8). Let m(o) be the first derivative of 1/2*o**4 - 10/3*o**3 - 8*o + 8*o**2 + w. Factor m(d).
2*(d - 2)**2*(d - 1)
Let x(p) be the first derivative of p**3/9 + 67*p**2/3 + 4489*p/3 + 810. Determine i, given that x(i) = 0.
-67
Find x, given that -11*x**2 - 5*x + 11*x**2 - 6*x**2 - 2*x - 1 = 0.
-1, -1/6
Suppose 70 = -11*l + l. Let d be l/(-21) - (1 - (-24)/(-9)). Factor 4/9*v**d + 10/9*v**5 + 2*v**3 + 0*v + 0 + 8/3*v**4.
2*v**2*(v + 1)**2*(5*v + 2)/9
Let x = -849 - -849. Let u(r) be the third derivative of -1/80*r**5 + 0*r + 0*r**4 + 1/160*r**6 + 3*r**2 + x + 0*r**3. Let u(d) = 0. Calculate d.
0, 1
Let g be ((-8)/(-6))/(2/15*5). Solve 118*o**3 + 25*o**g + 5 - 88*o - 24*o**4 - 6 + 35*o**2 - 18*o**5 - 47 = 0.
-3, -2/3, 1, 2
Let u be (14/21)/(2/90). Let x(k) = k**4 + k. Let o(z) = -4*z**5 - 15*z**4 - 6*z**3 - z**2 - 6*z. Let g(s) = u*x(s) + 5*o(s). Suppose g(w) = 0. Calculate w.
-1, -1/4, 0
Let i = -2/99 - -76/495. Let r(y) be the first derivative of -i*y**5 + 2/9*y**3 + 1/6*y**2 + 0*y + 7 - 1/18*y**6 + 0*y**4. Find m such that r(m) = 0.
-1, 0, 1
Suppose -q = 16 - 14. Let x be (-16)/(-6) + q/(-6). Suppose 4*h**3 + 0*h**3 - 2*h**x - 4*h**4 + 6*h**4 = 0. What is h?
-1, 0
Suppose 59 = 4*j + 43. Let h(s) be the first derivative of -j*s - s**4 - 1 + 4/3*s**3 + 2*s**2. Factor h(c).
-4*(c - 1)**2*(c + 1)
Let w(g) = -6 - g**3 - 2 - 4*g + 7*g**2 + 3. Let q be w(6). Find b such that 0*b**4 + q*b**3 + b**4 + b**4 - b + 2*b**2 + 2*b**4 = 0.
-1, 0, 1/4
Let o(f) = 2*f**4 - 86*f**3 + 396*f**2 + 2688*f + 3073. Let v(r) = r**4 + 2*r**3 - 1. Let z(k) = -o(k) - v(k). Solve z(w) = 0 for w.
-2, 16
Let s(o) be the third derivative of o**6/120 - o**5/15 + o**4/24 + o**3 - 9*o**2 - 4. Find x such that s(x) = 0.
-1, 2, 3
Let c(y) be the first derivative of y**8/15120 - y**7/7560 - y**6/1620 - 4*y**3/3 - 12. Let l(p) be the third derivative of c(p). Suppose l(x) = 0. What is x?
-1, 0, 2
Factor 17/5*q - 1/5*q**2 - 16/5.
-(q - 16)*(q - 1)/5
Let p(y) be the second derivative of -y**6/210 - 38*y**5/35 - 650*y**4/7 - 10000*y**3/3 - 125000*y**2/7 + 438*y. Factor p(w).
-(w + 2)*(w + 50)**3/7
Suppose 11*s - 13 = 9. Factor -8*f**2 - 844*f - f**2 - 3*f**s + 12 + 889*f.
-3*(f - 4)*(4*f + 1)
Let g(a) = -a**2 - 4*a - 4. Suppose -r - 1 = z + 2*z, 2*z + 3*r - 11 = 0. Let n be g(z). Solve 18/7*o**3 + n + 4/7*o + 22/7*o**2 = 0 for o.
-1, -2/9, 0
Let o be (-50)/(-13) + 2/13. Suppose -36*m + 48*m - 24 = 0. Factor -1/3*h**5 + 0*h - 1/3*h**3 - 2/3*h**o + 0 + 0*h**m.
-h**3*(h + 1)**2/3
Let d(h) be the second derivative of -h**5/70 - h**4/6 + h**3/21 + h**2 - 5*h + 3. Factor d(x).
-2*(x - 1)*(x + 1)*(x + 7)/7
Factor 47/3*w - 20/3*w**2 + 1/3*w**3 + 68/3.
(w - 17)*(w - 4)*(w + 1)/3
Let o(c) be the second derivative of c**7/147 + 2*c**6/105 - 3*c**5/70 - 2*c**4/21 + 4*c**3/21 + 3*c + 1. What is t in o(t) = 0?
-2, 0, 1
Let f = -277 - -280. Let r(c) be the third derivative of -10*c**2 + 0*c + 0*c**4 + 1/10*c**5 + 0 + 1/70*c**7 + 3/40*c**6 + 0*c**f. Factor r(a).
3*a**2*(a + 1)*(a + 2)
Let k(i) = -57*i**3 + 296*i**2 - 278*i + 80. Let q(m) = -14*m**3 + 74*m**2 - 70*m + 20. Let y(g) = -4*k(g) + 18*q(g). Let y(p) = 0. What is p?
1/2, 2/3, 5
Let s(g) be the first derivative of 1/16*g**4 - 7/2*g**2 - 1/80*g**6 - 9 - 1/12*g**3 + 1/120*g**5 + 0*g. Let l(c) be the second derivative of s(c). Factor l(v).
-(v - 1)*(v + 1)*(3*v - 1)/2
Factor 284*w + 244 - w**2 + 73 - 29 - 3*w**2.
-4*(w - 72)*(w + 1)
Let s(z) be the second derivative of 7*z**5 - 59*z**4/3 + 56*z**3/3 - 8*z**2 + 494*z. Factor s(h).
4*(h - 1)*(5*h - 2)*(7*h - 2)
Factor -40*p**2 - 98/3*p**4 - 84*p**3 + 0 - 16/3*p.
-2*p*(p + 2)*(7*p + 2)**2/3
Let c be (-1 - 2/(-1)) + -1. Suppose 44*a - 85*a = 0. Find q, given that 2/7*q**5 + 0 + 0*q**3 + c*q**2 + a*q**4 + 0*q = 0.
0
Let t(y) be the third derivative of 0*y**4 + 1/30*y**5 + 4*y**2 + 0*y**3 + 0 + 0*y. Factor t(h).
2*h**2
Let x(f) be the second derivative of 27*f**2 + 0 + 73/10*f**5 + 3/2*f**4 - 27*f**3 + 4/21*f**7 + 32/15*f**6 + f. Factor x(r).
2*(r + 3)**3*(2*r - 1)**2
Let v(b) be the third derivative of b**5/270 - 127*b**4/27 + 64516*b**3/27 - 3*b**2 + 130. Factor v(y).
2*(y - 254)**2/9
Suppose 0 = -5*w + 54 - 14. Suppose -2*y + w = 2*y. Let -y*f - 4 + 6 - 2*f**4 + 4*f**3 - 2*f = 0. What is f?
-1, 1
Let n = 9 + 117. Let m be 24/n*6/4. Solve 4/7*k + 0 - m*k**2 = 0.
0, 2
Let r(c) be the second derivative of -c**5/40 + 19*c**4/24 + 5*c**3/3 + 49*c + 2. Factor r(x).
-x*(x - 20)*(x + 1)/2
Suppose -26*u = 26*u - 39*u - 26. Factor 1/2*n**u + 1/8*n**3 + 0 + 1/2*n.
n*(n + 2)**2/8
Solve 3*c**2 + 32*c + 2*c**2 - 95*c + 31*c + 37*c = 0.
-1, 0
Let y be (-15)/21 + 3/6*2. Let x be 9/(126/16) + -1. Let -y*u**3 + 0 + 0*u - 1/7*u**2 - x*u**4 = 0. What is u?
-1, 0
Let g(n) be the second derivative of n**5/20 + n**4/6 - 13*n**3/6 + 5*n**2 + 2*n - 47. Find l such that g(l) = 0.
-5, 1, 2
Let d = 55 + -48. Let t be d - 2 - (-40)/(-8). Let 3/2*g**2 + 9/2*g + t = 0. What is g?
-3, 0
Let f(r) = r**3 + 7*r**2 - 2*r - 10. Let a be f(-7). Let z(m) be the first derivative of -m**2 - 2 - 9*m**3 - 3*m**a - 8*m**2 + m - 4*m. Factor z(w).
-3*(w + 1)**2*(4*w + 1)
Factor 0 - 45/2*a**2 + 75/2*a - 3/2*a**4 - 27/2*a**3.
-3*a*(a - 1)*(a + 5)**2/2
Let c = 4 + 8. Factor 3 - 8*p**3 - 3*p**3 + 7*p**3 - 7 - c*p - 12*p**2.
-4*(p + 1)**3
Let g = -9 + 12. Let k(l) = l - 1. Let i be k(g). Factor 2*d**3 + 8*d + 0*d**3 - 14*d**3 - 4*d**i + 4*d**4 + 4*d**5.
4*d*(d - 1)**2*(d + 1)*(d + 2)
Suppose -u + 7 = -m - 19, m + 5*u + 8 = 0. Let b be (m/138)/(2/(-6)). Factor 1/2*g**2 + b*g - 1.
(g - 1)*(g + 2)/2
Let f(s) be the second derivative of 0*s**2 + 1/10*s**5 + 0 - 5/6*s**4 + 4/3*s**3 + 20*s. Suppose f(u) = 0. Calculate u.
0, 1, 4
Suppose 0 = 4*m - 39*m. Let v(g) be the second derivative of 1/9*g**3 + m + 0*g**2 - 4*g + 1/30*g**5 + 1/9*g**4. Solve v(j) = 0.
-1, 0
Let m(w) = -2*w**4 - w**3 + w**2 - w. Let g(q) = 25*q**4 + 20*q**3 - 25*q**2 - 10*q + 20. Let b(c) = -g(c) - 10*m(c). Find h, given that b(h) = 0.
-2, 1
Let b(y) be the third derivative of -2*y**7/105 - 7*y**6/3 - 431*y**5/5 - 1190*y**4/3 - 2312*y**3/3 - 2*y**2 + 5. Find u such that b(u) = 0.
-34, -1
Suppose 10*q - 40 = 5*q. Determine b, given that -q + 5 + 4*b**2 + 2 - 3 = 0.
-1, 1
Let t be (-8)/18*12/(-8). Let v(b) be the second derivative of b - 1/6*b**4 - b**2 + t*b**3 + 0. Factor v(k).
-2*(k - 1)**2
Let l = -247 - -250. Let a(t) be the second derivative of 0*t**l - 1/6*t**4 + 0 + 0*t**2 - 3*t. Factor a(c).
-2*c**2
Let j(l) be the first derivative of -36*l**5/5 - 88*l**4 - 496*l**3/3 + 64*l**2 - 316. Find i, given that j(i) = 0.
-8, -2, 0, 2/9
Let f be (-2)/(-2) + 1403/5. Let g = 10106/5 - 2016. Solve 4/5 - f*d**4 + g*d - 160*d**3 - 72/5*d**2 = 0.
-1/4, 2/11
Let k be (-303)/210*-2 - 9/15. Factor -4/7*w**2 - k - 16/7*w.
-4*(w + 2)**2/7
Let p(m) be the second derivative of -1/210*m**6 + 0 - 1/84*m**4 + 0*m**2 + 0*m**3 - 1/70*m**5 - 12*m. Find i, given that p(i) = 0.
-1, 0
Let f = 162 + -162. Let u(q) be the first derivative of f*q - 1/4*q**4 - q**3 - q**2 + 5. Solve u(a) = 0 for a.
-2, -1, 0
Factor 5/2*a**3 + a + 39/4*a**2 - 13 - 1/4*a**4.
-(a - 13)*(a - 1)*(a + 2)**2/4
Let f be (-16)/(-256)*136 - 14/2. Factor 0 - 3/4*a + 0*a**4 + 2*a**2 + 1/4*a**5 - f*a**3.
a*(a - 1)**3*(a + 3)/4
Let i(s) = s**3 - 5*s**2 + 9*s - 4. Let f be i(2). Let l(a) be the first derivative of -1/5*a**3 + 2 - 3/10*a**f + 0*a. Find w such that l(w) = 0.
-1, 0
Factor -12*k + 22 + 21 + 11 + k**2 - 67.
(k - 13)*(k + 1)
Let i = 17037 + -67577/4. Let n = i - 142. Determine a, given that 3/4*a**2 - n + 0*a = 0.
-1, 1
Let -4*b**2 - 1/3*b**3 - 64/3 - 16*b = 0. Calculate b.
-4
Let f be 0 + (-8 - -6 - (-1 - 6)). Factor -15*k**3 - 9*k**2 + 5*k**4 - 2*k**2 + k**2 + 5*k**2 + 10*k + f*k**5.
5*k*(k - 1)**2*(k + 1)*(k + 2)
Let k(w) be the second derivative of 7*w**6/6 + 2*w**5 + 5*w**4/12 - 10*w + 2. Solve k(d) = 0 for d.
-1, -1/7, 0
Let b = 405 + -362. Let u = 43 - b. Determine c so that -3/4*c**2 - 1/2*c - 1/4*c**3 + u = 0.
-2, -1, 0
Let n(y) = -y**3 - 15*y**2 + y + 22. Let f be n(-15). Suppose -2*z + 5*s - f = 2*z, -z - s = -5. Suppose 1/4 + 0*d - 1/4*d**z = 0. Calculate d.
-1, 1
Let z(j) be the first derivative of -j**6/840 + 8*j**3/3 + 10. Let g(o) be the third derivative of z(o). Solve g(t) = 0 for t.
0
Let g = 6 - 3. Let l = -31 