4 + 7*y - 4*y**3 + 3*y**4 + 3 + 7*y**2. Let p(u) = 3*b(u) - 28*k(u). Factor p(j).
4*j*(j - 1)*(j + 1)**2
Suppose -53*v**2 - 9 + 154*v**2 - 3*v - 59*v**2 - 3*v**3 - 61*v**2 - 30*v = 0. What is v?
-3, -1/3
Suppose 8*n = -n - 99. Let z = -9 - n. Let 0 - o + 0*o**3 + 1/2*o**4 - 3/2*o**z = 0. What is o?
-1, 0, 2
Let o(s) be the first derivative of s**6/18 + s**5/3 + s**4/3 - 16*s**3/9 - 16*s**2/3 - 16*s/3 - 845. Factor o(m).
(m - 2)*(m + 1)*(m + 2)**3/3
Factor -1/8*v**2 - 59/8 + 15/2*v.
-(v - 59)*(v - 1)/8
Let y(z) be the first derivative of -z**4/3 - 7*z**3/9 - z**2/3 + z/3 + 9. Let y(k) = 0. What is k?
-1, 1/4
Let k(p) be the first derivative of p**6/2 - 9*p**5/5 + 9*p**4/4 - p**3 - 128. Factor k(b).
3*b**2*(b - 1)**3
Let b(s) = 65*s**3 + 155*s**2 - 300*s - 780. Let n(m) = 5*m**3 + 12*m**2 - 23*m - 60. Let i(t) = 3*b(t) - 40*n(t). Determine o so that i(o) = 0.
-3, -2, 2
Factor 6*n**2 - 5*n**3 - 3*n**3 - 2*n**3 + 5*n + 11*n**3.
n*(n + 1)*(n + 5)
Let l be (1*-130)/(8*9/72). Let s be (-1046)/l + (-114)/(-741). Suppose -s*q**2 - 4/5 + 5*q**5 + 9*q**4 - 24/5*q - 1/5*q**3 = 0. Calculate q.
-1, -2/5, 1
Let n be 4/1 - (35 - 34). Let i(a) be the first derivative of 0*a - 9/4*a**4 - 1 + 9/2*a**2 + a**n - 3/5*a**5. Factor i(q).
-3*q*(q - 1)*(q + 1)*(q + 3)
Let z(n) be the first derivative of 4/15*n**5 + 0*n + 0*n**2 + 35 + 16/9*n**3 - 4/3*n**4. What is b in z(b) = 0?
0, 2
Let m(j) = 9*j**2 - 5*j + 4. Let s be m(1). Factor -15*f - 48 - 16*f + s*f - 3*f**2 - f.
-3*(f + 4)**2
Let q(g) be the first derivative of -2*g**5/105 - 41*g**4/42 - 26*g**3/21 + 41*g**2/21 + 80*g/21 - 169. Suppose q(h) = 0. What is h?
-40, -1, 1
Let u(i) be the third derivative of 0*i**3 + 0 + 0*i**4 + 0*i + 0*i**6 - 1/280*i**7 + 1/80*i**5 + 18*i**2. Factor u(c).
-3*c**2*(c - 1)*(c + 1)/4
Let q = 76 - 62. Factor 17*l**5 - 3*l**3 - 39*l**5 + q*l**5 + 11*l**5.
3*l**3*(l - 1)*(l + 1)
Let o(s) be the third derivative of -6*s**2 + 1/1155*s**7 + 0 + 7/132*s**4 + 2/33*s**3 + 0*s + 3/110*s**5 + 1/132*s**6. Factor o(f).
2*(f + 1)**3*(f + 2)/11
Factor 4305*x - 4312*x + x**5 + 5*x**4 - 2*x**2 + 2 - 5 + 6*x**3.
(x - 1)*(x + 1)**3*(x + 3)
Suppose 3*z = 2*s - 24 + 5, 4 = -3*s - 2*z. Factor 17*p**s + 25*p + 6 + 13*p**2 - 6.
5*p*(6*p + 5)
Let i(x) be the second derivative of -x**2 + 1/6*x**4 - 10*x + 0 - x**3 + 3/10*x**5. Determine b so that i(b) = 0.
-1, -1/3, 1
Find w, given that -16/23 - 52/23*w + 10/23*w**3 - 26/23*w**2 = 0.
-1, -2/5, 4
Let k be (20/30)/((-6)/81) - -11. What is v in 15/8*v**5 + 3/4*v**3 + 0 + 0*v**k + 0*v - 21/8*v**4 = 0?
0, 2/5, 1
Let u(h) = 2*h**2 - 7. Let i be u(0). Let y = i + 9. Factor d**2 + y*d**3 + 4 + 3*d + 7*d + 5*d**2 + 2*d**2.
2*(d + 1)**2*(d + 2)
Solve -85*v**4 - 45*v**3 + 40*v**4 + 4 - 6*v**2 + 42*v**4 + 81*v**2 - 76 + 3*v**5 + 42*v = 0 for v.
-4, -1, 1, 2, 3
Suppose 2*q = -q - 2*m + 227, q - 89 = -4*m. Let g = -71 + q. Solve 0 + 2/11*y**g - 2/11*y**4 + 0*y + 0*y**3 = 0.
-1, 0, 1
Let g = -144/17 - -2534/255. Let u = g - 34/105. Solve -u*w**2 - 6/7*w + 0 = 0.
-3/4, 0
Let j(h) = 2*h + 11. Let l be j(-5). Suppose -l - 14*c**2 - 3*c + 1 + 8*c**2 = 0. Calculate c.
-1/2, 0
Let j(i) = i**3 + i**2 - i + 1. Let s(r) = 2*r + 3*r**2 + 9 - 6*r**3 + 35*r**4 - 14*r**4 - 11*r. Let o(m) = 9*j(m) - s(m). Factor o(p).
-3*p**2*(p - 1)*(7*p + 2)
Let g = -202/33 - -2792/165. Determine j, given that 0 + g*j + 132/5*j**3 - 21/5*j**4 - 45*j**2 = 0.
0, 2/7, 3
Let n(s) be the third derivative of 0*s - 7/132*s**4 - 4/33*s**3 + 1/660*s**6 + 0 - 20*s**2 - 1/165*s**5. Factor n(j).
2*(j - 4)*(j + 1)**2/11
Let d be (-2)/(-4) - (-1)/(-18). Let x be 664/996 + 4/3. Determine k so that 0 + 2/3*k**3 + 0*k + d*k**x = 0.
-2/3, 0
Suppose 4*a - 4*r - 40 = r, -5*r = 4*a. Let o be 576/120 + (16/10)/(-2). Find s, given that s - s + 0*s - s**a - 4*s**2 - s - o*s**4 - 6*s**3 = 0.
-1, 0
Let f = 74/1809 + -3/134. Let z(x) be the third derivative of 0*x - 1/270*x**5 - 1/27*x**3 + 0 + 5*x**2 - f*x**4. Solve z(j) = 0 for j.
-1
Let p(l) = l**3 + 8*l**2 - 3*l - 22. Let q be p(-8). Factor 6*x**q + 11*x - 9*x - 2*x + 2*x**3.
2*x**2*(x + 3)
Find h such that -5/6*h**5 + 0 - 5/6*h + 10/3*h**2 + 10/3*h**4 - 5*h**3 = 0.
0, 1
Let a(n) be the third derivative of n**7/945 - 11*n**6/270 + 2*n**5/3 - 325*n**4/54 + 875*n**3/27 + 404*n**2. Suppose a(k) = 0. What is k?
5, 7
Let -2/3*u**3 - 46/3*u + 6*u**2 + 10 = 0. Calculate u.
1, 3, 5
Let w(t) = -t**3 - 5*t**2 + 3*t - 14. Let v be w(-6). Factor o**v - 21*o**3 - 17*o**4 + o**3 - 4*o**2.
-4*o**2*(o + 1)*(4*o + 1)
Let t be 36/130 - (-141)/(-1833). Suppose -4/5*i + 0 + 4/5*i**3 + 1/5*i**2 - t*i**4 = 0. What is i?
-1, 0, 1, 4
Let y(f) be the first derivative of f**6/15 - f**5/2 + 4*f**4/3 - 4*f**3/3 - 15*f + 6. Let v(o) be the first derivative of y(o). Factor v(s).
2*s*(s - 2)**2*(s - 1)
Let a(q) be the third derivative of q**8/22680 + q**7/22680 + 7*q**5/60 + 11*q**2. Let g(v) be the third derivative of a(v). Factor g(s).
2*s*(4*s + 1)/9
Let r(s) = -20*s + 120. Let v be r(6). Suppose -11*u + 6*u = v. Factor u*n + 3*n**2 + 0 - 9/2*n**4 - 3/2*n**3.
-3*n**2*(n + 1)*(3*n - 2)/2
Let -3025/2*y - 1/6*y**3 + 166375/6 + 55/2*y**2 = 0. What is y?
55
Let l(g) be the first derivative of g**3/6 - 27*g**2/4 - 14*g - 277. Factor l(p).
(p - 28)*(p + 1)/2
Let w = -1 - -84. Let t = 4 + -1. Let 83*z**2 - 8*z**4 - z + 3*z**5 - w*z**2 + 6*z**t = 0. Calculate z.
-1/3, 0, 1
Let r(t) be the second derivative of t**8/2240 + t**7/280 - t**6/240 - 3*t**5/40 + 3*t**4/4 - 2*t. Let x(u) be the third derivative of r(u). Factor x(f).
3*(f - 1)*(f + 1)*(f + 3)
Let m(k) be the second derivative of k**7/105 - 14*k**6/75 + 18*k**5/25 - 17*k**4/15 + 11*k**3/15 + k - 73. Factor m(l).
2*l*(l - 11)*(l - 1)**3/5
Let o(q) be the third derivative of -q**5/150 - 7*q**4/10 + 43*q**3/15 + 12*q**2. Determine k, given that o(k) = 0.
-43, 1
Let c(h) be the first derivative of h**5/35 - 5*h**4/14 - h**3/21 + 5*h**2/7 + 91. Factor c(t).
t*(t - 10)*(t - 1)*(t + 1)/7
Determine y, given that 2/9*y**2 + 0 - 2/9*y**3 + 8/3*y = 0.
-3, 0, 4
Suppose 5*u - 2*i - 25 = 0, u = 3*i + i + 23. Suppose -2*n = 2*j - 4, 5*n - u*j + 7*j = 10. Solve -1/5*y - 1/5*y**n + 0 = 0.
-1, 0
Let a be (8/(-20) - (-38)/95)/(-1). Factor 0*o + a + 0*o**2 - 4/3*o**3 + 2/3*o**4 + 2/3*o**5.
2*o**3*(o - 1)*(o + 2)/3
Let p(k) = k**2 + k + 1. Let n(r) = 9*r**2 - 41*r + 19*r + 19*r + 6. Let h(b) = -n(b) + 6*p(b). Factor h(o).
-3*o*(o - 3)
Let h be (-6)/(3 - (-40)/(-12)). Let r = h + -16. Factor -r*p - 2*p**3 + 10*p**3 - 6*p**3.
2*p*(p - 1)*(p + 1)
Let c = -107/2 + 55. Let n = 149 - 593/4. Factor c*o - 9/4 + n*o**2.
3*(o - 1)*(o + 3)/4
Let g(s) be the second derivative of -2*s**5/135 - s**4/27 - s**3/27 + 11*s**2/2 + 18*s. Let r(a) be the first derivative of g(a). Find k such that r(k) = 0.
-1/2
Let l(k) = k**2 + k. Let h(m) = -2*m**3 - 2. Let o be 18/4 + (-15)/(-10). Let c(g) = o*l(g) - h(g). Suppose c(r) = 0. Calculate r.
-1
Let f(g) be the second derivative of g**6/720 + g**5/240 - g**4/24 - g**3/6 + 18*g. Let j(t) be the second derivative of f(t). Determine u, given that j(u) = 0.
-2, 1
Let i(b) be the second derivative of -b**5/10 + 19*b**4/2 - 56*b**3/3 + 514*b. Solve i(c) = 0 for c.
0, 1, 56
Let p(a) = -3*a**4 - 10*a**3 + 52*a**2 + 18*a - 45. Let t(d) = -7*d**4 - 19*d**3 + 105*d**2 + 37*d - 89. Let f(w) = -9*p(w) + 4*t(w). Solve f(z) = 0.
-1, 1, 7
What is d in 2/9*d - 2/9*d**3 + 2/9*d**2 - 2/9 = 0?
-1, 1
Let z = -69 - -97. Suppose n - 6 = a, -4*n + 2*a = -3*a - z. What is s in 7/2*s**n + 2/3 + 4*s - 49/6*s**3 = 0?
-2/7, 1
Factor 21 + 9 - l**2 - 3*l**2 + 0*l**2 - 6 - 20*l.
-4*(l - 1)*(l + 6)
Determine a, given that -272*a - 115*a**3 + 199*a**3 - 12*a**4 + 96 - 112*a**3 + 216*a**2 = 0.
-6, 2/3, 1, 2
Suppose 4*b + 5*r - 31 = 0, -56*b + 52*b = 4*r - 28. Solve 0*h**3 + 0 + 0*h + 1/6*h**2 - 1/6*h**b = 0 for h.
-1, 0, 1
Suppose 0 + 0*t - 6/17*t**5 + 8/17*t**4 - 2/17*t**3 + 0*t**2 = 0. What is t?
0, 1/3, 1
Factor 22/7 - 1/7*p**2 - 9/7*p.
-(p - 2)*(p + 11)/7
Let c(d) = 106*d**3 + 44*d**2 - 6*d. Let j be ((-88)/(-11))/(1/2). Let y(k) = -21*k**3 - 9*k**2 + k. Let l(w) = j*y(w) + 3*c(w). Suppose l(r) = 0. Calculate r.
-1/3, 0
Determine w so that -6/17*w**2 + 346/17*w - 228/17 = 0.
2/3, 57
Let t(y) be the third derivative of -y**5/270 + 5*y**4/36 + 16*y**3/27 + 2*y**2 - 169. Factor