 h(t) be the second derivative of -22*t - 12*t**2 - 7/6*t**4 - 16/3*t**3 + 0 - 1/10*t**5. Factor h(x).
-2*(x + 2)**2*(x + 3)
Let o(p) be the third derivative of p**8/1260 + 2*p**7/315 + p**6/54 + p**5/45 - p**3/6 + 23*p**2. Let x(i) be the first derivative of o(i). Factor x(j).
4*j*(j + 1)**2*(j + 2)/3
Let b(l) = -l**3 + 57*l**2 + 72*l - 806. Let k be b(58). What is x in k*x + 6*x**2 + 0 + 3/2*x**3 = 0?
-2, 0
Let j(w) be the first derivative of -80*w - 20*w**2 + 2 - 5/3*w**3. Solve j(o) = 0.
-4
What is m in -7*m**4 - 29*m**2 + 3*m**4 - 20 - 43*m**2 + 27*m + 32*m**3 + 37*m = 0?
1, 5
Solve -2/11*d**2 - 1058/11 + 92/11*d = 0.
23
Let v = 2321/415 - 16/83. Suppose 3*i - 9 = 3*m, 2*i + 2*m - 5 = 1. Factor 3/5*b**i + 81/5 + 81/5*b + v*b**2.
3*(b + 3)**3/5
Let v(r) be the first derivative of -r**4/32 - 55*r**3/24 - 91*r**2/2 + 98*r + 92. Factor v(f).
-(f - 1)*(f + 28)**2/8
Let 51*l + 6*l**2 - 39*l - 10*l**2 + l**2 = 0. Calculate l.
0, 4
Suppose -c + 4*c = 6. Suppose 3*i = -21, -9*i + 7*i - 2 = 4*n. Factor 2*d**2 - 2*d**4 + 1/2*d**5 + 3/2*d**n - c*d + 0.
d*(d - 2)**2*(d - 1)*(d + 1)/2
Let l(k) be the third derivative of 4*k**7/525 - 2*k**6/25 + 3*k**5/10 - 9*k**4/20 - 71*k**2. Determine a so that l(a) = 0.
0, 3/2, 3
Let w(c) = 6*c - 6. Let k(u) be the third derivative of u**5/60 - u**3/6 - 10*u**2. Let t(h) = 2*k(h) - w(h). Suppose t(g) = 0. What is g?
1, 2
Let u(d) be the third derivative of -d**7/105 + 73*d**6/60 + 191*d**5/15 + 155*d**4/3 + 104*d**3 + 122*d**2. Solve u(h) = 0 for h.
-2, -1, 78
Suppose 0 = 2*h + 5*o + 23, -h + 4*o + 26 = 5. Let g(b) = 9*b**3 + 31*b**2 + 75*b + 49. Let j(i) = -i**3 + i**2 - 1. Let x(d) = h*g(d) + 4*j(d). Factor x(v).
5*(v + 1)*(v + 3)**2
Let u be ((-152)/95)/(-4 + 72/20). Solve 315/2*a**u - 490*a**2 - 240*a - 100*a**3 - 32 - 49/2*a**5 = 0 for a.
-1, -2/7, 4
Let m(k) be the third derivative of -k**5/12 + 25*k**4/8 - 65*k**3/3 + 457*k**2. Factor m(g).
-5*(g - 13)*(g - 2)
Let v(g) = -5*g**4 + 5*g**3 + 3*g**2 - 10*g + 4. Let m(u) = u**4 - u**3 + u**2. Suppose 0*i - i = 6. Let r(a) = i*m(a) - 2*v(a). Factor r(x).
4*(x - 1)**3*(x + 2)
Let h(d) be the third derivative of d**6/15 + d**5/15 - 2*d**4/3 - 2*d**3 - 18*d**2 + 1. Factor h(z).
4*(z + 1)**2*(2*z - 3)
Let v be 6/21 + 3/14. Suppose 0 = -3*y + 3*a + 15, 20 = -3*y - 4*a. Solve -1/2*g**4 + 0*g - g**3 + y - v*g**2 = 0.
-1, 0
Suppose 0 = -3*z + 2*q + 16, q + 359 - 350 = 2*z. Factor -4/3*w**z - 44/9*w + 16/9.
-4*(w + 4)*(3*w - 1)/9
Let y(t) be the first derivative of -2*t**3/3 + 62*t**2 - 1922*t + 57. What is f in y(f) = 0?
31
Factor -2/11*l + 0*l**2 + 2/11*l**3 + 0.
2*l*(l - 1)*(l + 1)/11
Let c(w) be the third derivative of -w**6/30 + 17*w**5/120 - 5*w**4/24 + w**3/12 - 27*w**2. Determine k, given that c(k) = 0.
1/8, 1
Let h(k) be the second derivative of -k**4/8 + 6*k**3 - 131*k. Let h(s) = 0. What is s?
0, 24
Let p(q) = 12*q**2 + 95*q - 168. Let n(h) = 5*h**2 + 47*h - 84. Let g(c) = -14*n(c) + 6*p(c). Determine b so that g(b) = 0.
2, 42
Let x be ((-6)/(-5))/(4*(-570)/400 - -6). Factor -6/5*v**3 + 4/5*v**2 + 0 + 8/15*v**x - 2/15*v.
2*v*(v - 1)**2*(4*v - 1)/15
Let q(w) = -w**3 + 18*w**2 - 23*w. Let o(a) = 4*a**3 - 73*a**2 + 91*a. Let l(t) = -6*o(t) - 22*q(t). Factor l(b).
-2*b*(b - 20)*(b - 1)
Let v = 16594 + -16594. Factor 2/3*i**3 + v - 2/3*i - 2/3*i**2 + 2/3*i**4.
2*i*(i - 1)*(i + 1)**2/3
Let l(h) = 3*h**2 - 5*h - 8. Let p(a) = -142*a**2 + 72*a**2 + 73*a**2 - 4*a - 7. Let v(o) = 5*l(o) - 4*p(o). Let v(s) = 0. What is s?
-1, 4
Let q(g) be the first derivative of -g**3/15 - 11*g**2/10 - 18*g/5 - 239. Factor q(z).
-(z + 2)*(z + 9)/5
Let t(u) = -14*u**3 - 10*u**2 - 14*u - 6. Let h(j) = 31*j**3 + 21*j**2 + 27*j + 11. Let d(b) = -6*h(b) - 13*t(b). Solve d(f) = 0 for f.
-1, 3
Let i(o) be the third derivative of o**6/168 - 2*o**5/35 - 5*o**4/24 - o**3/7 - 30*o**2. Suppose i(k) = 0. What is k?
-1, -1/5, 6
Suppose -4 = 4*f - 6*f. Let a(v) be the first derivative of 2*v**3 - 5 + v**f - v**3 + v**3 - 3. What is b in a(b) = 0?
-1/3, 0
Suppose 2*b + 3*b - 3*r + 88 = 0, -32 = b + 3*r. Let l be (-22)/(-40) - 4/b. Factor l*d**2 - 3*d + 3.
3*(d - 2)**2/4
Factor -1936/3 - 4/3*d**2 - 176/3*d.
-4*(d + 22)**2/3
Suppose 5*b - 4 = 21. Suppose 5*a - 9*y = -4*y, b*y - 28 = -2*a. Factor 4*f + f**2 - a*f + 3*f**2 - 4.
4*(f - 1)*(f + 1)
Factor 94*c**3 + 40*c - 46*c**3 - 205*c**2 - 23*c**3.
5*c*(c - 8)*(5*c - 1)
Suppose -4*u + m + 22 = 0, -3*m - 10 = -8*m. Suppose -26 = -4*g - 18. Find y such that 2 - 5*y + 0*y + u*y**g - y - 3*y**3 + y**3 = 0.
1
Let 0 + 20/3*c + 2/3*c**2 = 0. Calculate c.
-10, 0
Let q = 9251 + -9249. Determine o, given that -22/7*o**5 + 4/7*o**4 - 8/7*o**q - 22/7*o + 4/7 + 44/7*o**3 = 0.
-1, 2/11, 1
Let i(q) be the second derivative of q**5/20 - 7*q**4/24 - 5*q**3/4 - 449*q. Solve i(j) = 0.
-3/2, 0, 5
Let z(a) be the first derivative of a**3/9 + 23*a**2/6 - 64. Factor z(q).
q*(q + 23)/3
Let c be 3 - (15 - (-4)/(-1)). Let a be -1 - 3 - (4 + c). Factor -2/9*w**2 + 0*w + 0 + a*w**3 + 2/9*w**4.
2*w**2*(w - 1)*(w + 1)/9
Suppose 33*w**2 + 18*w**4 - 28617*w + 8*w**2 + 42*w**3 - 3*w**2 + 28629*w + 2*w**5 = 0. What is w?
-6, -1, 0
Let k(c) = -c**2 - 12*c + 3. Let s be k(-12). Suppose s*j = -3*o - 9, -5*j = 2*o + 2*o + 17. Factor 9*b**3 + 23 - 15*b**2 + 9*b + 4*b**o - 13*b**2 - 17.
3*(b - 2)*(b - 1)*(3*b + 1)
Suppose -4*a + 8*a - 8 = -2*h, a + 4*h - 16 = 0. Let b(r) be the first derivative of 7 - 1/20*r**4 + a*r**2 + 0*r - 1/5*r**3. Let b(w) = 0. What is w?
-3, 0
Let z(x) = -x**3 + 12*x - 7. Let i be z(3). Factor 282*v - 282*v - 2*v**3 + i*v**4.
2*v**3*(v - 1)
Let n(q) be the second derivative of -q**4/12 - q**3/3 - q**2/2 - 68*q. Factor n(d).
-(d + 1)**2
Let z(i) = i**2 - i. Let b be (-2)/10 + (16/(-20) - 0). Let j(k) = k**2 - 10*k - 3. Let t(n) = b*j(n) + 4*z(n). Solve t(y) = 0.
-1
Let q = 16178/7 - 2311. Determine z, given that -2/7 - 3/7*z - q*z**2 = 0.
-2, -1
Find d, given that 8*d - 242 - 2*d**2 + 18*d - 70*d = 0.
-11
Let q(t) = t**5 - t**4 - 2*t**3 - 3*t**2 - t + 1. Let c(p) = -9*p**5 - 18*p**4 - 36*p**3 + 72*p**2 + 249*p + 156. Let i(v) = -c(v) - 6*q(v). Factor i(a).
3*(a - 2)*(a + 1)*(a + 3)**3
Let m(f) be the first derivative of 1/9*f**3 + 5 - 1/15*f**5 + 0*f + 1/24*f**4 - 1/12*f**2. Determine i, given that m(i) = 0.
-1, 0, 1/2, 1
Suppose -3*d = 2*p + 8, p + d = 4*d + 14. Factor -u + 2*u**2 - 2*u + 3*u**2 - 6*u**p.
-u*(u + 3)
Let n(w) be the first derivative of 0*w + 1/4*w**3 + 1/20*w**5 - 1/8*w**2 - 3/16*w**4 + 5. Determine x so that n(x) = 0.
0, 1
Suppose 10 = 5*n, 4*n = 2*o + 2*n + 44. Let z be (-29)/(-10) - 2/o. What is a in -41*a**2 - 39*a**2 + 77*a**2 - z*a**3 = 0?
-1, 0
Let w(a) be the second derivative of -1/42*a**7 + 2*a**2 + 0*a**3 - 7/12*a**4 - 15*a + 1/10*a**6 + 1/20*a**5 + 0. Factor w(n).
-(n - 2)**2*(n - 1)*(n + 1)**2
Let n(l) be the third derivative of l**7/42 - l**6/24 - l**5/3 + 5*l**4/6 + 13*l**2 - 4*l. Factor n(c).
5*c*(c - 2)*(c - 1)*(c + 2)
Let j(s) be the third derivative of 45*s**7/14 + 157*s**6/8 + 119*s**5/3 + 65*s**4/2 + 40*s**3/3 - 301*s**2. Solve j(h) = 0 for h.
-2, -1, -4/15, -2/9
Suppose 4*z + 5 + 97 = f, -f = 4*z - 110. Solve -1 + k - f*k**2 + 105*k**2 + 3 = 0.
-1, 2
Let u(w) be the first derivative of w**5/10 - 5*w**4/8 + 2*w**3/3 - 87. Factor u(v).
v**2*(v - 4)*(v - 1)/2
Let r(f) = 10*f - 4. Let j be r(1). Suppose 81 = j*q - 147. Factor 0 + 35*w**2 - w**3 - 1 - q*w**2 - 3*w.
-(w + 1)**3
Let r(g) be the second derivative of g**6/9 + 37*g**5/45 - 7*g**4/54 - 10*g**3/27 - 2*g - 32. Determine t, given that r(t) = 0.
-5, -1/3, 0, 2/5
Let v be (9/12)/((-1)/4 + 124/160). Factor -v*j**2 + 4 + 66/7*j.
-2*(j - 7)*(5*j + 2)/7
Suppose 36 = 3*x + 12. Let p be (-28)/21 - x/(-3). Suppose 1/3 - 5/3*s + s**2 + 5/3*s**3 - p*s**4 = 0. What is s?
-1, 1/4, 1
Let a(j) = -141*j - 65. Let k(o) = o**2 - 71*o - 32. Let h(u) = 2*a(u) - 5*k(u). Solve h(w) = 0 for w.
-2/5, 15
Solve -20/9*i - 14/3 - 2/9*i**2 = 0.
-7, -3
Determine i so that 1/6*i**2 - 10/3 - 1/6*i = 0.
-4, 5
Let k(r) be the third derivative of -3*r**6/80 + r**5/4 + 27*r**4/16 - 5*r**3/2 - 5*r**2 - 12. Factor k(p).
-3*(p - 5)*(p + 2)*(3*p - 1)/2
Factor 0 + 1/8*h**4 + 95/8*h + 97/8*h**3 + 191/8*h**2.
h*(h + 1)**2*(h + 95)/8
Solve 44*r**2 - 252/5*r**4 - 112/5*r + 108/5*r**5 - 12/5*r**3 + 16/5 = 0.
-1, 1/3, 2/3, 