et w(i) be the second derivative of -35*i + i**4 + 0 + 0*i**2 + 4/3*i**3. Find d such that w(d) = 0.
-2/3, 0
Let h = 44 - 48. Let y be (27/h - 0)/(-7 - -4). Factor -1/4*x**2 - y - 3/2*x.
-(x + 3)**2/4
Suppose 3*z - 384 = -0*z. Let u be z/22 - 2/(-11). Solve u*h**2 - 3*h**5 - 15*h**3 + 5*h**4 - h**4 + 8*h**4 = 0 for h.
0, 1, 2
Suppose -4*f + 10 = -5*q, -5*f = q + 2 - 29. Let z = -2 - -7. What is t in 4*t - 5*t**2 + 0*t**2 + 12*t**q - z*t**2 = 0?
-2, 0
Let -67/6*b + 65/3 + 1/6*b**2 = 0. What is b?
2, 65
Let s = -24 + 19. Let w(k) = -6*k**3 - 3*k**2. Let m(g) = g**4 - 11*g**3 - 6*g**2 + g. Let z(o) = s*w(o) + 3*m(o). Factor z(c).
3*c*(c - 1)**2*(c + 1)
Let m be ((-20)/6)/5*(4 - 7). Let p(h) be the third derivative of 0 - 1/54*h**5 - 1/135*h**6 + 0*h**3 - 1/108*h**4 - 6*h**m + 0*h. Factor p(n).
-2*n*(n + 1)*(4*n + 1)/9
Let i = 15586 - 15583. Suppose 7/9*n**2 + 1/9*n**4 + 0 - 5/9*n**i - 1/3*n = 0. Calculate n.
0, 1, 3
Let v(p) = 8*p**3 + p**2 - p**3 - 2*p**2 + 1 + p. Let h = 10 + -13. Let q(u) = -6*u**3. Let i(r) = h*v(r) - 4*q(r). Determine j so that i(j) = 0.
-1, 1
Let x(z) be the second derivative of z**4/114 - 2*z**3/57 - 15*z**2/19 + 45*z + 1. Suppose x(p) = 0. Calculate p.
-3, 5
Let m(n) = n - 7. Let v be m(9). Suppose a = -u + 3*a + 12, 5*u - 28 = v*a. Factor 6*l**2 - 6*l**3 - 2 - 12*l**4 + 13*l**u + 7*l**2 + 6 - 12*l.
(l - 2)**2*(l - 1)**2
Let h(v) be the third derivative of -v**8/448 + 3*v**7/280 + v**6/160 - 3*v**5/80 - 22*v**2 + 3*v. Let h(o) = 0. What is o?
-1, 0, 1, 3
Factor -17/2*x**3 + 150*x + 20*x**2 + 1/2*x**4 + 0.
x*(x - 10)**2*(x + 3)/2
Let v be (8 - 9) + (-12)/(-3). Factor -5*g**4 + 5*g**2 - 5*g**v - 92*g + 52*g + 45*g.
-5*g*(g - 1)*(g + 1)**2
Let d(l) = -l + 1. Let c be (-3 + 40/12)*-9. Let f(h) = h**2 + 4*h - 4. Let x(k) = c*f(k) - 12*d(k). Factor x(b).
-3*b**2
Let h(b) = -7*b**4 - 22*b**3 + 6*b**2 + 28*b - 16. Let y(i) = 13*i**4 + 43*i**3 - 11*i**2 - 54*i + 32. Let g(m) = 5*h(m) + 2*y(m). Find n, given that g(n) = 0.
-2, 2/3
Let g = -26 - -30. Factor 3*r**3 + g*r**2 + r**5 - 173 - 4*r**4 - 4*r + 173.
r*(r - 2)**2*(r - 1)*(r + 1)
Let f be 16/(-64) + ((-11)/4 - -1). Let k be ((-6)/(-24))/(f/(-24)). Solve -20/3*p**2 + 10/3*p + 20/3*p**k - 2/3 - 10/3*p**4 + 2/3*p**5 = 0.
1
Let p(h) = -h**2 - 10*h + 2. Let y be p(-10). Factor -9*g**y - 9*g**3 - 3*g**2 + 12*g**3.
3*g**2*(g - 4)
Let l = 0 + 2. Let d = 0 + l. Suppose 31*m**4 - 24*m**4 + 10*m**d - 2*m - 16*m**3 + m**2 = 0. Calculate m.
0, 2/7, 1
Let c(o) = -o**2 + 2*o**3 - 3*o**3 + 110 - 108. Let j(n) = -n**2 - n - 1. Let y(r) = c(r) + 2*j(r). Factor y(a).
-a*(a + 1)*(a + 2)
Factor 10*x - 10*x**2 + 9*x + 6*x - 25*x**2 + 10.
-5*(x - 1)*(7*x + 2)
Let h(u) = u**3 + 5*u**2 - 6*u - 6. Let a be h(-6). Let w be (-32)/a + 1 + -6. Determine z, given that 1/3*z**2 + w*z**3 + 0 + 0*z = 0.
-1, 0
Solve -417*j + 210*j + 12*j**2 + 247*j + 8 + 0 + 4 = 0.
-3, -1/3
Let c(y) be the first derivative of y**7/210 + 2*y**6/45 + y**5/10 + 5*y**3 - 7. Let l(f) be the third derivative of c(f). Solve l(z) = 0.
-3, -1, 0
Let z(i) = 460*i**4 - 120*i**3 - 35*i**2 + 35*i + 35. Let k(u) = 27*u**4 - 7*u**3 - 2*u**2 + 2*u + 2. Let p(r) = -35*k(r) + 2*z(r). Factor p(d).
-5*d**3*(5*d - 1)
Suppose -4 = 4*v + 3*a + 10, -4*v - a = 10. Let y be (-34)/(-10) + (v - -1). Factor 0*w + y*w**4 - 18/5*w**5 + 0 + 0*w**2 - 2/5*w**3.
-2*w**3*(3*w - 1)**2/5
Let j(v) be the second derivative of -3*v**5/20 + 8*v**4 - 128*v**3 - 2*v - 2. Factor j(u).
-3*u*(u - 16)**2
Suppose -12 = 3*n - 5*n. Factor -13*q**3 + q**3 + n + 24*q - 1 - 44*q**2 + 27.
-4*(q - 1)*(q + 4)*(3*q + 2)
Factor -20/7*y + 2/7*y**2 + 6.
2*(y - 7)*(y - 3)/7
Factor -2/5*p**2 + 24/5*p + 0.
-2*p*(p - 12)/5
Let v(i) = i**5 - i**4 - i**3 + 1. Let u = -21 - -22. Let x(p) = -p**5 + p**4 - p**3 + p**2 + 2*p - 2. Let a(d) = u*x(d) + 2*v(d). Factor a(k).
k*(k - 2)*(k - 1)*(k + 1)**2
Let o be ((-9)/30 - 3/6)*(-145)/580. Factor 0*x + 0 - o*x**2.
-x**2/5
Let r(a) be the first derivative of -a**4/14 - 20*a**3/21 + 11*a**2/7 + 110. Factor r(f).
-2*f*(f - 1)*(f + 11)/7
Suppose -2*w + 18 = -3*l, 0*w = -3*w + 3*l + 21. Factor -2*q**4 - 10*q**2 + 3*q**4 - 4*q**w + 4*q**4 - q**3.
5*q**2*(q - 2)*(q + 1)
Let u(n) be the third derivative of -1/12*n**4 + 0*n**5 + 1/30*n**6 + 20*n**2 - 1/168*n**8 + 0 + 0*n + 0*n**3 + 0*n**7. Factor u(m).
-2*m*(m - 1)**2*(m + 1)**2
Suppose l + l - 16 = 0. Suppose 0 = f - 2*k - 10, -3*f - k + l = 4*k. Factor 6 - 2*y + 1 - f*y**3 + 2*y**4 - 7 + 6*y**2.
2*y*(y - 1)**3
Let i(z) be the second derivative of 3/2*z**4 + 7/3*z**3 + 0 + 30*z + 1/15*z**6 + 1/2*z**5 + 2*z**2. Factor i(x).
2*(x + 1)**3*(x + 2)
Let g(u) be the first derivative of 3/2*u**4 + 0*u + 2 - 20/3*u**3 + 3*u**2. Determine b, given that g(b) = 0.
0, 1/3, 3
Let w be (-5 + (-12)/24)/(-11). Factor 2 - n - w*n**2 + 1/4*n**3.
(n - 2)**2*(n + 2)/4
Let k(g) be the third derivative of g**5/20 - 11*g**4/8 + 12*g**3 + 289*g**2. Factor k(s).
3*(s - 8)*(s - 3)
Factor -32*o**2 + 480*o - 10*o**3 - 3*o**4 + 2*o**4 - 512*o.
-o*(o + 2)*(o + 4)**2
Let m(v) be the second derivative of -20*v**2 + 6*v - 155/6*v**4 + 0 + 110/3*v**3 + 21/4*v**5. Let m(y) = 0. Calculate y.
2/7, 2/3, 2
Let w(m) = 5*m**3 - m**2 - 5. Let c(s) = 6*s**3 - s**2 - 4. Let k(g) = 4*c(g) - 5*w(g). Let h be k(0). Factor 55*i - 10 - 2 - h*i**2 - 34*i.
-3*(i - 1)*(3*i - 4)
Suppose 4*b + 422 = 422. Let l(q) be the second derivative of 0*q**5 + 2/21*q**7 + b*q**4 + 0*q**3 + 0*q**2 + 2/15*q**6 + 14*q + 0. Factor l(k).
4*k**4*(k + 1)
Let y(b) be the first derivative of -b**4/4 - b**3/3 - b**2/2 - b + 18. Let t(r) = 7*r**3 - r**2 + 3*r + 3. Let g(w) = -t(w) - 3*y(w). Factor g(c).
-4*c**2*(c - 1)
Let l(b) = 3*b**2 - 41*b - 41. Let o be l(-1). Factor 0 + 4/3*g**o - 2/9*g**2 - 2*g**4 + 0*g.
-2*g**2*(3*g - 1)**2/9
Let h(y) be the second derivative of y**6/270 + y**5/60 + y**4/54 + 55*y + 1. Suppose h(k) = 0. Calculate k.
-2, -1, 0
Let v(g) be the first derivative of 22*g**3/9 + 134*g**2/3 + 16*g + 257. Suppose v(x) = 0. Calculate x.
-12, -2/11
Suppose 2*x = 4*d - 42, -7*d + 4*x = -2*d - 48. Factor -9*n + 14 - 15*n**2 - 5 - 6 + 9*n**3 + d*n**4.
3*(n - 1)*(n + 1)**2*(4*n - 1)
Let y(w) be the second derivative of w**6/90 - w**5/15 - 7*w**3/3 + 6*w. Let t(n) be the second derivative of y(n). What is i in t(i) = 0?
0, 2
Let z(j) = 6*j**2 - 26*j - 20. Let q(t) = -11*t**2 + 51*t + 41. Let k(w) = -4*q(w) - 7*z(w). Factor k(d).
2*(d - 12)*(d + 1)
Let f(c) be the second derivative of 7*c**6/90 + c**5/15 + 13*c**3/6 - 4*c. Let r(q) be the second derivative of f(q). Factor r(y).
4*y*(7*y + 2)
Suppose -84*g**2 - 10*g**2 - 180*g - 6*g**2 + 37*g**3 + 41*g**3 - 83*g**3 = 0. Calculate g.
-18, -2, 0
Let v(m) = -m**2 + m + 1. Let x(u) = -20*u**3 - 120*u**2 - 35*u - 5. Let s(a) = 5*v(a) + x(a). Factor s(t).
-5*t*(t + 6)*(4*t + 1)
Let i(z) = -3*z**3 - z**2 - 7*z + 11. Let u(j) = -2*j**3 - 4*j + 6. Let l(b) = -b**2 - 17*b - 11. Let o be l(-16). Let y(f) = o*u(f) - 3*i(f). Factor y(v).
-(v - 3)*(v - 1)*(v + 1)
Suppose 4*x + 4 = 38*s - 35*s, 0 = -s - 5*x - 5. Factor 0 + 2/15*f**5 - 2/5*f**3 + 4/15*f**2 + 0*f**4 + s*f.
2*f**2*(f - 1)**2*(f + 2)/15
Let o be (4 - 1)*(-60 + 9 + 0). Let k = o + 769/5. Find x, given that k*x + 1/5*x**2 + 3/5 = 0.
-3, -1
Let p be (-4)/20*-3 - (-3 - 396/(-210)). Factor p*d + 12/7*d**2 + 3/7*d**3 + 0.
3*d*(d + 2)**2/7
Let 2/5*r - 2/5*r**3 + 0*r**2 + 0 = 0. What is r?
-1, 0, 1
Let h(l) be the third derivative of -5*l**7/2772 + l**6/396 - l**5/660 + l**4/12 + l**2. Let a(w) be the second derivative of h(w). Factor a(k).
-2*(5*k - 1)**2/11
Let h(i) = 7*i**3 + 135*i**2 + 300*i + 8. Let z(r) = -5*r**3 - 90*r**2 - 200*r - 5. Let t(v) = -5*h(v) - 8*z(v). Suppose t(u) = 0. Calculate u.
-5, -4, 0
Suppose -j = -5*d, -23 = -5*j + 3*d - d. Suppose -j*m - 3*b = -12, 12 = 2*b + 4. Find u such that -2*u + 0*u**2 + m - 3/2*u**5 - u**4 + 9/2*u**3 = 0.
-2, -2/3, 0, 1
Suppose 0 = 2*t + 230 + 16. Let y be t/21 + 6 + 26/14. Factor 2/7*m**3 - 6/7*m**y - 4/7 + 2/7*m**4 - 10/7*m.
2*(m - 2)*(m + 1)**3/7
Let p(f) be the third derivative of -f**7/42 + f**6/10 + 3*f**5/20 + 28*f**2 - 2*f. Factor p(q).
-q**2*(q - 3)*(5*q + 3)
Let o = 7045 + -49312/7. Factor -1/7*w**3 + 2/7 + o*w + 0*w**2.
-(w - 2)*(w + 1)**2/7
Let f(p) be the second derivative of p**6/30 - p**4/2 + 4*p**3/3 - 9*p**2 - 24*