*r - 2)
Factor -188*s + s**2 - 384 - 24*s**3 + 4*s**4 - 356*s + 3*s**4 - 241*s**2 - 3*s**4.
4*(s - 12)*(s + 2)**3
Suppose -3*d - 2*w - 28 = d, -4*d - 40 = -w. Let a = d + 21. Suppose -1 + 14*q - 2*q + 6*q**2 - 9*q**4 + 0*q**2 - a*q**3 + 4 = 0. Calculate q.
-1, -1/3, 1
Let b(g) = 7*g**3 - 72*g**2 + 389*g - 581. Let a(p) = 3*p**3 - 34*p**2 + 194*p - 290. Let q(n) = 5*a(n) - 2*b(n). Determine c so that q(c) = 0.
2, 12
Let p = 2431 + -2429. Let 0 - 1/2*u**4 + 1/4*u**p + 0*u - 1/4*u**3 = 0. What is u?
-1, 0, 1/2
Let m be -2 + (-4842)/(-606) - 6. Let g = m + 205/303. Determine w so that 0*w + 2/3 - g*w**2 = 0.
-1, 1
Suppose 2*r - 49 = 9. Factor -24*z**4 + 64*z**4 - r*z**4 - 25*z**4 + 34*z**3 + 12*z + 2*z**5 - 34*z**2.
2*z*(z - 3)*(z - 2)*(z - 1)**2
Let r(i) be the first derivative of -1/26*i**4 + 2 - 16/13*i - 12/13*i**2 - 4/13*i**3. Factor r(c).
-2*(c + 2)**3/13
Factor -3/5*y**4 - 1323/5 + 252*y - 426/5*y**2 + 12*y**3.
-3*(y - 7)**2*(y - 3)**2/5
Let z(x) = -x**4 + x**3 - 3*x**2 + 3*x + 4. Let g(u) = u**3 + u + 1. Let c(k) = -4*g(k) + z(k). Factor c(l).
-l*(l + 1)**3
Let w = -13 + 15. Solve 8*p - 12 - 7*p**w - 11*p**2 - 7*p**2 + 29*p**2 = 0.
-3, 1
Let l = 44 + -34. Factor 5*z**3 - 6*z + 2*z - l*z**4 + 4*z.
-5*z**3*(2*z - 1)
Let a = -245 - -137. Let l be (-2)/8 + -17*3/a. Suppose l*b**5 + 16/9*b + 8/9 - 10/9*b**3 + 2/9*b**2 - 2/9*b**4 = 0. Calculate b.
-1, 2
Suppose -6*c = -0*c - 60. Determine k so that -5*k**4 + 5*k**2 - 177 + c*k**3 - 10*k + 177 = 0.
-1, 0, 1, 2
Let t be (-2)/(-5)*(-115)/(-207). Let r be 4/22 - 341/(-121). What is o in 2/3*o**4 + 0 - 8/9*o**r + t*o**2 + 0*o = 0?
0, 1/3, 1
Let v be (3*3)/((-3)/90*-5). Let j = 56 - v. Factor 4/5 + 1/5*l**j + 4/5*l.
(l + 2)**2/5
Let n be 69/15 + (-6)/(-15). Suppose w = n*h + 21, -w - 3*h = -4*h - 21. Factor w*m**2 + 42*m + 14 - 2 + 33*m - 27*m.
3*(m + 2)*(7*m + 2)
Let t(y) be the third derivative of -y**5/140 + 13*y**4/28 - 169*y**3/14 + 30*y**2 - 2*y. Factor t(c).
-3*(c - 13)**2/7
Let z = 62 + -59. Factor 4 + 2*k - 4*k**3 + 5*k + 4 - z*k - 8*k**2.
-4*(k - 1)*(k + 1)*(k + 2)
Let q(m) be the third derivative of -11*m**2 + 0*m**4 + 0*m - 1/84*m**8 + 0 + 2/105*m**7 + 1/30*m**6 - 1/15*m**5 + 0*m**3. Factor q(f).
-4*f**2*(f - 1)**2*(f + 1)
Let x(z) be the third derivative of -z**6/1800 - z**5/25 - 6*z**4/5 + 31*z**3/6 - 22*z**2. Let d(a) be the first derivative of x(a). Let d(c) = 0. What is c?
-12
Suppose 0 = 2*r - 3*h - 4, -6*r = -r + 4*h - 10. Find y such that 3*y**2 - 11*y**2 - 3*y**3 - 17*y**3 - 2*y**5 - r*y**5 - 16*y**4 = 0.
-2, -1, 0
Let t(o) be the third derivative of -1/16*o**4 + 1/8*o**3 + 0*o + 1/80*o**5 - 27*o**2 + 0. Suppose t(v) = 0. Calculate v.
1
Let u(s) be the first derivative of 0*s + 3*s**2 + 4/5*s**5 - 1/9*s**6 - 4/3*s**3 - 4/3*s**4 - 25. Suppose u(n) = 0. What is n?
-1, 0, 1, 3
Let r(w) be the third derivative of w**6/40 - w**5/30 - w**4/24 + w**3/3 - 14*w**2. Let d be r(1). Suppose 0 - 6*b**2 + 3*b**d - 3 - 1 + 8*b = 0. What is b?
2/3, 2
Let m(g) be the first derivative of g**6/15 + g**5/5 + g**4/6 + 9*g - 15. Let a(y) be the first derivative of m(y). Let a(b) = 0. What is b?
-1, 0
Let t(y) = -3*y**3 + 6*y**2 + 27*y - 3. Let n(f) = -3*f**3 + 5*f**2 + 26*f - 4. Let o(j) = 3*n(j) - 4*t(j). Suppose o(p) = 0. Calculate p.
-2, 0, 5
Factor -12*d**2 - 9/4*d**3 - 51/4*d - 3.
-3*(d + 1)*(d + 4)*(3*d + 1)/4
Let q(d) be the first derivative of -121*d**5/5 - 275*d**4/4 - 757*d**3/12 - 75*d**2/4 - 9*d/4 - 465. Find k, given that q(k) = 0.
-1, -3/22
Let u be (12/(-14))/((-27)/126). Let l be (-3)/(-4) + (5 - u) + -1. Factor -1 + l*x**2 + x.
(x + 2)*(3*x - 2)/4
Let k(a) be the second derivative of a**4/36 - 17*a**3/18 - 19*a**2/3 + 2*a - 368. Find z, given that k(z) = 0.
-2, 19
Find m such that 6/7*m**2 - 26/7*m + 2/7*m**3 - 30/7 = 0.
-5, -1, 3
Let v = 12269 - 12269. Let -2*r**3 + 32/5*r**2 - 8/5*r + v - 14/5*r**4 = 0. What is r?
-2, 0, 2/7, 1
Factor -307*m - 20*m**3 + 28*m**4 - 76*m**2 + 291*m + 12*m**2.
4*m*(m - 2)*(m + 1)*(7*m + 2)
Let j(g) = -g**2 - 13*g + 5. Let v(d) = 4*d**2 + 36*d - 16. Let k(u) = 8*j(u) + 3*v(u). Factor k(c).
4*(c - 1)*(c + 2)
Let v(a) be the first derivative of -a**6/21 + 12*a**5/35 + 19*a**4/14 - 16*a**3/7 + 673. What is u in v(u) = 0?
-3, 0, 1, 8
Let l(p) = -6*p**3 + p**2 - 8*p + 13. Let o(i) = -i**3 + i**2 - i + 1. Let j(x) = 3*l(x) - 21*o(x). Find w such that j(w) = 0.
-1, 1, 6
Let k(b) = -8*b**2 + 82*b + 199. Let z(d) = 95*d**2 - 985*d - 2385. Let y(s) = -35*k(s) - 3*z(s). Solve y(g) = 0.
-2, 19
Let z(k) be the first derivative of 2*k**6/15 - k**5/5 - k**4/3 + 2*k**3/3 + 8*k - 2. Let w(o) be the first derivative of z(o). What is c in w(c) = 0?
-1, 0, 1
Let q(b) be the third derivative of -b**5/270 + 5*b**4/54 + 8*b**3/9 + 16*b**2. Factor q(u).
-2*(u - 12)*(u + 2)/9
Let r be 14/(-105) + (-124)/(-30). Suppose 127*c + 19 - 132*c - 15*c**2 + 5*c**3 - r = 0. Calculate c.
-1, 1, 3
Let j be (-3)/(-7) + (-54)/(-21). Factor 2*z**j + 0*z**2 - 2*z**2 - z**4 - 113*z + 111*z + 3*z**4.
2*z*(z - 1)*(z + 1)**2
Let c(p) be the second derivative of 0*p**3 + 18*p - 1/5*p**4 + 1/10*p**5 + 0 - 1/75*p**6 + 0*p**2. Factor c(d).
-2*d**2*(d - 3)*(d - 2)/5
Let n(u) = -8*u**3 - 12*u + 11. Let v(g) = g**3 + g - 1. Suppose f - 3*w = -11, -f + 1 = -2*f + w. Let c(h) = f*n(h) + 36*v(h). Factor c(b).
4*(b - 1)**2*(b + 2)
Let u(r) = -r**5 + r**3 + 2*r**2 + r + 2. Let l(k) = -k**5 - 32*k**4 + 97*k**3 - 102*k**2 + 53*k + 10. Let p(v) = -l(v) + 5*u(v). Find o such that p(o) = 0.
0, 1, 2, 3
Let t = -143 + 143. Let u(j) be the second derivative of t - 2*j - 7/12*j**4 + 0*j**2 - 1/6*j**3 - 49/80*j**5. Factor u(k).
-k*(7*k + 2)**2/4
Suppose 1 = -3*u + x, -4*u - 7 = x - 8. Solve -5/7*t**3 + 2/7*t**4 + u + 0*t + 5/7*t**5 - 2/7*t**2 = 0.
-1, -2/5, 0, 1
Let y(i) be the second derivative of -1/2*i**3 - 1/16*i**4 - 9/8*i**2 + 0 + 21*i. Solve y(g) = 0.
-3, -1
Let m be (-2)/(-5)*(-4 + 9). Factor 0 + 1/9*t**3 - 1/9*t + 0*t**m.
t*(t - 1)*(t + 1)/9
Let r be ((-31)/(-124))/((-45)/(-24)). Find d such that r*d**2 + 0 - 4/15*d = 0.
0, 2
Let q(o) be the second derivative of -28*o**4/3 - 8*o**3 - 18*o**2/7 - 23*o + 1. Suppose q(v) = 0. Calculate v.
-3/14
Suppose 0 = 4*v - 5*g + 25, 63*g - 10 = -3*v + 61*g. Determine f so that v + 2/3*f**2 - 2*f = 0.
0, 3
Let z(l) = l**3 - 2*l**2 - 22*l + 35. Let h be z(5). Factor 1/2*c**2 - 7/4*c**4 + h*c + 5/4*c**3 + 0.
-c**2*(c - 1)*(7*c + 2)/4
Let t(i) = -i**2 + 11*i - 34. Let y(k) = -k**2 + 7*k - 2. Let f(j) = -2*t(j) + 6*y(j). Let f(o) = 0. Calculate o.
-2, 7
Let y(k) be the second derivative of -k**7/10080 - 7*k**6/2880 - k**5/48 + 7*k**4/4 + 3*k. Let g(w) be the third derivative of y(w). Factor g(p).
-(p + 2)*(p + 5)/4
Let a(g) be the first derivative of 0*g**2 + 9/10*g**5 - 1/3*g**4 + g - 10 + 0*g**3 - 7/15*g**6. Let w(u) be the first derivative of a(u). Factor w(r).
-2*r**2*(r - 1)*(7*r - 2)
Let s be 3 - (5/(20/16) - 1). Let c(o) be the third derivative of -6*o**2 + 0*o - 1/60*o**4 - 1/300*o**5 + 0*o**3 + s. Factor c(g).
-g*(g + 2)/5
Suppose 4/3*z + 8/3 - 4/3*z**3 + 4/3*z**4 - 4*z**2 = 0. Calculate z.
-1, 1, 2
Let w(v) be the second derivative of 32*v - 5/48*v**4 - 7/24*v**3 + 0 - 1/80*v**5 - 3/8*v**2. Factor w(n).
-(n + 1)**2*(n + 3)/4
Let x(k) be the third derivative of -k**6/90 + 2*k**5/15 - 2*k**4/3 + 16*k**3/9 - 537*k**2. Factor x(a).
-4*(a - 2)**3/3
Let i(b) be the third derivative of -2/3*b**3 - 1/30*b**5 - 5/12*b**4 + 0*b + 1/30*b**6 + 0 + 5*b**2. Find r such that i(r) = 0.
-1, -1/2, 2
Let l(u) be the second derivative of 0*u**2 + 0 + 19*u + 1/15*u**4 + 1/25*u**5 - 4/15*u**3. Factor l(r).
4*r*(r - 1)*(r + 2)/5
Let c(v) be the first derivative of -v**3/6 - 35*v**2/4 - 33*v - 267. Factor c(w).
-(w + 2)*(w + 33)/2
Let h = 2322001/600 - 3870. Let o(k) be the third derivative of 0*k + 1/40*k**4 + 7*k**2 + h*k**6 + 1/30*k**3 + 1/100*k**5 + 0. Factor o(y).
(y + 1)**3/5
Suppose 0 = 5*y + 3*o, -4*y - 4*o - 1 = 7. Suppose -y*r = -8*r. Determine s so that s**4 + 3*s**3 - 3*s + r*s - s = 0.
-2, 0, 1
Let a = 1001 + -999. Let o(j) be the first derivative of -a + 0*j + 0*j**2 - 1/24*j**4 - 1/9*j**3 + 1/15*j**5 + 1/36*j**6. Find i, given that o(i) = 0.
-2, -1, 0, 1
Let i(c) be the first derivative of -c**8/4200 + c**7/2100 + c**6/900 - c**5/300 + c**3 + 17. Let o(a) be the third deriva