52. Factor 0 - 1/4*h**g + 1/4*h.
-h*(h - 1)/4
Let w(a) = -6*a**3 + 3*a**2 + 4*a + 7. Let z be w(5). Let v be ((-192)/z)/(1/3). Factor 10/9*d - 2/9 + v*d**3 - 16/9*d**2.
2*(d - 1)*(2*d - 1)**2/9
Let t(u) be the first derivative of -u**4 - 40*u**3/3 + 48*u**2 - 20. Solve t(x) = 0.
-12, 0, 2
Let s(l) be the second derivative of 1/30*l**5 - 1/3*l**4 + 4/3*l**3 + l + 0 + 7/2*l**2. Let r(w) be the first derivative of s(w). Let r(k) = 0. What is k?
2
Let f(t) be the first derivative of 3 + 1/16*t**4 + 1/2*t**3 + 9/8*t**2 - 6*t. Let q(v) be the first derivative of f(v). Factor q(n).
3*(n + 1)*(n + 3)/4
Let d(r) be the first derivative of -r**6/150 + 3*r**5/100 + r**4/12 - r**3/10 - 2*r**2/5 + 35*r + 25. Let g(f) be the first derivative of d(f). Factor g(s).
-(s - 4)*(s - 1)*(s + 1)**2/5
Let a = -11/86 - -557/3010. Let g(x) be the first derivative of -5/42*x**6 - a*x**5 - 3/14*x**2 + 0*x + 2/21*x**3 - 1 + 2/7*x**4. Solve g(z) = 0.
-1, 0, 3/5, 1
Let i(u) = -2*u**4 + 94*u**3 + 6*u - 6. Let n(r) = -r**4 + 95*r**3 + 5*r - 5. Let j(f) = -5*i(f) + 6*n(f). Factor j(l).
4*l**3*(l + 25)
Let o(p) be the second derivative of p**7/21 - 8*p**6/15 + 17*p**5/10 - 5*p**4/3 - 57*p - 2. Find m, given that o(m) = 0.
0, 1, 2, 5
Let d = -260 - -483. Factor -d*v + 0*v**4 - 4*v**4 + 4 + 231*v - 8*v**3.
-4*(v - 1)*(v + 1)**3
Let u(c) be the third derivative of -2*c**7/105 + 11*c**6/30 - 3*c**5/5 - 11*c**4/6 + 20*c**3/3 + 469*c**2. Factor u(z).
-4*(z - 10)*(z - 1)**2*(z + 1)
Let p(l) = 9*l - l**2 - 12 + 13*l + 25*l - 24*l. Let f(j) = 12*j - 6. Let g(c) = 5*f(c) - 3*p(c). Let g(b) = 0. What is b?
1, 2
Factor -30*r**3 - 20*r**2 + 115 - 6*r + 104 - 194 + 18*r - 5*r**4 + 18*r.
-5*(r - 1)*(r + 1)**2*(r + 5)
Let f be 1 - -3 - (19 - -57). Let n = f + 75. Factor -3/2*u + 1 + 0*u**2 + 1/2*u**n.
(u - 1)**2*(u + 2)/2
Let o = 1093 + -1093. Factor -2/7*h**2 + 0*h - 2/7*h**3 + o.
-2*h**2*(h + 1)/7
Let o(u) be the third derivative of -u**5/8 - 37*u**4/192 + u**3/24 + 333*u**2. Determine c, given that o(c) = 0.
-2/3, 1/20
Let 1/4*i + 3*i**4 + 1/4*i**5 - 1/2*i**3 + 3 - 6*i**2 = 0. What is i?
-12, -1, 1
Factor -45*n - 1/4*n**2 - 2025.
-(n + 90)**2/4
Factor -147/2*w + 1/2*w**5 + 8*w**4 + 28*w**2 + 0 + 37*w**3.
w*(w - 1)*(w + 3)*(w + 7)**2/2
Suppose -4*o = -2*x - 2, -2*x + 5*x = -5*o + 19. Factor -7*b**2 - 79*b**3 + 3*b**2 + 81*b**x + b + b.
2*b*(b - 1)**2
Let j(t) be the third derivative of t**6/360 - 7*t**5/180 - t**4/72 + 7*t**3/18 - 2*t**2 + 53*t. Factor j(x).
(x - 7)*(x - 1)*(x + 1)/3
Let g be (-14 + 2)*11/(-33). Factor 9 + 3*v + 7 - 4*v**2 - g*v + v**3 - 12.
(v - 4)*(v - 1)*(v + 1)
Let w(f) be the second derivative of 5*f**4/12 - 55*f**3/6 + 25*f**2 - 2*f + 7. Factor w(m).
5*(m - 10)*(m - 1)
Let g be 3/6 - (-3)/(-6). Let b(u) = -u + 4. Let z be b(g). Factor -8*q**z - 4*q**3 - 2*q**2 + 0*q**2 + 14*q**4 - 8*q**4.
-2*q**2*(q + 1)**2
Suppose 5*n + 1 = 11. Suppose n*a - 2*h + 8 = 0, 5 = -4*a - 3*h + 17. Factor 0 + a*v**2 - 3/2*v**3 + 3/2*v**4 + 0*v.
3*v**3*(v - 1)/2
Suppose 0 = -2*d + 3*t - 8, t + 5 = -d + 1. Let f = d - -10. Factor u**3 + 3*u**2 - 4 - 7*u + u + f*u.
(u - 1)*(u + 2)**2
Let b(m) = -4 - 4*m**2 + m**2 + 2*m**2 + 5*m. Let o be b(3). Determine n so that 2 + 0 - 2*n**o - 4*n**3 - n**3 + 5*n = 0.
-1, -2/5, 1
Suppose c + 15 = -c - 5*y, -5*c = 5*y. Suppose 4*i = -5*s + 27, 0*i = -c*s + 4*i + 3. Factor -10*f**4 - 74*f**4 + 6*f**3 + f**s + 5*f**3 + 147*f**5.
3*f**3*(7*f - 2)**2
Suppose -320/9*b + 40/9*b**4 - 80/9*b**2 + 4/9*b**5 + 100/9*b**3 + 256/9 = 0. Calculate b.
-4, 1
Let z = -566 + 566. Let u(q) be the third derivative of -1/240*q**6 + 0*q + 0 + 0*q**4 + 7*q**2 + z*q**5 - 1/420*q**7 + 0*q**3. Factor u(s).
-s**3*(s + 1)/2
Factor 6/5*x - 1/5*x**4 - 6/5*x**3 + 8/5*x**2 - 7/5.
-(x - 1)**2*(x + 1)*(x + 7)/5
Let q(r) be the first derivative of 2*r**3/27 - 256*r**2/9 + 32768*r/9 - 24. Find x such that q(x) = 0.
128
Let w(k) be the second derivative of -5*k - 11/45*k**6 + 0*k**2 + 0 + 5/21*k**7 - 4/15*k**5 + 2/9*k**4 + 0*k**3. Solve w(v) = 0.
-2/3, 0, 2/5, 1
Let 3 - 17*z + 250*z**2 - 8*z - 252*z**2 - 3*z + 27 = 0. Calculate z.
-15, 1
Let m = 55 + -20. Factor 2*o**2 - m*o + 16*o + 26*o + 3.
(o + 3)*(2*o + 1)
Let r = 2409/494 - -154/247. Factor r*x**3 + 13/3*x**2 + 16/3 + 5/6*x**4 - 16*x.
(x - 1)*(x + 4)**2*(5*x - 2)/6
Let r(w) be the first derivative of -3*w**4/4 - 11*w**3/3 + 2*w**2 + 175. Suppose r(j) = 0. What is j?
-4, 0, 1/3
Let c(g) be the second derivative of 3*g - 15/2*g**2 + 0 - 5/12*g**4 + 10/3*g**3. Find b such that c(b) = 0.
1, 3
Let v(t) = -5*t + t + t - 7. Let x be v(-5). Determine h, given that -6*h + 7 - 3*h**2 - 15 + x = 0.
-2, 0
Suppose 0 = 2*v - 9 + 1. Let -34 - 13*d**3 + 2 + 4*d**v + 24*d**2 + 16*d - 7*d**3 = 0. What is d?
-1, 2
Suppose 0 = -5*s - 1 + 16. Let l(i) be the first derivative of 2*i**s - 9 - 3*i**3 - i**2 - 2*i**2 - 9*i + 2*i**3. Factor l(o).
3*(o - 3)*(o + 1)
Let f(r) = r**2 + r - 3. Let a be f(-3). Factor -113*d**3 + 4 - 3*d + d**2 - 4 - d**4 + 116*d**a.
-d*(d - 3)*(d - 1)*(d + 1)
Let u(b) be the second derivative of b**7/420 - b**5/60 + 13*b**3/2 + 5*b. Let s(d) be the second derivative of u(d). Factor s(t).
2*t*(t - 1)*(t + 1)
Let l be (8 + (-632)/80)/((-4)/(-5)). Let g(o) be the first derivative of 1/2*o**3 - 1/10*o**5 + o + l*o**4 + 4 - 5/4*o**2. Factor g(a).
-(a - 1)**3*(a + 2)/2
Find l, given that -17/3*l - 1/3*l**2 + 0 = 0.
-17, 0
Let v(n) be the third derivative of n**5/15 + 5*n**4/3 - 64*n**2. Factor v(s).
4*s*(s + 10)
Let z = 35038 + -349893/10. Let s = z + -206/5. Determine q, given that 0 + s*q**2 - 7/2*q**3 - 9/2*q + 1/2*q**4 = 0.
0, 1, 3
Let a(l) be the third derivative of 841*l**5/120 + 29*l**4/8 + 3*l**3/4 + 7*l**2 - 4. Let a(v) = 0. What is v?
-3/29
Let i(t) be the third derivative of 0 + 2/15*t**5 + 0*t**3 + 0*t + 0*t**7 + 8*t**2 + 1/10*t**6 + 0*t**4 - 1/84*t**8. Factor i(f).
-4*f**2*(f - 2)*(f + 1)**2
Let g be (-2490)/(-1743) + (-54)/77. Factor g*z + 0 + 2/11*z**3 - 8/11*z**2.
2*z*(z - 2)**2/11
Let o(t) be the second derivative of -t**10/10080 - t**9/420 - 9*t**8/560 + 19*t**4/12 - 17*t. Let l(a) be the third derivative of o(a). Factor l(k).
-3*k**3*(k + 6)**2
Let v be (-1)/(-2) + ((-91)/234 - 0). Let z(a) be the third derivative of -1/90*a**5 + 0*a - v*a**3 - 1/18*a**4 + 0 - 3*a**2. Let z(p) = 0. What is p?
-1
Let r(f) be the second derivative of -f**4/4 - 5*f**3 - 88*f. Solve r(g) = 0 for g.
-10, 0
Let w be (-1136)/852*6/(-4). Determine j, given that -4/9*j**4 + 0 - 4/9*j**3 + 0*j**w + 0*j = 0.
-1, 0
Let y = -1 + 5. Suppose 6 = h + y. Solve 3 + 4*u**3 - 6*u**4 - 16 + 12*u**2 + h*u**4 + 5 - 4*u = 0 for u.
-1, 1, 2
Let p(s) be the second derivative of -s**6/240 + 7*s**5/160 - 5*s**4/96 - 7*s**3/48 + 3*s**2/8 + 14*s - 2. Factor p(c).
-(c - 6)*(c - 1)**2*(c + 1)/8
Factor -5*y**2 + 317*y - 12532 - 2048 + 223*y.
-5*(y - 54)**2
Let y(c) = 24*c + 624. Let h be y(-26). What is m in h - 3/2*m**2 - m - 1/2*m**3 = 0?
-2, -1, 0
Let k(l) be the first derivative of 4*l**5/5 - l**4 - 12*l**3 - 22*l**2 - 16*l + 24. Factor k(b).
4*(b - 4)*(b + 1)**3
Solve -t**2 + 114*t**2 + 21*t + 15*t**2 - 117*t + 18 = 0 for t.
3/8
Let d(u) be the third derivative of u**7/315 - u**6/36 + 4*u**5/45 - u**4/9 + 25*u**2. Factor d(w).
2*w*(w - 2)**2*(w - 1)/3
Let j(o) be the third derivative of 1/3*o**3 + 1/14*o**4 - 1/210*o**5 + 0*o + 0 - 10*o**2. Factor j(f).
-2*(f - 7)*(f + 1)/7
Let t(x) be the third derivative of x**5/330 - x**4/22 - 7*x**3/33 - 25*x**2. Let t(p) = 0. What is p?
-1, 7
Let k(g) be the second derivative of 4*g**2 - 2*g + 0 + 1/168*g**7 + 1/3*g**4 - 2*g**3 + 1/10*g**5 - 1/20*g**6. Factor k(m).
(m - 2)**4*(m + 2)/4
Let x(n) be the third derivative of 0 - 3/8*n**4 - 1/40*n**6 + 1/2*n**3 + 3/20*n**5 + 0*n - 3*n**2. Find s, given that x(s) = 0.
1
Let s be 18/8 + 1/(-4) - 6. Let o = s - -4. Determine d so that -1/5*d**3 + 0*d**2 + o + 1/5*d = 0.
-1, 0, 1
Suppose 13 = -3*b + 73. Let g = b + -18. What is q in -1/2*q**4 + 0*q - q**g - 3/2*q**3 + 0 = 0?
-2, -1, 0
Let n(o) be the first derivative of -o**4/4 - 4*o**3 + 2*o**2 + 48*o - 69. Suppose n(h) = 0. What is h?
-12, -2, 2
Let y(h) be the third derivative of h**8/8400 - h**7/2100 + 4*h**3 - 2*h**2. Let c(j) be the first derivative of y(j). Factor c(q).
q**3*(q - 2)/5
Let c(f) be the second derivative of 0 - 5*