 8*r**3/9 + 40*r**2. Factor h(k).
2*(k - 1)*(k + 8)/3
Suppose -2*i + 13 = -5*j, -3*j - 3 = -0. Suppose -d + i = k, -12 = -0*d + d - 3*k. Factor 1/2*b**3 + 0*b**2 + 0 + d*b.
b**3/2
Let w(g) be the third derivative of g**8/2520 + g**7/420 + g**5/3 + 6*g**2. Let v(j) be the third derivative of w(j). Determine c so that v(c) = 0.
-3/2, 0
Let f(h) = -25*h**4 - 67*h**3 - 18*h**2 + 20*h - 2. Let g(k) = 75*k**4 + 202*k**3 + 53*k**2 - 60*k + 7. Let t(m) = 7*f(m) + 2*g(m). Factor t(j).
-5*j*(j + 1)*(j + 2)*(5*j - 2)
Let c = 9705/106513 + -2/9683. Find o, given that -4/11*o - 4/11 - c*o**2 = 0.
-2
Let o(d) be the second derivative of 2*d**7/21 - 16*d**6/15 + 24*d**5/5 - 34*d**4/3 + 46*d**3/3 - 12*d**2 + 454*d. Determine z so that o(z) = 0.
1, 2, 3
Let g = 3 + 20. Suppose 5*v = -4*z + 56, -3*z - g = -4*z + v. Factor -10*d + 4*d**4 + z*d - 11*d + 6*d**3.
2*d*(d + 1)**2*(2*d - 1)
Let c(p) be the second derivative of -35/9*p**4 + 343/135*p**6 + 0 - 11*p + 49/90*p**5 - 8/9*p**2 + 76/27*p**3. Factor c(s).
2*(s + 1)*(7*s - 2)**3/9
Let r(g) = 11*g**3 - 15*g**2 + 10*g + 8. Let z(b) = 10*b**3 - 14*b**2 + 8*b + 8. Let n(y) = -6*r(y) + 7*z(y). Let n(h) = 0. What is h?
-1, 1, 2
Let y(u) be the first derivative of u**6/120 - u**4/2 + 9*u**3 + 26. Let q(h) be the third derivative of y(h). Factor q(i).
3*(i - 2)*(i + 2)
Suppose 0 = -0*a + a - 9. Solve -15*z - 9 + a*z - 3*z**3 - 3*z**2 + 21*z = 0 for z.
-3, 1
Let f(k) = -k**3 + 12*k**2 - 4*k + 22. Let v be f(12). Let h be (-4)/(-1) - v/(-16)*2. Factor 1/4*p**2 + p + h.
(p + 1)*(p + 3)/4
Let p be (-1708)/(-305) - (-128)/(-24). Factor 0 - 2/15*g**2 - p*g.
-2*g*(g + 2)/15
Let z = 21 + -18. Let y be (z + -1)*(2 + -1). Factor -2*b**y - 66 + 66 + 8*b.
-2*b*(b - 4)
Let u(w) be the second derivative of -w**6/150 + 3*w**5/100 + w**4/10 - 14*w**3/15 + 12*w**2/5 - 398*w. Factor u(g).
-(g - 2)**3*(g + 3)/5
Let p(u) be the first derivative of -5*u**4/12 - 5*u**3/6 - 13*u + 13. Let n(y) be the first derivative of p(y). Suppose n(x) = 0. Calculate x.
-1, 0
Determine q so that 32/3*q - 8/3 - 22/3*q**3 + 8/3*q**5 - 26/3*q**2 + 16/3*q**4 = 0.
-2, 1/2, 1
Suppose 25*a = 7*a. Let u(d) be the first derivative of -d**4 + 0*d**2 - 5 + a*d - 8/3*d**3. Suppose u(h) = 0. What is h?
-2, 0
Let a(u) be the third derivative of -u**6/600 - u**5/60 + u**4/120 + u**3/6 - 30*u**2 + 3. Factor a(o).
-(o - 1)*(o + 1)*(o + 5)/5
Find c, given that -2*c**5 + 11*c + 15*c**3 + 8*c**4 - 3*c - 21*c**3 - 8*c**2 = 0.
-1, 0, 1, 2
Let d(j) be the first derivative of 4/7*j**2 - 10/21*j**3 + 1/7*j**4 - 32 - 2/7*j. Solve d(h) = 0 for h.
1/2, 1
Let x(w) = -129*w**3 + 24*w**2 + 108*w - 24. Let g(z) = 18*z**3 + 21*z**3 - 27*z - 7*z**3 + 6 - 6*z**2. Let c(f) = -21*g(f) - 5*x(f). Solve c(a) = 0 for a.
-1, 2/9, 1
Suppose -4*x - 3*m = -23, m + 3*m - 22 = -x. Let c = 13/15 + -1/5. Suppose -1/3*n**x + 0 - n**3 + c*n = 0. What is n?
-1, 0, 2/3
Let a = 45 - 42. Factor 20 + 37*o**3 + 13*o**4 - 8*o**4 - 52*o**a + 15*o - 25*o**2.
5*(o - 4)*(o - 1)*(o + 1)**2
Let j(f) be the second derivative of 0 - 5/21*f**3 - 1/42*f**4 + 3*f + 0*f**2. Suppose j(r) = 0. What is r?
-5, 0
Let u(d) be the second derivative of d**5/5 - 2*d**4/3 - 14*d**3/3 - 8*d**2 - 22*d. Let u(z) = 0. What is z?
-1, 4
Let s be -3*4/(-30) + (-26)/(-65). Let i(r) be the second derivative of 24/5*r**2 + s*r**3 + 9*r + 1/20*r**4 + 0. Determine g, given that i(g) = 0.
-4
Let y(t) = 8*t - 8*t + t**3 - t**5 + 1. Let k(q) = -8*q**5 + 11*q**3 - 2*q**2 - 3*q + 9. Let g(i) = -2*k(i) + 14*y(i). Determine x, given that g(x) = 0.
-2, -1, 1
Let v(a) be the second derivative of 1/2*a**2 - 18*a + 25/12*a**4 - 5/3*a**3 + 0. Factor v(g).
(5*g - 1)**2
Let l(b) be the third derivative of 49*b**6/60 + 7*b**5/6 - 13*b**4/12 + b**3/3 - 2*b**2 - 54. Factor l(z).
2*(z + 1)*(7*z - 1)**2
Let b(q) = 2*q + 2. Suppose -w - 5*y + 25 = 0, -5*y = -4*w - 29 + 4. Let x be b(w). Factor 9*a - 5*a + 4*a + 4*a**x.
4*a*(a + 2)
Let x be -12 + (11 - (-8 - -5)). Factor 2/5*t + 4/5 - 2/5*t**x.
-2*(t - 2)*(t + 1)/5
Suppose 4*q - 17 = 4*n - 5, -5*q + n + 23 = 0. Suppose 3*a - 12 = -4*t, -4*a - 15 = -q*t - 0*t. Solve a + 0*i + 2/3*i**2 = 0 for i.
0
Let j(y) = 7*y**2 - 8*y - 15. Let l(a) be the second derivative of -11*a**4/12 + 2*a**3 + 23*a**2/2 + 23*a. Let m(v) = 8*j(v) + 5*l(v). Factor m(k).
(k - 5)*(k + 1)
Let o = 4253/15 + -850/3. Let 8/5*l - 16/5 - o*l**2 = 0. Calculate l.
4
Let u(k) = k**2 + k - 1. Suppose -p + 3 = 13. Let x = -9 - p. Let y(i) = 6*i**2 + 18*i + 2. Let a(j) = x*y(j) - 10*u(j). Factor a(s).
-4*(s - 3)*(s + 1)
Let g(n) be the third derivative of -n**5/60 - n**3/6 - 14*n**2. Let w(u) = -u**2 + u - 2. Let b(f) = -10*g(f) + 5*w(f). Factor b(q).
5*q*(q + 1)
Let q be (-1)/(-4) + 34/56. Let o = -72127 - -504891/7. Factor q*a**2 + 0 + 0*a**3 - 4/7*a - o*a**4.
-2*a*(a - 1)**2*(a + 2)/7
Let a = 442/5 - 883/10. Solve -a*k**4 + 0 + 1/5*k**5 - 1/5*k - 3/5*k**3 + 7/10*k**2 = 0 for k.
-2, 0, 1/2, 1
Let q = -67/9 + 1678/225. Let u(d) be the third derivative of -8*d**2 - 1/525*d**7 + 0*d**4 - 1/15*d**3 + 0*d + 0*d**6 + q*d**5 + 0. Factor u(n).
-2*(n - 1)**2*(n + 1)**2/5
Suppose 41 - 51 = -5*k. Suppose -3*g + 4 = -8. Let -k*r**5 - 13*r**3 - 2*r**g - r + 19*r**3 + 2*r**2 - 3*r = 0. What is r?
-2, -1, 0, 1
Let f(q) be the first derivative of 2*q**3/3 + 10*q**2 + 50*q + 125. Solve f(i) = 0.
-5
Suppose 11*q + 49*q = 0. Let j(s) be the first derivative of -12 + 0*s**2 + q*s + 1/3*s**3. Factor j(a).
a**2
Let w = 50167 + -50165. Factor 2/5*j**w + 8/5*j - 2.
2*(j - 1)*(j + 5)/5
Let x(d) = 2*d**2 + 8*d - 6. Let s be x(-6). Let f = s + -14. Find i such that -4*i**3 + 2*i**3 - 5*i**4 - 3*i**3 - 5*i**5 + 15*i**f = 0.
0, 1
Solve 3200/7 - 72/7*l**2 - 480/7*l - 2/7*l**3 = 0 for l.
-20, 4
Let q be (-94)/8 + (42 - 30). Factor q*v**3 + 3/4*v**2 + 0 + 1/2*v.
v*(v + 1)*(v + 2)/4
Let o(m) = -23*m**2 + 124*m + 260. Let 