of 1/24*n**6 - 35/4*n**5 + 0*n + 100*n**2 + 6125/8*n**4 + 0 - 214375/6*n**3. Determine j so that k(j) = 0.
35
Let i(j) be the first derivative of -35*j**6/27 + 232*j**5/45 + 46*j**4/9 + 32*j**3/27 + 3997. Suppose i(z) = 0. What is z?
-2/5, -2/7, 0, 4
Let b(p) = -27*p**3 - 29 + 34 - 82*p + 30*p**3 - 40*p**2. Let m(h) = -h**3 + 20*h**2 + 40*h - 2. Let r(x) = 6*b(x) + 15*m(x). Determine d, given that r(d) = 0.
-18, -2, 0
Suppose 6*t - 8 = h - 21, -15 = 5*t. Let g(k) = -k**2 - 9*k - 18. Let r be g(h). Solve 0 + 0*l**r - 2/15*l**5 + 0*l**4 + 4/15*l**3 - 2/15*l = 0.
-1, 0, 1
Let z = -2046 + 2050. Let b(l) be the first derivative of -9/7*l**2 - 2 + 12/35*l**5 + 3/7*l + 13/7*l**3 - 9/7*l**z. Factor b(h).
3*(h - 1)**2*(2*h - 1)**2/7
Let z be 818/(-1227)*(-24)/14. Factor 0*r**2 - z + 4/7*r**3 - 12/7*r.
4*(r - 2)*(r + 1)**2/7
Let s(d) be the first derivative of -40/3*d - 13 - 7*d**2 - 2/9*d**3. Find c, given that s(c) = 0.
-20, -1
Let c = -884677/3 + 294893. Suppose -128/3 - c*y**2 - 32/3*y = 0. What is y?
-8
Determine g, given that -98*g - 40*g**4 + 490*g + 36*g**4 + 20*g**4 + 72*g**3 - 399*g**2 = 0.
-8, 0, 7/4
Factor -z**4 + 3*z**4 - 12330*z**2 + 495*z - 108*z**3 + 93*z + 2*z**4 + 12806*z**2.
4*z*(z - 21)*(z - 7)*(z + 1)
Let g(b) be the first derivative of 40*b + 51*b**2 + 5/3*b**3 - 244. Suppose g(o) = 0. Calculate o.
-20, -2/5
Let b(a) = -7*a**3 - 826*a**2 + 1167*a - 330. Let w(t) = -15*t**3 - 1651*t**2 + 2334*t - 658. Let d(p) = -5*b(p) + 2*w(p). Let d(j) = 0. Calculate j.
-167, 2/5, 1
Let q(u) be the second derivative of u**7/56 + 447*u**6/40 + 151857*u**5/80 + 149185*u**4/16 + 18537*u**3 + 36963*u**2/2 + 6295*u. Factor q(a).
3*(a + 1)**3*(a + 222)**2/4
Suppose -l + 270 = 2*p + 79, -5*l + p = -900. Suppose -4*w = 41 - l. Suppose -16*d**4 + w*d**3 - 4*d**4 + d**2 - 6*d - 11*d**2 + d = 0. What is d?
-1/4, 0, 1
Suppose 26*i = 33*i. Suppose -y = -4*b + 9, -5*b + i*y - 4*y = -27. Factor g + g**4 - b*g**4 + 130*g**3 - 133*g**3.
-g*(g + 1)**2*(2*g - 1)
Let i(u) be the first derivative of -4*u**3/3 - 20*u**2 + 300*u - 270. Let i(g) = 0. What is g?
-15, 5
Let t be ((-846)/(-1034))/((-21)/(-77)). Factor -2*z**2 + 32/3*z + 2/3*z**4 + 8 - 4*z**t.
2*(z - 6)*(z - 2)*(z + 1)**2/3
Let z(t) be the first derivative of -9*t**3 + 21/2*t**2 + 15/4*t**4 - 3/5*t**5 + 65 - 6*t. Let z(x) = 0. What is x?
1, 2
Let l(q) be the first derivative of q**5/35 + q**4/7 - 38*q**3/21 + 30*q**2/7 - 27*q/7 + 10423. Determine a, given that l(a) = 0.
-9, 1, 3
Factor -3969/2*p**2 - 257298363/2 - 3/2*p**3 - 1750329/2*p.
-3*(p + 441)**3/2
Let n(q) be the second derivative of -q**4/8 - 55*q**3/12 - 125*q**2/2 + 1876*q. Factor n(j).
-(j + 10)*(3*j + 25)/2
Let v(f) = 6*f - 41. Let x be v(13). Let w(n) = 28*n**2 - x*n**2 - 1 + 10. Let i(j) = -8*j**2 + 8. Let y(t) = -6*i(t) + 5*w(t). Solve y(o) = 0 for o.
-1, 1
Let f(j) = 2*j**4 + j**2 + j + 1. Let h(g) = -8*g**4 - 8*g**3 + 131*g**2 - 223*g - 3. Let a(w) = 3*f(w) + h(w). Find p, given that a(p) = 0.
-11, 0, 2, 5
Suppose -4*q + 25 = p, -5 = -3*p - p + 3*q. Suppose 32*r - 211 + 83 = 0. Factor -3*g**r - 2*g**5 - 6*g**3 + p*g**5 - 3 + 3*g + 3*g**2 + 12*g**2 - 9*g**2.
3*(g - 1)**3*(g + 1)**2
Let r(a) be the third derivative of a**6/240 + 19*a**5/80 + 131*a**3/6 - 166*a**2. Let g(j) be the first derivative of r(j). Let g(u) = 0. What is u?
-19, 0
Let v(j) be the second derivative of -j**5/40 + 5*j**4/6 - 17*j**3/3 + 16*j**2 - 3*j + 2617. Factor v(o).
-(o - 16)*(o - 2)**2/2
Let u(o) be the first derivative of o**6/540 + o**5/18 + 25*o**4/36 + 125*o**3/27 - o**2/2 - 9*o - 41. Let d(l) be the second derivative of u(l). Factor d(h).
2*(h + 5)**3/9
Let t(s) = 3*s**4 + 13*s**3 + 63*s**2 + 67*s + 16. Let w(h) = 3*h**4 - h**3 - h - 4. Let o(i) = t(i) - 2*w(i). Find c such that o(c) = 0.
-1, 8
Let h(d) be the first derivative of d**5/35 + 25*d**4/14 + 16*d**3/7 - 25*d**2/7 - 7*d - 11947. Suppose h(o) = 0. What is o?
-49, -1, 1
Factor -9/2*s + 11 - 1/2*s**2.
-(s - 2)*(s + 11)/2
Suppose -2/5*h**3 - 386201104/5 - 3468/5*h**2 - 2004504/5*h = 0. What is h?
-578
Let v(u) be the first derivative of u**8/2688 + u**7/420 + u**6/320 + 15*u**2 + 31. Let k(y) be the second derivative of v(y). Suppose k(q) = 0. What is q?
-3, -1, 0
Let i(t) = t**3 - 6*t**2 + 13*t. Let f be i(2). Find u, given that 3*u**5 + 100*u**2 + 24*u**4 - 131*u**3 - f*u**3 - 5*u**5 + 51*u**3 = 0.
0, 2, 5
Let w(k) be the third derivative of 1/168*k**4 - 11/420*k**5 + 1/84*k**6 + 0*k**3 + 0*k + 9*k**2 + 0. Suppose w(h) = 0. Calculate h.
0, 1/10, 1
Let -2394320 + 944*z + 4067*z + 4336*z - 5*z**2 - 2427*z + 0*z**2 = 0. Calculate z.
692
Factor 6*j**3 - 113*j**2 - 7260 - 193*j**2 + 890*j**2 + 6472*j + 9300 + 474*j**2.
2*(j + 6)*(j + 170)*(3*j + 1)
Let p(d) be the third derivative of d**9/10080 + d**8/2240 + 3*d**4/8 + d**3/3 - 26*d**2. Let g(t) be the second derivative of p(t). Factor g(j).
3*j**3*(j + 2)/2
Let 1/5*b**4 - 27/5*b**2 + 0*b**3 + 54/5*b + 0 = 0. What is b?
-6, 0, 3
Let h(n) be the second derivative of 11/14*n**3 + 1/70*n**6 + 0*n**2 - 1/28*n**4 + 0 + 175*n - 33/140*n**5. Solve h(r) = 0 for r.
-1, 0, 1, 11
Let k(f) be the second derivative of -f**4/18 - 4*f**3/3 - 11*f**2/3 - 968*f. Find r such that k(r) = 0.
-11, -1
Let c(y) be the second derivative of -6*y - 89/8*y**4 + 33/20*y**5 + 23*y**3 - 3*y**2 + 9. Factor c(o).
3*(o - 2)**2*(22*o - 1)/2
Let p = 2/675101 - -13502014/2025303. Find f such that 5/3*f**4 + 5/6*f**5 - 10/3*f**3 + 0 + 0*f - p*f**2 = 0.
-2, 0, 2
Let y = 120415/94 - 1281. Let t = 289/658 - y. Factor t - 3/7*f**2 + 0*f.
-3*(f - 1)*(f + 1)/7
Let p(r) = -1323*r + 4 + 3 + 1324*r. Let b be p(2). What is n in 32 + 21 + n**2 - 13 - 14*n + b = 0?
7
Let l = 638 + -1075. Let j = l - -439. Find o, given that -3/7*o**j + 0 + 2/7*o + 1/7*o**3 = 0.
0, 1, 2
Let n(z) be the second derivative of -z**7/6 - 43*z**6/15 - 201*z**5/10 - 72*z**4 - 261*z**3/2 - 81*z**2 - 23*z - 13. Determine y, given that n(y) = 0.
-3, -2/7
Let z(s) = s**2 - 21. Let u be z(-5). Factor 34 - 6*o**2 - 16*o - 34 + u*o**2.
-2*o*(o + 8)
Suppose 35*b - 37*b = 3*c, 0 = -2*c + 2*b. Let y(j) be the first derivative of c*j**2 + 1/20*j**5 + 6 + 0*j**3 + 0*j - 1/8*j**4. Solve y(d) = 0 for d.
0, 2
Find g such that -160000/3 + 800/3*g - 1/3*g**2 = 0.
400
Let b(y) be the second derivative of -y**6/225 + 149*y**5/75 - 20341*y**4/90 - 18476*y**3/3 - 57660*y**2 + y - 701. Factor b(l).
-2*(l - 155)**2*(l + 6)**2/15
Let n be 36830/15225 - (-78)/(-910). Suppose -n*z**4 + z**3 + 23/3*z**2 + 0 - 1/3*z**5 + 14/3*z = 0. What is z?
-7, -1, 0, 2
Suppose -28 - 51 - 27 = -53*o. Let i(l) be the first derivative of 2/3*l**3 + 0*l + 11 + o*l**2. Suppose i(q) = 0. Calculate q.
-2, 0
Let a(y) = 2*y**2 + 60*y + 3. Let v be a(-30). Let -v*z**4 + 17*z**3 + 9*z**3 - 32*z**3 + 15*z**2 + 18*z**3 = 0. Calculate z.
-1, 0, 5
Let o(l) be the third derivative of -l**6/120 - 7*l**5/40 + 61*l**3/6 + 27*l**2 - 1. Let p(k) be the first derivative of o(k). Factor p(i).
-3*i*(i + 7)
Let g(d) = 3*d**2 + 1884*d - 1887. Let s(f) = -5*f + 5. Let w(h) = g(h) - 3*s(h). Factor w(m).
3*(m - 1)*(m + 634)
Let s(g) be the first derivative of g**6/27 + 56*g**5/45 - 59*g**4/18 + 20*g**3/9 - 2394. Let s(f) = 0. What is f?
-30, 0, 1
Find m such that -100*m**2 + 15856*m**2 + 5260*m**3 + 36*m**4 + 10020*m + 11046*m + 5248 - 32*m**4 - 5318*m = 0.
-1312, -1
Let w(d) be the first derivative of d**6/30 + 17*d**5/25 + 53*d**4/10 + 58*d**3/3 + 65*d**2/2 + 25*d + 116. Determine a, given that w(a) = 0.
-5, -1
Let k = 639260/117 + -71026/13. Determine m so that -8/9*m - k*m**2 + 0 = 0.
-4, 0
Let x(a) be the second derivative of a**4/3 - 308*a**3/3 - 1590*a**2 - 8128*a. Factor x(j).
4*(j - 159)*(j + 5)
Let l = 265 + -237. Suppose -l + 16 = -4*r. Let -1/5*v**5 + 1/5*v**2 - 3/5*v**r + 0 + 0*v + 3/5*v**4 = 0. What is v?
0, 1
Let f(t) be the third derivative of 0 + 600*t**3 + 2/105*t**7 - 290*t**4 + 140*t**2 + 29/15*t**6 + 781/15*t**5 + 0*t. Factor f(b).
4*(b - 1)**2*(b + 30)**2
Suppose 0 = -2*f + 4*c - 0*c + 14, 20 = 4*f - 4*c. Let d be ((-40)/40)/((-1)/f). Factor -4 + 10*m + 7/2*m**d + 13*m**2.
(m + 2)**2*(7*m - 2)/2
Let q = 92 + -90. Let -q*d + 18*d**4 - 2272 + 15*d**2 + 2272 - 31*d**3 = 0. Calculate d.
0, 2/9, 1/2, 1
Let g(y) be the first derivative of 22*y - 1/3*y**3 - 186 + 9/2*y**2. Find r