= 0.
2/7, 22
Let b(q) be the second derivative of q**7/21 - 2*q**6/5 + 3*q**5/10 + 5*q**4/3 - 2*q + 424. Factor b(v).
2*v**2*(v - 5)*(v - 2)*(v + 1)
Solve 0 + 3/7*m**4 + 18/7*m**3 - 48/7*m**2 + 0*m = 0 for m.
-8, 0, 2
Let k(m) = 9*m**5 + 9*m**4 - 11*m**3 - 11*m + 11. Let x(q) = -5*q**5 - 5*q**4 + 6*q**3 + 6*q - 6. Let p(z) = -6*k(z) - 11*x(z). Factor p(b).
b**4*(b + 1)
Suppose -j = r + j + 5, 0 = -3*r - j + 5. Factor -15*u**2 + 6*u**2 - 6 - 15*u - 3*u**3 - r*u**2.
-3*(u + 1)**2*(u + 2)
Let w = 861/10 - 423/5. Solve -9/4*l - w - 3/4*l**2 = 0.
-2, -1
Factor 76 - 1062*j**3 - 1060*j**3 + 45*j - 18*j**2 + 2119*j**3 - 6*j**2 + 86.
-3*(j - 3)*(j + 2)*(j + 9)
Let u(j) = 15*j**2 + 15*j - 4. Let l(p) = -18*p**2 - 16*p + 4. Let s(d) = -4*l(d) - 5*u(d). Factor s(c).
-(c + 4)*(3*c - 1)
Suppose 0 = -157*d + 153*d. Let k(j) be the third derivative of 0*j**5 + 1/105*j**7 - 1/60*j**6 - j**2 + 0*j + 0*j**4 + d*j**3 + 0. Let k(m) = 0. What is m?
0, 1
Let z(j) = 58*j**3 + 2*j**2 + j - 3. Let h be z(1). Factor -2*f**2 + 24*f - h + 79 - 93.
-2*(f - 6)**2
Find x, given that -3/4*x + 3/4*x**3 + 9/4 - 9/4*x**2 = 0.
-1, 1, 3
Let -132*k**2 + 42*k**2 + 50*k**2 + 52*k**2 + 52 - 160*k = 0. What is k?
1/3, 13
Let o(n) be the second derivative of n**7/252 - n**6/90 + n**4/36 - n**3/36 + 65*n. Factor o(s).
s*(s - 1)**3*(s + 1)/6
Let v(f) be the third derivative of 6*f**7/175 - f**6/25 - 4*f**5/15 - 4*f**4/15 - 18*f**2. Factor v(j).
4*j*(j - 2)*(3*j + 2)**2/5
Let m be (-7 - (-3 + -3))*25/(-30). Let h(u) be the second derivative of -1/16*u**5 + m*u**3 + u**2 - 11*u + 0 - 1/24*u**4. Determine d, given that h(d) = 0.
-2, -2/5, 2
Suppose 728*j = 769*j - 123. Determine y, given that -24*y**2 - 6*y - 15/2*y**4 + 0 - 51/2*y**j = 0.
-2, -1, -2/5, 0
Let n(r) be the second derivative of r**4/12 + r**3/6 + 441*r. Factor n(m).
m*(m + 1)
Let r(t) be the second derivative of 1/20*t**5 - 1/168*t**7 + 1/24*t**4 - 1/4*t**2 - 1/8*t**3 + 0*t**6 - 37 + t. Find i, given that r(i) = 0.
-1, 1, 2
Let o(m) = -m**3 + 2*m**2 - 1. Let r be o(1). Suppose -2*j + r*j = -2*d + 12, 5*d = -j + 6. Factor -13*v**2 - 2*v**4 + 15*v**d + 2*v**2 - 2.
-2*(v - 1)**2*(v + 1)**2
Let v(k) = -k**3 + 19*k**2 + 21*k - 24. Let n be v(20). Let c be (-4)/3*(-15)/(-40)*n. Factor -4/9*u + 0 + 2/9*u**c.
2*u*(u - 2)/9
Let x(a) = 153 - 301 + 150. Let g(s) = 6*s - 5*s - 5 + s**2 - 5. Let j(o) = 2*g(o) + 10*x(o). Determine i, given that j(i) = 0.
-1, 0
Let k(i) be the first derivative of -3 - 12/5*i**5 + 2*i**2 - 20/3*i**3 + 0*i + 7*i**4. Suppose k(o) = 0. What is o?
0, 1/3, 1
Suppose 2/13*d**3 - 4/13*d**2 - 14/13*d - 8/13 = 0. Calculate d.
-1, 4
Let v be (-341)/372*20/(-22). Factor -1/6*d**3 + 0 + 2/3*d**2 + v*d.
-d*(d - 5)*(d + 1)/6
Let q(f) = -f**3 - 6*f**2 + 3*f - 7. Let n be q(-7). Let j be (7/n)/((-1)/(-6)). Factor 4*w + 2*w + 5 + 3*w**2 - j.
3*(w + 1)**2
Let u(c) be the first derivative of -4*c**3 - c**2/2 + c + 59. What is a in u(a) = 0?
-1/3, 1/4
Factor 16*n - 31*n**2 - 28*n**2 + 55*n**2 - 16.
-4*(n - 2)**2
Solve -2/3*h + 0 - 1/3*h**2 = 0 for h.
-2, 0
Let y(o) be the second derivative of o**5/20 + o**4/2 - 7*o**3/6 + 86*o. Factor y(d).
d*(d - 1)*(d + 7)
Factor -7*f - 1/2*f**4 + 2*f**3 + 4 + 3/2*f**2.
-(f - 4)*(f - 1)**2*(f + 2)/2
Let s = -862/13 + 7784/117. Let d = 652/693 - 4/77. Factor s*i**2 + d*i + 2/3.
2*(i + 1)*(i + 3)/9
Let d(t) be the first derivative of -10 + 1/5*t - 3/10*t**2 - 4/15*t**3. Factor d(i).
-(i + 1)*(4*i - 1)/5
Solve 140*a - 4*a**3 - 4*a**5 - 200*a**2 + 17 + 124*a**3 - 53 - 20*a**4 = 0.
-9, 1
Suppose 0 = 2*f - 2, -5*f = 5*l - 4*f - 21. Solve 2/9*r**3 + 0 - 4/9*r + 2/3*r**l + 2/9*r**5 - 2/3*r**2 = 0 for r.
-2, -1, 0, 1
Let h(p) be the second derivative of -p**6/90 + 2*p**5/45 - p**4/18 + 9*p**2 + 9*p. Let b(u) be the first derivative of h(u). Factor b(n).
-4*n*(n - 1)**2/3
Let o(d) = -7*d**2 + d + 2. Let q(l) = l**2 - 6*l + 6. Let s(p) = p - 1. Let n(w) = -q(w) - 6*s(w). Let i(j) = -6*n(j) + o(j). Factor i(m).
-(m - 2)*(m + 1)
Solve -39*s + 64 - 11 + s**2 - 5 + 17 + 9 = 0.
2, 37
Let j(u) be the first derivative of u**6/24 + 3*u**5/20 + u**4/16 - u**3/4 - u**2/4 + 17. Factor j(w).
w*(w - 1)*(w + 1)**2*(w + 2)/4
Let x(i) be the third derivative of i**5/15 + 7*i**4/6 + 4*i**3 + 32*i**2. Factor x(a).
4*(a + 1)*(a + 6)
Let f(b) be the first derivative of b**6/6 + 24*b**5 + 1200*b**4 + 64000*b**3/3 + 470. Factor f(c).
c**2*(c + 40)**3
Let b be (1/2)/(2/8). Let o = -2142 - -6431/3. Suppose -20/3*n - o*n**b - 20/3 = 0. What is n?
-2
Let i = 24 - 16. Suppose 2*z - 4*q - i = 0, 5*z - 43 = 2*q - 7. Find t such that -t**5 + 5*t**5 + 4*t + 0*t**5 - z*t**3 = 0.
-1, 0, 1
Let f be (0/2 - 2) + -25 + 30. Suppose -f*k + 4*k = 2. Determine b, given that 1/3*b**k + b + 2/3 = 0.
-2, -1
Suppose 0 = -251*q + 259*q - 16. Suppose -8/9*g - 8/9 - 2/9*g**q = 0. Calculate g.
-2
Let u(o) = -34 - 6 + 7 - 7*o. Let f be u(-5). Factor 2/9*t**4 + 2/3*t**3 - 4/9 + 2/9*t**f - 2/3*t.
2*(t - 1)*(t + 1)**2*(t + 2)/9
Determine n so that 1/9*n**2 + 106/9*n + 2809/9 = 0.
-53
Let 6/5*w**4 + 0*w - 1/5*w**5 - 32/5*w**2 + 0*w**3 + 0 = 0. Calculate w.
-2, 0, 4
Let q(y) = 3*y - 38. Let j be q(14). Suppose 2*a = -2*v + 2, 4*a - 8 - 3 = 3*v. Suppose -1/2*n**j - 1 + 7/2*n + 5/2*n**3 - 9/2*n**a = 0. Calculate n.
1, 2
Factor 448*o**2 - 14792*o**3 + 36 + 14498*o**3 - 69*o - 153*o.
-2*(3*o - 2)*(7*o - 3)**2
Let r(h) be the second derivative of h**4/6 - 3*h**3 + 14*h**2 - 100*h. Determine j, given that r(j) = 0.
2, 7
Suppose 23*u + 5*u = 56. Factor 3/5*r**4 + 0 - 9/5*r**u - 6/5*r + 0*r**3.
3*r*(r - 2)*(r + 1)**2/5
Let h(f) = -f**2 + 22*f + 3. Let y be h(0). Let b(u) be the first derivative of 5/2*u**4 - y + 6*u**3 + 4*u + 2/5*u**5 + 7*u**2. Solve b(v) = 0 for v.
-2, -1
Let g(v) = v**5 + 8*v**3 + 4*v + 4. Let b = -120 - -116. Let u(p) = p**5 + p**4 + 9*p**3 + 5*p + 5. Let i(a) = b*u(a) + 5*g(a). Find s such that i(s) = 0.
0, 2
Let k(h) = -h**3 + 6*h**2 + 2*h - 10. Suppose 0 = y + 4*y - 30. Let w be k(y). Factor 2*l**2 + l**4 + 2*l**2 - 3*l**w - 2*l**4.
-l**2*(l - 1)*(l + 1)
Let f(t) = -t**4 + 3*t**3 - t**2 + t. Let g(o) = 6 - o - 1 + o**4 - o**3 - 5. Let z(n) = -5*f(n) - 10*g(n). Solve z(m) = 0 for m.
-1, 0, 1
Determine c so that 17*c**2 + 26*c**2 + 29*c**2 - 68*c**2 - 140*c - 144 = 0.
-1, 36
Let c(d) be the third derivative of 0*d**3 - 8*d**2 + 0 + 0*d - 1/70*d**7 + 0*d**4 + 0*d**5 - 1/20*d**6. Determine v, given that c(v) = 0.
-2, 0
Let i(v) = 15*v**4 - 5*v**2 - 10*v + 20. Let d(x) = -x**4 - x**3 - x**2 - 1. Let k(h) = 20*d(h) + i(h). Factor k(s).
-5*s*(s + 1)**2*(s + 2)
Let o(n) = -26 + 79 - 8*n**2 - 9 - 10*n. Let c(r) = -r**2 - r + 5. Let y(f) = 52*c(f) - 6*o(f). Solve y(q) = 0.
1
Let b(i) be the first derivative of 4/33*i**3 + 0*i**4 + 0*i**2 - 2/55*i**5 - 33 - 2/11*i. Factor b(j).
-2*(j - 1)**2*(j + 1)**2/11
Let m(a) be the first derivative of a**4/27 - 64*a**3/27 + 512*a**2/9 + 52*a - 23. Let f(l) be the first derivative of m(l). Factor f(z).
4*(z - 16)**2/9
Suppose 0 = 3*k + 4*f - 22, 0 = 4*k + 5*f + 9 - 37. Factor -2 - 13 - 3*s**k - 1 + 7*s**2.
4*(s - 2)*(s + 2)
Let w = 36 + -32. Factor w*i - 23*i + 36 + 4*i**2 + 43*i.
4*(i + 3)**2
Let h(x) = -x**3 + 5*x**2 + 6*x + 8. Let f be h(7). Let b be 3/(-7) - f/112. What is j in 1/4*j**2 + 0 - 1/4*j**4 + 0*j + b*j**3 = 0?
-1, 0, 1
Let d = -104 - -109. Suppose -4*u = -2*j - 10, -u - d*j = -0*u - 8. Factor -1/3*p**2 + 0 + 0*p + 1/6*p**u.
p**2*(p - 2)/6
Factor -5*c**4 + 198*c**3 + 136*c**2 - 79*c**2 - 78*c - 172*c**2.
-c*(c - 39)*(c - 1)*(5*c + 2)
Suppose 4 = w + 57. Let i = -48 - w. Find n such that 22/3*n**3 + 6*n**2 + 13/3*n**4 + n**i + 7/3*n + 1/3 = 0.
-1, -1/3
Let h = 3622 - 3620. Factor -16/13*g**h - 42/13*g - 2/13*g**3 - 36/13.
-2*(g + 2)*(g + 3)**2/13
Let h(a) = -a**3 + 14*a**2 + 12*a + 45. Let o be 16/(-152) - (-287)/19. Let c be h(o). Factor 2/5*b + b**4 - b**2 - 2/5*b**3 + c.
b*(b - 1)*(b + 1)*(5*b - 2)/5
Suppose 134 = -3*r + 29. Let o be (-6)/r*90/27. Determine q, given that -2*q**2 - 18/7*q - o = 0.
-1, -2/7
Suppose -3 = 4*r + j, 0 = 4*j - 6*j - 6. Let c(u) be the second derivative of -3/2*u**2 + 1/2*u**4 - 1/10*u**6 + 0 + 7*u + r*u**3 + 0*u**5. Factor c(h).
-3*(h - 1)**2*(h + 1)**2
Let f(d) be the first derivative of 2*d**3/27 + 8*d**2/9 + 32*d/9 - 36. Factor f(k).
2*(k + 4)**2/9
Let t(g) be the t