*a.
2*(c - 1)*(c + 7)
Let x be (-25)/2*(3 + -5). Solve -22*j + 2*j**3 - 3*j**3 - 2*j**3 + x*j = 0 for j.
-1, 0, 1
Let m(u) be the third derivative of -2*u**7/105 + u**6/6 - u**5/3 - 5*u**4/6 + 4*u**3 - 2*u**2 - 12*u. Determine o so that m(o) = 0.
-1, 1, 2, 3
Let f(b) be the first derivative of -b**7/420 + b**6/90 - b**5/60 - 2*b**3 + 11. Let z(x) be the third derivative of f(x). What is h in z(h) = 0?
0, 1
Suppose 3*r + 44 = 3*p + 7*r, 0 = -4*p - 4*r + 52. Suppose 2*q = -d + 2, -3*d + p = -q + 2. Determine z, given that 4/5*z + 2/5 + 2/5*z**d = 0.
-1
Let h be 3 + 186/(-136) + ((-49)/7)/(-28). Determine f so that -h + 0*f**2 + 2/17*f**3 - 24/17*f = 0.
-2, 4
Let t = 73 - 78. Let d be 4 - (8/t)/(-4 + 6). Let 0 - d*o**3 - 14/5*o**4 - 6/5*o**2 + 4/5*o = 0. Calculate o.
-1, 0, 2/7
Suppose 0 = -3459*f + 3447*f + 24. Let -3/2*j**5 + 0*j**4 + 9/2*j**3 + 0*j + 0 - 3*j**f = 0. What is j?
-2, 0, 1
Let v be ((0/(-17))/(-15))/(-2). Factor -40/7*i**4 + 0 + v*i + 0*i**2 + 6*i**5 + 8/7*i**3.
2*i**3*(3*i - 2)*(7*i - 2)/7
Let x(q) be the second derivative of 2/9*q**3 - 9*q - 3/2*q**2 - 5/18*q**6 - 11/36*q**5 + 1/18*q**4 + 0. Let z(l) be the first derivative of x(l). Factor z(f).
-(4*f - 1)*(5*f + 2)**2/3
Let r = 2369/4744 - -3/4744. Factor -7/2*w + 1 + r*w**4 + 9/2*w**2 - 5/2*w**3.
(w - 2)*(w - 1)**3/2
Let v(l) be the first derivative of -21 + 10*l + l**5 - 5/2*l**2 + 5/4*l**4 - 5*l**3. Factor v(h).
5*(h - 1)**2*(h + 1)*(h + 2)
Let w(r) be the second derivative of 0*r**3 + 0 + 2*r**2 - 1/30*r**5 + 3*r - 1/6*r**4. Let h(z) be the first derivative of w(z). Solve h(m) = 0 for m.
-2, 0
Let d(m) = -38*m + 110*m + 4*m**3 + m**3 - 32*m**2 - 45. Let q(f) = -35*f**3 + 225*f**2 - 505*f + 315. Let y(l) = -20*d(l) - 3*q(l). Factor y(u).
5*(u - 3)**2*(u - 1)
Let o(v) = 11*v - 9. Let d be o(-4). Let b = -157/3 - d. Factor 4/9*m - 10/9*m**2 + b*m**3 + 0.
2*m*(m - 1)*(3*m - 2)/9
Suppose -2*d - 5*x - 40 = 3*d, 3*x + 12 = 0. Let v be 0/(-2) - (d - 16/(-4)). Factor -2/3*g**2 - 2*g + v.
-2*g*(g + 3)/3
Suppose 2*d + 12 = 3*l - d, -d - 1 = 0. Determine n so that 15 + 3*n**3 - 15 - 6*n + l*n**2 = 0.
-2, 0, 1
Suppose -16 = 2*x + 4*o, x + 4*o + 14 = -2*x. Factor 10*m - m**2 + 15 + 0*m**2 - 4*m**x.
-5*(m - 3)*(m + 1)
Let y(i) be the second derivative of -4*i + 0 + 0*i**3 + 1/10*i**5 + 1/6*i**4 + 0*i**2. Solve y(p) = 0.
-1, 0
Let j(u) be the second derivative of u**5/510 - 4*u**3/51 - 9*u**2 - 35*u. Let q(m) be the first derivative of j(m). Solve q(o) = 0.
-2, 2
Let u be 2/(-6) + (-183)/(-9). Find o such that -7*o + 39*o**2 + u*o**3 + 9*o + 10*o - 7*o**2 = 0.
-1, -3/5, 0
Let f(x) be the third derivative of x**7/1050 + x**6/40 + 19*x**5/150 + x**4/5 - 6*x**2. Factor f(l).
l*(l + 1)*(l + 2)*(l + 12)/5
Suppose 2*y + y = 0, -3*y - 1944 = -3*r. Factor 3*m**3 - r + 6*m**2 + 648.
3*m**2*(m + 2)
Let z(d) be the second derivative of d**7/42 - d**6/10 - 9*d**5/20 - 5*d**4/12 - 2*d + 17. Factor z(k).
k**2*(k - 5)*(k + 1)**2
Let x(h) be the first derivative of 2/35*h**5 + 9 + 1/14*h**4 - 2/21*h**3 + 0*h - 1/7*h**2. Factor x(a).
2*a*(a - 1)*(a + 1)**2/7
Let r(f) = -40*f**3 - 36*f**2 - 89*f + 143. Let y(s) = -22*s**3 - 18*s**2 - 44*s + 72. Let c(b) = 6*r(b) - 11*y(b). Determine k so that c(k) = 0.
-3, 1, 11
Let -3/4*j**4 - 3*j**3 - 3/2*j - 15/4*j**2 + 0 = 0. Calculate j.
-2, -1, 0
Let g(o) be the third derivative of -1/60*o**4 + 1/600*o**6 + 0*o + 0*o**3 + 0 - 2*o**2 + 1/300*o**5. Determine q so that g(q) = 0.
-2, 0, 1
Suppose 361 = 63*q - 80. Let x(s) be the second derivative of 0 + 0*s**4 + 0*s**2 - q*s - 1/130*s**5 + 1/39*s**3. Factor x(n).
-2*n*(n - 1)*(n + 1)/13
Let v be (-2)/(-28)*-8*((-10)/4 - 8). Find q such that -6*q**2 + 0 + v*q**3 - 3/2*q**4 + 0*q = 0.
0, 2
Let a(m) = 5*m**2 + m + 4. Let n(x) = -12*x**2 - x - 9. Let v(s) = -5*a(s) - 2*n(s). Solve v(w) = 0.
-2, -1
Let y(g) be the second derivative of 19*g - 7/48*g**4 - g**2 - 5/4*g**3 + 0. Factor y(c).
-(c + 4)*(7*c + 2)/4
Let c(v) = -15*v**3 - 15*v**2 - 5*v. Let q(m) = 8*m**3 + 8*m**2 + 3*m. Let w(f) = -3*c(f) - 5*q(f). Solve w(p) = 0.
-1, 0
Let t(k) be the second derivative of k**5/10 + k**4/14 + 55*k - 1. Suppose t(x) = 0. Calculate x.
-3/7, 0
Suppose -n = 32*w - 33*w + 5, -3*w - 4*n = 6. Factor 6*p**w + 3 + 27/2*p.
3*(p + 2)*(4*p + 1)/2
Let v(g) be the third derivative of 1/40*g**6 + 0*g - 7*g**2 + 1/48*g**4 + 0 + 1/105*g**7 + 1/30*g**5 + 1/672*g**8 + 0*g**3. Factor v(o).
o*(o + 1)**4/2
Suppose 0 = -13*w + 5 - 5 + 26. Determine r so that 1/4*r**4 - 3/2*r**2 + r + w - 1/4*r**3 = 0.
-2, -1, 2
Let l(d) be the third derivative of -1/630*d**6 - 7*d**2 + 1/3528*d**8 + 1/105*d**5 + 0 + 1/252*d**4 + 0*d - 1/735*d**7 - 1/21*d**3. Find r such that l(r) = 0.
-1, 1, 3
Let 2/5*k**2 + 84*k + 4410 = 0. What is k?
-105
Let d = 400 + -14399/36. Let g(f) be the second derivative of 0 - 1/72*f**4 + d*f**3 + 4*f + 0*f**2. Determine i so that g(i) = 0.
0, 1
Let b(t) be the first derivative of -5*t**4/4 - 80*t**3/3 - 145*t**2/2 - 70*t + 141. Let b(d) = 0. Calculate d.
-14, -1
Let u(g) be the first derivative of -g**3/3 + 9*g**2/2 + 9. Factor u(n).
-n*(n - 9)
Let b(t) = 45*t**3 - 362*t**2 + 371*t - 56. Let a(s) = -s**3 + 2*s**2 + s. Let z(l) = a(l) + b(l). Factor z(v).
4*(v - 7)*(v - 1)*(11*v - 2)
Let k(g) = -g**3 - g**2 + 7*g + 10. Let i be k(-1). Factor -5/3*p**5 + 0*p**2 + 0 + 10/3*p**i - 5/3*p**4 + 0*p.
-5*p**3*(p - 1)*(p + 2)/3
Determine d so that 40*d**3 - 208 - 28*d**3 + 176*d - 188*d**2 + 256*d = 0.
2/3, 2, 13
Let g(u) be the second derivative of 0 - 11/20*u**5 + 1/2*u**2 - 2/15*u**6 - 8*u - 1/6*u**3 - 3/4*u**4. Factor g(b).
-(b + 1)**3*(4*b - 1)
Determine f, given that -1080/7*f**2 - 162/7 - 702/7*f - 96*f**3 - 128/7*f**4 = 0.
-3, -3/4
Let w be (-30)/(-8) - (-2)/8. Factor 16*h**4 - 25*h**3 - 10*h**2 + 45*h**4 - h**w.
5*h**2*(3*h - 2)*(4*h + 1)
Let z(q) be the third derivative of -1/24*q**4 - 1/10*q**5 + 0 + 1/120*q**6 + 0*q - 19*q**2 + q**3. Factor z(v).
(v - 6)*(v - 1)*(v + 1)
Let f = -22801 + 22801. Factor 0*t + 2/3*t**2 + f + 2/3*t**3.
2*t**2*(t + 1)/3
Let j(p) be the third derivative of p**3 - 1/20*p**5 + 0 + 0*p - 2*p**2 - 1/8*p**4. Factor j(g).
-3*(g - 1)*(g + 2)
Let c = -7/3 - -43/15. Let q(p) be the first derivative of -p**2 - c*p**3 - 6 - 1/10*p**4 - 4/5*p. Solve q(a) = 0.
-2, -1
Let c(v) be the second derivative of v**7/7 - 8*v**6/15 + 3*v**5/10 + v**4/3 - 13*v - 3. Determine k, given that c(k) = 0.
-1/3, 0, 1, 2
Let v(u) = 2*u + 1. Let d(g) = 5*g**3 + 60*g**2 + 237*g + 256. Let b(r) = -d(r) + 6*v(r). Factor b(x).
-5*(x + 2)*(x + 5)**2
Let x be 2*6/3 - 0. Suppose x*t - 3*g - 10 = 3, -3*t = 5*g - 17. Factor -y**t + 5*y**3 - 3*y**3 - 10*y - y**4 + 6*y**2 + 4 + 0.
-2*(y - 1)**3*(y + 2)
Let j(d) = 29*d + 1. Let o be j(1). Let a be (-6)/4 + (4 - (-9)/o). Factor -a*b**2 + 0 + 8/5*b**3 - 4/5*b.
2*b*(b - 2)*(4*b + 1)/5
Let m(r) be the second derivative of 2*r**7/21 - 2*r**6/3 + 7*r**5/5 - r**4 + 225*r. Determine n, given that m(n) = 0.
0, 1, 3
Suppose -6*o = -15*o. Let a(w) be the first derivative of o*w + 0*w**3 + 6 - 1/22*w**4 + 1/11*w**2. Factor a(p).
-2*p*(p - 1)*(p + 1)/11
Let -4/17*j**2 - 20/17*j**3 + 10/17 + 2/17*j**5 + 18/17*j - 6/17*j**4 = 0. Calculate j.
-1, 1, 5
Let m**5 + 28*m**2 - 11 + 27 + 15*m**4 + 31*m**3 + 45*m + 42*m**2 + 19*m**3 - 5 = 0. What is m?
-11, -1
Let w(g) be the first derivative of g**5/25 + g**4/10 - g**3/5 - 2*g**2/5 + 4*g/5 - 57. Factor w(x).
(x - 1)**2*(x + 2)**2/5
Let g(f) be the second derivative of f**7/1680 + f**6/720 - 3*f**3/2 - 5*f. Let z(h) be the second derivative of g(h). Factor z(y).
y**2*(y + 1)/2
Let l(c) be the second derivative of 3*c**5/20 + 6*c**4 + 93*c**3/8 + 69*c**2/8 + 176*c. Factor l(t).
3*(t + 23)*(2*t + 1)**2/4
Let q(i) = i**3 + 9*i**2 + 2*i + 22. Let y be q(-9). Let b(o) be the first derivative of 0*o + 0*o**2 + 6 - 1/8*o**y + 1/20*o**5 + 1/12*o**3. Factor b(c).
c**2*(c - 1)**2/4
Let z(v) be the third derivative of -v**8/10080 - v**7/630 - v**5/5 - 16*v**2. Let g(a) be the third derivative of z(a). Determine f, given that g(f) = 0.
-4, 0
Let k(a) = 3*a - 9. Let u be k(4). Find n, given that 5*n - n**2 - 11*n**3 + 12*n**u - 5*n = 0.
0, 1
Let s(j) be the second derivative of j**6/40 + j**5/60 - j**4/3 + 2*j**3/3 + j**2 - j. Let k(g) be the first derivative of s(g). Factor k(z).
(z - 1)*(z +