/21*y**3. Factor g(s).
s*(s - 1)**2*(s + 7)/7
Let b(f) be the second derivative of 0 + 12*f + 1/2*f**2 - 1/480*f**5 - 3/16*f**3 + 1/32*f**4. Let y(i) be the first derivative of b(i). Factor y(x).
-(x - 3)**2/8
Factor 0 - 1/4*s**2 - 11/4*s.
-s*(s + 11)/4
Let a(k) = k**3 - 17*k**2 + k - 13. Let p be a(17). Let 21*u + 40 - 21*u**4 - 75*u**3 - 34 - 21*u**p - 18*u**2 = 0. What is u?
-1, -2/7, 1/2
Let h = 640 + -638. Let m(z) be the first derivative of -16/21*z**3 - 5/14*z**4 + 4/7*z - 7 - 1/7*z**h. Factor m(a).
-2*(a + 1)**2*(5*a - 2)/7
Let o = -53 - -69. Suppose 5*g = -o*g + 63. Solve 2/5*x**g + 0*x**4 + 0 + 4/15*x**2 - 2/15*x**5 + 0*x = 0.
-1, 0, 2
Let o = -42 + 15. Let z = -25 - o. Solve 0*u + 1/4*u**z + 0 + 1/4*u**3 = 0 for u.
-1, 0
Let w(v) be the second derivative of v**5/70 + 25*v**4/42 + 8*v**3/7 - 299*v. Determine b, given that w(b) = 0.
-24, -1, 0
Let r = 1925 - 1922. Let l(i) be the first derivative of -5*i**2 - 10 + 3/2*i**4 - 8/3*i**r + 4*i. Factor l(w).
2*(w - 2)*(w + 1)*(3*w - 1)
Factor -12*z - 9*z**2 - 10*z**2 - 8*z**2 + 11*z**2 - 4*z**3.
-4*z*(z + 1)*(z + 3)
Let f(q) be the third derivative of q**5/420 - 19*q**4/56 + 55*q**3/21 + 8*q**2 + 33*q. Factor f(t).
(t - 55)*(t - 2)/7
Let q(a) be the first derivative of -a**6/9 + 14*a**5/45 - a**4/9 - 2. Determine n, given that q(n) = 0.
0, 1/3, 2
Let l = -742154/9 + 82605. Let a = -143 + l. Factor -a*p**3 + 2/9*p**4 + 2/9*p**5 + 2/9*p - 4/9*p**2 + 2/9.
2*(p - 1)**2*(p + 1)**3/9
Let f = 55 - 52. What is h in 2*h**f - 5*h**3 + 6*h**3 - 3*h**4 = 0?
0, 1
Let u = 200 - 95. Find t such that -u*t - 4*t**2 - 82 - 818 - 15*t = 0.
-15
Let s(d) be the second derivative of -1/300*d**6 + 1/50*d**5 + 0 + 0*d**3 + 7/2*d**2 - 1/30*d**4 - 8*d. Let m(b) be the first derivative of s(b). Factor m(l).
-2*l*(l - 2)*(l - 1)/5
Suppose 51*b - 3 = 2*u + 48*b, u = b. Let a(v) be the third derivative of -2/3*v**4 - 16/3*v**3 + 0*v - u*v**2 + 0 - 1/30*v**5. Factor a(l).
-2*(l + 4)**2
Let j(z) = -2*z - 14. Let l be j(-9). Factor l*p**3 + 5*p**3 - 5*p**3 - 4*p.
4*p*(p - 1)*(p + 1)
Suppose -y = 7*y + 416. Let r = -155/3 - y. Factor 2/3 - r*u**2 - 1/3*u.
-(u - 1)*(u + 2)/3
Suppose -3*i = 5*c + 9, -3*c - 9 = -c + 3*i. Let y(w) be the first derivative of -1 + w - 1/3*w**3 + c*w**2. Find k such that y(k) = 0.
-1, 1
Let w be 12/(-18) - -2 - -15*(-8)/144. Determine i, given that 1/4*i**2 - w*i - 1/4*i**4 + 3/4*i**3 - 1/4*i**5 + 0 = 0.
-2, -1, 0, 1
Let w(t) = -3*t**2 + 2*t + 5. Let h be w(-1). Let 0 + h*c + 3/4*c**3 - 9/4*c**2 = 0. What is c?
0, 3
Let u be (353/(-360) + 1)*(-15)/(-70). Let v(n) be the third derivative of -1/6*n**3 + 0 - u*n**5 + 3*n**2 + 0*n - 1/24*n**4. Determine b so that v(b) = 0.
-2
Find z, given that -63/2 + 21/4*z**2 + 129/4*z - 3/4*z**4 - 21/4*z**3 = 0.
-7, -3, 1, 2
Let z(t) be the first derivative of t**7/840 + t**6/120 + t**5/40 + t**4/24 + 20*t**3/3 + 19. Let j(k) be the third derivative of z(k). Factor j(l).
(l + 1)**3
Let o(g) be the first derivative of -4*g**3/21 + 12*g**2/7 - 20*g/7 - 117. What is y in o(y) = 0?
1, 5
Let l = -28 - -30. Factor -12*v**2 + 4*v**2 + 98 - 28*v + 10*v**l.
2*(v - 7)**2
Let l = 201/2 + -99. Factor l*b**4 + 0 - 3/2*b**3 + 0*b - 3*b**2.
3*b**2*(b - 2)*(b + 1)/2
Let q = -44/15 + 103/30. Let h(s) be the second derivative of 0*s**2 - q*s**3 - 3*s + 0 - 1/4*s**4. What is k in h(k) = 0?
-1, 0
Let a(s) be the first derivative of 2*s**3/3 + 20*s**2 + 72*s - 341. Factor a(m).
2*(m + 2)*(m + 18)
Factor 1/5*c**3 - 22/5*c - 16/5 - c**2.
(c - 8)*(c + 1)*(c + 2)/5
Let y(p) be the third derivative of p**7/280 - 51*p**6/320 - 7*p**5/40 + 51*p**4/64 + 13*p**3/8 - 703*p**2. What is t in y(t) = 0?
-1, -1/2, 1, 26
Let d(z) be the second derivative of -z**6/72 - z**5/12 + 7*z**3/6 - 26*z. Let w(v) be the second derivative of d(v). What is g in w(g) = 0?
-2, 0
Let f(j) be the second derivative of -1/190*j**5 + 1/57*j**4 + 0*j**2 - 5*j - 1/57*j**3 + 0. Find z such that f(z) = 0.
0, 1
Find h such that 86*h**2 - 98*h**2 - 3*h**3 - 10*h + 18 + 6*h + h = 0.
-3, -2, 1
Let w = 61 - 56. Factor 149*l**4 - 145*l**4 - 4*l**w + 2*l**5.
-2*l**4*(l - 2)
Find t, given that 30/13*t + 14/13*t**2 + 2/13*t**3 + 18/13 = 0.
-3, -1
Let z(h) be the first derivative of -16*h**3/3 - 9*h**2 - 2*h + 63. Suppose z(d) = 0. What is d?
-1, -1/8
Let q(c) = -8*c**2 + 8*c + 10. Let u(i) = 51 + 161*i**2 - 105*i - 56*i**2 - 104 - 77. Let x(s) = 40*q(s) + 3*u(s). Factor x(o).
-5*(o - 2)*(o + 1)
Let a be (-5)/((-75)/2) + (-2552)/(-660). Suppose 12/7*z**3 - 8/7*z**a + 16/7*z**2 - 8/7 - 12/7*z = 0. Calculate z.
-1, -1/2, 1, 2
Let a(i) = 8*i**2 + 3757*i + 234389. Let w(l) = -3*l**2 - 1252*l - 78129. Let o(b) = 2*a(b) + 7*w(b). What is v in o(v) = 0?
-125
Factor -6*v - 1/4*v**2 + 25/4.
-(v - 1)*(v + 25)/4
Determine a, given that 22/15*a**2 - 44/15 + 238/15*a = 0.
-11, 2/11
Let m(s) = -19*s**2 + 21*s + 76. Let f(x) = -22*x**2 + 23*x + 77. Let v(l) = 6*f(l) - 7*m(l). Find g such that v(g) = 0.
-5, 14
Let w(f) be the first derivative of 27*f**5/40 + 63*f**4/4 + 419*f**3/4 + 189*f**2/2 + 243*f/8 - 3. Factor w(z).
3*(z + 9)**2*(3*z + 1)**2/8
Suppose j = -1, 0 = 103*l - 98*l + 4*j - 6. Let r(o) be the second derivative of 0*o**l + 1/48*o**4 + 0*o**3 + 0 - 7*o - 1/80*o**5. Let r(m) = 0. What is m?
0, 1
Suppose 0 = -3*l + l. Suppose -4*c - 3*j = -48 + 16, -5*j + 20 = l. Solve 40*o**c + 4 + 46*o**3 - 7*o - 8*o + 94*o**4 + o - 26*o**2 = 0.
-1, 1/4, 2/5
Let j = -621 + 621. Let i(u) be the third derivative of 0 + 1/120*u**5 + 4*u**2 - 1/24*u**4 + 0*u + j*u**3. Let i(b) = 0. What is b?
0, 2
Suppose 134*a - 410 = -71*a. Factor 0 - b + 1/2*b**a.
b*(b - 2)/2
Solve 4/3*p**4 + 4/3*p**3 + 0 - 16/3*p**2 - 1/3*p**5 + 0*p = 0.
-2, 0, 2, 4
Suppose 0 = -2*d - 33*d + 70. Let i(x) be the first derivative of 6/13*x**d - 1 + 18/13*x + 2/39*x**3. Factor i(c).
2*(c + 3)**2/13
Let q(f) = 15*f**5 + 16*f**4 - 93*f**3 + 11*f**2 + 93*f - 37. Let u(d) = -d**5 - d**3 + d**2 - d + 1. Let c(t) = -q(t) - 5*u(t). Find r such that c(r) = 0.
-4, -1, 2/5, 1, 2
Factor -72 + 28*w**3 + 4*w**4 - 12*w - 195*w**2 + 118*w**2 + 129*w**2.
4*(w - 1)*(w + 2)*(w + 3)**2
Suppose 4*b = -13 + 29. Let i(a) be the third derivative of 4*a**2 + 0*a**b + 1/180*a**6 + 0*a + 0*a**3 + 0 - 1/90*a**5. Factor i(w).
2*w**2*(w - 1)/3
Suppose 29*z + 133 - 278 = 0. Let m(f) be the second derivative of 2*f - 1/3*f**2 + 1/24*f**4 + 0 - 1/9*f**3 - 1/180*f**6 + 1/60*f**z. Factor m(o).
-(o - 2)**2*(o + 1)**2/6
Suppose 61*y - 84*y = 0. Let p(q) be the third derivative of -6*q**2 + 1/2*q**3 + 1/4*q**4 + 0*q + y + 1/20*q**5. Suppose p(j) = 0. What is j?
-1
Let d(c) be the second derivative of c**6/240 + 7*c**5/240 + c**4/24 + c**3/2 + 21*c. Let i(u) be the second derivative of d(u). Factor i(o).
(o + 2)*(3*o + 1)/2
Let u = 77 + -67. Suppose 2*j + 9 = 5*h, 11 = 3*j + 4*h - u. Factor -5/2*l + 1/2*l**j - 1/2*l**4 + 3/2*l**2 + 1.
-(l - 1)**3*(l + 2)/2
Find n such that -6*n - 1/2*n**3 + 0 + 13/2*n**2 = 0.
0, 1, 12
Suppose 0 = -37*a - 51*a. Let b(c) be the third derivative of 1/48*c**6 + a*c + 0 + 10*c**2 + 1/24*c**5 - 5/12*c**4 - 5/3*c**3. Factor b(v).
5*(v - 2)*(v + 1)*(v + 2)/2
Let m(j) = j**4 + 146*j**3 + 247*j**2 - 6135*j - 18432. Let g(y) = 72*y**3 + 124*y**2 - 3068*y - 9216. Let f(l) = 9*g(l) - 4*m(l). Factor f(t).
-4*(t - 12)**2*(t + 4)**2
Suppose -24 = -s - 3*s. Let d be (9/(-6))/(s/(-4)). Solve 2*c**2 - 5*c**2 + d + 2*c**2 = 0 for c.
-1, 1
Let y(n) = -n**2 + n. Let p be ((-24)/(-1))/6 - (3 - 0). Let r(u) = -9*u**2 - 7*u. Let h(j) = p*r(j) - 5*y(j). Factor h(g).
-4*g*(g + 3)
Let j = 1184 - 1180. Suppose -5*i + 27 = 3*n - 6, -2*i = -4*n + 18. Factor j*l**3 - n*l + 2*l - 4*l**5 + 4*l.
-4*l**3*(l - 1)*(l + 1)
Let z(i) be the first derivative of i**4/3 + 8*i**3/9 - 14*i**2/3 + 16*i/3 - 12. Factor z(d).
4*(d - 1)**2*(d + 4)/3
Let a be 1 + (-897)/(-27) + 2/(-9). Let i = a - 32. Factor -2 + 15/2*r**2 + i*r.
(3*r + 2)*(5*r - 2)/2
Let g(j) be the third derivative of -2*j**7/175 - 2*j**6/75 + 2*j**5/75 + 2*j**4/15 + 2*j**3/15 - j**2 + 13. Determine o so that g(o) = 0.
-1, -1/3, 1
Let b be 5/(-25) + (-22)/(-10) + 27. What is d in b*d**2 + 2*d - 46*d - 28*d**3 + 8 + 35*d**2 = 0?
2/7, 1
Let w = 25744/63 - 3670/9. Factor 92/21*k**3 + 22/7*k**4 + w*k**5 + 20/7*k**2 + 2/21 + 6/7*k.
2*(k + 1)**3*(3*k + 1)**2/21
Let b = 3/103