 4. Factor 3*h**3 + 3*h**2 - 3/2*h**4 - 3/2 - 3/2*h - 3/2*h**z.
-3*(h - 1)**2*(h + 1)**3/2
Determine g so that 1/5*g**3 + 0 - 1/5*g**2 + 0*g = 0.
0, 1
Let b = -339 - -491. Let t = -150 + b. Solve 21/4*d**t - 3/2*d + 15/4*d**4 - 27/4*d**3 + 0 - 3/4*d**5 = 0 for d.
0, 1, 2
Let a(n) be the first derivative of 3*n**6/160 - n**5/80 + 2*n**2 + 19. Let q(z) be the second derivative of a(z). Let q(k) = 0. What is k?
0, 1/3
Determine l, given that 36*l**4 + 48*l**4 + 207*l**3 + 216*l**2 + 12*l**5 - 32*l + 113*l = 0.
-3, -3/2, -1, 0
Let y(d) = -26*d - 1298. Let g be y(-50). Factor -1/5*w**3 + 0 - 4/5*w**g - 3/5*w.
-w*(w + 1)*(w + 3)/5
Suppose 0 = -0*k - 2*k - 6, -2*k = 5*s + 1. Let i be -1*(-1 + -2)*s. Factor 4*z**2 + i*z**3 - 13*z**3 + 4*z**2 - 2*z**2 + 4*z.
-2*z*(z - 1)*(5*z + 2)
Let r(c) be the second derivative of 0*c**4 - 3*c + 0 - 1/10*c**5 + c**3 - 2*c**2. Factor r(y).
-2*(y - 1)**2*(y + 2)
Let f(p) be the first derivative of 23*p**4/10 + 14*p**3/5 - 2*p**2/5 + 74. Solve f(y) = 0.
-1, 0, 2/23
Let f(q) be the first derivative of 2*q**3/11 - 36*q**2/11 - 168*q/11 - 112. Factor f(i).
6*(i - 14)*(i + 2)/11
Let b be (15/18)/((-39)/234) - -8. Solve 8/3*o + 10/3*o**5 - 6*o**b - 16/3*o**4 + 0 + 16/3*o**2 = 0.
-1, -2/5, 0, 1, 2
Factor 55*g**3 + 3837*g - 3820*g + 54*g**2 + 24*g**2 - 6.
(g + 1)*(5*g + 3)*(11*g - 2)
Let f be (2/(-24))/((-17)/1377). Let -18*o**2 + 0*o**3 - 16*o - 4 + f*o**4 = 0. Calculate o.
-2/3, 2
Let f(w) be the third derivative of w**8/1008 - 11*w**7/630 + 19*w**6/360 - w**5/20 + 2*w**2 + 7. Factor f(t).
t**2*(t - 9)*(t - 1)**2/3
Let d(x) be the second derivative of 5*x**7/112 + 3*x**6/80 - 111*x**5/160 - 51*x**4/32 - x**3/4 + 9*x**2/4 - 2*x + 10. Find j such that d(j) = 0.
-2, -1, 2/5, 3
Suppose k = 2*f - 1, -4*k + 0*f - 5*f + 61 = 0. Let y = -7 + k. Factor j**4 - 7*j**3 + 7*j**3 - j**y.
j**2*(j - 1)*(j + 1)
Suppose 282*f = 278*f + 80. What is x in -2*x**3 - 10*x**2 + 19*x - 10*x**3 + 7*x**3 + 16*x - f = 0?
-4, 1
Let z(j) = -7*j - 11. Let l be z(-5). Factor -4 - 5 + 9*r - 3*r**3 + 3 - l*r - 12*r**2.
-3*(r + 1)**2*(r + 2)
Let t(b) be the third derivative of -b**8/168 - 13*b**7/420 - b**6/16 - 7*b**5/120 - b**4/48 - 12*b**2. Let t(y) = 0. What is y?
-1, -1/4, 0
Let k(r) be the first derivative of r**4/22 + 16*r**3/33 - 53. Let k(h) = 0. What is h?
-8, 0
Let r(n) = -51*n**4 + 1497*n**3 - 27231*n**2 - 30. Let x(h) = 7*h**4 - 214*h**3 + 3890*h**2 + 4. Let u(t) = 2*r(t) + 15*x(t). Suppose u(q) = 0. Calculate q.
0, 36
Let r(b) be the first derivative of -b**6/12 + b**5/10 + 9*b**4/8 + 11*b**3/6 + b**2 - 45. Factor r(j).
-j*(j - 4)*(j + 1)**3/2
Let q(h) be the first derivative of 4 - 45/8*h**2 + 9/16*h**4 + 2*h**3 + 3*h. Find y such that q(y) = 0.
-4, 1/3, 1
Let t(q) be the third derivative of -1/84*q**4 - 1/42*q**3 + 0 - 1/420*q**5 + 0*q + 15*q**2. Factor t(a).
-(a + 1)**2/7
Factor -4*k**3 + 11*k**2 - 52*k + 44*k**2 + 21*k**2 - 20*k**2.
-4*k*(k - 13)*(k - 1)
Suppose 8*n**2 + 40*n + 34*n**3 - 64*n**3 - 16*n + 24*n**3 - 2*n**4 = 0. What is n?
-3, -2, 0, 2
Let r(u) = -2*u**2 - 218*u + 180. Let a(v) = -v**2 - 144*v + 120. Let t(q) = -8*a(q) + 5*r(q). Determine x, given that t(x) = 0.
1, 30
Let r(w) be the first derivative of w**4/12 + 5*w**3/6 + 3*w**2 - 14*w + 11. Let p(x) be the first derivative of r(x). Solve p(c) = 0 for c.
-3, -2
Let y(t) be the second derivative of t**5/90 + t**4/6 - 12*t**2 + 736*t. What is n in y(n) = 0?
-6, 3
Let z(i) be the second derivative of i**8/7560 - i**6/540 - i**5/270 + 13*i**3/6 + 7*i. Let n(q) be the second derivative of z(q). Suppose n(p) = 0. What is p?
-1, 0, 2
Let n(k) be the first derivative of -k**7/168 - k**6/18 - 5*k**5/24 - 5*k**4/12 - 14*k**3 - 4. Let o(j) be the third derivative of n(j). Factor o(t).
-5*(t + 1)**2*(t + 2)
Let k(g) be the third derivative of 1/6*g**3 - 2 - 1/12*g**4 - 1/480*g**6 - 14*g**2 + 1/48*g**5 + 0*g. What is r in k(r) = 0?
1, 2
Let j(z) be the first derivative of -7*z**6/2 + 69*z**5/5 - 9*z**4/2 - 72. Factor j(t).
-3*t**3*(t - 3)*(7*t - 2)
Let p(n) be the third derivative of n**7/350 + n**6/10 - 144*n**2. Factor p(w).
3*w**3*(w + 20)/5
Let w = -175 + 127. Let r be 4*(179/90 - w/(-80)). Factor r + 20/9*a + 2/9*a**2.
2*(a + 5)**2/9
Determine w, given that -40/3*w - 8 + 2/3*w**4 + 4/3*w**3 - 14/3*w**2 = 0.
-2, -1, 3
Let w = -3275/321 + -14/107. Let q = w - -13. Let 1/6*t**2 + 4/3*t + q = 0. What is t?
-4
Let h(t) be the second derivative of -t**4/66 - 34*t**3/33 - 3*t**2 - 478*t. Solve h(w) = 0.
-33, -1
Let b(j) = j**3 - 3*j**2 - j - 8. Let x be b(4). Let d be ((-4 - 2)/12)/((-1)/x). Factor 33/4*u + 12*u**5 + 129/4*u**d + 3/4 + 42*u**4 + 219/4*u**3.
3*(u + 1)**3*(4*u + 1)**2/4
Let p be (-63)/21*-2*(-2)/(-6). Factor -139 + 139 + p*s**5.
2*s**5
Let t(p) = -2*p**3 + 90*p**2 - 1060*p - 4. Let k(b) = 8*b**3 - 359*b**2 + 4241*b + 18. Let w(f) = 4*k(f) + 18*t(f). Factor w(c).
-4*c*(c - 23)**2
Let r(y) be the first derivative of -1/10*y**6 - 13 + 0*y**2 + 0*y**3 - 3/10*y**4 + 9/25*y**5 + 0*y. What is c in r(c) = 0?
0, 1, 2
Let l(y) be the first derivative of -11 + 1/5*y**3 + 0*y**2 + 0*y - 3/25*y**5 + 0*y**4. Let l(b) = 0. Calculate b.
-1, 0, 1
Let a(u) = -u**2 + 5*u - 2. Let f(y) = 9*y**2 + 147*y - 180. Let l(h) = 12*a(h) + f(h). Find j such that l(j) = 0.
1, 68
Let j(v) be the second derivative of 5*v**6/2 - 207*v**5/4 + 316*v**4 - 426*v**3 + 240*v**2 + 238*v. Find p, given that j(p) = 0.
2/5, 5, 8
Let z be ((-72)/(-90))/(2/(-50)). Let s be 1/(-1)*z/60. Factor -1/2*n**3 + s*n + 0 - 1/6*n**2.
-n*(n + 1)*(3*n - 2)/6
Let l = -39216 - -39218. Let j = 38/75 + 4/25. Factor 0*i**l - j*i**4 + 4/3*i - 4/3*i**3 + 2/3.
-2*(i - 1)*(i + 1)**3/3
Factor 120/7*k**2 + 87/7*k + 51/7*k**3 + 18/7.
3*(k + 1)**2*(17*k + 6)/7
Let w(t) be the second derivative of 2/9*t**2 - 9*t + 0 + 4/27*t**4 - 17/27*t**3. Factor w(q).
2*(q - 2)*(8*q - 1)/9
Let f(d) be the second derivative of -d**6/150 - d**5/50 - 246*d. Factor f(w).
-w**3*(w + 2)/5
Let y(s) = -6*s**2 - 14*s + 14. Let o(n) = 4*n**2 + 13*n - 13. Let p(u) = -4*o(u) - 3*y(u). Let a be p(1). Factor 2/3*b**3 + 0 - 2/3*b**a + 0*b.
2*b**2*(b - 1)/3
Let g(a) = -6*a**4 + 26*a**3 - 18*a**2 + 2*a. Let i(l) = l**5 - 7*l**4 + 26*l**3 - 17*l**2 + 3*l. Let j(z) = -6*g(z) + 4*i(z). Solve j(o) = 0.
-5, 0, 1, 2
Let s(f) = -21*f**3 + 45*f**2 - 15*f - 9. Let h(d) = -22*d**3 + 45*d**2 - 15*d - 8. Let n = 1 - -3. Let v(u) = n*h(u) - 3*s(u). Factor v(j).
-5*(j - 1)**2*(5*j + 1)
Let l(v) be the first derivative of 0*v - 1/10*v**2 - 1/6*v**3 + 12. Let l(p) = 0. Calculate p.
-2/5, 0
Let o = -562 - -565. Let -2/3*w**o + 0 - 2/3*w**2 + 4/3*w = 0. Calculate w.
-2, 0, 1
Let o(h) be the third derivative of -h**8/1008 - h**7/126 + h**6/120 + 17*h**5/180 + 5*h**4/36 + 12*h**2 + 5. Suppose o(v) = 0. Calculate v.
-5, -1, 0, 2
Solve -2*s**4 - 37/2*s + 23*s**2 + 7/2*s**3 - 6 = 0 for s.
-3, -1/4, 1, 4
Let t(p) be the third derivative of p**6/900 + p**5/90 + 7*p**4/180 + p**3/15 + 26*p**2. Factor t(g).
2*(g + 1)**2*(g + 3)/15
Determine t, given that -148*t**3 + 34*t**3 + 168*t**4 + 137*t**3 + 70*t**3 + 12*t**2 - 48*t**5 + 0*t**2 = 0.
-1/4, 0, 4
Let j(w) be the first derivative of w**6/1620 + w**5/180 + w**4/54 + 19*w**3/3 - 20. Let m(q) be the third derivative of j(q). Suppose m(k) = 0. Calculate k.
-2, -1
Let f = -82 + 331/4. Let z(u) be the first derivative of 0*u**3 - 5 + f*u**4 + 0*u - 3/2*u**2. Find b such that z(b) = 0.
-1, 0, 1
Let u(n) be the second derivative of n**9/52920 - n**7/8820 - 13*n**4/12 + 2*n. Let c(y) be the third derivative of u(y). Factor c(b).
2*b**2*(b - 1)*(b + 1)/7
Determine r, given that 2944 - 3640*r - 479 + 265*r**2 - 5*r**3 + 915 = 0.
1, 26
Let z = -1196 + 1196. Suppose 0 - b**4 + 1/3*b**5 + z*b + b**3 - 1/3*b**2 = 0. What is b?
0, 1
Let w(y) be the third derivative of 0*y**3 - 1/108*y**4 - 1/135*y**5 + 3*y**2 + 0*y + 0 - 1/540*y**6. Determine x, given that w(x) = 0.
-1, 0
Let v(d) = 96 + 92*d - 9*d**2 + 18*d - 14*d. Let k(b) = 25*b + 17 - b**2 - 13*b - 5. Let g(q) = -33*k(q) + 4*v(q). Factor g(h).
-3*(h + 2)**2
Let w(f) be the second derivative of -f**5/20 - 13*f**4/12 - 2*f**3/3 + 3*f**2/2 - 26*f. Let z(n) = n**3 + n**2 + 1. Let x(d) = w(d) + 5*z(d). Factor x(j).
4*(j - 2)*(j - 1)*(j + 1)
Let x(o) be the second derivative of o**6/90 - 4*o**5/5 + 311*o**4/18 - 