1
Let m(u) be the first derivative of u**3/9 + 50*u**2/3 + 2500*u/3 - 205. Factor m(l).
(l + 50)**2/3
Let w be (-4 + -1)/(10/(-4)). Factor -10*q**2 + 6 - 7 + 26*q - w*q**3 - 13.
-2*(q - 1)**2*(q + 7)
Let u be 18*(4/(-18) + (-272)/(-576)). Let i(l) be the first derivative of -l**3 + 15/4*l**2 - 3 + u*l. Determine z so that i(z) = 0.
-1/2, 3
Let g be (-4)/3*3 - (-7 - 3). Let b be (g - 0)/(-18)*-1. Solve 1/3*x**2 + 0 + b*x = 0 for x.
-1, 0
Let b(v) be the first derivative of v**6/600 - v**5/100 + v**4/60 - 7*v**2/2 - 6. Let u(j) be the second derivative of b(j). Let u(w) = 0. Calculate w.
0, 1, 2
Let d(j) = -3*j**2 - 12*j - 12. Suppose 0 = 7*w - 9 - 12. Let n(x) = 6*x**2 + 24*x + 24. Let c(t) = w*n(t) + 5*d(t). Solve c(o) = 0.
-2
Let u be 24/(-10)*90/(-36). Suppose -14 = j + 4*b, -4*b = 6*j - j + u. Factor -9*l - 6*l**j + 3*l**5 + 6*l**3 - 8*l**4 + 1 + 16*l**4 + l**4 - 4.
3*(l - 1)*(l + 1)**4
Let l(w) be the first derivative of 4/11*w**2 + 9/22*w**4 - 4/55*w**5 + 0*w - 36 - 8/11*w**3. Factor l(s).
-2*s*(s - 2)**2*(2*s - 1)/11
Factor 90/23 + 2/23*q**3 + 22/23*q**2 + 78/23*q.
2*(q + 3)**2*(q + 5)/23
Suppose 2 - 28 = -13*n. What is v in -n + 10*v**2 + 5*v + 2 + 5*v**3 = 0?
-1, 0
Let z(w) be the first derivative of 5*w**4/4 - 10*w**3/3 + 5*w**2/2 - 123. Let z(m) = 0. What is m?
0, 1
Let r = -11057173/380 + 116393/4. Let f = -1/38 + r. Let -f + 2/5*y**4 + 4/5*y**3 + 0*y**2 - 4/5*y = 0. What is y?
-1, 1
Let z = -5606849/1274630 - -4983/1946. Let n = -5/131 - z. Determine j so that n*j**2 + 0*j**3 + 0 - 3/5*j**4 + 6/5*j = 0.
-1, 0, 2
Suppose -2*j + 2*g - 8 = -3*j, -2*j + 2*g = 2. Factor -3*a**j - 2*a**4 + a**2 + 1 + 3*a**4.
(a - 1)**2*(a + 1)**2
Let r(o) = 7*o**2 - 16*o - 2. Let f(w) = -w**2 + 3*w - 1. Let n(t) = 6*f(t) + r(t). Factor n(c).
(c - 2)*(c + 4)
Suppose -x + 394 = 5*y - 484, -5*x - 860 = -5*y. Find c, given that -20 + 45*c**2 + 91*c**3 - 13*c - 67*c + 139*c**3 - y*c**4 = 0.
-2/5, -2/7, 1
Let h(g) be the third derivative of -g**8/2352 + g**7/294 - 2*g**2 - 14. Factor h(z).
-z**4*(z - 5)/7
Let o = -30 + 35. Suppose -3*n - 4 = u + n, o*u = -4*n + 12. Factor 0 - 2/5*t**5 + 4/5*t**2 + 0*t + 6/5*t**3 + 0*t**u.
-2*t**2*(t - 2)*(t + 1)**2/5
Suppose 2*n = -5*u + 28, 6*n + 11 = 2*u + 7*n. Let q(l) be the second derivative of 0*l**4 - 1/9*l**3 - 1/90*l**u - 2*l + 1/30*l**5 + 0 + 1/6*l**2. Factor q(t).
-(t - 1)**3*(t + 1)/3
Let j(q) = -15*q**2 + 15*q + 170. Let y = -54 - 31. Let u(k) = k**2 - k - 12. Let l(z) = y*u(z) - 6*j(z). Factor l(i).
5*i*(i - 1)
Let h(g) = 8*g**2 + 134*g + 974. Let q(c) = -15*c**2 - 270*c - 1950. Let l(x) = 5*h(x) + 3*q(x). Factor l(f).
-5*(f + 14)**2
Solve -3*t**2 + 56*t**4 + 24*t**4 + 115*t**3 + 15*t**5 - 75 - 140*t + 35 - 27*t**2 = 0 for t.
-2, -1/3, 1
Let w(g) be the third derivative of g**7/210 - g**6/30 - 11*g**5/60 - g**4/4 + 662*g**2. Let w(l) = 0. What is l?
-1, 0, 6
Let o = -33577/2 - -16789. Factor -o - 49/2*c**3 - 18*c**2 - 23/4*c - 31/2*c**4 - 15/4*c**5.
-(c + 1)**4*(15*c + 2)/4
Let f = -950 + 142501/150. Let h(g) be the third derivative of 0 + 0*g**4 + 0*g**3 + 1/600*g**6 - 3*g**2 + f*g**5 + 0*g. Determine d, given that h(d) = 0.
-2, 0
Let n be (-25344)/(-2912) - (-4)/26. Let g = 131/14 - n. Factor 0*a + a**2 - 1/2*a**4 - g + 0*a**3.
-(a - 1)**2*(a + 1)**2/2
Let k = 7726 + -7721. Factor 0 - 1/6*a**k - 7/6*a**3 - 5/6*a**4 + 0*a - 1/2*a**2.
-a**2*(a + 1)**2*(a + 3)/6
Let i(k) be the third derivative of -k**7/280 - k**6/80 + k**5/80 + k**4/16 + 5*k**2 + 65. Find m such that i(m) = 0.
-2, -1, 0, 1
Let q(b) be the second derivative of b**4/60 - 4*b**3/15 + 2*b - 22. Factor q(j).
j*(j - 8)/5
Let z(k) be the third derivative of k**5/24 + 5*k**4/12 - 3*k**2 + 23*k. Factor z(v).
5*v*(v + 4)/2
Let g(t) = t**2 - 7*t + 15. Let v be g(5). Let i be v - 1*66/18. Factor 5/3*x**2 - 1/3*x**3 - 8/3*x + i.
-(x - 2)**2*(x - 1)/3
Let f(s) be the first derivative of s**6/24 - 7*s**5/20 + 7*s**4/16 + 23*s**3/12 - 11*s**2/2 + 5*s - 202. Let f(z) = 0. What is z?
-2, 1, 2, 5
Let k(q) be the second derivative of 0 - 20*q + 2/45*q**4 + 0*q**2 + 2/75*q**5 + 1/225*q**6 + 0*q**3. Factor k(u).
2*u**2*(u + 2)**2/15
Let d(n) be the third derivative of n**7/4200 - n**5/150 + 19*n**3/6 - 15*n**2. Let l(c) be the first derivative of d(c). Factor l(z).
z*(z - 2)*(z + 2)/5
Let y(h) be the second derivative of 13*h + 1/5*h**2 + 0 + 1/2*h**3 + 13/60*h**4. Factor y(w).
(w + 1)*(13*w + 2)/5
Find m, given that -1/9*m**5 + 20/9*m**2 + 19/9*m + 2/3 + 2/3*m**3 - 2/9*m**4 = 0.
-2, -1, 3
Let j(a) be the third derivative of a**5/30 - 55*a**4/6 + 3025*a**3/3 - 68*a**2 + a. Suppose j(s) = 0. Calculate s.
55
Let h(z) = -30*z**3 + 381*z**2 - 1059*z + 42. Let d(b) = 3*b**3 - 38*b**2 + 106*b - 4. Let v(m) = 21*d(m) + 2*h(m). Factor v(s).
3*s*(s - 6)**2
Let s = 24/53 - 211/583. Let k(x) be the first derivative of 0*x - 2/11*x**3 - 12 + s*x**2. Determine y so that k(y) = 0.
0, 1/3
Factor -24*b - 64/7*b**4 - 292/7*b**2 - 36/7 - 32*b**3.
-4*(b + 1)**2*(4*b + 3)**2/7
Let p(u) = u**2 - 6*u - 9. Let j(c) = 6*c**2 - 42*c - 63. Let g(x) = -2*j(x) + 15*p(x). Find t, given that g(t) = 0.
-1, 3
Let i(w) be the third derivative of w**5/12 + 125*w**4/12 + 3125*w**3/6 + 31*w**2 + 2. Factor i(b).
5*(b + 25)**2
Let u(s) be the second derivative of 2*s**6/15 - 2*s**5/5 - 4*s**4 + 80*s**3/3 - 64*s**2 - 23*s. Factor u(x).
4*(x - 2)**3*(x + 4)
Let q(d) = -2*d**2 - 3*d + 51. Let a(i) = -2*i**2 - 4*i + 44. Let j(o) = -3*a(o) + 4*q(o). Factor j(t).
-2*(t - 6)*(t + 6)
Factor 80/3*l**4 - 472/3*l**3 + 0 - 4/3*l**5 + 240*l**2 - 108*l.
-4*l*(l - 9)**2*(l - 1)**2/3
Let l(u) be the first derivative of -2*u**3/3 + 10*u**2 + 22*u - 34. Factor l(k).
-2*(k - 11)*(k + 1)
Suppose 0 + 0*p - 32/7*p**2 - 2/7*p**4 + 16/7*p**3 = 0. What is p?
0, 4
Let k(j) = -95*j**2 + 40*j + 1. Let z(l) = -21*l + 32*l**2 - 37*l + 18*l + 64*l**2. Let c(x) = -4*k(x) - 5*z(x). Suppose c(v) = 0. What is v?
1/5
Solve -51/4*v**2 - 31/4*v**3 - 3 - 9/4*v**4 - 10*v - 1/4*v**5 = 0.
-3, -2, -1
Let y(p) be the second derivative of -25/12*p**4 + 28*p + 0 - 9/2*p**2 + 5*p**3. Factor y(f).
-(5*f - 3)**2
Let x(y) be the first derivative of 5/2*y**5 - 15*y**2 + 265/24*y**4 - 20/3*y + 41 + 25/3*y**3. Determine d, given that x(d) = 0.
-2, -1/5, 2/3
Factor -768/7*n - 120/7*n**2 - 4/7*n**3 + 2048/7.
-4*(n - 2)*(n + 16)**2/7
Let l(s) be the first derivative of 3*s**4/4 + 3*s**3 - 6*s**2 - 96. Factor l(h).
3*h*(h - 1)*(h + 4)
Factor -16*x**4 + x**3 + 30*x**4 - 7*x**3 - 12*x**4 - 20*x**2.
2*x**2*(x - 5)*(x + 2)
Let w = 41973/2 + -20986. Find c, given that w*c + 1/4 + 1/4*c**2 = 0.
-1
Factor 14*t**3 + 36 - 26*t**2 + 284*t**4 + 0*t - 286*t**4 - 6*t.
-2*(t - 3)**2*(t - 2)*(t + 1)
Suppose 3*b - 31 + 29 = g, -4*b + 33 = 3*g. Suppose -10/3*h**b + 16/3*h - 14/3*h**2 + 8/3 = 0. Calculate h.
-2, -2/5, 1
Let y(s) = 2*s + 2. Let f be y(-6). Let l(z) = -3*z - 28. Let k be l(f). Factor -1/4*q - 1/4*q**k + 0.
-q*(q + 1)/4
Suppose 3*b - 8*b - 1 + 16 = 0. Suppose -8/7 + 0*g + 2*g**2 - 6/7*g**b = 0. Calculate g.
-2/3, 1, 2
Let b(f) be the third derivative of f**9/1008 + 37*f**8/6720 - f**7/210 - f**6/60 - 2*f**5/5 - 16*f**2. Let y(k) be the third derivative of b(k). Factor y(u).
3*(u + 2)*(4*u + 1)*(5*u - 2)
Let y be (12/28)/((-6)/(-4)). Let o(v) = -7*v + 46. Let n be o(6). Factor 0*u + 2/7*u**2 - y*u**n + 0 + 0*u**3.
-2*u**2*(u - 1)*(u + 1)/7
Let y(j) be the first derivative of 0*j**4 - 2/5*j**6 - 2/7*j**7 + 0*j**2 + 2 - 3/20*j**5 + 0*j**3 - 2*j. Let n(k) be the first derivative of y(k). Factor n(l).
-3*l**3*(2*l + 1)**2
Let k be 1541/2208 - 8/256. Determine r, given that -2/3*r**4 + 0*r + k*r**2 + r**3 - r**5 + 0 = 0.
-1, -2/3, 0, 1
Let f(v) be the first derivative of -1/2*v**4 - 5*v**2 - 8/3*v**3 + 3 - 4*v. Factor f(h).
-2*(h + 1)**2*(h + 2)
Let i be 30/90 + (1/(-4) - (-138)/72). Solve 2/9*z**4 + 8/9 + 26/9*z**i + 4/3*z**3 + 8/3*z = 0 for z.
-2, -1
Suppose -4*m + 4*a + 7 = -5, -2*m - 5*a - 15 = 0. Suppose u - 3 = -m*u. Suppose 5 - u*h + 2 - 2*h**2 - h**2 - 1 = 0. What is h?
-2, 1
Let i be ((-455)/182)/(1/(-2)). Solve 1/7*w**i - 8/7*w + 23/7*w**2 - 16/7 - w**4 + w**3 = 0.
-1, 1, 4
Let o(h) be the second derivative of 1/10*h**5 + 1/63*h**7 + 0*h**2 + 0 + 4/45*h**6 - 2/9*h**4 - 4/9*h**3 + 7*h. Determine v so that o(v) = 0.
-2, -1, 0, 1
Let g be (12/(-36))/((-1)/15)