h**2 + 42*h - 14. Let g be i(8). Suppose 7*f = -m + 3*f + 44, -81 = -4*m + 3*f. Factor 4*x**2 - x**g - 2 + m*x + 11 - 12*x.
3*(x + 1)*(x + 3)
Let h be 1/((-1)/(-15)*-1)*-1. Suppose -h*u = -12*u. Factor -1/2*w**4 - 1/2*w**3 + u*w**2 + 0 + 0*w.
-w**3*(w + 1)/2
Let z = 47 + -29. Let b be ((-10)/(-8))/((-3)/z + 1). Solve -3/2*s**2 - b*s + 0 = 0 for s.
-1, 0
Let t = 156 + -72. Let r be 45/t - (-1)/(-4). Factor -4/7*u + r + 2/7*u**2.
2*(u - 1)**2/7
Let h = -14 + 18. Suppose 2*j + 4*o + 4 = 0, -3*j - 2*o - 3*o - 4 = 0. Factor -1 + 4*p**h + 4*p**3 - 12*p - p**4 + p**j + 8*p - 3*p**2.
(p - 1)*(p + 1)**2*(3*p + 1)
Let i(t) be the third derivative of t**7/210 - t**6/30 - t**5/20 + 5*t**4/12 + 4*t**3/3 - 8*t**2 + t. Let i(v) = 0. What is v?
-1, 2, 4
Factor -47*v**3 - 10 + 171*v**2 + 14*v**4 - 27*v**3 - 70*v - 53*v**2 + 22.
2*(v - 3)*(v - 1)**2*(7*v - 2)
Let t(k) be the third derivative of -k**5/60 - 5*k**4/12 - 8*k**3/3 - 41*k**2 + 1. Factor t(n).
-(n + 2)*(n + 8)
Let h(m) be the first derivative of -4/9*m**3 - 5 + 0*m**2 - 1/3*m**4 + 0*m - 1/15*m**5. Let h(c) = 0. What is c?
-2, 0
Suppose -3*b + 8 = u, -5*b + 5 = -0*b. Let q(g) = -g**3 + 4*g**2 + 5*g + 2. Let z be q(u). Factor 8*f**4 - f**5 - 5*f**4 - 2*f**z - f**3 - f**2 + 2*f.
-f*(f - 2)*(f - 1)**2*(f + 1)
Let a(j) be the second derivative of 10/7*j**3 + 23/21*j**4 + 20*j + 4/7*j**2 + 0 - 3/7*j**5 - 10/21*j**6. Suppose a(i) = 0. Calculate i.
-1, -2/5, -1/5, 1
Let x(a) be the third derivative of a**7/210 + a**6/40 - a**5/20 - 7*a**4/24 + a**3 - 182*a**2. Factor x(j).
(j - 1)**2*(j + 2)*(j + 3)
Factor 10*s**2 - 49*s**2 - 53*s + 10*s**3 + 13*s + 5*s**4 - 16*s**2 + 160 - 5*s**2.
5*(s - 2)**2*(s + 2)*(s + 4)
Suppose 44*r - 11454 = -11454. Solve 1/4*j**3 - 1/4*j**2 + r - 1/2*j = 0 for j.
-1, 0, 2
Suppose 2/3*t**4 - 4 - 17/3*t**2 - 26/3*t - 1/2*t**3 + 1/6*t**5 = 0. Calculate t.
-2, -1, 3
Suppose 33 + 25 = 4*o - 3*t, -5*o + 57 = 4*t. Factor -g**5 - o*g**4 - 6*g**3 - 1 + 6*g**2 + 4 + 4*g**4 - 2*g**5 + 9*g.
-3*(g - 1)*(g + 1)**4
Let q(g) be the second derivative of -3/100*g**5 - 1/20*g**4 - 12*g + 0*g**2 - 1/30*g**3 - 1/150*g**6 + 0. What is v in q(v) = 0?
-1, 0
Let t(w) = -w**2 - 2*w + 50. Let b be t(6). Let j be (-5)/30*b*-1. Factor 0 - 1/3*i + j*i**2.
i*(i - 1)/3
Factor -2/11*l + 8/11*l**2 + 0.
2*l*(4*l - 1)/11
Factor -52900*r - 12167000/3 - 230*r**2 - 1/3*r**3.
-(r + 230)**3/3
Let h(j) be the third derivative of j**7/1260 + j**6/240 - j**5/360 - j**4/48 - 58*j**2. Find o, given that h(o) = 0.
-3, -1, 0, 1
Suppose -t - 3 = 3*p - 11, -4*t - 16 = -4*p. Let u be (4/25)/((-4)/(-90)). Solve 0 + u*m**p + 4/5*m**2 + 14/5*m**4 + 0*m = 0.
-1, -2/7, 0
Let i = -39 + 41. Determine j, given that 3*j - 12*j**i - j - 2*j**3 - j - 11*j = 0.
-5, -1, 0
Factor y**4 - 2/7*y - 3/7 + 18/7*y**3 + 12/7*y**2.
(y + 1)**3*(7*y - 3)/7
Let d(y) = -10*y**2 - 2665*y - 176855. Let o(l) = 15*l**2 + 3997*l + 265286. Let u(n) = 7*d(n) + 5*o(n). Determine t so that u(t) = 0.
-133
Let o(d) be the second derivative of -5*d**4/12 - 100*d**3/3 + 205*d**2/2 + 4*d + 68. Solve o(u) = 0.
-41, 1
Let n = 8 - 2. Let u(m) = m**3 - 7*m**2 + 5*m + 6. Let f be u(n). Suppose b**4 - b**2 + f*b**2 + 2*b**5 - 7*b**4 + 9*b**2 = 0. Calculate b.
-1, 0, 2
Let n(o) be the second derivative of 49*o**5/5 - 231*o**4 + 496*o**3 - 416*o**2 + 85*o. Factor n(g).
4*(g - 13)*(7*g - 4)**2
Suppose 160*y = -49*y. Determine n, given that y + 3/2*n**2 + 21/4*n**3 + 0*n + 6*n**4 + 9/4*n**5 = 0.
-1, -2/3, 0
Suppose 0 = 5*q - 488 - 27. Let g = -74 + q. What is m in 2*m**2 - g + 29 + 4*m = 0?
-2, 0
Let u = 8101/36 + -225. Let n(s) be the second derivative of -1/24*s**4 - 1/180*s**6 - u*s**3 - 1/40*s**5 + 0 + 5*s + 0*s**2. Factor n(c).
-c*(c + 1)**3/6
Suppose -z - 4*i - 8 = 4, 4*i = -5*z - 12. Suppose -2*l = -z*l - 10. Factor 0*c + 0*c**3 + 3*c - l*c**3 + 2*c.
-5*c*(c - 1)*(c + 1)
Let f(c) be the second derivative of 3*c - 1/2*c**2 + 0 - 1/3*c**3 - 1/12*c**4. Factor f(z).
-(z + 1)**2
Let w(n) = 5*n**4 + 17*n**3 + 7*n**2 - 29. Let q(h) = 36*h**4 - 34*h**4 + h**3 + 2*h**2 + 5*h**3 - 10. Let p(s) = 17*q(s) - 6*w(s). Factor p(a).
4*(a - 1)**2*(a + 1)**2
Let 6/5*a + 3/5 + 3/5*a**2 = 0. Calculate a.
-1
Suppose -23*w + 344*w = 0. Factor 0*r + w - 14/19*r**3 - 2/19*r**5 - 6/19*r**2 - 10/19*r**4.
-2*r**2*(r + 1)**2*(r + 3)/19
Let v be -6 - -3 - -3 - -3. Determine x, given that -v*x**2 - 6 + 4*x - 3*x + 4*x**2 + 0*x = 0.
-3, 2
Let b(w) be the second derivative of w**6/2 - 33*w**5/10 + 2*w**4 - 97*w. Determine o, given that b(o) = 0.
0, 2/5, 4
Let b(j) = 100*j**2 + 280*j - 110. Let i(z) = 11*z**2 + 31*z - 12. Let c(v) = -6*b(v) + 55*i(v). Factor c(d).
5*d*(d + 5)
Factor 1/2*f**2 - 5/2 + 2*f.
(f - 1)*(f + 5)/2
Suppose 3*p = -s + 6*p + 9, -p = -2*s + 8. Factor 6 - 520*j**2 + 29*j - 2*j + 448*j**2 + 39*j**s.
3*(j - 1)**2*(13*j + 2)
Suppose v - l = l + 4, l = -3*v - 23. Let f = -4 - v. Factor -f + 2*m**2 - m**2 + 0*m**2 + 1.
(m - 1)*(m + 1)
Suppose 41*h + 29 = 3*u + 46*h, -h + 4 = 0. Let n(v) be the first derivative of 0*v**2 + 7 + 0*v - 1/6*v**4 + 0*v**u - 2/15*v**5. Factor n(c).
-2*c**3*(c + 1)/3
Factor -7/6*b**3 - 5/6*b**4 - 1/2*b**2 - 1/6*b**5 + 0*b + 0.
-b**2*(b + 1)**2*(b + 3)/6
Factor 0*f**2 + 0*f**2 - 8*f**5 + 4*f**3 + 6*f**5 - 2*f**5.
-4*f**3*(f - 1)*(f + 1)
Suppose 18*v = 226 - 190. Factor 1/6*w**v + 3/2 + 5/3*w.
(w + 1)*(w + 9)/6
Let t = 21 + -33. Let s be (12/(-88))/(t/16). Factor -2/11*d + 2/11*d**3 - 2/11*d**2 + s.
2*(d - 1)**2*(d + 1)/11
Let n(w) be the first derivative of -w**6/42 + 2*w**5/35 - 178. Solve n(a) = 0 for a.
0, 2
Suppose 12*t - 90*t**2 - 2/5 = 0. Calculate t.
1/15
Let z(q) be the third derivative of 0*q + 3*q**2 - 1/15*q**5 - 1/60*q**6 + 1/4*q**4 + 0*q**3 + 0. Factor z(u).
-2*u*(u - 1)*(u + 3)
Let q(c) = 3*c**2 - 19*c + 6. Let n(k) = 2*k**2 - 14*k + 6. Let v(m) = m. Let g(b) = -n(b) + 4*v(b). Let i(f) = 4*g(f) + 5*q(f). Factor i(j).
(j - 3)*(7*j - 2)
Factor -j**2 + 32 - 10*j + 9*j + 9 + 25*j + 16*j.
-(j - 41)*(j + 1)
Let u be (1/(-2))/((-4)/208). Suppose -4*x + 26 + x**2 - 5*x**2 - u = 0. Calculate x.
-1, 0
Let v(l) = -1 + 6*l**3 - 5*l**3 + l + l**4 + 1 - 1. Let o(s) = -15*s**4 - 15*s**3 - 18*s + 18. Let z(a) = -o(a) - 18*v(a). Solve z(d) = 0.
-1, 0
Let h(q) be the first derivative of -3*q**4 - 25 + 6*q**3 + 3/2*q**6 + 3/2*q**2 - 6*q - 12/5*q**5. Factor h(l).
3*(l - 1)**3*(l + 1)*(3*l + 2)
Suppose -10*f = -14*f + 12. Factor -s + 3*s**2 - 2 + 0*s**2 - s**4 - 2*s**4 + 2*s**4 + s**f.
-(s - 2)*(s - 1)*(s + 1)**2
Let w = 404 + -401. Let t(v) be the first derivative of -w - 3/2*v**2 + 1/4*v**4 + 0*v**3 - 2*v. Solve t(i) = 0.
-1, 2
Let h(d) = 3*d**3 + 16*d**2 - 24*d. Let i(l) = 27*l**2 + 4*l**3 - 60*l + 13*l**2 + 4*l**3. Let b(t) = 12*h(t) - 5*i(t). Find r, given that b(r) = 0.
-3, 0, 1
Let s(h) = 1014*h**2 - 317*h + 19. Let t(u) = -507*u**2 + 159*u - 9. Let m(k) = -3*s(k) - 5*t(k). Factor m(v).
-3*(13*v - 2)**2
Let y be (-56)/(-3) - (-6)/18. Factor -151*j + 8*j**4 - 5*j**3 - 6*j**4 + 108*j**2 + 162 - 65*j - y*j**3.
2*(j - 3)**4
Let s(a) = -a**3 + 13*a**2 + 4*a - 25. Let o(n) = 4*n**3 - 66*n**2 - 22*n + 126. Let v(g) = -3*o(g) - 14*s(g). Determine m so that v(m) = 0.
-7, -2, 1
Let c(g) be the third derivative of g**8/1512 - 2*g**7/315 + 7*g**6/540 + g**5/15 - 11*g**4/27 + 8*g**3/9 - 53*g**2 + g. Let c(w) = 0. Calculate w.
-2, 1, 2, 3
Let k = -66 - -60. Let n(r) = -3*r**2 + 47*r + 93. Let y(s) = -2*s**2 + 46*s + 94. Let d(a) = k*n(a) + 7*y(a). Solve d(v) = 0 for v.
-5
Let y(z) be the third derivative of z**8/336 - z**7/15 - z**6/8 + 2*z**2 - 6. Factor y(w).
w**3*(w - 15)*(w + 1)
Let q(f) be the second derivative of -f**4/12 - 3*f**3 - 17*f**2/2 + 8*f - 5. Suppose q(w) = 0. What is w?
-17, -1
Suppose 160 - 16*d + 2/5*d**2 = 0. What is d?
20
Let z be ((-8)/14)/(-2) + (-1044)/(-756). Let j(t) be the second derivative of -5*t + 0*t**2 + 0 + 5/4*t**4 - 1/4*t**5 - z*t**3. Find d, given that j(d) = 0.
0, 1, 2
Let z = -5607 + 5609. Factor 0*w + 0 + 0*w**z - 4/3*w**3.
-4*w**3/3
Let g(u) = -13*u**3 + 38*u**2 + 31*u - 23. Let l(s) = 92*s**3 - 264*s**2 - 216*s + 162. Let v(f) = -44*g(f) - 6*l(f). Factor v(n).
4*(n - 5)*(n + 1)*(5*n - 2)
Let m(p) = 2*p**3 - 133*p**2 - 202*p - 133. Let h be m(68). Factor 38/5*u**h + 32/5*u - 8/5 - 14/5*u**4 + 2/5*u**5 - 10*u**2.
2*(u - 2)**2*(u - 1)**3/5
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