 188. Determine h, given that f(h) = 0.
-17, -15
Let z(x) be the second derivative of -1/40*x**5 + 0*x**3 - 4 - 13*x + 0*x**2 + 1/24*x**4. Find w such that z(w) = 0.
0, 1
Let v(n) = 2*n - 7. Let l be v(6). Suppose q + q - l*t - 13 = 0, 3*q - 3*t - 33 = 0. Factor 15*z**4 + 19*z**4 + 3*z**2 - 51*z**4 + q*z**4.
-3*z**2*(z - 1)*(z + 1)
Let u = 1184757 - 1184755. Factor 23/6*h**u + 40 - 68/3*h - 1/6*h**3.
-(h - 15)*(h - 4)**2/6
Let q(p) be the second derivative of -2*p**6/15 + 6*p**5 - 99*p**4 + 1936*p**3/3 - 39*p + 14. Solve q(s) = 0 for s.
0, 8, 11
Let b(z) = -z**2 - 21*z - 18. Let x be b(-20). Suppose -10 = x*f, 0 = 2*o + 5*f + 8 + 3. Solve 5 - 13*w**3 + o*w - 2*w**3 + 5*w + 3*w**4 - 29 + 18*w**2 = 0.
-1, 2
Let n(i) be the first derivative of -2*i**3/39 + 129*i**2/13 + 20*i + 1803. Factor n(r).
-2*(r - 130)*(r + 1)/13
Suppose 0 = -2*b - 2 - 10. Let q(u) = u**3 + 1. Let p(n) = -9*n**3 - 39*n**2 + 87*n - 51. Let o(a) = b*q(a) - p(a). Solve o(y) = 0 for y.
-15, 1
Let u(v) = 20*v**2 + 6212*v + 1376. Let g(o) = 81*o**2 + 24838*o + 5500. Let z(i) = 2*g(i) - 9*u(i). Factor z(c).
-2*(c + 346)*(9*c + 2)
Let t be 1218/29 + (-8534)/204. Factor t*k**5 + 1/3*k**2 + 1/2 - 5/6*k**4 - 7/6*k + k**3.
(k - 3)*(k - 1)**3*(k + 1)/6
Let v be (-62)/(-5)*(9 + -4). Let m = 64 - v. Suppose 5*h**m - 15*h - 5*h - 6*h + 6*h = 0. What is h?
0, 4
Suppose 6*k + 4*j - 12 = 0, 259*j = 2*k + 255*j - 4. Suppose 1/2*w**4 + k - 5/2*w**2 - 5/4*w**3 + w + 1/4*w**5 = 0. What is w?
-2, -1, 1, 2
Factor -10 + 101/2*u**2 - 11/2*u**3 + 46*u.
-(u - 10)*(u + 1)*(11*u - 2)/2
Let v(f) be the third derivative of -15/2*f**3 + 0 - 4*f**2 + f + 17/16*f**4 - 1/40*f**5. Find k such that v(k) = 0.
2, 15
Suppose -23*s - 22*s - 118215 = 0. Let i = 18391/7 + s. Factor -2/7*d**5 - 6/7*d**2 + 10/7*d**3 - i*d**4 + 0*d + 0.
-2*d**2*(d - 1)**2*(d + 3)/7
Let v = -95524/9 - -668965/63. Factor -v - 3/7*m + 33/7*m**2 + 3/7*m**3.
3*(m - 1)*(m + 1)*(m + 11)/7
Let a(c) be the first derivative of -1/2*c - 5/12*c**3 + 66 + 7/8*c**2. Factor a(m).
-(m - 1)*(5*m - 2)/4
Let k(z) be the second derivative of -z**5/30 + 133*z**4/18 + 275*z**3/3 + 417*z**2 + 33*z - 1. Suppose k(p) = 0. Calculate p.
-3, 139
Suppose 9*i = -10*i + 76. Let k be i*(26/(-14)*1 + 2). Suppose -2/7*c**5 + 6/7 - k*c**2 - 10/7*c - 2/7*c**4 + 12/7*c**3 = 0. Calculate c.
-3, -1, 1
Suppose -111*t + 56*t + 55*t - 427*t**2 + 226*t**2 + 3*t**3 = 0. Calculate t.
0, 67
Suppose -5*q + 0*k - 3*k + 13 = 0, 2*q + 1 = 5*k. Find u, given that 5*u + 660*u**2 + 652*u**2 - 1317*u**q + 10 = 0.
-1, 2
Let g(b) be the first derivative of b**6/120 + b**5/8 + 27*b**3 + 71. Let v(c) be the third derivative of g(c). Solve v(x) = 0 for x.
-5, 0
Let l(q) be the first derivative of q**4/4 - 5*q**3 + 19*q**2 + 144*q + 2280. Factor l(t).
(t - 9)*(t - 8)*(t + 2)
Let -3/4*v**4 - 60 - 33/4*v**3 + 0*v**2 + 69*v = 0. What is v?
-10, -4, 1, 2
Let q = 910 + -1296. Let d = 1545/4 + q. Let -d*z + 0 - 1/4*z**4 + 1/4*z**3 + 1/4*z**2 = 0. What is z?
-1, 0, 1
Factor -10*j**2 - 27/10*j**4 - 21*j**3 - 1/10*j**5 + 300*j + 0.
-j*(j - 3)*(j + 10)**3/10
Suppose -1 = -l - 4. Let q be (12 + -6)/(l/(-2)). Suppose 2 + q*g**2 - g**2 - 4*g**2 + g = 0. What is g?
-1, 2
Let v(s) be the third derivative of s**6/840 + 13*s**5/60 - s**4/168 - 13*s**3/6 + 1294*s**2. Suppose v(c) = 0. Calculate c.
-91, -1, 1
Suppose -3*v = -5*v - 4, 4*v = 4*s + 40. Let o be s/(-21)*8/16. Factor -2/7*c**4 + o*c - 2/7*c**3 + 2/7*c**2 + 0.
-2*c*(c - 1)*(c + 1)**2/7
Let l = 5259 + -5254. Let g(k) be the first derivative of 5*k**3 - l*k**2 + 1/4*k**5 - 15/8*k**4 + 0*k - 14. Factor g(a).
5*a*(a - 2)**3/4
Let p(g) be the second derivative of -g**4/24 - g**3/4 + 9*g**2/2 + 177*g + 1. Find r such that p(r) = 0.
-6, 3
Let w(y) = -y**3 + y**2 + 2*y - 5. Let v be w(-2). Let d be v - 91/49 - 16/28. Suppose d - 18/7*u - 6/7*u**3 + 20/7*u**2 = 0. What is u?
1/3, 1, 2
Let 0*b + 0 + 28/11*b**2 + 8/11*b**4 - 38/11*b**3 + 2/11*b**5 = 0. Calculate b.
-7, 0, 1, 2
Let a(p) be the third derivative of 4*p**2 + 1/280*p**7 - 2*p + 1/80*p**6 - 19/80*p**5 - 3/2*p**3 + 0 + 7/8*p**4. Let a(m) = 0. What is m?
-6, 1, 2
Factor -79*q - 5*q**2 - 70*q + 25*q - 3*q - 63*q.
-5*q*(q + 38)
Let s be (1 - 1) + 270/90. Let r(a) be the first derivative of -a - 3/4*a**2 + 5/6*a**s - 8. Determine i so that r(i) = 0.
-2/5, 1
Let s(i) be the second derivative of i**7/210 + 2*i**6/45 + 2*i**5/15 - 19*i**3/6 + 10*i. Let m(w) be the second derivative of s(w). Factor m(x).
4*x*(x + 2)**2
Let h be 16/(-5984)*11*(-12 + 8). Determine x so that 1920/17*x + 1800/17 + 122/17*x**2 + h*x**3 = 0.
-30, -1
Let b(z) be the first derivative of -68/3*z**3 + 74*z**2 + 130 - 76*z - z**4. Let b(u) = 0. What is u?
-19, 1
Let n be (2 - 2) + (-69881)/(-536). Let v = 529/4 - n. Determine w so that -9/4*w**2 + v*w**3 + 3/4*w**4 + 0*w - 3/8*w**5 + 0 = 0.
-2, 0, 1, 3
Let t(v) be the second derivative of 1/42*v**4 - 38/21*v**3 + 361/7*v**2 + 2*v - 8. Determine q so that t(q) = 0.
19
Suppose -5*f - 74 = 5*o - 44, 4*o + 10 = 3*f. Let g be (-8)/f - 30*(-7)/(-63). Factor -4/3*h**2 + 2/3*h + 0 + g*h**3.
2*h*(h - 1)**2/3
Suppose -5*q - 27 - 233 = -5*d, 3*d + q - 156 = 0. Let u be (-4)/22 + -6*d/(-143). Factor 0*o + 8/5*o**3 - u*o**4 + 0 + 4/5*o**5 - 2/5*o**2.
2*o**2*(o - 1)**2*(2*o - 1)/5
Let -5 + 404*u**2 - 25 + 68*u - 34 - 810*u**2 + 402*u**2 = 0. What is u?
1, 16
Let u(p) = p**3 + 35*p**2 - 134*p. Let f(c) = 11*c**3 + 349*c**2 - 1356*c. Let o(y) = 2*f(y) - 21*u(y). Suppose o(l) = 0. Calculate l.
0, 3, 34
Let w(d) be the first derivative of 20*d**3/3 - 1925*d**2/2 + 480*d - 1031. Let w(g) = 0. Calculate g.
1/4, 96
Let j be 35/(-2)*(-80)/28. Factor 17*r + 28*r**2 - j*r + 4*r**3 - 6*r**3 - 42*r - 23*r.
-2*r*(r - 7)**2
Let d(y) = -24*y - 14 - 4 - 3*y**2 + 19*y**3 - 14*y. Let q(l) = -515*l**3 + 80*l**2 + 1025*l + 485. Let w(n) = 55*d(n) + 2*q(n). Factor w(x).
5*(x - 2)*(x + 1)*(3*x + 2)
Suppose 4*w - 16 = 0, v + 4*v = 5*w + 5570. Let d = -4457/4 + v. Find l, given that -d*l**2 - 3/2 + 21/4*l = 0.
2/5, 1
Let -2898 + 534*j + 3378 - 34*j + 5*j**3 + 140*j**2 = 0. Calculate j.
-24, -2
Suppose 5*x - 45 = -t - 4*t, 4*x - 2*t = 6. Let r(l) be the first derivative of -6 + 1/15*l**5 + 0*l - 1/3*l**2 - 1/3*l**3 + 0*l**x. What is h in r(h) = 0?
-1, 0, 2
Let b = 249 - 247. Factor 0*m**2 - 7*m**2 + 4*m**4 - 11*m**2 + b*m**2 + 8*m**3 - 32*m.
4*m*(m - 2)*(m + 2)**2
Let n = -23 - -17. Let z be n/(-8) + 51/(-68). Factor 3*k**2 + z*k**2 - 5*k**3 + 0*k**2 - 4*k**2 - 4*k**4.
-k**2*(k + 1)*(4*k + 1)
Suppose -1809 = -583*m - 60. Let 1/6*j - 1/3*j**2 + 1/6*j**m + 0 = 0. Calculate j.
0, 1
Let r(x) be the third derivative of 1/30*x**4 - 4/5*x**3 - x**2 + 34/75*x**5 + 1/140*x**8 + 8/105*x**7 - 76 + 22/75*x**6 + 0*x. What is n in r(n) = 0?
-3, -2, -1, 1/3
Let i(h) be the first derivative of 3*h**5/10 - 51*h**4 + 2379*h**3 - 6834*h**2 + 13467*h/2 - 94. Factor i(v).
3*(v - 67)**2*(v - 1)**2/2
Suppose 5*g - 46 = 10*g - 4*a, -30*g + 74 = a. Let p be (-1*(-3)/(-2))/(-3). Solve -p*v**g + 1/4 + 1/4*v + 1/4*v**5 - 1/2*v**3 + 1/4*v**4 = 0 for v.
-1, 1
Let f(p) be the second derivative of p**6/255 + 13*p**5/170 - 15*p**4/34 + 47*p**3/51 - 16*p**2/17 - 6260*p. What is k in f(k) = 0?
-16, 1
Let m(l) be the third derivative of -1/140*l**5 + 1/4*l**4 + 0*l + 30 + 2*l**2 + 0*l**3. Suppose m(x) = 0. What is x?
0, 14
Let g be (-4452)/(-318) + -2*40/6. Suppose -4/9 + 2/9*o**4 + 2/9*o**2 - g*o**3 + 2/3*o = 0. Calculate o.
-1, 1, 2
Factor 25*i + 35*i - 18*i**3 + 3*i**4 + 12*i + 15*i**2 - 108.
3*(i - 3)**2*(i - 2)*(i + 2)
Let l be (-23)/4*13675/(-1094). Factor 49/8*f**2 - l*f - 1/8*f**3 - 625/8.
-(f - 25)**2*(f + 1)/8
Factor 2 - 69*y + 15876*y**2 - 142*y + 15 - 797*y - 1.
4*(63*y - 2)**2
Let f(w) be the first derivative of 484*w**5/5 + 440*w**4 - 6496*w**3/3 + 1088*w**2 - 192*w - 1969. What is y in f(y) = 0?
-6, 2/11, 2
Let a = -2649 + 4202. Let d = a + -1553. Determine v so that 0*v**4 + d + 0*v - 21/5*v**3 + 27/5*v**5 - 6/5*v**2 = 0.
-2/3, -1/3, 0, 1
Let v(p) be the first derivative of 27*p**5/4 + 15*p**4/2 + 10*p**3/3 - p**2/2 - 55*p - 43. Let l(n) be the second derivative of v(n). Let l(x) = 0. What is x?
-2/9
Let v(k) be the first derivative of 3*k**4/2 - 272*k**3/3 + 177*k**2 - 88*k - 413. Suppose v(s) = 0. Calculate s.
1/3, 1, 44
Let p(m) be the thir