6. Let s be n(16). Let d be s/(-80)*(-15)/9. What is h in -32/7 + 2*h**4 - 32/7*h**d + 32/7*h + 16/7*h**2 - 2/7*h**5 = 0?
-1, 2
Let z = -174 + 170. Let w be 8 - (6 + 4) - (2 + z). Factor 2/9*r**2 + w*r + 0 - 4/9*r**3.
-2*r**2*(2*r - 1)/9
Let t(o) = 3*o - 9*o**2 + 0*o**3 + o**3 + 6*o**2 + 8. Let n be t(5). Determine h, given that 10 - 30*h + 5*h**4 - 28*h**2 + n*h**2 - 25*h**3 - 19*h + 14*h = 0.
1, 2
Let w(q) be the third derivative of -1/20*q**5 + 41*q**2 + 0*q**3 + 7/4*q**4 + 0*q - 1. Factor w(y).
-3*y*(y - 14)
Let i(f) be the first derivative of -41 - 8/75*f**5 - 4/45*f**3 - 1/45*f**6 - 1/6*f**4 + 0*f**2 + 0*f. Find o such that i(o) = 0.
-2, -1, 0
Let q(v) be the first derivative of -v**6/9 + 14*v**5/15 + 49*v**4/3 + 68*v**3 + 117*v**2 + 90*v + 1306. Determine t so that q(t) = 0.
-3, -1, 15
Let j(s) be the first derivative of -105 + 42*s**2 + 26*s**3 + 19/4*s**4 + 8*s. Suppose j(h) = 0. What is h?
-2, -2/19
Let h(g) be the second derivative of g**5/10 - 17*g**4/6 - 188*g**3/3 - 300*g**2 - 29*g - 52. Factor h(o).
2*(o - 25)*(o + 2)*(o + 6)
Let s(f) be the third derivative of f**5/240 - 77*f**4/24 - 103*f**3/8 - 2*f**2 - 25*f. Determine t, given that s(t) = 0.
-1, 309
Suppose 0*t = -t + 7. Let q(u) = 2*u**2 - 10*u - 3. Let s be q(t). Factor -12*y**2 - 89 + 15*y**3 + 13*y**3 + s - 27*y**3 + 48*y.
(y - 4)**3
Let k(d) = -20*d - 30. Let j(o) = -o**2 - 97*o - 151. Let s(q) = 2*q**2 - 4*q - 8. Let z be s(-3). Let g(b) = z*k(b) - 4*j(b). Let g(c) = 0. Calculate c.
-1, 14
Suppose 0 = m - 78 + 89. Let y be (-5)/(20/16) + m/(-1). Suppose y*d**2 - 2*d**2 - 4*d + 29*d - 30 = 0. What is d?
-6, 1
Let u = 4966/1293 + -75/431. Factor 2 + 1/3*q**3 + 4/3*q**2 - u*q.
(q - 1)**2*(q + 6)/3
Suppose -5*m - 2*j = -7, -5*j - 9 = 5*m - 4. Suppose 3*g = -5*b + 12, 0 = m*b + 2*g - 26 + 19. Factor -1/5*u**b + 0 - 1/5*u**2 + 0*u.
-u**2*(u + 1)/5
Let x(c) be the first derivative of c**5/70 + 17*c**4/42 - 6*c**3/7 + 51*c - 183. Let t(s) be the first derivative of x(s). Determine z so that t(z) = 0.
-18, 0, 1
Let l = 437 + -435. Suppose 4*w = 3*w + 29. Let 0*v**4 - l*v**4 - 27*v**3 + w*v**3 = 0. What is v?
0, 1
Factor 2050*k**2 - 231*k**3 + 0 + 49/6*k**4 - 17500/3*k.
k*(k - 14)*(7*k - 50)**2/6
Let t(u) be the first derivative of 177 + 9/4*u**4 + 0*u - 3*u**5 + 0*u**3 + 0*u**2 + u**6. Let t(o) = 0. Calculate o.
0, 1, 3/2
Let x = 5/1546 - -9221/17006. Suppose x*o**2 - 96/11*o + 384/11 = 0. What is o?
8
Let k(j) be the second derivative of j**4/28 + 40*j**3/7 + 237*j**2/14 - 2*j - 85. Find d, given that k(d) = 0.
-79, -1
Let i(f) be the first derivative of 0*f**2 + 15*f**4 - 64 + 0*f + 20/3*f**3 + 5*f**5. Factor i(x).
5*x**2*(x + 2)*(5*x + 2)
Let a be (3/8)/(495/30360) - 21. Factor 44376/7*j**3 + 13675204/7*j - 1272112/7*j**a + 0 - 688/7*j**4 + 4/7*j**5.
4*j*(j - 43)**4/7
Let p(y) = -y**3 + 4*y**2 + 135*y - 47. Let u be p(-10). Factor -9/2*o**u + 81/4*o**2 + 0 + 0*o + 1/4*o**4.
o**2*(o - 9)**2/4
Let r be (-2)/9 - 8/((-4032)/154). Let b(n) be the third derivative of -15*n**2 + 0*n + 0 + 1/48*n**5 + r*n**4 + 1/6*n**3 + 1/480*n**6. Factor b(y).
(y + 1)*(y + 2)**2/4
Let x(f) = -3*f**3 + 31*f**2 - 5*f - 44. Let a be x(10). Let h(s) be the first derivative of 21/4*s**4 - 6/5*s**5 - a + 15/2*s**2 - 3*s - 9*s**3. Factor h(r).
-3*(r - 1)**3*(2*r - 1)
Let p = 9 + 3. Let a = p + -9. Let -5*l**2 - 4*l**a + 5*l**2 - 4*l**2 = 0. What is l?
-1, 0
Let u be (-12)/(-30)*10/14. Let g be (-108)/14*(-19)/57. Factor -54/7 + u*k**3 - g*k**2 + 54/7*k.
2*(k - 3)**3/7
Let r(m) be the first derivative of 2*m**3/21 + 4*m**2 + 374*m/7 - 2334. Factor r(y).
2*(y + 11)*(y + 17)/7
Let l(j) = -j**4 + j**2 + j + 1. Let h = 88 + -92. Let w(c) = -14*c**4 + 6*c**3 - 4 - 14*c**4 + 29*c**4 - 4*c - 7*c**2. Let p(s) = h*l(s) - w(s). Factor p(b).
3*b**2*(b - 1)**2
Let t = -176 + 180. Let 756*b**4 - 4*b**3 - b**3 - t*b**3 - 3*b**5 - 768*b**4 = 0. Calculate b.
-3, -1, 0
Let f(z) = 3*z**4 - 23*z**3 - 61*z**2 + 3*z + 108. Let n(i) = -i**4 - i**3 - i**2 + i - 4. Let k(h) = f(h) + 5*n(h). Find x, given that k(x) = 0.
-11, -2, 1
Let h be 3*8/(-160)*5/(60/(-32)). Let p(o) = -o**3 + 5*o**2 + 4*o + 14. Let v be p(6). Factor -2/5 + n - h*n**v.
-(n - 2)*(2*n - 1)/5
Let a(z) be the third derivative of -z**4/24 - 10*z**2. Let c be a(-5). Solve 41*x**c - 10*x**5 - 16*x**5 - 12*x**5 = 0.
0
Factor 4*x**3 + 6471 - 9*x**3 + 85*x**2 - 400*x - 6151.
-5*(x - 8)**2*(x - 1)
Let q(c) be the first derivative of -c**6/12 + 63*c**5/10 - 351*c**4/8 + 171*c**3/2 + 171. Factor q(b).
-b**2*(b - 57)*(b - 3)**2/2
Let w be 38508/(-198) + 18/(-99). Let n = w - -1754/9. Let -70/9*r - n*r**3 - 26/9*r**2 + 98/9 = 0. Calculate r.
-7, 1
Let h(v) = -13*v**2 - 4604*v - 2420. Let m(l) = l**2 + 24. Let p(b) = -h(b) - 5*m(b). Factor p(i).
4*(i + 575)*(2*i + 1)
Factor 596/7*g + 2/7*g**2 - 598/7.
2*(g - 1)*(g + 299)/7
Let x(v) = -v**3 - 75*v**2 + 65*v - 833. Let q be x(-76). Let a(h) be the second derivative of -1/66*h**4 + 0 + 11*h - 4/11*h**2 + 4/33*h**q. Factor a(w).
-2*(w - 2)**2/11
Let f be (6314/(-132) - -49)*(-6)/(-21). Factor 10/3*i + 11/3 - f*i**2.
-(i - 11)*(i + 1)/3
Find u such that 56/5*u**3 + 1004/5*u**2 - 4/5*u**4 - 1056/5*u + 0 = 0.
-11, 0, 1, 24
Let h(x) = -17*x**2 + 335*x - 225. Let r be h(19). Factor 5/2*d**2 - 1/2*d**r + 3*d + 0.
-d*(d - 6)*(d + 1)/2
Let y = -486 + 822. Let w = -334 + y. Factor 0 + 6/7*u + 2/7*u**w.
2*u*(u + 3)/7
Let s(m) be the second derivative of -2*m**7/21 + 6*m**6/5 + 13*m**5/5 - 29*m**4/3 - 8*m**3 + 40*m**2 + 33*m - 2. Suppose s(h) = 0. Calculate h.
-2, -1, 1, 10
Let i(c) be the second derivative of c**7/3780 - 7*c**6/405 - 33*c**3/2 + c**2 + 69*c. Let n(x) be the second derivative of i(x). Factor n(g).
2*g**2*(g - 28)/9
Suppose 5*y - 136 = 259. Let b = 79 - y. Solve 5*w**2 - 15 + 0*w**2 + 0*w**2 + b*w - 10*w = 0 for w.
-1, 3
Let u(c) be the second derivative of 2*c**7/21 - 12*c**5 + 170*c**4/3 - 110*c**3 + 108*c**2 - 6*c + 7. Factor u(j).
4*(j - 6)*(j - 1)**3*(j + 9)
Let g(a) be the first derivative of -4*a**5/5 + 20*a**4 + 228*a**3 - 796*a**2 + 832*a + 3170. Factor g(w).
-4*(w - 26)*(w - 1)**2*(w + 8)
Let i(k) be the first derivative of -36*k**5/5 + 178*k**4 + 1708*k**3/3 + 568*k**2 + 176*k + 1009. Solve i(j) = 0.
-1, -2/9, 22
Let z = 590 - 591. Let u be ((4/(-12))/(z/18))/3. Factor 5/6*x**u - 10/3*x + 10/3.
5*(x - 2)**2/6
Factor -43*j - 212*j + 39*j + 1000*j**2 - j**3 - 1058*j**2.
-j*(j + 4)*(j + 54)
Let h(i) = i**2 - i - 3. Let s(m) = 3*m - 404 + 402 + m + 4*m**2. Let k(b) = 2*h(b) - s(b). Let k(a) = 0. What is a?
-2, -1
Let y be ((-1)/(-35)*2)/(20/600). Let x = 1421 - 1421. Find q such that -3/7*q**2 + x - y*q = 0.
-4, 0
Let q(k) be the first derivative of -5*k**4/24 + 17*k**3/3 - 55*k**2/3 + 12*k + 438. Determine b, given that q(b) = 0.
2/5, 2, 18
Let u(x) be the first derivative of -3*x**5/5 + 27*x**4/4 + 11*x**3 - 27*x**2/2 - 30*x + 601. Determine g, given that u(g) = 0.
-1, 1, 10
Let u be 6/(-27) + (4 - (-544)/(-144)). Let m(t) be the second derivative of -3*t + u - 1/24*t**4 - 4/3*t**3 + t**2 + 1/10*t**5. Factor m(g).
(g - 2)*(g + 2)*(4*g - 1)/2
Let l(w) be the second derivative of -1/9*w**3 + 0 + 1/90*w**4 + 2/5*w**2 - 88*w. Factor l(f).
2*(f - 3)*(f - 2)/15
Let z(u) be the first derivative of 1/27*u**3 + 17/18*u**2 - 155 - 2*u. Factor z(n).
(n - 1)*(n + 18)/9
Suppose 4232*t + 295*t**2 - 836273 - 299*t**2 - 283091 = 0. What is t?
529
Let f(k) be the first derivative of k**5/15 - 7*k**4/4 - 23*k**3/9 + 7*k**2/2 + 22*k/3 - 3324. Find t, given that f(t) = 0.
-1, 1, 22
Let x = -4369/8 + 83123/152. Let k(h) be the first derivative of 0*h**2 + 0*h + 3/19*h**6 + x*h**4 - 15 + 16/57*h**3 + 12/19*h**5. Factor k(d).
2*d**2*(d + 2)*(3*d + 2)**2/19
Let w = -5857 + 5860. Let u(a) be the second derivative of 1/2*a**4 + 1/2*a**w + 0*a**2 + 0 + 3/20*a**5 - 6*a. Suppose u(q) = 0. Calculate q.
-1, 0
Let y(l) = 6*l**3 - 14*l**2 - 32*l + 140. Let b(m) = -31*m**3 + 68*m**2 + 159*m - 699. Let q(r) = -4*b(r) - 21*y(r). Factor q(n).
-2*(n - 12)*(n - 2)*(n + 3)
Let y = -419 - -496. Let b be y/121*(36/14 - 2). Find z, given that -b*z**2 + 0 + 2/11*z**4 + 0*z - 2/11*z**3 = 0.
-1, 0, 2
Let t = 92891 + -92889. Let 5/7 - 1/7*m**3 + 9/7*m + 3/7*m**t = 0. What is m?
-1, 5
Let z = 405316/283829 + 22/40547. Factor -z - 1/7*y**3 + y + 4/7*y**2.
