(n - 2)**2
Let i(t) be the third derivative of 1/30*t**4 + 0*t + 1/75*t**5 - 2/525*t**7 - 1/150*t**6 + 0 + 0*t**3 - 2*t**2. Let i(f) = 0. What is f?
-1, 0, 1
Factor 2/3*r**4 + 0*r - 4*r**3 + 0*r**2 + 2/3*r**5 + 0.
2*r**3*(r - 2)*(r + 3)/3
Let s = -1 + 0. Let z be (s + (-14)/(-8))*24/45. Factor 1/5*y**3 + 1/5*y + z*y**2 + 0.
y*(y + 1)**2/5
Factor 4/3*y - 8/9*y**3 + 0 - 2/9*y**4 - 2/9*y**2.
-2*y*(y - 1)*(y + 2)*(y + 3)/9
Let o(a) be the third derivative of a**8/672 - a**7/105 + a**6/80 + a**5/30 - a**4/12 - 86*a**2. Factor o(l).
l*(l - 2)**2*(l - 1)*(l + 1)/2
Let t(i) be the second derivative of 1/21*i**3 + 1 - 1/84*i**4 + 4/7*i**2 + 4*i. Determine j, given that t(j) = 0.
-2, 4
Let d(g) be the second derivative of g**7/6 - g**6/15 - 7*g**5/20 + g**4/6 - 37*g - 5. Solve d(v) = 0 for v.
-1, 0, 2/7, 1
Let k = 160 - 153. Let w(h) = h**2 + 3*h. Let j be w(-4). Factor o - 2*o**3 - j*o**4 - k*o + 4*o**2 + 2*o + o**5 + 5*o**3.
o*(o - 2)**2*(o - 1)*(o + 1)
Let b(m) be the first derivative of -5*m**4 - 8/3*m**3 - 4/5*m**5 + 9 + 16*m**2 + 0*m. Factor b(a).
-4*a*(a - 1)*(a + 2)*(a + 4)
Factor -8*c**5 - 3*c**5 - 12*c**4 + 92*c**3 - 306*c**4 - 3*c**5.
-2*c**3*(c + 23)*(7*c - 2)
Let z(h) be the second derivative of -7*h**10/10800 + h**9/1350 - h**8/4200 - 43*h**4/12 + 4*h + 9. Let x(t) be the third derivative of z(t). Factor x(b).
-2*b**3*(7*b - 2)**2/5
Let o = -7 + 12. Let h be (-2 - (-48)/20)*o. Factor g**h - g - 1/3*g**3 + 1/3.
-(g - 1)**3/3
Let r = 217 + -211. Suppose -25 = -4*k + 5*i, 2*k - 10 = r*i - 4*i. Factor 0 + k*q - 3/2*q**2.
-3*q**2/2
Let b = 1693 + -1684. Let k(z) be the first derivative of 2/33*z**3 + 1/11*z**2 + 0*z + b. Solve k(u) = 0 for u.
-1, 0
Let u(m) = 5*m**3 - 4*m**2 - 3*m - 7. Let f be u(-3). Let b = 169 + f. What is v in 2/11*v**2 + b*v + 0 = 0?
0
Suppose 0 = -6*s + 3*s + h + 106, 0 = -3*h + 6. Let k = -36 + s. Solve -3/8*n**5 + 0*n + 3/8*n**3 + k*n**2 + 0 + 0*n**4 = 0.
-1, 0, 1
Let o(x) be the first derivative of 1/3*x**3 + 3/2*x**2 + 0*x - 39. Factor o(a).
a*(a + 3)
Let 0 - 6/5*x**4 - 16/5*x + 2/5*x**5 - 4/5*x**3 + 24/5*x**2 = 0. Calculate x.
-2, 0, 1, 2
Let s = -4 + 7. Suppose 89*i**2 + i**s - 92*i**2 - 4*i**3 = 0. Calculate i.
-1, 0
Let j(k) be the second derivative of -k**7/63 - k**6/45 + k**5/6 + k**4/18 - 8*k**3/9 + 4*k**2/3 + 177*k. Factor j(p).
-2*(p - 1)**3*(p + 2)**2/3
Let y(h) be the second derivative of h**5/15 + h**4/3 + 9*h**2/2 - 3*h. Let s(q) be the first derivative of y(q). Let s(n) = 0. Calculate n.
-2, 0
Let d = -4 + 10. Suppose 8 - 62 = -d*b. Factor 1 - 1 + 181*f - 183*f - 11*f**2 - b*f**3.
-f*(f + 1)*(9*f + 2)
Let v be (26/104)/((-18)/(-16)). Factor -4/9 + v*o**3 - 10/9*o - 2/3*o**2 + 2/9*o**4.
2*(o - 2)*(o + 1)**3/9
Let x(r) be the first derivative of 8*r**3/3 - 19*r**2 + 9*r + 16. Factor x(c).
(2*c - 9)*(4*c - 1)
Suppose 26*l - 2590 = 12*l. Let u = l - 553/3. Factor 0 - u*b + 1/3*b**2.
b*(b - 2)/3
Let w be -1 + 15*8*2/48. Let k(p) be the second derivative of 0 - 2/45*p**3 - 1/15*p**2 + 11*p - 1/90*p**w. Factor k(x).
-2*(x + 1)**2/15
Let t(b) = -5*b**4 - 2*b**3 + 5*b**2 - 2*b + 4. Let z(c) = -3 + 5 - c + c**2 - c**4 - 3 + 2. Let y(l) = -5*t(l) + 20*z(l). Suppose y(n) = 0. Calculate n.
-2, -1, 0, 1
Let j(s) = 7*s**2 + 3*s - 2. Let a(b) = -11*b + 5*b + 11 - 36*b**2 - 8*b + 0. Suppose -5*u + 1 = -9. Let m(l) = u*a(l) + 11*j(l). Factor m(z).
5*z*(z + 1)
Let b(g) be the second derivative of 4*g**6/165 + g**5/22 + g**4/66 + 96*g. Factor b(z).
2*z**2*(z + 1)*(4*z + 1)/11
Let w = -23016 + 23020. Find d such that -20*d**2 + 0 - 25*d**3 - 5/4*d**5 - 10*d**w + 0*d = 0.
-4, -2, 0
Let l = -317 + 317. Factor -2/9*d**3 + 0 + l*d**2 + 2/9*d.
-2*d*(d - 1)*(d + 1)/9
Let j(z) be the second derivative of z**7/63 + 2*z**6/45 - 23*z**5/30 - 14*z**4/9 + 112*z**3/9 - 64*z**2/3 - 29*z - 5. What is w in j(w) = 0?
-4, 1, 4
Let i(d) = -3*d**5 - 2*d**3 - 2*d**2 - 2. Let o(f) = 10*f**5 + 7*f**3 + 7*f**2 + 7. Suppose 0 = -2*l + 32 - 4. Let b(j) = l*i(j) + 4*o(j). Factor b(h).
-2*h**5
Suppose 0 = v + 3, 3*n - 4*v - 3 = -6*v. Let j(s) be the third derivative of 0*s**n - 1/64*s**4 + 0 + 0*s**5 + 1/320*s**6 + 0*s - 8*s**2. Factor j(i).
3*i*(i - 1)*(i + 1)/8
Let p(z) be the first derivative of -z**3/24 - 5*z**2/16 + 7*z/4 + 48. Determine q so that p(q) = 0.
-7, 2
Let t be (-3)/5*(-2030)/10962. Solve t*g**2 + 0 - 10/9*g = 0 for g.
0, 10
Factor 5*o**3 + 2*o**2 - o**3 + 60*o + 34*o**2 + 160 - 132.
4*(o + 1)**2*(o + 7)
Let 4*p**3 + 18 - 376/3*p + 310/3*p**2 = 0. Calculate p.
-27, 1/6, 1
Let x = 211 + -206. Let c(t) be the third derivative of 0*t - 1/30*t**4 - 1/10*t**3 + 0 - 1/300*t**x - 11*t**2. Factor c(p).
-(p + 1)*(p + 3)/5
Let s(o) be the first derivative of -o**3/4 + 75*o**2/8 + 39*o/2 + 126. Factor s(x).
-3*(x - 26)*(x + 1)/4
Let q(c) be the second derivative of -c**6/33 - 2*c**5/55 + 7*c**4/66 + 2*c**3/11 - 143*c. Solve q(s) = 0.
-1, 0, 6/5
Let a be (-15)/24*(-7)/735. Let x(v) be the second derivative of 0*v**3 + 0 + 0*v**6 + 7*v + 0*v**4 - a*v**7 + 0*v**5 + 0*v**2. Factor x(q).
-q**5/4
Let y(l) = -13*l**3 - 17*l**2 - 5*l - 5. Let n(f) = -15*f**3 - 18*f**2 - 6*f - 6. Let p(a) = 5*n(a) - 6*y(a). Factor p(v).
3*v**2*(v + 4)
Factor 3*r - 2 + 92*r**3 - 195*r**3 + 102*r**3.
-(r - 1)**2*(r + 2)
Let b(d) = d**2 + 11*d + 21. Suppose 63 - 27 = -4*a. Let c be b(a). Factor 0*n**2 + 0 + 12/7*n - 9/7*n**c - 3/7*n**4.
-3*n*(n - 1)*(n + 2)**2/7
Factor 41*l**3 - 42*l**3 + 3*l**2 - 3*l - 6*l**2 - 1.
-(l + 1)**3
Suppose -5*o = -8*o + 12. Let -o*h**4 - 4 + 4 + 69*h - 20*h**2 + 16*h**3 - 61*h = 0. What is h?
0, 1, 2
Let m(v) = 5*v**3 + 2*v**2 + v. Let r(t) = -6*t**3 - 3*t**2 - t. Suppose 7 = -4*n + 127. Suppose 5*x = -10 + n. Let k(d) = x*r(d) + 5*m(d). Factor k(l).
l*(l - 1)**2
Suppose -62*k = -67*k + 50. Let v be (-1)/k*(-2 - 20). Determine z so that 1/5*z**4 + 6/5*z**3 - 1/5*z**5 - 3/5 + v*z - 14/5*z**2 = 0.
-3, 1
Let g(r) be the third derivative of -r**7/280 - r**6/120 + r**5/40 + r**4/8 - r**3/6 + 4*r**2. Let l(b) be the first derivative of g(b). Solve l(a) = 0.
-1, 1
Suppose 2 = 2*d - 38. Let -2*k**2 - 16 - k**2 - d*k - 4 - 2*k**2 = 0. What is k?
-2
Suppose 62*l + 39 = 114 + 111. Factor -l*b - 3/2*b**2 + 0.
-3*b*(b + 2)/2
Let h(f) be the first derivative of f**6/24 + f**5/20 - 9*f**4/16 + 11*f**3/12 - f**2/2 + 606. Factor h(p).
p*(p - 1)**3*(p + 4)/4
Let y(t) = -8*t**2. Let m(s) = -95*s**2. Let j(k) = -10 - 10*k - k**3 - 17*k + 22*k - 9*k**2. Let i be j(-9). Let h(r) = i*y(r) - 3*m(r). Factor h(c).
5*c**2
Let y(l) = -17*l**2 - 9*l + 13. Let t(n) = 8*n**2 + 4*n - 6. Suppose 0 = 3*p + 4 - 22. Let b(o) = p*y(o) + 13*t(o). Solve b(h) = 0.
0, 1
Let c(d) = -6*d**3 + 23*d**2 + 65*d + 33. Let x(a) = 21*a**3 - 68*a**2 - 195*a - 98. Let m(f) = 8*c(f) + 3*x(f). Suppose m(p) = 0. Calculate p.
-1, -2/3, 3
Let c = 2167 + -2165. Factor 0 - 1/3*m**c - 1/3*m**3 + 0*m.
-m**2*(m + 1)/3
Let p = 113 - 903/8. Let r(q) be the first derivative of 0*q - 1/2*q**2 - 1 + p*q**4 + 1/6*q**3. Factor r(u).
u*(u - 1)*(u + 2)/2
Let m be 1/3 + (-13)/3. Let t be (2 + m/(-6))*3. Factor t*z**2 - z + 4*z + 5*z**3 + z**2 + z**3.
3*z*(z + 1)*(2*z + 1)
Let t = 89 - 89. Suppose 14*g - 18*g = t. Factor g + 2/11*o**4 + 8/11*o**3 + 8/11*o**2 + 0*o.
2*o**2*(o + 2)**2/11
Let x(o) = o**2 + 5*o - 10. Let k be x(-11). What is d in 1 - 31*d - 9 + 4*d**3 + k*d - 37*d = 0?
-1, 2
Let l(m) = 3*m**4 + 3*m**3 + 10*m**2 + 4*m. Let d(k) = -2*k**4 - 5*k**3 + 30*k**2 - 51*k**2 - 8*k - 5*k**4. Let a(y) = -4*d(y) - 10*l(y). Factor a(j).
-2*j*(j + 1)*(j + 2)**2
Let m(u) be the second derivative of 2*u**7/21 + 2*u**6/15 - u**5 - 5*u**4/3 + 8*u**3/3 + 8*u**2 + 87*u. Let m(r) = 0. What is r?
-2, -1, 1, 2
Let n = 13361/80 + -167. Let h(w) be the third derivative of 0 + 0*w + 0*w**3 + 0*w**4 + n*w**6 + 0*w**5 - 6*w**2. Factor h(g).
3*g**3/2
Suppose 2*f + 9 = 5*x + 30, 9 = 4*f + x. Let n(c) = 4*c**2 - 12*c. Let b(i) = -2*i**2 + 6*i. Let l(h) = f*n(h) + 5*b(h). Factor l(s).
2*s*(s - 3)
Let v(r) be the second derivative of r**6/20 + 63*r**5/20 + 57*r**4/2 + 110*r**3 + 216*r**2 - 141*r. Suppose v(n) = 0. Calculate n.
-36, -2
Let s(d) be the first derivative of -4*d**3/3 - 16*d**2 - 60*d + 101. Factor s(w).
-4*(w + 3)*(w + 5)
Let a(b) = 3*b - 39. Let v be a(14). Find i such that 5*i**3 - 4*i**4 - 5*i**v - 6*i**5 - 8*i**5 = 0.