7306. Determine z, given that r(z) = 0.
-3, 0, 9
Let z = -2634143/4 - -658537. Factor 25/4*p**2 - 10*p + z*p**3 + 4 - 5/4*p**4 - 1/4*p**5.
-(p - 1)**3*(p + 4)**2/4
Let g(a) be the third derivative of -1/10*a**4 + 0 + 16/15*a**3 - 204*a**2 - 1/150*a**5 + 0*a. Factor g(p).
-2*(p - 2)*(p + 8)/5
Let n(t) be the second derivative of 9*t**2 + 0 + 10/3*t**3 - 4/3*t**4 - 1/15*t**6 + 18*t - t**5. Solve n(i) = 0 for i.
-9, -1, 1
Suppose 14*z + 1072 = 22*z. Factor t**3 - 4*t**3 - z*t**2 + 164*t**2 + 42 - 69*t.
-3*(t - 7)*(t - 2)*(t - 1)
Suppose 0 = -3*v + 4*w - 3, -8*v + 9*v = -5*w + 18. Let y(f) be the first derivative of 0*f - 1 + 0*f**2 + 1/4*f**4 - 1/3*f**v. Factor y(j).
j**2*(j - 1)
Let g(h) be the second derivative of -11/8*h**4 + 3/40*h**5 + 13/2*h**3 - 12*h**2 + 0 + 150*h. Determine a, given that g(a) = 0.
1, 2, 8
Let z = 1093 - 1091. Let m be (40/36)/(z/9). Solve -f**4 + 6/5*f + f**2 - 1/5*f**m - f**3 + 0 = 0 for f.
-3, -2, -1, 0, 1
Let h(p) be the third derivative of 0 - 7/24*p**6 + 1/12*p**5 + 0*p**3 + 35/24*p**4 - 1/42*p**7 + 0*p - 23*p**2. Solve h(l) = 0 for l.
-7, -1, 0, 1
Let a be (-1*(0 + 30))/(19 + -17). Let t(i) = 3*i**3 + 46*i**2 + 17*i + 30. Let k be t(a). Factor 0*l**3 + k*l - 3/5*l**4 + 3/5*l**2 + 0.
-3*l**2*(l - 1)*(l + 1)/5
Let b(w) be the first derivative of -w**3 + 207*w**2/2 + 117. Factor b(a).
-3*a*(a - 69)
Let g(t) = -4*t**3 + 215*t**2 - 417*t + 208. Let u(f) be the first derivative of -f**4/4 + 2*f**3/3 + f + 150. Let v(j) = g(j) - u(j). Factor v(a).
-3*(a - 69)*(a - 1)**2
Let q = 1 + 2. Let y(u) = -214*u + 13496. Let a be y(63). Factor a*r**q + 4*r + 0*r**4 - 20*r**2 - 12*r**4 + 14*r**3.
-4*r*(r - 1)**2*(3*r - 1)
Let x(t) be the first derivative of -66 - 2/27*t**3 - 338/9*t + 26/9*t**2. Solve x(d) = 0.
13
Let m = 3 - 1. Suppose 24 = 2*x - 2*v - 3*v, 18 = 5*x - m*v. Factor 0 - 12*f - 2 - 6*f**x - f.
-(f + 2)*(6*f + 1)
Let r(m) be the second derivative of m**6/6 - 17*m**5/20 - 73*m**4/4 - 105*m**3/2 + 81*m**2 + 820*m - 3. Factor r(v).
(v - 9)*(v + 3)**2*(5*v - 2)
Let q(d) be the third derivative of -11/20*d**5 + 0*d**3 + 0*d + 3/4*d**4 + 97*d**2 + 0. Find w such that q(w) = 0.
0, 6/11
Suppose 2*p + 9 = c, 4*p = -4*c - 23 - 13. Let f(u) = -u**3 - 2*u**2 + u. Let q(l) = l**3 + 47*l**2 - 86*l + 60. Let k(y) = p*f(y) - q(y). Factor k(a).
5*(a - 3)*(a - 2)**2
Let g(c) be the first derivative of c**6/24 - 35*c**4/24 - 5*c**3 + 7*c**2 + 2. Let m(o) be the second derivative of g(o). Suppose m(h) = 0. Calculate h.
-2, -1, 3
Let a be 4/(-14) + (-3140)/(-14). Suppose -d + 1 = -3*h + 4, 2*h + 3*d - 13 = 0. Factor -w**3 + 222*w**5 + 4*w**h + 7*w**3 - a*w**5.
-2*w**2*(w - 2)*(w + 1)**2
Let x(d) be the first derivative of -2*d**3/33 - 73*d**2/11 - 144*d/11 + 2349. Factor x(s).
-2*(s + 1)*(s + 72)/11
Suppose 0 - 1/6*r**2 + 555/2*r = 0. Calculate r.
0, 1665
Factor -60*r**4 + 5*r**5 + 105*r**3 + 594*r**2 + 638*r**2 - 1282*r**2.
5*r**2*(r - 10)*(r - 1)**2
Let f(c) = 2*c**3 + 288*c**2 - 1142*c + 1132. Let j(x) = -10*x**3 - 1150*x**2 + 4567*x - 4526. Let k(b) = 9*f(b) + 2*j(b). Let k(y) = 0. Calculate y.
2, 142
Let q = -802847/48 - -16726. Let i(s) be the second derivative of 0*s**2 - 33*s + q*s**4 + 0 - 5/24*s**3. Factor i(x).
x*(x - 5)/4
Let a(s) = -s**3 + 19*s**2 - 31*s - 48. Let z be a(17). Suppose 0*c + 2*c + 35*c**2 - 54*c**2 + 28*c**2 - 5*c**z = 0. Calculate c.
-1/5, 0, 2
Let x(l) = -l**2 - 6*l + 1. Let j(k) = -4*k**3 + 43*k**2 - 158*k + 161. Let w(v) = -j(v) + x(v). Suppose w(u) = 0. Calculate u.
2, 4, 5
Let q(h) be the first derivative of h**7/105 - h**6/60 - h**5/6 - h**4/4 + 9*h**2/2 - 61. Let k(n) be the second derivative of q(n). Let k(z) = 0. What is z?
-1, 0, 3
Factor 0*n + 22*n**2 - 2/3*n**4 + 0 - 16/3*n**3.
-2*n**2*(n - 3)*(n + 11)/3
Let d(i) be the first derivative of -1/6*i**4 + 20/9*i**3 - 48*i - 93 - 4*i**2. Solve d(v) = 0 for v.
-2, 6
Let w be 73 - 72 - -1*1. Find a, given that 12*a**3 + 979*a**2 + 3*a - w*a**5 + 3*a - 995*a**2 = 0.
-3, 0, 1
Factor -6498/13*d + 34/13*d**2 + 764/13.
2*(d - 191)*(17*d - 2)/13
Let h(z) be the second derivative of z**4/8 + 197*z**3/4 + 147*z**2 + 11*z + 77. Factor h(j).
3*(j + 1)*(j + 196)/2
Let o(c) be the first derivative of 0*c**5 - 15 + 5*c + 0*c**2 + 0*c**4 + 1/150*c**6 + 0*c**3. Let i(v) be the first derivative of o(v). Factor i(b).
b**4/5
Let h be ((-3)/36)/((-5)/(-180)*-4). Let y(w) be the first derivative of -h*w**4 + 0*w + w**3 + 2 + 3*w**2. Factor y(f).
-3*f*(f - 2)*(f + 1)
Suppose 6/5*l**2 + 1084/15*l + 16 = 0. Calculate l.
-60, -2/9
Let m(y) = -53*y**2 - 28*y + 199. Let q(l) = -9*l**2 + 2. Let z(b) = -5*m(b) + 30*q(b). Find c, given that z(c) = 0.
11, 17
Let y be 8/10*(10/(-4) - -4). Factor 0 - y*l + 2/5*l**4 - 2/5*l**3 - 2*l**2.
2*l*(l - 3)*(l + 1)**2/5
Suppose 4*h = 0, -3*i + 6 = h - 4*h. Factor 63*m**i - 36*m**2 - 40*m - 31*m**2 - 36.
-4*(m + 1)*(m + 9)
Let c be (3 + 7 + -9)*(0 + 99). Factor c*t + 21 + 57*t - 13 + 7*t**2 + 36.
(t + 22)*(7*t + 2)
Suppose q = 4*b - 5 - 123, 2*b - 78 = -3*q. Suppose -y - 30 + b = 0. Let -4 - 3*d**2 + 8 + 4*d**y + 70*d**4 + 4*d - 71*d**4 - 8*d**3 = 0. Calculate d.
-2, -1, 1
Factor 32/3 - 20/3*h + 2/3*h**2.
2*(h - 8)*(h - 2)/3
Let s = -298/13 - -687/26. Let k(f) be the third derivative of 0 + 0*f + 49/20*f**5 - 2*f**2 + 2*f**3 - s*f**4. Factor k(w).
3*(7*w - 2)**2
Factor -2/9 - 6962*c**2 + 236/3*c.
-2*(177*c - 1)**2/9
Let j(m) = m - 21. Let w be j(22). Let c = w + 24. What is s in 0*s**4 - 4*s**4 - 25*s - 20*s**2 + 15 - 6*s**4 + 15*s**2 + c*s**3 = 0?
-1, 1, 3/2
Let h = 64 + -62. Suppose 3*c - 6 = 4*y + 7, 0 = 3*c - h*y - 11. Factor -92*x**2 + 80*x**2 - 3*x**5 + 6*x**4 + c*x**4.
-3*x**2*(x - 2)**2*(x + 1)
Let a be 28/189*53/848. Let g(m) be the third derivative of -1/270*m**5 + 0*m + 4*m**2 + 0 + 2/9*m**3 - a*m**4. Factor g(j).
-2*(j - 2)*(j + 3)/9
Let k = 595103 + -595043. Find x, given that -48*x - 24 - k*x**3 + 21/2*x**4 + 108*x**2 = 0.
-2/7, 2
Factor 143*o**2 + 44*o**3 - 29*o + 0*o**3 - 135*o**2 - 15*o - 8.
4*(o - 1)*(o + 1)*(11*o + 2)
Let x be -6*9/27 - (-1028)/(-2). Let v = 8822/17 + x. What is c in -2/17*c**2 - v - 20/17*c = 0?
-5
Let o(k) be the third derivative of k**5/300 - 41*k**4/120 + 19*k**3/5 - k**2 + 35*k - 14. Let o(v) = 0. What is v?
3, 38
Determine u so that -72/7*u + 0 - 2/7*u**3 + 74/7*u**2 = 0.
0, 1, 36
Let p(h) be the third derivative of 7*h**6/30 + 4141*h**5/30 - 445*h**4/6 - 592*h**3/3 + 270*h**2 - 6*h. Solve p(m) = 0.
-296, -2/7, 1/2
Let y(d) be the first derivative of d**5/5 + 5*d**4/14 - 12*d**3/7 - 20*d**2/7 + 32*d/7 - 1513. Factor y(p).
(p - 2)*(p + 2)**2*(7*p - 4)/7
Let n(g) be the first derivative of -13*g**5/3 - 185*g**4/12 + 95*g**3/9 + 185*g**2/6 - 10*g - 474. What is t in n(t) = 0?
-3, -1, 2/13, 1
Let h be ((-82)/(-205))/(4/((-12960)/(-264))). Find z, given that -1080/11*z**3 + 7200/11*z**2 + h*z**4 - 16000/11*z + 0 = 0.
0, 20/3
Let s(k) = 2*k**3 - 15*k**2 + 2*k + 25. Let q be s(8). Factor 10*n - 5*n**3 - 45*n - 80*n**2 - q*n + 0*n.
-5*n*(n + 2)*(n + 14)
Factor -277*x**2 + 587*x**2 - 1120*x + 61857 - 375457 - 311*x**2.
-(x + 560)**2
Suppose -273*y + 5 = 5. Let z(f) be the second derivative of 1/336*f**7 + 11*f + 0*f**4 + 0*f**6 + y*f**3 - 1/160*f**5 + 0 + 0*f**2. Let z(b) = 0. What is b?
-1, 0, 1
Let a(g) be the third derivative of 0 - 4/3*g**3 + 0*g + 1/180*g**5 - 23/72*g**4 + 147*g**2. Let a(c) = 0. What is c?
-1, 24
Suppose -o = q - 4*q, 0 = 4*o - 3*q + 5*q. Let -c + 1/4*c**2 + 1/8*c**3 + o = 0. Calculate c.
-4, 0, 2
Let j be (-12)/(-26) + (-770)/(-97240)*432. Factor -j - 2/17*a + 66/17*a**2 + 2/17*a**3.
2*(a - 1)*(a + 1)*(a + 33)/17
Let a(z) be the second derivative of 0 + 128*z + 1/12*z**4 - 5*z**2 + 13/4*z**3. Factor a(i).
(i + 20)*(2*i - 1)/2
Let y(g) = 5*g**2 - 8*g + 9. Let k(p) = -7*p**2 + 7*p - 9. Suppose 10*t + 23 = -7. Let v(b) = t*y(b) - 2*k(b). Factor v(x).
-(x - 9)*(x - 1)
Let f(a) be the third derivative of a**7/70 + 7*a**6/30 + 13*a**5/15 - 2*a**4 - 3523*a**2. Let f(x) = 0. Calculate x.
-6, -4, 0, 2/3
Determine d so that 9*d**5 - 255*d**4 + 437*d - 5830*d**2 + 1963*d**3 + 458*d + 131*d**4 - 18*d**5 + 305*d = 0.
-24, 0, 2/9, 5
Let o = -123 - -140. Factor -135*f - 108 - o*f**2 + 30*f**3 - 22*f**2 - f**4 - 2*f**4 - 45*f.
-3*(f - 6)**2*(f + 1)**2
Let r(p) be the first derivative of p**3/27 - 25*p**2