/17
Let n = -32774 + 295091/9. Factor -n + 1/9*j**4 + 20/3*j**2 - 50/9*j - 14/9*j**3.
(j - 5)**3*(j + 1)/9
Let z(b) be the first derivative of -2*b**5/35 + 4*b**4/7 + 6*b**3/7 - 90. Factor z(l).
-2*l**2*(l - 9)*(l + 1)/7
Let m(c) = c**2 - 20*c + 54. Let k be m(17). Let n(b) be the first derivative of -3 + 2/7*b - 2/7*b**2 - 2/7*b**k. Factor n(x).
-2*(x + 1)*(3*x - 1)/7
Let g(y) = 11*y**2 + 12*y + 93. Let q(z) = 5*z**2 + 6*z + 46. Let r(a) = -6*g(a) + 13*q(a). Factor r(s).
-(s - 10)*(s + 4)
Let w(a) be the second derivative of -a**4/66 + 16*a**3/33 - 15*a**2/11 + 148*a + 3. Solve w(k) = 0.
1, 15
Let w(h) be the first derivative of -4*h**5/5 - 61*h**4/4 + 39*h**3 - 35*h**2/2 - 17*h + 55. Let w(n) = 0. What is n?
-17, -1/4, 1
Let y = -2 + 10. Suppose 0 = -4*b + y - 0. Factor b - 24*w - 1 + 8*w**3 + 2*w + 5 + 16*w**2.
2*(w + 3)*(2*w - 1)**2
Suppose -108 - 44*g + 10*g**4 + 20*g**4 + 15*g**4 - 525*g**5 + 8*g + 1023*g**2 + 1521*g**3 = 0. What is g?
-1, -3/5, 2/7, 2
Suppose -444*f - 294 = -1182. Solve -3/4*j**f + 27/2*j - 243/4 = 0.
9
Determine w, given that -2*w**4 - 10*w**4 + 5*w**2 - 2*w**4 + 6*w - 2*w**3 + 23*w**4 - 10*w**4 = 0.
-3, -1, 0, 2
Suppose -4*m = d - 22, 0 = -5*d - 2*m - 2 + 22. Factor 1/9*k**d - 14/9*k + 49/9.
(k - 7)**2/9
Let x(b) = 7*b**4 + 10*b**3 + 7*b**2 - 8*b + 4. Let g(c) = -c**4 - c**3 - 2. Let d(w) = -24*g(w) - 3*x(w). What is q in d(q) = 0?
-2, -1, 2, 3
Let k(b) = 4*b**5 - 24*b**3 + 20*b + 16. Let r(p) = -p**3 + p**2 + p + 1. Let q be 8 + 0*(-3)/(-9). Let l(j) = q*r(j) - k(j). Suppose l(g) = 0. What is g?
-1, 1, 2
Let w(q) be the third derivative of q + 1/168*q**8 + 0*q**4 - 6/5*q**5 + 0*q**3 + 0 + 2/5*q**6 + 11/105*q**7 + 18*q**2. Factor w(i).
2*i**2*(i - 1)*(i + 6)**2
Let q = 9 + -6. Let m(j) = j**3 + j**2 - 17*j + 19. Let s be m(3). Suppose -1/2*d**q + d**2 + 2*d - s = 0. Calculate d.
-2, 2
Let c(w) be the third derivative of -w**5/48 - 65*w**4/24 - 845*w**3/6 - w**2 + 6*w. Let c(v) = 0. Calculate v.
-26
Factor -10*z**4 - 9*z**4 - 46*z**4 + 86*z + 99*z - 45 + 210*z**3 + 20*z**5 - 15*z**5 - 290*z**2.
5*(z - 9)*(z - 1)**4
Suppose 2*h = -7*y + 4*y - 2, -3*y = -5*h - 26. Let l(n) be the first derivative of 0*n - 3/4*n**4 - 3/2*n**y - 2*n**3 + 7. Suppose l(w) = 0. Calculate w.
-1, 0
Let a = -913 + 923. Let v(b) be the first derivative of 0*b - 1/3*b**3 - a + 0*b**2 - 1/5*b**5 + 1/2*b**4. Factor v(q).
-q**2*(q - 1)**2
Let i(p) be the first derivative of -3*p**5/110 + 5*p**4/22 + p**3/11 - 15*p**2/11 + 15*p - 9. Let y(m) be the first derivative of i(m). Factor y(t).
-6*(t - 5)*(t - 1)*(t + 1)/11
Suppose 2*c = -3*x - 3, -c + 2*x + 2 = c. Factor -16/9*h**2 + 8/9*h + c + 10/9*h**3 - 2/9*h**4.
-2*h*(h - 2)**2*(h - 1)/9
Let k(a) be the third derivative of -25*a**8/336 - 47*a**7/42 - 51*a**6/8 - 209*a**5/12 - 305*a**4/12 - 20*a**3 + 125*a**2. Determine h so that k(h) = 0.
-4, -3, -1, -2/5
Let j(r) = 4*r - 116. Let q be j(30). Let p(x) be the first derivative of 0*x**3 + 3 + 0*x**2 - 3/4*x**q + 0*x. Factor p(u).
-3*u**3
Let g be -2*(-1)/(4 + 1). Suppose -6*j - 7*j + 26 = 0. Factor 2/5 - g*q**j + 0*q.
-2*(q - 1)*(q + 1)/5
Solve -3*v + 7072*v**2 + 28*v - 25*v**4 - 7167*v**2 - 145*v**3 = 0.
-5, -1, 0, 1/5
Let x(v) = -v**3 - 5*v**2 + 32*v + 6. Let r be x(-9). Let y be 54/45*20/r. Factor -4/7*u**2 + 0*u + 0 + y*u**3.
4*u**2*(u - 1)/7
Let f = 14 + -9. Suppose 3*d**2 + 180 + 60*d + 7*d**2 - f*d**2 = 0. What is d?
-6
Solve 2/11*i**3 + 8/11*i + 0 - 8/11*i**2 = 0 for i.
0, 2
Let d be (-1 - -1 - (-8 + 4)) + 28. What is i in 5*i**3 + d - 32 + 5*i**2 = 0?
-1, 0
Factor -495 - 3*i**2 - 139*i + 37*i - 372.
-3*(i + 17)**2
Suppose -14 - 34 = -12*h. Let w be (-140)/56 - (1 - h). Solve 0 - 1/2*g + w*g**3 + 0*g**2 = 0 for g.
-1, 0, 1
Let p(s) be the third derivative of 53*s**5/30 + 101*s**4/30 - 8*s**3/15 + 201*s**2. Suppose p(l) = 0. What is l?
-4/5, 2/53
Let x(w) be the second derivative of -w**6/255 + 12*w**5/85 - 59*w**4/51 - 104*w**3/17 - 169*w**2/17 - 2*w + 72. Determine s, given that x(s) = 0.
-1, 13
Let s be (7 + 2 + -5)/(0 + 3). Let r(p) be the second derivative of -1/3*p**4 + s*p**3 - 1/5*p**5 + 0*p**2 - 3*p + 0. Factor r(c).
-4*c*(c - 1)*(c + 2)
Let b be (10 + -6)*(1 - 0). Determine h, given that 0*h - h**3 - 3/2*h**b + 9/2*h**2 - 2 = 0.
-2, -2/3, 1
Let g(u) be the third derivative of -12321*u**5/80 - 111*u**4/16 - u**3/8 + 29*u**2 + 3. Factor g(s).
-3*(111*s + 1)**2/4
Suppose -9*n - 214 = 1010. Let v be 16/n - 6/(-51). Suppose -1/6*f**3 + v + 1/3*f**2 - 1/6*f = 0. What is f?
0, 1
Let n(h) be the third derivative of h**7/630 + h**6/30 - 3*h**5/20 + 7*h**4/36 - 62*h**2. Find u such that n(u) = 0.
-14, 0, 1
Let h = 432/1055 + -2/211. Suppose 0 - h*f**2 - 1/5*f - 1/5*f**3 = 0. What is f?
-1, 0
Let x(k) be the first derivative of k**6/3 + 3*k**5/5 - 9*k**4/4 - 8*k**3/3 + 6*k**2 + 585. Factor x(s).
s*(s - 1)*(s + 2)**2*(2*s - 3)
Let o(l) = -l**3 - 16*l**2 + 19*l + 34. Let t be o(-17). Let y(a) be the second derivative of 1/18*a**4 + 2/9*a**3 + a + t + 0*a**2. Solve y(v) = 0.
-2, 0
Let m(o) = -o**2 - 1. Let s(v) = -v**2 + 1. Let w(i) = m(i) + 3*s(i). Let n(p) = -3 - p + 4 + 21*p**2 - 10. Let t(q) = -4*n(q) - 22*w(q). Factor t(g).
4*(g - 1)*(g + 2)
Let b(j) = -9*j**3 + 23*j**2 + 4*j + 4. Let y(z) = 26*z**3 - 72*z**2 - 11*z - 11. Let n(v) = 11*b(v) + 4*y(v). Let n(k) = 0. Calculate k.
0, 7
Let j(g) be the second derivative of g**5/20 - 83*g**4/12 + 280*g**3 + 882*g**2 + 15*g. Solve j(y) = 0.
-1, 42
Let w be -4*(-1235)/4200 - 1/(-2). Let d = -12/35 + w. Let d*z + 2 - 2/3*z**2 = 0. Calculate z.
-1, 3
Suppose 3*x = -3*o, 0*o = 4*o + 16. Solve 6*d**4 - 21*d + 5*d**5 + 0*d**3 - x - 24*d**2 - 2 - 2*d**5 - 6*d**3 = 0 for d.
-1, 2
Let m(l) be the second derivative of l**5/40 + l**4/24 - l**3/6 + 7*l - 7. Factor m(q).
q*(q - 1)*(q + 2)/2
Let l(c) be the second derivative of c**7/504 - c**6/72 - c**4/12 + 4*c. Let p(a) be the third derivative of l(a). Determine j, given that p(j) = 0.
0, 2
Let l be (665/(-399) - 1/3)*2/(-24). Suppose -1/6*u**4 + 1/6*u**2 + 0*u - 1/6*u**5 + l*u**3 + 0 = 0. Calculate u.
-1, 0, 1
Let u be (4*-1)/((1 - 6) + 4). Let x be u/(-54)*-3 - (-32)/18. Find j, given that 3/2*j**5 + 0 + 9/2*j**3 + 0*j - 3/2*j**x - 9/2*j**4 = 0.
0, 1
Suppose 0 = -j + 9*j + 5*j - 39. Solve 0 - 5/3*d**j + 10/3*d - 5/3*d**2 = 0.
-2, 0, 1
Suppose 5*i + 34 - 44 = 0. Let n be (5 - 2)/(i - 1). Factor 0 + 2/13*w**2 + 0*w + 2/13*w**n.
2*w**2*(w + 1)/13
Let y(s) be the first derivative of s**6/60 + 2*s**5/35 + s**4/28 - 2*s**3/21 + 11*s**2/2 + 4. Let o(h) be the second derivative of y(h). Factor o(z).
2*(z + 1)**2*(7*z - 2)/7
Let k(f) be the first derivative of 4/39*f**3 + 2/13*f**5 + 7/26*f**4 - 14 + 0*f + 0*f**2. Find t such that k(t) = 0.
-1, -2/5, 0
Let a = 1/30 - -13/10. Let x(q) be the first derivative of 1 - 3/2*q**4 + 0*q + 1/3*q**6 + a*q**3 + 0*q**2 + 0*q**5. Factor x(d).
2*d**2*(d - 1)**2*(d + 2)
Let d(g) be the second derivative of -2*g**6/45 - g**5/5 - 2*g**4/9 - 193*g. Solve d(t) = 0 for t.
-2, -1, 0
Let y(m) be the third derivative of -m**7/315 - 11*m**6/180 - 43*m**5/90 - 23*m**4/12 - 4*m**3 + 13*m**2 + 26*m. Let y(p) = 0. Calculate p.
-4, -3, -1
Let m(g) be the first derivative of -3*g**4/8 + 2*g**3 + 15*g**2/4 - 209. Factor m(z).
-3*z*(z - 5)*(z + 1)/2
Suppose -4*g = x - 17 + 6, -3*x + 5*g = 1. Factor -3*m**x + 35 + 5*m**3 + 6*m - 8*m**2 - 35.
2*m*(m - 3)*(m - 1)
Let v(c) be the first derivative of 0*c + 5/12*c**4 - 8/9*c**3 - 1/15*c**5 + 2/3*c**2 + 6. Find g, given that v(g) = 0.
0, 1, 2
Let c = -19 - -34. Suppose -3 = 3*j - c. Factor -4 + j + 3*v**2 - 5 + 2.
3*(v - 1)*(v + 1)
Let x be -3 + 0 + 1 + 1 + 6. Factor v**3 - v - 6*v**3 + x*v + v.
-5*v*(v - 1)*(v + 1)
Suppose 0 = -3*k - k + 8. Factor -8*q**2 - 32*q**3 + 24*q**3 + q**2 + q**2 - k*q**4.
-2*q**2*(q + 1)*(q + 3)
Suppose -52*u + 3*u**2 + u**2 + 33*u**2 + 2*u**3 + 5*u**2 + 4*u**2 - 96 = 0. Calculate u.
-24, -1, 2
Let u(x) = -7*x + 7. Let b be u(5). Let v be 5*1 - b/(-14). Factor -5 + 4 - v*t**2 + 16 - 3.
-3*(t - 2)*(t + 2)
Factor -9*n**4 - 12*n**3 - 773*n**5 + 36*n**2 + 0*n**4 + 776*n**5.
3*n**2*(n - 3)*(n - 2)*(n + 2)
Let d(c) = -10*c**4 + 49*c**3 - 48*c**2. Let u(s) = 2*s**4 - 12*s**3 + 12*s**2. Let k(t) = 2*d(t) + 9*u(t). Let k(h) = 0. Calculate h.
-6, 0, 1
Let w = -790 + 796. Let h(o) = o**3 -