 164. Suppose t(g) = 0. What is g?
-1, 2/3, 3/2
Let g = 561947 + -561947. Factor 1/2*q - q**2 + g + 1/2*q**3.
q*(q - 1)**2/2
Let x be (14/(-4)*24/294)/(2/(-28)). Let h(u) be the second derivative of -1/8*u**x + 0 + 1/2*u**3 - 3/4*u**2 - 8*u. Let h(g) = 0. Calculate g.
1
Let g be (-1)/(-2)*(-3 - (10 - (-1053)/(-78))). Factor 0 + 15/4*n**2 + 4*n - g*n**3.
-n*(n - 16)*(n + 1)/4
Let t(i) be the third derivative of -i**5/300 + i**4/24 + 5*i**3 - 1465*i**2 - i. Factor t(n).
-(n - 15)*(n + 10)/5
Suppose -4*y + 189 - 77 = 96. Let t(a) be the first derivative of -2*a**2 + 26/27*a**3 - 2/9*a**5 - 39 - 16/9*a + a**y. Find m, given that t(m) = 0.
-1, -2/5, 1, 4
Let x be (-3 - 2)/(12/12). Let t(j) = -2*j**2 - j - 1. Let d(o) = -15*o**2 - 635*o - 19850. Let v(h) = x*t(h) + d(h). Factor v(w).
-5*(w + 63)**2
Let k(n) be the second derivative of 27*n - 1/16*n**4 - 1 - 3/2*n**2 + 1/2*n**3. Suppose k(r) = 0. What is r?
2
Let d = -112 - -169. Suppose 3*z - d = -27. Factor -5*i**3 - 29*i**2 - 32*i**2 + 76*i**2 - z*i.
-5*i*(i - 2)*(i - 1)
Suppose -39*s + 36*s = -9. Solve -2 + 4*z - 5 + 2*z**2 + 4*z - s = 0 for z.
-5, 1
Let u(s) be the first derivative of -2/15*s**5 - 81 - 17/18*s**4 - 4/3*s**2 + 0*s - 56/27*s**3. What is h in u(h) = 0?
-3, -2, -2/3, 0
Let q = -65/557 + 1569/3899. Factor 0*i**4 + 2/7*i**3 - q*i**5 + 0 + 0*i**2 + 0*i.
-2*i**3*(i - 1)*(i + 1)/7
Find w, given that -1/5*w**4 - 7/10*w**3 - 1/5*w**2 + 3/10*w + 0 = 0.
-3, -1, 0, 1/2
Let f(a) be the third derivative of -a**6/420 - 2*a**5/105 + a**4/84 + 4*a**3/21 + 2406*a**2. Factor f(y).
-2*(y - 1)*(y + 1)*(y + 4)/7
Let z(v) = -v**2 - 8*v - 11. Let s be z(-5). Factor -50*x - s*x**3 + 18*x + 15*x - x**4 + 6*x**2 + 21*x - 5.
-(x - 1)**2*(x + 1)*(x + 5)
Factor -860*y - 703584*y**2 + 351977*y**2 + 351903*y**2 + 568 - 4*y**3.
-4*(y - 71)*(y - 2)*(y - 1)
Suppose 0*q**3 + 0 - 1/6*q**4 + 1/2*q**2 + 1/3*q = 0. Calculate q.
-1, 0, 2
Factor -45 - 21 + 20 - 14*m - 2*m**2 + 62*m.
-2*(m - 23)*(m - 1)
Let b(z) be the third derivative of z**8/588 + 83*z**7/735 + 547*z**6/420 + 1291*z**5/210 + 377*z**4/28 + 102*z**3/7 - 1073*z**2. Suppose b(d) = 0. What is d?
-34, -3, -1, -1/2
Let u = -35 + 69. Factor 34*k - 2*k**3 - u*k**2 + 5*k - 19 - 19 + 35*k.
-2*(k - 1)**2*(k + 19)
Let u be (-2 - (-28)/6) + 22/(-33). Let -2*f - 18*f**4 - 40615*f**2 - 5*f**3 + u*f + 40640*f**2 + 5*f**5 - 7*f**4 = 0. Calculate f.
-1, 0, 1, 5
Let d(n) be the third derivative of n**6/720 + n**5/10 - 85*n**4/36 + 44*n**3/3 - 691*n**2. Suppose d(y) = 0. Calculate y.
-44, 2, 6
Let u(i) = 3*i**3 + 815*i**2 + 882*i + 5. Let p(z) = -3*z**3 - 829*z**2 - 882*z - 4. Let r(x) = -5*p(x) - 4*u(x). Suppose r(y) = 0. What is y?
-294, -1, 0
Let z(v) be the third derivative of 5/2*v**3 + 2*v**2 + 5/24*v**4 - 1/24*v**6 - 1/4*v**5 + 0 + v. Determine c, given that z(c) = 0.
-3, -1, 1
Let x = -1511 - -1515. Let m(a) be the second derivative of -15*a - 1/30*a**5 + 0*a**2 + 0*a**3 + 0*a**x + 0 + 1/90*a**6. Factor m(q).
q**3*(q - 2)/3
Let f(m) = -4114*m + 69941. Let w be f(17). Factor 1/6*s**2 + 0 + w*s.
s*(s + 18)/6
Let l = 2551039/892871 + 3/127553. Factor 1/7*d**5 + l*d**2 + 0 - 39/7*d**3 + 0*d + 18/7*d**4.
d**2*(d - 1)**2*(d + 20)/7
Let o = -13114 + 1036026/79. Let t = 197/158 + o. Determine y, given that -3/4*y + 3/4*y**3 + t*y**4 + 0 - 3/2*y**2 = 0.
-1, -1/2, 0, 1
Let n(z) be the third derivative of z**8/2856 - 134*z**7/1785 + 433*z**6/85 - 22997*z**5/255 + 40931*z**4/204 - 2941*z**2 + z. Determine b, given that n(b) = 0.
0, 1, 11, 61
Let x(m) be the first derivative of -4/3*m**3 - 1296*m - 82 - 72*m**2. Let x(g) = 0. What is g?
-18
Let q = -324027 + 324030. Factor 39/5*n**2 + 0 - 3/5*n**q - 66/5*n.
-3*n*(n - 11)*(n - 2)/5
Factor 148/5*x**4 + 340736/5 - 3992/5*x**3 - 216832/5*x - 2/5*x**5 + 9328*x**2.
-2*(x - 22)**3*(x - 4)**2/5
Let k(l) be the second derivative of 0*l**2 + 0*l**3 + 2/33*l**4 + 22*l - 1/55*l**6 - 1/231*l**7 + 2 + 0*l**5. Factor k(y).
-2*y**2*(y - 1)*(y + 2)**2/11
Let k(j) be the second derivative of 0*j**2 + 0 - 2/75*j**5 + 1/900*j**6 + 36*j + 11/6*j**3 + 0*j**4. Let d(w) be the second derivative of k(w). Factor d(s).
2*s*(s - 8)/5
Suppose -7*i - 52*i - 105 = -80*i. Factor -2/3 - 19/3*d**3 + 2*d**i - 5/3*d**4 + 9*d**2 - 7/3*d.
(d - 1)**3*(d + 2)*(6*d + 1)/3
Let j(w) be the third derivative of w**8/420 - w**6/90 + 181*w**3/6 + 66*w**2. Let i(m) be the first derivative of j(m). Let i(g) = 0. What is g?
-1, 0, 1
Determine x so that 484/3 + 75*x**2 + 220*x = 0.
-22/15
Let v(m) = 13*m**3 + 20*m**2 - 54*m - 3. Let a be v(5). Let r = -9248/5 + a. What is i in -r*i**2 + 0 + 12/5*i**3 + 0*i - 3/5*i**4 = 0?
0, 2
Let o(m) be the third derivative of -m**2 - 40/33*m**4 - 3 + 6400/33*m**3 + 1/330*m**5 + 0*m. Factor o(l).
2*(l - 80)**2/11
Let w(h) be the second derivative of -h**4/32 + 83*h**3/4 - 993*h**2/16 - 167*h + 2. Find a, given that w(a) = 0.
1, 331
Let m = 4025464 - 5382044972/1337. Let s = m + -2/191. Factor 2/7*n**2 + 0*n - s*n**4 + 0 + 2/7*n**5 - 2/7*n**3.
2*n**2*(n - 1)**2*(n + 1)/7
Let b(i) be the second derivative of i**4/24 + 17*i**3/2 + 297*i**2/4 + 2423*i. Factor b(r).
(r + 3)*(r + 99)/2
Let h(i) = -i**2 + i + 1. Let g(s) be the second derivative of s**5/4 + 7*s**4/6 - 29*s**3/6 - 17*s**2 - 2*s. Let c(v) = -g(v) - 4*h(v). Solve c(n) = 0.
-3, -1, 2
Let u(b) be the first derivative of -b**3/12 - 17*b**2/8 - 15*b + 1057. Solve u(t) = 0 for t.
-12, -5
Let v(s) be the first derivative of 27*s**5/5 + 237*s**4/4 + 54*s**3 - 24*s**2 + 3204. Solve v(n) = 0.
-8, -1, 0, 2/9
Suppose -3*j + 5*j = 4. Suppose 4*k = -2*d + 326, 0*k - 157 = -j*k + 5*d. Find g such that k*g**3 + 7*g - 77*g**3 - 7*g + 20*g**2 = 0.
-5, 0
Let m(n) be the first derivative of -2*n**5/35 - 26*n**4/7 - 664*n**3/7 - 8320*n**2/7 - 51200*n/7 - 512. Determine r so that m(r) = 0.
-16, -10
Let v = -18715 - -393019/21. Let o(k) be the second derivative of 0*k**2 - 32*k + v*k**3 - 1/105*k**6 - 4/21*k**4 + 1/14*k**5 + 0. Determine l so that o(l) = 0.
0, 1, 2
Suppose 5*r - 4066*q - 9 = -4069*q, 0 = q - 3. Factor -16/7*g + r - 18/7*g**2 - 2/7*g**3.
-2*g*(g + 1)*(g + 8)/7
Let s(m) be the third derivative of 5/14*m**4 - 1/210*m**5 + 2*m**2 - 2 + 0*m - 75/7*m**3. Let s(x) = 0. What is x?
15
Find q such that 0 - 252*q - 51*q**3 + 93/4*q**4 - 327*q**2 - 3/4*q**5 = 0.
-2, -1, 0, 6, 28
Let p = 1331 + -1331. Let x(v) be the first derivative of -v**3 + 0*v**2 + 3/5*v**5 + p*v**4 + 16 + 0*v. Let x(j) = 0. Calculate j.
-1, 0, 1
Let q(z) = -5*z**3 - z**2 - 2*z. Let p(u) = 68*u**3 + 26*u**2 + 138*u. Let r(d) = -p(d) - 14*q(d). Factor r(h).
2*h*(h - 11)*(h + 5)
Let q(u) = -7*u**3 + 3*u**2 - 2*u + 2. Let l(i) = i - 1. Let h(p) = 6*l(p) + 3*q(p). Factor h(k).
-3*k**2*(7*k - 3)
Let u(a) = -11*a**3 + 29*a**2 + 256*a + 1008. Let i(c) = 12*c**3 - 30*c**2 - 256*c - 1056. Let w(n) = -9*i(n) - 10*u(n). Factor w(r).
2*(r - 18)*(r + 4)**2
Let d = 216 + -210. Let o be 1*60/(-45)*d/(-4). Find m such that 2/7*m**3 - 2/7 - 2*m**o + 16/7*m**4 + 8/7*m**5 - 10/7*m = 0.
-1, -1/2, 1
Let j(p) = 4*p**2 - 75*p - 3. Let d(a) = 3*a**2 - 75*a - 2. Let v(i) = -3*d(i) + 2*j(i). Factor v(l).
-l*(l - 75)
Let u(f) be the second derivative of f**6/90 + 53*f**5/60 - 61*f**4/3 + 1528*f**3/9 - 2080*f**2/3 + 3801*f. Factor u(o).
(o - 4)**3*(o + 65)/3
Let n(r) be the second derivative of 16/21*r**3 - 63*r - 5/21*r**4 + 1/35*r**5 + 0 - 8/7*r**2. Factor n(p).
4*(p - 2)**2*(p - 1)/7
Let z = 337478 + -337476. Factor 22/5*k**4 - 2/5*k**5 - 16/5*k + 0 - 54/5*k**3 + 10*k**z.
-2*k*(k - 8)*(k - 1)**3/5
Suppose -300 - 55/3*o + 5/3*o**2 = 0. Calculate o.
-9, 20
Let c(g) = -g**2 - 5*g - 1. Suppose -9*a = 17 + 10. Let h be c(a). Solve -8*t**5 + 3*t**5 - 9*t**4 + h*t**2 + 5*t**3 + 4*t**4 = 0.
-1, 0, 1
Let c(a) be the first derivative of -1/9*a**3 - 300*a + 87 - 10*a**2. Factor c(b).
-(b + 30)**2/3
Factor 265 + 5/4*n**2 + 135*n.
5*(n + 2)*(n + 106)/4
Let u be (-44)/(-154) + (1 - 2/7). Let f be u/10 + 1/15. Factor 2 - 8/3*l + 7/6*l**2 - f*l**3.
-(l - 3)*(l - 2)**2/6
Let f(w) be the second derivative of -1/20*w**4 + 39/10*w**2 + 89*w + 6/5*w**3 + 0. Factor f(m).
-3*(m - 13)*(m + 1)/5
Let l(x) = -4*x**5 + 28*x**3 - 8*x**2 - 47*x + 32. Let m(z) = z. Suppose -3*i = -5*d - 3 - 4, 3*d + 1 = i. Let c(u) = d*l(u) - m(u). Solve c(a) = 0.
-2, 1, 2
Let f(u) be the second deri