16. Let i(v) be the second derivative of 0 + 1/5*v**2 - 10*v + 1/200*v**5 + g*v**4 + 2/15*v**3. Suppose i(w) = 0. Calculate w.
-2, -1
Let p(m) be the third derivative of -119/96*m**4 + 49/12*m**3 + 0*m + 130*m**2 + 3/80*m**5 + 1/840*m**7 + 0 + 11/480*m**6. Suppose p(n) = 0. What is n?
-7, 1, 2
Suppose 6*v + 90 = 102. Factor -63*a - 4*a**3 + 39*a**v + a**3 + 52*a - 25*a.
-3*a*(a - 12)*(a - 1)
Let a be (-1144)/(-156) + (-2574)/351. Factor -20/7*j**3 + 20/7*j + a - 1/7*j**4 + 1/7*j**2.
-j*(j - 1)*(j + 1)*(j + 20)/7
Let j = -6/3265 - -659/3265. Factor j*f**2 + 3/5*f + 2/5.
(f + 1)*(f + 2)/5
Let i be (9/27)/((-20)/13425). Let h = -223 - i. Find o, given that -3/8 - 3/8*o**2 + h*o = 0.
1
Factor 0 + 3/5*z**2 - 1122/5*z.
3*z*(z - 374)/5
Let z(l) be the third derivative of 0*l**4 + 1/210*l**7 + 0*l**3 + l**2 + 6 + 0*l - 1/60*l**5 + 0*l**6. Factor z(p).
p**2*(p - 1)*(p + 1)
Suppose 3*y + 2*p - 49 = 0, -y + 16 = -0*y + p. Let j = y - 14. Factor -n - j*n**2 - 2*n**2 + 4*n**2 + 2.
-(n - 1)*(n + 2)
Let n(j) be the first derivative of -1/12*j**6 - 21/4*j**4 + 13/10*j**5 - 37/4*j**2 + 29/3*j**3 + 9/2*j - 178. Let n(i) = 0. What is i?
1, 9
Suppose -338*b - 568*b + 613 = -630 - 569. Factor 0 + 0*p - 31/7*p**3 + 1/7*p**4 + 0*p**b.
p**3*(p - 31)/7
Let n(j) be the third derivative of -j**6/240 - j**5/20 + 22*j**3/3 - 8*j**2 + j. Let u(h) be the first derivative of n(h). Solve u(a) = 0.
-4, 0
Let m(c) = -3*c**2 + 6*c + 7. Suppose -49 = 7*t - 14. Let a(y) = -6*y**2 + 12*y + 13. Let i(l) = t*m(l) + 2*a(l). Determine x, given that i(x) = 0.
-1, 3
Let u be 22/242 - 1520/22. Let g = -45 - u. Find y, given that -g - 4*y**2 + 16 + 4*y**2 + 2*y**2 = 0.
-2, 2
Suppose -100/3*v - 35/6*v**2 - 130/3 = 0. What is v?
-26/7, -2
What is z in -64/15*z**2 - 2/15*z**4 + 8/3*z + 26/15*z**3 + 0 = 0?
0, 1, 2, 10
Suppose -41 + 6 = -7*g. Suppose y = g*y - 20. Factor 40*z + z**2 + y*z**4 + 5*z**5 - 6*z**2 - 76*z**3 - 20 + 51*z**3.
5*(z - 1)**3*(z + 2)**2
Suppose -3*q + 5*x = 6, x + 9 = 5*q - 3. Suppose -2 = c + u - q*u, -c + 16 = 4*u. Suppose 8*k**2 + 3*k**c - k**4 + 4*k**3 + 4*k**3 = 0. What is k?
-2, 0
Let b(h) be the second derivative of h**5/140 - 25*h**4/84 + 52*h**3/21 - 40*h**2/7 + 1191*h. Factor b(i).
(i - 20)*(i - 4)*(i - 1)/7
Let h(d) = 4*d**2 - 1722*d - 3418. Let k(y) = y**2 - 574*y - 1140. Let r(g) = -4*h(g) + 14*k(g). Factor r(f).
-2*(f + 2)*(f + 572)
Let s(n) = -n**3 - 10*n**2 - 152*n - 917. Let m be s(-7). Let i(o) be the third derivative of 0*o**3 - 1/420*o**5 + 0*o + 13*o**2 + m - 5/168*o**4. Factor i(w).
-w*(w + 5)/7
Let l be (63/9)/(3/9). Let d be -2*(-3)/6 + -1 + l. Factor -6*f**2 - d*f**4 + 3 + 7*f - 2*f**5 - 24*f**3 - f - 4*f**5 + 0*f**5.
-3*(f + 1)**4*(2*f - 1)
Let u(p) be the second derivative of 27*p**2 + 21/20*p**5 - 4*p - 63/2*p**3 + 2 - 1/2*p**4. Factor u(s).
3*(s - 3)*(s + 3)*(7*s - 2)
Suppose 0 = 12*m - 10*m - 8. Suppose -3*j - 4 = 5*k - 29, 2*k + 16 = m*j. Factor -2*r**2 + 126*r + 3*r**k + 1 - 247*r + 123*r.
(r + 1)**2
Let o = 698/27 - 1369/54. Let k(y) be the first derivative of 1 + 5/6*y**3 + o*y**4 + 0*y + 1/4*y**2. Solve k(m) = 0 for m.
-1, -1/4, 0
Let y(j) be the first derivative of -4/45*j**5 + 0*j - 1/18*j**2 + 75 - 4/27*j**3 - 1/54*j**6 - 1/6*j**4. Find p, given that y(p) = 0.
-1, 0
Let z(p) = 3*p + 10*p - 15*p - 1 + 3*p**2 - 2*p**2 + 4*p. Let j(i) = -4*i**3 + 18*i**2 + 36*i - 38. Let g(m) = j(m) - 6*z(m). Factor g(n).
-4*(n - 4)*(n - 1)*(n + 2)
Let d = -178570 + 178570. Factor -23/5*t + 1/5*t**2 + d.
t*(t - 23)/5
Let b = -672 + 674. Suppose -9 = m - 3*k, -8*m + b*k - 6 = -3*m. Suppose m*v**2 - 2/3 - v + 1/3*v**3 = 0. What is v?
-1, 2
Let z = 1/426337 - -2984357/852674. Let -7/2*j - 15/2 + z*j**2 - 1/2*j**3 = 0. What is j?
-1, 3, 5
Let d(t) be the third derivative of 0*t - 10*t**2 + 1/330*t**5 + 16/33*t**3 + 0 - 2/33*t**4. Factor d(a).
2*(a - 4)**2/11
Let v = 2719921/105 - 25904. Let z(a) be the third derivative of 0 + 27*a**2 + 0*a - 2/21*a**3 + v*a**5 + 1/420*a**6 - 1/84*a**4. Factor z(r).
2*(r - 1)*(r + 1)*(r + 2)/7
Suppose -248/3*g - 2/3*g**2 + 0 = 0. What is g?
-124, 0
Suppose 0 = 36*y - 84 - 60. Factor 4*r - 47*r**4 - 2 + y*r**3 + 88*r**4 + 3 - 40*r**4 + 6*r**2.
(r + 1)**4
Let c = 190590 - 571768/3. Factor 32/3*u - 16/3*u**2 + 32/3 - 32/3*u**3 - 14/3*u**4 - c*u**5.
-2*(u - 1)*(u + 2)**4/3
Suppose -5*s + r - 2*r = -140, -2*s - 5*r + 33 = 0. Factor 24 + 20*a + s*a**2 - 72 - 9*a**2 + 24*a.
4*(a + 3)*(5*a - 4)
Let t(n) = 146*n + 6*n**2 + 55 + 62 + 111 + 75*n. Let q(d) = d**2 + 37*d + 38. Let m(x) = -39*q(x) + 6*t(x). Find h, given that m(h) = 0.
-38, -1
Determine z, given that 3*z**5 + 425*z + 486*z**3 + 1020*z**2 - 48230*z**4 + 48308*z**4 + 270 + 454*z = 0.
-18, -5, -1
Let v = 423/286 - -42717/11726. Let h = 21/164 + v. Let -3/4*x**5 - 3/2*x - 15/4*x**4 - h*x**2 - 27/4*x**3 + 0 = 0. Calculate x.
-2, -1, 0
Suppose -2*o + 4*t = -28, 2*o + 0*o - 5*t = 31. Suppose o = 12*a - 8*a. Find v, given that -8 + 0*v**3 + 60*v**a - 90*v**2 + 21*v + 10*v**4 + 11*v - 4*v**3 = 0.
-2, 2/5, 1
Let a(s) be the first derivative of 3*s**4/8 - 59*s**3/2 + 306*s**2 + 6550. Suppose a(j) = 0. What is j?
0, 8, 51
Let q(j) be the second derivative of -j**4/78 + 6476*j**3/39 - 10484644*j**2/13 + 9343*j. Solve q(x) = 0 for x.
3238
Factor 60*m**2 + 4/5*m**4 + 148/5*m + 156/5*m**3 + 0.
4*m*(m + 1)**2*(m + 37)/5
Factor -450/11 - 144/11*r + 2/11*r**2.
2*(r - 75)*(r + 3)/11
Let s(f) = -135*f**3 - 540*f**2 - 675*f - 380. Let l(w) = -20 + 25*w + 45 - 11 + 20*w**2 + 3*w**3 + 2*w**3. Let z(r) = -55*l(r) - 2*s(r). Factor z(n).
-5*(n + 1)**2*(n + 2)
Suppose -608*l**2 + 23*l**3 - 27*l**3 - 10240 + 2806*l + 2250*l = 0. What is l?
-160, 4
Let w(f) be the second derivative of 3*f**4/4 - 158*f**3/3 + 35*f**2/2 - 1388*f. Factor w(l).
(l - 35)*(9*l - 1)
Suppose 53*w - 35*w = 0. Let m be w - -1 - 117/819. Solve 0 + 9/7*l**2 - 15/7*l**4 + 0*l - m*l**3 = 0.
-1, 0, 3/5
Factor 5/4*o - 33/2 + 1/4*o**3 + 3*o**2.
(o - 2)*(o + 3)*(o + 11)/4
Let k(c) be the first derivative of -77*c**4/2 - 1072*c**3/3 + 628*c**2 - 192*c - 845. Solve k(u) = 0 for u.
-8, 2/11, 6/7
Let o(k) be the second derivative of 1/2*k**3 - 18*k + 0*k**2 + 1/1620*k**6 + 0*k**4 + 0 - 1/90*k**5. Let w(m) be the second derivative of o(m). Factor w(l).
2*l*(l - 6)/9
Find b, given that 1/3*b**4 + 46/3 + 7*b - 7*b**3 - 47/3*b**2 = 0.
-2, -1, 1, 23
Suppose 32*l - 65942 = -6774. Let -98*j + 64*j + 120*j + j**2 + l = 0. Calculate j.
-43
Let o(l) = -354*l**2 - 108*l + 219. Let u(a) = 12 + 12 - 25 + a**3 - a**2. Let b(n) = -o(n) + 9*u(n). Factor b(i).
3*(i + 1)*(i + 38)*(3*i - 2)
Let w be (8 - 4)*(-3)/12 + 4. Factor -13 + 12*i**2 - 5605*i + 5569*i + 33 + 4*i**w.
4*(i - 1)**2*(i + 5)
Factor 973*i**2 + 275*i + 46*i - 970*i**2.
3*i*(i + 107)
Factor 80*v**4 + 5*v**5 - 5*v**5 - 120*v**2 + 512*v**3 + 4*v**5 + 1144*v**2.
4*v**2*(v + 4)*(v + 8)**2
Suppose -491 + 16 = -19*s. Let j be (s + -26)/(-2 + 1 + -4). Factor -2/5*v**5 + 0*v - j*v**2 + 3/5*v**4 + 0 + 0*v**3.
-v**2*(v - 1)**2*(2*v + 1)/5
Let v(f) be the second derivative of -f**5/20 + f**4/6 + 4*f**3/3 + f**2 - 25*f. Let t be v(4). Factor 2*w + 18 - 15 - 6*w**t + w.
-3*(w - 1)*(2*w + 1)
Let l = -23 + 26. Let i be ((-12)/(-21))/((744/224)/31). Determine n so that 2/3 - i*n + 26/3*n**2 - 4*n**l = 0.
1/6, 1
Find m, given that -422/7*m**2 + 66992/7*m + 2/21*m**3 - 199712/21 = 0.
1, 316
Let m(f) be the second derivative of 5*f**7/42 + f**6/5 - 59*f**5/20 - f**4 - 86*f. Let m(t) = 0. Calculate t.
-4, -1/5, 0, 3
Let p(y) be the first derivative of y**4/10 + 94*y**3/15 - 97*y**2/5 + 98*y/5 - 93. Determine c so that p(c) = 0.
-49, 1
Determine g, given that 2*g**5 - 3*g - 1324*g**2 - 9598 - 76*g**4 - 1159*g - 600*g**3 + 9238 = 0.
-4, -1, 45
Let r = -14020/51 - -690791/561. Let c = 957 - r. Factor 0 - 18/11*f - c*f**2.
-6*f*(f + 3)/11
Factor 13*g**3 + 10*g**2 - 7*g**2 + 165*g**4 + 10*g**3 + 25 - 169*g**4 - 12*g**2 - 35*g.
-(g - 5)*(g - 1)**2*(4*g + 5)
Let h(z) be the second derivative of z**4/12 + 13*z**3/2 + 19*z**2 + 7*z + 2. What is n in h(n) = 0?
-38, -1
Let d(b) = -49*b**3 - 8*b**2 + 16*b + 17. Let g(n) = 13*n**3 + 2*n**2 - 4*n - 4. Let h(r) = 4*d(r) + 15*g(r). Factor h(x).
-(x - 2)*(x + 2)**2
Let g = 30/59 + 6690/767. Let l = 1/297 - -5927/3861. Factor l*s**2 - 144/13 - 2/13*s**5 - g*s + 30/13*s**3 + 0*