 24. Let w = g - 28. Suppose -2/7*j**3 + 0*j - 4/7*j**2 + w = 0. Calculate j.
-2, 0
Let g(a) be the third derivative of a**6/840 - a**4/56 - a**3/21 - 14*a**2 - 3. Factor g(b).
(b - 2)*(b + 1)**2/7
Let z be 27/126*7*50/15. Solve -z - 5/4*v**3 - 10*v - 25/4*v**2 = 0 for v.
-2, -1
Let f = 6 + -3. Let h(g) = -2 + 9*g + 1 - 8*g - g**2 - 7*g. Let c(i) = i**2 + 5*i. Let t(v) = f*h(v) + 4*c(v). Find z such that t(z) = 0.
-3, 1
Let b = -7654 + 7656. Find k such that 7/4*k + 0 + 1/4*k**b = 0.
-7, 0
Let g = 32 - -39. Let m = 356/5 - g. Factor -2/5*l**2 + 0 + 0*l - m*l**4 - 3/5*l**3.
-l**2*(l + 1)*(l + 2)/5
Factor 0 + 2/9*y**2 - 2/9*y.
2*y*(y - 1)/9
Let k be (-17)/(-4) + (-13)/52. Let v(g) be the first derivative of 1/6*g**6 - 3/4*g**k + g**2 + 0*g + 1/5*g**5 + 7 - 1/3*g**3. Suppose v(m) = 0. What is m?
-2, -1, 0, 1
Let k be (-15)/40*(-15)/(-9) + 1. Let d(w) be the second derivative of 0*w**2 - k*w**3 - 5*w + 0 + 5/16*w**4. Factor d(f).
3*f*(5*f - 3)/4
Let u(i) = -40*i**4 - 30*i**3 + 50*i**2 + 30*i. Let x(c) = -20*c**4 - 15*c**3 + 25*c**2 + 15*c - 1. Let k(a) = 2*u(a) - 5*x(a). Factor k(t).
5*(t - 1)*(t + 1)**2*(4*t - 1)
Let j = -2950 - -141595/48. Let l = j + 697/240. Suppose 2/5*r**5 - 4/5 - 4/5*r**3 - l*r + 4/5*r**4 - 16/5*r**2 = 0. Calculate r.
-1, 2
Let p(n) be the first derivative of -n**6/2 + 6*n**5/5 - 2*n**3 + 3*n**2/2 + 27. Solve p(i) = 0 for i.
-1, 0, 1
Let w be 6/(-21) + (-2)/(-7). Suppose 0 = -z - 4, 7*d - 3*d + 4*z + 8 = w. Find r, given that -3/4*r**5 + 0 - 1/4*r**4 + 0*r + 0*r**d + 0*r**3 = 0.
-1/3, 0
Suppose 2*f + 2 = 6. Find w such that -26*w**4 - 25*w + 2 + 9*w**2 - 25*w**f + 34*w**3 + 24*w + 7*w**5 = 0.
-2/7, 1
Factor 65*a**2 + 85/2 + 427/4*a + 3/4*a**3.
(a + 1)*(a + 85)*(3*a + 2)/4
Let u be ((-27)/6 - -4)/(2/4). Let s be u/(-2) + (66/4)/11. Factor 60/7*w**s + 72/7*w - 50/7*w**3 + 16/7.
-2*(w - 2)*(5*w + 2)**2/7
Factor -163 + 2*n**2 - 229 + 616 + 44*n.
2*(n + 8)*(n + 14)
Let w(z) = -z**5 - z**2 + z - 1. Let m(d) = -10*d**5 + 50*d**4 - 165*d**3 + 195*d**2 - 75*d - 5. Let y(l) = -m(l) + 5*w(l). Let y(i) = 0. Calculate i.
0, 1, 4
Suppose -39 = -3*m + 24. Suppose m = 3*u - w, w - 7 = -u - 0. Factor 21*s**2 + 24 + 61*s - 10*s**2 + u*s**2 - 25*s + 3*s**3.
3*(s + 2)**3
Let v(a) be the third derivative of -a**7/420 + 19*a**6/240 - 7*a**5/24 + 17*a**4/48 - 5*a**2 + 29*a. Determine l, given that v(l) = 0.
0, 1, 17
Let f(o) = -2*o**2 + 26*o + 25. Let q(n) = -n**2 + 12*n + 13. Let w(b) = -3*f(b) + 7*q(b). Find k, given that w(k) = 0.
-2, 8
Factor 8*q**2 + 18*q - 42*q + 24*q - 2*q**3 - 2*q**4 + 16*q**2.
-2*q**2*(q - 3)*(q + 4)
Let j be (-36)/48 - 105/(-138). Let m = 11/46 + j. Factor m*a**2 + 1/4 + 1/2*a.
(a + 1)**2/4
Let k(n) = -n**3 - 3*n**2 - n - 1. Let j be k(-3). Let l be 1/2 + (-85)/(-10). Factor -j*d**2 - 9*d - l + 5 + 3*d.
-2*(d + 1)*(d + 2)
Suppose 134 + 26 = 5*u. Let k = u - 30. Solve -16/3*o - 5*o**k - 4/3 = 0 for o.
-2/3, -2/5
Let h(k) be the third derivative of -1/480*k**6 + 0 + 1/120*k**5 - 18*k**2 + 0*k + 0*k**4 + 0*k**3. Factor h(a).
-a**2*(a - 2)/4
Let t(x) = 9*x**5 + 77*x**4 + 191*x**3 + 180*x**2 + 55*x - 1. Let z(l) = l**5 - l**4 + l**3 - l + 1. Let w(c) = -t(c) - z(c). Let w(d) = 0. Calculate d.
-3, -1, -3/5, 0
Let r(m) be the second derivative of m**5/120 + m**4/24 + m**3/12 - 41*m**2/2 - 45*m. Let d(a) be the first derivative of r(a). Factor d(l).
(l + 1)**2/2
Solve 4 + 34/5*j + 2/5*j**3 + 16/5*j**2 = 0 for j.
-5, -2, -1
Let l(j) be the first derivative of -j**6/60 + 21*j**4/40 + 2*j**3/3 + 34. Solve l(i) = 0.
-4, -1, 0, 5
Suppose 66 = 6*f + 5*f. Determine z so that -199*z**3 + 200*z**3 - 2*z**2 - 5*z + f*z**2 = 0.
-5, 0, 1
Suppose 4*x - 12 = -4*c - c, 0 = 5*c + x - 3. Suppose -187*m + 5*z = -192*m, 2*z = m - 6. Factor c - 3/2*j**m + 9/2*j.
-3*j*(j - 3)/2
Suppose -8 = 5*w + 7. Let r(y) = -y**2 - 10*y - 18. Let k be r(w). Determine m, given that -4/11*m - 8/11*m**4 + 0 + 10/11*m**k + 14/11*m**2 = 0.
-1, 0, 1/4, 2
Let -172*x**3 + 177*x**3 - 160*x - 11*x**2 - 59*x**2 = 0. Calculate x.
-2, 0, 16
Let p(n) = 5*n**2 - 11*n + 13. Let m(c) be the third derivative of -c**5/20 + c**4/4 - c**3 + 15*c**2. Let l(z) = -11*m(z) - 6*p(z). Factor l(t).
3*(t - 2)*(t + 2)
Let v(q) be the second derivative of 5*q**7/42 + 11*q**6/10 + 33*q**5/10 + 7*q**4/3 - 4*q**3 + 41*q. Factor v(m).
m*(m + 2)**2*(m + 3)*(5*m - 2)
Let z be (-8)/(-6)*(-3)/2. Let q be 2 + z + (2 - (1 - -1)). Suppose 6/7*v**4 + q*v**2 - 2/7*v**3 + 0*v + 0 + 8/7*v**5 = 0. What is v?
-1, 0, 1/4
Let f(n) be the first derivative of n**4/3 + 2*n**3/9 - 4*n**2/3 - 2*n + 67. Factor f(u).
2*(u + 1)**2*(2*u - 3)/3
Let w(r) = 7*r**4 + 4*r**3 + 5*r**2 + 2*r + 6. Let m(j) = -6*j**4 - 5*j**3 - 7*j**2 - 3*j - 5. Let v(g) = -6*m(g) - 5*w(g). Find h, given that v(h) = 0.
-8, -1, 0
Let w(h) = -h**3 - 2 - 3*h + 6 - 5*h**2 - 1 - h. Let l be w(-4). Factor s**5 + 3*s**2 - l*s**4 + s**3 - s**2 - 2*s**5 + s**4.
-s**2*(s - 1)*(s + 1)*(s + 2)
Factor -2/3*d - 8/3 + 1/3*d**2.
(d - 4)*(d + 2)/3
Let s(m) be the first derivative of -5*m**4/8 + 50*m**3 - 1500*m**2 + 20000*m + 37. Factor s(i).
-5*(i - 20)**3/2
Let i = 177/4 - 44. Let q be 81/(-216) - (-10)/16. Factor 1/2*z - q*z**3 - i*z**2 + 0.
-z*(z - 1)*(z + 2)/4
Let v(o) be the second derivative of -o**8/7560 + o**7/11340 - o**4/4 - 6*o. Let w(i) be the third derivative of v(i). Determine g, given that w(g) = 0.
0, 1/4
Let d = -15 + 340. Let p be 115/d - (-1)/(-5). Suppose -2/13*w + 0 - p*w**2 = 0. What is w?
-1, 0
Let d(q) be the second derivative of -16*q + 0 + 405/2*q**2 + 5/12*q**4 - 15*q**3. Factor d(l).
5*(l - 9)**2
Suppose -67*d - 22 + 22 = 0. Let 0 - 2/5*x**4 + 0*x**3 + d*x - 2/5*x**5 + 0*x**2 = 0. Calculate x.
-1, 0
Factor 10*h + 2/7*h**3 - 38/7*h**2 - 34/7.
2*(h - 17)*(h - 1)**2/7
Let k(x) be the first derivative of -2*x**3/21 - 30*x**2/7 - 58*x/7 + 261. Suppose k(i) = 0. Calculate i.
-29, -1
Let f be 272/72 - 4/(-18). Suppose -2*l = -f*i - 20, -4*l + 2 - 14 = 5*i. Let 1/3*g**4 - 1/3*g**l - 2/3*g + 2/3*g**3 + 0 = 0. Calculate g.
-2, -1, 0, 1
Factor -5/2*f**3 - 3/2*f**2 + 0 - 1/2*f**4 + 0*f + 1/2*f**5.
f**2*(f - 3)*(f + 1)**2/2
Factor 18*p + 114*p**2 - 113*p**2 - 20*p - 8.
(p - 4)*(p + 2)
Factor -3/4*f**2 + 3/4*f**3 + 0*f + 0.
3*f**2*(f - 1)/4
Let y(n) be the third derivative of n**10/75600 - n**9/30240 - n**8/10080 + n**7/2520 + n**5/5 + 8*n**2. Let h(c) be the third derivative of y(c). Factor h(p).
2*p*(p - 1)**2*(p + 1)
Let k(o) be the third derivative of -o**6/140 + 13*o**5/210 + 11*o**4/84 - 5*o**3/21 + 9*o**2 + o. Factor k(d).
-2*(d - 5)*(d + 1)*(3*d - 1)/7
Let r = 11 + -63. Let t = -52 - r. Factor 2/7*g**3 + t + 8/7*g**2 + 8/7*g.
2*g*(g + 2)**2/7
Determine z, given that 42*z + 74*z - 2*z**3 - 50*z + 66*z**2 - z**3 + 312 + 234*z = 0.
-2, 26
Let c be ((-12)/(-18))/(2/9). Suppose 2*p - 12 = -c*d, -4*p + 9 = p - 3*d. Find u such that 4*u**3 - u**4 - u**3 - u**3 + p*u**4 = 0.
-1, 0
Let b(x) be the first derivative of -x**3/33 + 3*x**2/11 + 16*x/11 + 93. Suppose b(i) = 0. Calculate i.
-2, 8
Let x(d) be the second derivative of d**6/10 - 63*d**5/10 + 397*d**4/4 + 462*d**3 + 726*d**2 + d + 121. Find f such that x(f) = 0.
-1, 22
Let t be (-234)/(-72) + (-1)/4. Factor 2*f**4 - 5*f**t + 15*f**3 + 9*f**2 + 8 + 17*f**2 + 2*f**3 + 24*f.
2*(f + 1)**2*(f + 2)**2
What is p in 7847*p**5 - 24*p + p**4 + 28*p**3 - 4*p**2 + 3*p**4 - 7851*p**5 = 0?
-2, -1, 0, 1, 3
Let a = -23 - -47. Suppose 0 = -6*n - 6*n + a. Factor 0 + 2/7*z - 2/7*z**n.
-2*z*(z - 1)/7
Let i(n) be the first derivative of 4*n**3/15 - 6*n**2/5 - 16*n/5 + 418. Find u, given that i(u) = 0.
-1, 4
Let i = 49163/132 + -2225/6. Let s = i - 15/11. Factor 1/2*t**2 - s*t**4 - 1/4*t**3 + 0*t + 0.
-t**2*(t - 1)*(t + 2)/4
Suppose -n = 3*r + 14, 5*n - 2*r - 9 = -28. Let c be 2*n/15*9/(-14). Determine u so that 1/7*u**3 + c*u + 1/7 + 3/7*u**2 = 0.
-1
Let a(m) = -2*m**3 - 39*m**2 - 24*m - 63. Let c be a(-19). Let w be c/24 + 4/6. Factor 50/7*j**3 + 2/7 + 32/7*j**5 - 10/7*j**w + 80/7*j**4 - 10/7*j.
2*(j + 1)**3*(4*j - 1)**2/7
Let y(k) be the third derivative of -1/360*k**6 + 0*k**3 + 1/1008*k**8 + 0*k + 0*k**4 + 0*k**7 + 0 + 0*k**5 - 10*k**2. Find j such that y(j) = 0.
-1, 0, 1
Let m = -4441 + 13327/3. Factor -m*x**2 + 4/3*x + 0.
-4*x*(x - 1)/3
Let g be 6/(-4)*(-8)/(-6). Let l(w) = -3*w**3 + 7*w**2 - 10*w - 4.