
Let h(o) = 10*o**3 - 100*o**2 + 334*o - 313. Let v(g) = 5*g**3 - 50*g**2 + 168*g - 156. Let x(q) = -4*h(q) + 7*v(q). Solve x(c) = 0 for c.
2, 4
Factor -32*u - 24*u**4 + 2*u**3 - 27*u**4 + 4*u**3 + 50*u**4.
-u*(u - 4)**2*(u + 2)
Suppose 9*m - 6 = -105. Let p be ((-8)/1*7/14)/m. Factor -2/11*n + 6/11*n**3 + 0 + p*n**5 - 2/11*n**2 + 10/11*n**4.
2*n*(n + 1)**3*(2*n - 1)/11
Let v be 1 + 1 - (1 + -2). Let o = 9 + -6. Factor -2*c**v - o*c**4 - 5*c**4 + 7*c**4.
-c**3*(c + 2)
Let y be (-1 - 2 - -21)*1. Let j = -16 + y. Factor -4*i + 24*i**2 + 14*i**4 + 9*i**4 + j*i**4 - 45*i**3.
i*(i - 1)*(5*i - 2)**2
Factor 1/3*n**4 - 4*n**2 - 28/3*n + 1/3*n**3 - 16/3.
(n - 4)*(n + 1)*(n + 2)**2/3
Suppose 0 = 17*w - 25*w. Let v(q) be the first derivative of q**2 + w*q + 0*q**3 + 8 - 1/2*q**4. Factor v(a).
-2*a*(a - 1)*(a + 1)
Let n(d) = 7*d**2 + 71*d + 88. Let w(h) = 27*h**2 + 288*h + 351. Let o(r) = -15*n(r) + 4*w(r). What is c in o(c) = 0?
-28, -1
Let w(z) be the second derivative of -4/15*z**3 + 1/10*z**7 + 0 + 13*z + 43/150*z**6 - 9/20*z**4 + 7/100*z**5 + 2/5*z**2. Find i such that w(i) = 0.
-1, 2/7, 2/3
Let y(d) = -9*d**3 - d**2 + 13*d + 1. Let n(u) = -17*u**3 - 3*u**2 + 27*u + 3. Let q(c) = 2*n(c) - 5*y(c). Factor q(a).
(a - 1)*(a + 1)*(11*a - 1)
Suppose 0 = -2*j + b - 0*b + 70, 2*b + 177 = 5*j. Suppose j*c**3 + 2 + 40*c**2 + 2 + 3*c**3 + 20*c + 20*c**4 + 4*c**5 = 0. Calculate c.
-1
Let m(l) = -26*l + 43*l - 11*l**4 - 29*l**2 + 3*l**5 - 4*l**2 - 5 + 27*l**3. Let x(i) = -i**5 - i**4 + i**3 + i**2 + i + 1. Let h(w) = m(w) + x(w). Factor h(r).
2*(r - 2)*(r - 1)**4
Let m(u) = -7*u**2 - u - 3. Let i(x) be the first derivative of 5*x**3 + x**2/2 + 7*x - 2. Let p(g) = -3*i(g) - 7*m(g). Suppose p(o) = 0. What is o?
-1, 0
Let y(i) be the second derivative of -i**7/98 - i**6/70 + 9*i**5/70 + i**4/7 - 4*i**3/7 - 2*i - 41. Let y(x) = 0. What is x?
-2, 0, 1, 2
Let f(b) be the first derivative of 1/7*b**4 - 1/21*b**6 - 4/7*b - 16/21*b**3 + b**2 + 4/35*b**5 - 6. Factor f(v).
-2*(v - 1)**4*(v + 2)/7
Let f(o) be the third derivative of 11*o**2 - 1/160*o**5 + 3/64*o**4 + 0 + 0*o + 0*o**3. Factor f(v).
-3*v*(v - 3)/8
Let y(r) be the second derivative of -1/12*r**4 + 0*r**2 + 36*r - 1/2*r**3 + 0. Factor y(u).
-u*(u + 3)
Let r = 57/14 + -93/28. Let 9/4*n + 3 - r*n**2 = 0. Calculate n.
-1, 4
Suppose -3*g - 6 = -3. Let x be ((-42)/(-77))/((6/(-8))/g). Suppose -2/11*c - 8/11*c**2 + 0 - x*c**3 = 0. What is c?
-1/2, 0
Let k(f) be the second derivative of -7*f**4/6 - 52*f**3/3 - 21*f**2 + 128*f. Factor k(z).
-2*(z + 7)*(7*z + 3)
Let t(v) be the third derivative of -v**8/10080 - v**7/840 + v**6/90 - 7*v**5/20 - 15*v**2. Let c(h) be the third derivative of t(h). Factor c(q).
-2*(q - 1)*(q + 4)
Let j(s) = s**2 + 10*s + 18. Let z be j(-8). Determine y, given that -2*y - 20 - 8*y + 2*y**4 + z*y**2 + 14 + 12*y**3 + 2*y**2 - 2*y**5 = 0.
-1, 1, 3
Suppose 0 = f + 2*f - 4*y - 63, 5*y + 32 = f. Suppose f + 10 = 9*b. Factor -1/3 + 1/3*z**2 - 4/3*z**b + 4/3*z.
-(z - 1)*(z + 1)*(4*z - 1)/3
Let l(a) be the first derivative of a**5/30 - 61*a**4/24 + 133*a**3/2 - 2205*a**2/4 - 3087*a - 66. Factor l(y).
(y - 21)**3*(y + 2)/6
Let b be -19 - -24 - 1*-1. Suppose -b*z - 8 = -10*z. Factor z*h + h**2 + h**2 + 8 - 10 - 2*h**3.
-2*(h - 1)**2*(h + 1)
Let d be (-2)/2 - (1 + -4). Factor -6*f**2 - 25 + 6*f**d + 20*f + 2*f**2 + 3*f**2.
5*(f - 1)*(f + 5)
Let g be (-793)/610 - (-27)/15. Factor -2/3*n + 1/6*n**3 - g*n**2 + 0.
n*(n - 4)*(n + 1)/6
Let a(v) be the second derivative of v**5/130 + 3*v**4/13 - v**3/39 - 18*v**2/13 + 125*v. Suppose a(m) = 0. What is m?
-18, -1, 1
Suppose 4*j - 64 = 3*c, -3*j - c = -5*c - 55. Suppose -g + 3*g - j = 3*o, g + 4 = -2*o. Factor g*v**3 + 1 + 2 + 10*v - 1 + 8*v**2 + 2.
2*(v + 1)**2*(v + 2)
Let x(u) be the first derivative of -u**7/5460 - u**6/234 - 5*u**5/156 + u**3 - 9. Let b(y) be the third derivative of x(y). Find i such that b(i) = 0.
-5, 0
Factor 120/19 - 10/19*c**2 + 2/19*c**3 - 112/19*c.
2*(c - 10)*(c - 1)*(c + 6)/19
Let w(y) = 3*y**3 + 3*y**2 - 3*y. Let n(k) = 3*k**2 - k - 2*k - 2*k**2 + 4*k. Let p(i) = 3*n(i) + w(i). Factor p(u).
3*u**2*(u + 2)
Let o(r) be the second derivative of -2*r**3/3 + 6*r**2 - 14*r. Let d be o(3). Factor -2/7*g**2 + 0*g + d + 0*g**3 + 2/7*g**4.
2*g**2*(g - 1)*(g + 1)/7
Let b be 4 + -1 + -3 + 195. Suppose b*h = 197*h. Solve 27/7*c + 3/7*c**3 - 18/7*c**2 + h = 0.
0, 3
Let f(b) = -b**3 - 2*b**2 + b + 8. Let s(u) = 5*u**3 + 9*u**2 - 5*u - 42. Let l(z) = -11*f(z) - 2*s(z). Determine x, given that l(x) = 0.
-4, -1, 1
Suppose 0 = 9*s - 15*s - 24. Let b be ((-3)/6)/(1/s). Factor 2/11*o**b + 0*o + 0 - 2/11*o**3.
-2*o**2*(o - 1)/11
Let w(s) be the second derivative of -11*s**6/60 + 29*s**5/40 + s**4/2 - 11*s**3/3 - 4*s**2 - 50*s. Determine n, given that w(n) = 0.
-1, -4/11, 2
Let b be (-720)/(-35) - (-5 - (-1 + -2)). Let d = b + -309/14. Factor 1/4 + 3/4*c + d*c**2 - 3/4*c**4 - 1/4*c**5 - 1/2*c**3.
-(c - 1)*(c + 1)**4/4
Let x be 2 + (2 - (-1 - -2 - -1)). Factor 4*b**3 + b**4 - b**2 - 2*b**3 - 3*b**3 - b**3 + x*b.
b*(b - 2)*(b - 1)*(b + 1)
Let k = 60 - 69. Let r be (-3 - -1) + 2 - 4/k. Factor -r*b + 0 - 2/9*b**4 + 4/9*b**3 + 2/9*b**2.
-2*b*(b - 2)*(b - 1)*(b + 1)/9
Let -2*b + 7/3 - 1/3*b**2 = 0. What is b?
-7, 1
Let k(l) be the second derivative of l**5/4 - 295*l**4/6 + 2800*l**3 + 18000*l**2 - 2*l + 186. Let k(n) = 0. Calculate n.
-2, 60
Let v(a) = -a**4 + 4*a**3 + a**2 + 4. Let f(l) = 12 - l**4 + 7*l**3 - 14 + 9 + l**2. Let m(s) = -4*f(s) + 7*v(s). Factor m(q).
-3*q**2*(q - 1)*(q + 1)
Let c be 27/72*4 + (-38)/36. Suppose -2 + 7 = j. What is u in 0*u - 2/9 + 4/9*u**3 - 2/3*u**4 + 8/9*u**2 - c*u**j = 0?
-1, 1/2, 1
Let g(l) be the first derivative of l + 4 + 1/10*l**6 - 2*l**3 - 3/4*l**5 + 2*l**4 + 0*l**2. Let o(v) be the first derivative of g(v). Factor o(h).
3*h*(h - 2)**2*(h - 1)
Let o(s) be the third derivative of -s**6/280 + s**5/35 + 11*s**4/56 + 3*s**3/7 + 118*s**2. Factor o(c).
-3*(c - 6)*(c + 1)**2/7
Suppose -3*p = -4*p + 3. Find q such that -5*q**4 - 21*q**3 - 5*q**3 - 4*q**p - 45*q**2 = 0.
-3, 0
Factor 159*b**2 + 54 + 2*b**3 + 9 - b**3 + 12 - 228*b - 7*b**3.
-3*(b - 25)*(b - 1)*(2*b - 1)
Let a(q) be the third derivative of -q**8/336 + 31*q**7/210 - 127*q**6/60 + 97*q**5/30 + 85*q**4/8 - 75*q**3/2 - 865*q**2. What is b in a(b) = 0?
-1, 1, 15
Let i(t) be the first derivative of -t**4/14 + 6*t**3/7 - 2*t**2 - 48*t/7 + 146. Factor i(z).
-2*(z - 6)*(z - 4)*(z + 1)/7
Let a(s) = -s**2 - 6*s + 2. Let b be a(-6). Factor m**3 + 14 - m**3 - b + 3*m**3 - 9*m**2.
3*(m - 2)**2*(m + 1)
Let r(a) be the third derivative of -a**6/300 + a**5/25 - a**4/12 - 54*a**2 - 4*a. Let r(y) = 0. What is y?
0, 1, 5
Suppose -15*b + b + 154 = 0. Factor 22*o + b + 2*o + 3*o**2 - 18 - 20.
3*(o - 1)*(o + 9)
Suppose 4*y - b = 22, -44*y + 5*b = -41*y - 42. Factor 14/5*l**y - 38/5*l**3 - 2/5*l - 4/5 + 6*l**2.
2*(l - 1)**3*(7*l + 2)/5
Let q(v) be the second derivative of -2*v**6/15 - 8*v**5/5 - 20*v**4/3 - 32*v**3/3 - 12*v + 1. Factor q(k).
-4*k*(k + 2)**2*(k + 4)
Let z(x) be the second derivative of x**7/399 - 2*x**6/285 - x**5/38 + x**4/19 + 130*x. Solve z(l) = 0.
-2, 0, 1, 3
Let p(a) = a - 1. Suppose 20 + 0 = -2*t. Let u(m) = -7*m + 11*m + 7 - 18*m + 7*m**2. Let b(y) = t*p(y) - 2*u(y). Factor b(q).
-2*(q - 1)*(7*q - 2)
Suppose 43*z + 273 = 134*z. Factor 14*p + 2/3*p**z + 12 + 16/3*p**2.
2*(p + 2)*(p + 3)**2/3
Suppose -5*o - 5*v = -6*v - 54, -3*v = -3. Factor 3 - 6*n**2 - 17 + o*n + 9.
-(n - 1)*(6*n - 5)
Let h = 51 - 53. Let o(y) = -6*y**3 + 8*y**2 - 2*y + 2. Let j(s) = -31*s**3 + 40*s**2 - 9*s + 11. Let d(r) = h*j(r) + 11*o(r). Factor d(m).
-4*m*(m - 1)**2
Let i(l) be the second derivative of 0 + 3/80*l**5 - 32*l + 1/2*l**4 + 13/8*l**3 + 9/4*l**2. Find u, given that i(u) = 0.
-6, -1
Let k(x) be the first derivative of x**6/18 - 4*x**5/5 + 19*x**4/4 - 134*x**3/9 + 26*x**2 - 24*x + 200. What is c in k(c) = 0?
2, 3
Let w(p) be the third derivative of -p**7/42 + 3*p**6/8 - 7*p**5/4 + 95*p**4/24 - 5*p**3 - 34*p**2. Factor w(z).
-5*(z - 6)*(z - 1)**3
Let n = 11714/3 - 3904. Find f such that -2/3*f**2 - 4/3*f - n = 0.
-1
Let a(v) be the third derivative of v**5/30 - 7*v**4/4 + 661*v**2. Determine b, given that a(b) = 0.
0, 21
Let t(s) be the third derivative of -s**6/160 + s**5/30 + s**4/24