**3 - 27*r**2/2 - 54*r - 76. Determine x so that s(x) = 0.
-3, -1/4, 2/5, 1, 3
Let r(k) = -10*k**2 + 5*k - 5. Let a(s) = 5*s**2 - 2*s + 1. Let p(i) = -5*a(i) - 2*r(i). Factor p(t).
-5*(t - 1)*(t + 1)
Let l(i) be the first derivative of -1/420*i**5 + 0*i - 3 + 1/3*i**3 + 1/168*i**4 + 0*i**2 + 1/2520*i**6. Let o(h) be the third derivative of l(h). Factor o(z).
(z - 1)**2/7
Let x = -15 - -8. Let s = -27/4 - x. Suppose 0*k + s*k**2 + 1/4*k**3 + 0 = 0. Calculate k.
-1, 0
Let p be -4 + (-687)/(-51) + -24 + 15. Let -32/17*o + 2/17*o**4 - 2/17*o**5 + p*o**2 + 24/17*o**3 + 0 = 0. Calculate o.
-2, 0, 1, 4
Factor 0 + 88/13*b**2 - 16/13*b - 140/13*b**3 + 50/13*b**4.
2*b*(b - 2)*(5*b - 2)**2/13
Let y(n) = 8*n**4 - 97*n**3 - 3*n**2 + 6. Let r(f) = -65*f**4 + 775*f**3 + 25*f**2 - 50. Let p(k) = 3*r(k) + 25*y(k). Find l, given that p(l) = 0.
0, 20
Let l(d) = d**3 + d. Let y(i) = -3*i**4 - 22*i**3 - 81*i**2 - 88*i - 36. Let n(f) = 5*l(f) - y(f). What is s in n(s) = 0?
-4, -3, -1
Let j(i) be the first derivative of 21/4*i**4 + 2*i**3 + 0*i + i**6 - 14 + 0*i**2 + 21/5*i**5. Let j(s) = 0. What is s?
-2, -1, -1/2, 0
Find s such that 322*s**2 + 296*s**2 + 5*s**3 - 8*s**2 = 0.
-122, 0
Let a(v) be the third derivative of v**5/480 + 7*v**4/192 - v**3/6 + 19*v**2 - v. Find m, given that a(m) = 0.
-8, 1
Let a(n) be the third derivative of -1/84*n**8 + 1/15*n**5 + 3*n**2 + 2/35*n**7 + 0 + 0*n**4 - 1/10*n**6 + 6*n + 0*n**3. Factor a(x).
-4*x**2*(x - 1)**3
Let q = 19 + -17. Factor 2*b + 5*b**2 + 9*b**2 - 10*b**2 + q*b.
4*b*(b + 1)
Factor 2/7*o**4 - 8/7*o - 8/7*o**2 + 0 + 2/7*o**3.
2*o*(o - 2)*(o + 1)*(o + 2)/7
Let y(u) be the second derivative of 0 + 1/16*u**4 + 27/8*u**2 - 3/4*u**3 - 11*u. Factor y(p).
3*(p - 3)**2/4
Let r(t) be the second derivative of -t**7/84 + t**6/120 + t**5/16 + t**4/24 + 215*t. Find p, given that r(p) = 0.
-1, -1/2, 0, 2
Factor -4*h**3 + 24*h**4 - 32*h + 40*h**2 + 25*h**4 - 53*h**4.
-4*h*(h - 2)*(h - 1)*(h + 4)
Let m(g) be the third derivative of -1/30*g**5 - 1/315*g**7 + 0*g + 0 + 27*g**2 - 1/60*g**6 + 0*g**3 - 1/36*g**4. What is j in m(j) = 0?
-1, 0
Let t(z) be the first derivative of z**7/840 - z**6/480 + 20*z**2 + 36. Let h(m) be the second derivative of t(m). Factor h(k).
k**3*(k - 1)/4
Let b be (-32)/(-7) + (-8)/14 + -103. Let d be -6*(-12)/b*(-2 - -1). Determine y, given that 2/11*y**3 + 8/11 - d*y - 2/11*y**2 = 0.
-2, 1, 2
Suppose -w + 8 = -f + 16, 5*f + 5*w + 10 = 0. Find b such that 12/5*b**2 + 4/5 + 12/5*b + 4/5*b**f = 0.
-1
Factor -2048 - 24*w**2 + 1/2*w**3 + 384*w.
(w - 16)**3/2
Let g = -18035 + 198387/11. What is z in -72/11 - 24/11*z - g*z**2 = 0?
-6
Let a(l) be the third derivative of 0*l**3 + 23/360*l**6 - 68/945*l**7 + 1/216*l**4 - 24*l**2 - 7/270*l**5 + 0 + 0*l + 5/189*l**8. Suppose a(j) = 0. What is j?
0, 1/5, 1/4, 1
Let p(a) be the first derivative of 5*a**7/336 + 7*a**6/144 + 11*a**5/240 + a**4/48 + 4*a**3/3 + 14. Let n(y) be the third derivative of p(y). Factor n(q).
(q + 1)*(5*q + 1)**2/2
Let n be 19/(19/(-10)) + 13. Solve 6/5 - 3/5*m**n + 0*m**2 + 9/5*m = 0 for m.
-1, 2
Let q = -213 - 50. Let n = q + 1316/5. Factor n - 1/10*t**3 + 2/5*t**2 - 1/2*t.
-(t - 2)*(t - 1)**2/10
Let z(w) = -w**2 - 2*w + 104. Let y be z(9). Let t be (y - (-76)/(-16))*16/30. Find x such that 4/15*x**2 + 0 + 2/15*x + t*x**3 = 0.
-1, 0
Let d(p) be the second derivative of p**6/180 + p**5/12 + 11*p**4/24 + 11*p**3/9 + 5*p**2/3 - 71*p. Factor d(a).
(a + 1)*(a + 2)**2*(a + 5)/6
Factor 13 - 30*s**2 + 4*s**3 - 7*s + 56*s**2 - 3 + 39*s.
2*(s + 1)*(s + 5)*(2*s + 1)
Suppose -427 + 437 = 5*p. Let t(u) be the second derivative of -1/12*u**4 - 1/20*u**5 + 7*u + 0 + 0*u**p + 0*u**3. Solve t(j) = 0 for j.
-1, 0
Suppose 4/15*u**3 + 0*u**2 + 0 + 0*u - 14/15*u**4 = 0. What is u?
0, 2/7
Let y(h) be the second derivative of -1/2*h**2 - 1/240*h**5 - 3/8*h**3 + 3*h + 1/16*h**4 + 0. Let p(z) be the first derivative of y(z). Factor p(v).
-(v - 3)**2/4
Let q(r) = r - 12. Let j be q(10). Let o be j/(-4)*(9 - 1). Let -15*x**2 - 6 + 27*x**3 + 2*x**4 + 7*x**4 - 27*x + 12*x**o = 0. What is x?
-1, -2/7, 1
Let s(v) = -v**2 - 4*v - 8. Let x(n) = n**2 + n + 1. Let i(l) = -3*s(l) - 15*x(l). Factor i(f).
-3*(f + 1)*(4*f - 3)
Let t be 2/(-36)*3*1191. Let q = t - -199. Factor 1/6*k**3 - 1/2 + q*k**2 - 1/6*k.
(k - 1)*(k + 1)*(k + 3)/6
Let y be 6/(-40) + (1 - (-33)/(-44)). Factor -1/10*g**3 + y*g**5 + 0*g + 0*g**4 + 0*g**2 + 0.
g**3*(g - 1)*(g + 1)/10
Let d(w) be the first derivative of 5*w**4 - 22*w**3/3 - 2*w**2 + 6*w - 5. Determine u, given that d(u) = 0.
-1/2, 3/5, 1
Suppose -17*f + 18*f = 10. Factor 30*s - 18*s + 5*s**3 - f - 17*s + 10*s**2.
5*(s - 1)*(s + 1)*(s + 2)
Let y(f) be the second derivative of -f**7/10080 + f**6/120 - 3*f**5/10 - 7*f**4/3 + 45*f. Let d(p) be the third derivative of y(p). Solve d(q) = 0.
12
Let -14*y - 55/4 - 1/4*y**2 = 0. What is y?
-55, -1
Let z(p) = 5*p**4 + p**3 - 4*p - 5. Let g(u) = u**4 + u**2 - u - 2. Let o(d) = -6*g(d) + 2*z(d). Factor o(y).
2*(y - 1)*(y + 1)**2*(2*y - 1)
Let d be ((-36)/2870)/((-4)/56). Let k = d + 1/41. Determine c, given that 2/5*c + 0*c**3 - 3/5*c**2 + k*c**4 + 0 = 0.
-2, 0, 1
Let 34*f**3 + 69*f**4 - 14*f**3 - 25*f**2 + 10*f - 74*f**4 = 0. What is f?
0, 1, 2
Let d = 2724 + -2715. Let f(h) be the third derivative of 1/10*h**5 - 1/4*h**4 + 1/3*h**3 - d*h**2 - 1/60*h**6 + 0 + 0*h. Find y such that f(y) = 0.
1
Suppose 3*c - 505 = -100. Let a be ((-10)/(-100))/(0 + 6/c). Factor 0 + a*u**3 + 3/4*u + 3/4*u**4 + 9/4*u**2.
3*u*(u + 1)**3/4
Let d(c) be the second derivative of -c**6/720 - c**5/80 - c**4/24 - 5*c**3 + 21*c. Let n(v) be the second derivative of d(v). Find m such that n(m) = 0.
-2, -1
Suppose -820*p - 812*p + 1604*p + 2*p**2 = 0. What is p?
0, 14
Let y(q) be the second derivative of q**9/720 - 3*q**8/560 + q**7/280 + q**6/120 + 7*q**4/12 - 7*q. Let v(o) be the third derivative of y(o). Factor v(z).
3*z*(z - 1)**2*(7*z + 2)
Find c such that -7/3*c**3 + 0*c - 1/6*c**5 + 7/6*c**4 + 4/3*c**2 + 0 = 0.
0, 1, 2, 4
Let i(j) be the third derivative of j**7/1680 + j**6/360 - j**5/80 + 13*j**3/6 - 9*j**2. Let x(d) be the first derivative of i(d). Solve x(w) = 0 for w.
-3, 0, 1
Let q be 2/(-11) - (-230)/55. Suppose -2*j - 3*j + 6*j - q*j**2 = 0. What is j?
0, 1/4
Solve 8/5*f + 8/5 - 6/5*f**2 - 2/5*f**4 - 8/5*f**3 = 0.
-2, -1, 1
Suppose -6*f = -f - 15. Suppose f*h + 6 = 3*r, -3*r + 3*h - 2*h = -8. Suppose 0 - 2*k**4 - 2/3*k**5 + 4/3*k - 2/3*k**r + 2*k**2 = 0. What is k?
-2, -1, 0, 1
Suppose 4*q - 11 = 2*h - 3, -4*h + 23 = 5*q. Find i such that -h*i - 4*i**2 + 79 - 75 + i**3 + i**3 = 0.
-1, 1, 2
Let i = 12/1187 + 3501/5935. Solve 4/5*h**2 + 0*h - 1/5 + 2/5*h**3 - i*h**4 - 2/5*h**5 = 0.
-1, 1/2, 1
Factor -3099*j + 2325 - 480*j**3 + 1920*j**2 + 780*j - 3*j**5 - 1521*j + 60*j**4 + 747.
-3*(j - 4)**5
Factor -1/2 + 11/4*h + 13/4*h**2.
(h + 1)*(13*h - 2)/4
Let x = -121 + 262. Solve 137*d**2 + 24*d - x*d**2 + 3 - 3 = 0.
0, 6
Suppose 3*y - 6 = -0. Let n be 409 - 391 - (0 + 15). Solve 0*j**n - 4/15*j**4 + 2/15*j**5 - 2/15*j + 4/15*j**y + 0 = 0 for j.
-1, 0, 1
Let u(o) be the second derivative of -o**8/1680 + o**7/210 + 7*o**3/6 + 17*o. Let n(i) be the second derivative of u(i). Suppose n(p) = 0. Calculate p.
0, 4
Let m(y) be the third derivative of 0*y**3 + 1/240*y**5 + 1/24*y**4 + 0*y + 0 - 6*y**2. Factor m(t).
t*(t + 4)/4
Determine p so that -443*p**2 - 291*p**2 + 202*p**2 - 16 - 208*p = 0.
-2/7, -2/19
Let j(o) = -14 + 24 + o - 10. Let a be j(3). Factor 83*z + a*z**2 - 83*z.
3*z**2
Suppose -15*x = -18 - 57. Suppose -h + w = -5, -4*w = 4*h - 0*w - 4. What is c in x*c**3 + 12*c**2 + 0*c**h + 13*c - c - 2*c**3 = 0?
-2, 0
Let b = 37 + -35. Let r be (b/(-3))/(((-30)/9)/10). Factor -7/5*u + 9/5*u**r + 1/5*u**4 - u**3 + 2/5.
(u - 2)*(u - 1)**3/5
Let k(z) be the second derivative of 1/18*z**3 - 1/36*z**4 - 2*z + 1/3*z**2 + 0. Factor k(n).
-(n - 2)*(n + 1)/3
Suppose 11 = 5*w + 1. Let -7 + 14 - 6 - 12*t + 36*t**w = 0. What is t?
1/6
Let m be -1 - (3 - (-1 - -10)). Suppose 6 = -2*p + m*p. Let -11*n + 12*n**p + 5 - 2 + 9*n**3 - 1 + 0 = 0. Calculate n.
-2, 1/3
Let o = -13 + 17. Suppose o*s - 23 = 17. Factor 1 + 2*z**5 - z**5 - s*z**4 + z - 2*z**3 - 2*z**2 + 11*z**4.
(z - 1)**2*(z + 1)**3
Let j be ((-6)/(-10))/(4/20). Let n be (-8)/((-40)/15) + -2 + -1. Fa