ative of -z**4/24 + z**3/3 + 3*z**2/4 - 7*z/3 - 241. Factor f(u).
-(u - 7)*(u - 1)*(u + 2)/6
Let q be 11*(-3)/(3/2). Let s be (q/(-30) - (-4)/(-12)) + 0. Factor -1/5*b**2 - 1/5 + s*b.
-(b - 1)**2/5
Let h(g) = -14*g**4 + 62*g**3 - 68*g**2 - 20*g + 8. Let m(t) = -28*t**4 + 123*t**3 - 137*t**2 - 39*t + 18. Let c(f) = 9*h(f) - 4*m(f). Factor c(p).
-2*p*(p - 3)*(p - 2)*(7*p + 2)
Let s(w) be the first derivative of w**3/21 - 15*w**2/7 + 29*w/7 - 18. Factor s(v).
(v - 29)*(v - 1)/7
Let h(x) be the third derivative of x**6/240 - x**5/10 + 3*x**4/16 + 11*x**3/6 + x**2 - 130. Factor h(t).
(t - 11)*(t - 2)*(t + 1)/2
Let d(o) = -o**2 + 14*o + 4. Let c be d(16). Let a be -3 + c/(-12) - 20/(-18). Factor 46/9*k**4 + 0 + 26/9*k**2 + a*k + 6*k**3 + 14/9*k**5.
2*k*(k + 1)**3*(7*k + 2)/9
Let n(b) be the first derivative of b**6/3 + 77*b**5/10 + 223*b**4/8 + 247*b**3/6 + 113*b**2/4 + 8*b + 762. Suppose n(t) = 0. Calculate t.
-16, -1, -1/4
Let u = -7138479/55 + 129786. Let m = u + 52/11. Let -4/5*p + 1/5*p**4 + m + 6/5*p**2 - 4/5*p**3 = 0. Calculate p.
1
Let l(b) = -b**3 - 5*b**2 + 9*b + 20. Let t be l(-6). Suppose -4 = -2*j + 2. Factor -7*q + q + j*q**t + 0*q.
3*q*(q - 2)
Let j = -9/175 + 11/75. Let l(b) be the third derivative of -1/420*b**5 + 0*b - 4*b**2 - j*b**3 + 1/42*b**4 + 0. Suppose l(h) = 0. Calculate h.
2
Factor 0*y + 12/5*y**2 - 464/5*y**3 + 0 + 304/5*y**4.
4*y**2*(2*y - 3)*(38*y - 1)/5
Let j(m) be the third derivative of m**5/50 + 129*m**4/10 + 16641*m**3/5 - 12*m**2 + 2*m. Solve j(o) = 0 for o.
-129
Let z = 25/158 + 345/316. Factor 3/2*y**3 - 7/4*y + 1/4*y**5 + 3/4 + 1/2*y**2 - z*y**4.
(y - 3)*(y - 1)**3*(y + 1)/4
Let p = -4042/5 + 809. Let a(y) be the first derivative of 0*y**3 + 1/2*y**6 + 0*y**2 + p*y**5 + 0*y + 0*y**4 - 6. Factor a(w).
3*w**4*(w + 1)
Factor 31*j**2 - 72*j + 432 - 54*j**3 - 316*j**2 - 21*j**3.
-3*(j - 1)*(5*j + 12)**2
Suppose o - 1 - 1 = 0. Suppose -4*r + 6 = -o*r. Factor 78*u**r - 3*u**2 + 3*u - 3 + 6 - 81*u**3.
-3*(u - 1)*(u + 1)**2
Let w(k) = -k**3 - k**2 + k. Let d be w(-2). Let y be 6/(-12)*(-4 + 0). Suppose -13 + y*g**2 - 8*g + 5 - 4*g**d = 0. Calculate g.
-2
Solve 216*v + 3*v**2 - 238*v - 4*v**2 = 0 for v.
-22, 0
Find f such that 3/5*f**3 - 12/5 + 0*f + 9/5*f**2 = 0.
-2, 1
Suppose 0 = a - 3*f - 19 - 34, -57 = -a + 2*f. Factor a*r - 1 - r**2 - 27*r - 36*r.
-(r - 1)**2
Factor -126*x**2 - 107*x - 45 + 5*x - 40*x**3 + 16*x**2 - 5*x**4 - 18*x.
-5*(x + 1)**2*(x + 3)**2
Let d(i) be the second derivative of i**6/120 - 3*i**5/40 - 7*i**3/6 - 5*i. Let v(l) be the second derivative of d(l). Factor v(t).
3*t*(t - 3)
Let g be ((-1)/2)/((-15)/18). Let a = -3186 + 3188. Factor 0 - g*r + 3/5*r**a.
3*r*(r - 1)/5
Let d(u) be the third derivative of 6*u**2 + 0*u**4 - 1/20*u**6 + 0 + 0*u - 1/70*u**7 - 1/20*u**5 + 0*u**3. Factor d(w).
-3*w**2*(w + 1)**2
Suppose -50 = 4*k - 3*j + 22, 4*k + 5*j = -72. Let r = -16 - k. Determine i so that 4/3*i**r - 8/3*i + 4/3 = 0.
1
Let i be 1 + 6 - 3 - (-1426)/(-56). Let o = i - -91/4. Find l, given that 3/7*l**2 - o + 6/7*l = 0.
-3, 1
Let j(c) be the first derivative of 4/5*c**5 - 10 - 4*c**2 + 0*c**3 - 4*c + 2*c**4. Factor j(y).
4*(y - 1)*(y + 1)**3
Suppose 12 = 2*t + 4*j - 0*j, -t + 3*j - 4 = 0. Let m(b) be the first derivative of t*b**2 - 7 + b**4 + 0*b + 8/3*b**3. Factor m(p).
4*p*(p + 1)**2
Let s(q) be the second derivative of q**5/20 + 13*q**4/4 - 87*q**3/2 + 405*q**2/2 + 101*q + 1. Solve s(v) = 0.
-45, 3
Let y(l) be the first derivative of 0*l - 2/3*l**3 + 3/4*l**4 + 1/24*l**6 - 3/10*l**5 + 4 + 0*l**2. Factor y(n).
n**2*(n - 2)**3/4
Let n(p) = p**3 + 15*p**2 - 56*p - 40. Let c be n(-18). Let m(o) = -13*o - 50. Let a be m(c). Factor 10/7*g + 25/7 + 1/7*g**a.
(g + 5)**2/7
Let y(t) be the third derivative of -1/240*t**5 + t**2 - 1/8*t**3 - 1/24*t**4 + 0 + 0*t. What is o in y(o) = 0?
-3, -1
Solve -3/4*j**5 - 1293/4*j**3 + 27*j**4 + 1269*j**2 + 324*j - 1296 = 0 for j.
-1, 1, 12
Suppose -24/5*j**2 - 18*j - 2/5*j**3 - 20 = 0. What is j?
-5, -2
Let 4/17*f - 14/17*f**2 + 10/17 = 0. Calculate f.
-5/7, 1
Let r(v) = 8*v - 16. Let s be r(9). Suppose -2*o**5 - 2*o - s*o**4 - 64*o**2 + 7*o + 92*o**3 + 11*o + 14*o**5 = 0. Calculate o.
0, 2/3, 1, 2
Let -1/7*k**2 + 0*k - 3/7*k**4 + 3/7*k**3 + 1/7*k**5 + 0 = 0. What is k?
0, 1
Let o(r) = r**2 - 21*r + 3. Let c be o(21). Find v such that -4*v**3 + 9*v**2 - 9*v**4 - 6*v + 3*v**5 + 3*v**3 + 0*v**3 + 4*v**c = 0.
-1, 0, 1, 2
Suppose 11*t - 15 = 8*t. Factor r**2 - 2 - 4*r**3 + 2*r + 6*r**4 - 5*r**2 - 2*r + 6*r - 2*r**t.
-2*(r - 1)**4*(r + 1)
Factor -44/17 - 2/17*w**4 - 50/17*w**3 - 134/17*w - 138/17*w**2.
-2*(w + 1)**3*(w + 22)/17
Let t(z) be the third derivative of z**5/50 - 11*z**4/20 + 2*z**3 - 70*z**2. Find c, given that t(c) = 0.
1, 10
Let w(v) = v**3 - 12*v**2 + 4*v - 9. Let b be w(12). Find a, given that 2*a**3 - b*a**2 + 28*a**4 + 8*a + 11*a**2 - 8*a**3 - 2*a**3 = 0.
-1, 0, 2/7, 1
Suppose -56 = -14*x - 0*x. Let d(k) be the second derivative of 1/36*k**x + 0 - 2/9*k**3 + 5*k + 1/2*k**2. Find c such that d(c) = 0.
1, 3
Let p be 42/(-72) + 2/8. Let u = 5/12 - p. Factor 0 + 1/4*g**4 + u*g**2 - 1/4*g - 3/4*g**3.
g*(g - 1)**3/4
Let a(g) be the third derivative of g**7/5670 + g**6/180 + 19*g**4/12 - 15*g**2. Let l(p) be the second derivative of a(p). Factor l(z).
4*z*(z + 9)/9
Let h(k) = -2*k + 4. Let n be h(1). Suppose -3*w + n*c - 2 = 0, -3*c = -4*w - 0*c - 3. Factor -10/13*v**3 + w + 2*v**2 + 12/13*v.
-2*v*(v - 3)*(5*v + 2)/13
Let -3/2*z - 7/4*z**2 + 0 + 3/4*z**3 = 0. Calculate z.
-2/3, 0, 3
Let t(d) = 24*d**2 - 6*d - 9. Suppose -3*o = -5*y - 15, -o + 6 = -2*y - 0*o. Let r(w) = -w**2 - w - 1. Let v(f) = y*r(f) - t(f). Factor v(l).
-3*(l - 1)*(7*l + 4)
Let t(b) = 8*b - 1. Let q be t(1). Let y be 0 - (3 + (-25)/q). Solve y*m**3 - 2/7*m - 2/7*m**5 + 0*m**2 + 0*m**4 + 0 = 0 for m.
-1, 0, 1
Let n = -329/32670 + 5/363. Let g(m) be the third derivative of 5*m**2 + 0 + 0*m - 1/36*m**4 - n*m**5 + 0*m**3. Factor g(t).
-2*t*(t + 3)/9
Let l(y) = -2*y**3 - 8*y**2 - 4*y - 12. Let o be l(-4). Let h(i) = i**2 + i - 18. Let j be h(o). Let -3/2*b**j + 1/2*b**3 + 3/2*b - 1/2 = 0. Calculate b.
1
Determine j so that -845/2*j**3 + 256*j - 101/2*j**2 - 50*j**4 - 66 = 0.
-33/4, -1, 2/5
Suppose -6*i = -4*h + 24, -5*i = 2*h - 3*h + 13. Solve 14/5*m**2 - 12/5 + 8/5*m**h - 2*m = 0.
-2, -3/4, 1
Let t(v) be the first derivative of -v**4 + 8*v**3/3 + 10*v**2 - 24*v + 135. Factor t(a).
-4*(a - 3)*(a - 1)*(a + 2)
Let x(y) = -5*y**3 + 5*y**2 + 2*y + 4. Let h(j) = 9*j**3 - 9*j**2 - 4*j - 6. Let a(q) = -6*h(q) - 10*x(q). Factor a(m).
-4*(m - 1)**2*(m + 1)
Let z(r) = 3*r + 11. Let b be z(-6). Let i = 11 + b. Factor -2*v**5 - 2*v**4 + 0*v**5 + 2 + 4*v**3 - 4*v**2 + 4*v**i - 2*v.
-2*(v - 1)**3*(v + 1)**2
Suppose 6*q - 2*q - 4 = 2*b, -4*q - 3*b + 4 = 0. Let l be 13 - 7 - 2/q. Let 15*a**2 + 14*a**2 - 4*a + l*a**3 + 4 - 33*a**2 = 0. What is a?
-1, 1
Suppose 544*t - 541*t = 6. Let f(x) be the first derivative of x**4 - 1 + 3/2*x**3 - t*x**2 - 2*x - 1/2*x**5. Let f(b) = 0. What is b?
-1, -2/5, 1, 2
Let p be (-1 + -2 - 3) + 8. Determine v so that 3/7*v**3 - 3/7*v**4 + 0*v + 0*v**p + 0 = 0.
0, 1
Determine x so that 33/2*x**3 + 0 + 24*x**2 - 3/2*x**4 - 480*x = 0.
-5, 0, 8
Suppose t + f - 1 = 4*f, 4*t - f - 15 = 0. Factor 0*z**2 + 1/2*z**t + z**3 - 1/2 - z.
(z - 1)*(z + 1)**3/2
Let f = 13 + -10. Let b(m) = 7*m**3 + m**2 - 13*m - 19. Let w(h) = 36*h**3 + 4*h**2 - 64*h - 96. Let a(p) = f*w(p) - 16*b(p). Factor a(g).
-4*(g - 2)*(g + 1)*(g + 2)
Let g be 672/864*(-12)/(-28). Factor -2/3*p**3 + 0*p - g*p**4 - 1/3*p**2 + 0.
-p**2*(p + 1)**2/3
Let x(i) = 3*i**2 - 2*i - 1. Let d(a) = -a**2 + a. Let h(z) = 10*d(z) + 4*x(z). Factor h(b).
2*(b - 1)*(b + 2)
Let t(d) be the first derivative of 5*d**3/3 + 45*d**2 - 95*d - 5. Factor t(m).
5*(m - 1)*(m + 19)
Let l(y) = -3*y + 23. Let d be l(6). Let q(x) be the third derivative of 9*x**2 + 0*x - 1/6*x**4 + 1/90*x**d + x**3 + 0. Determine g, given that q(g) = 0.
3
Factor 20*s**2 + 718*s**3 + 44*s - 19*s - 723*s**3.
-5*s*(s - 5)*(s + 1)
Let j(f) be the second derivative of -1/3*f**2 - 1/3*f**3 + f - 1/40*f**5 + 2 - 11/72*f**4. Suppose j(n) = 0. Calculate n.
-2, -1, -2/3
Factor -193*j + j**2 - 31*j + 43*j**2 - 2*j**3 - 18*j.
-2*j*(j - 11)**2
Let l(k) be the second derivative of 5/4*k**4