- 56. Let a(n) = -23*n**2 + 187*n + 168. Let d(r) = 2*a(r) + 7*z(r). Factor d(c).
-4*(c + 1)*(c + 14)
Let n be (-2)/6*-9 - -27. Let o = n + -28. Let -8/11 + 24/11*j + 12/11*j**3 - 2/11*j**4 - 26/11*j**o = 0. What is j?
1, 2
Determine m, given that 3/5*m - 2/5*m**3 + 14/5*m**2 - 1/5*m**5 - 9/5 - m**4 = 0.
-3, -1, 1
Let h(f) be the third derivative of f**6/180 - f**5/18 - 11*f**4/18 - 16*f**3/9 + 17*f**2 - 2*f. Determine c, given that h(c) = 0.
-2, -1, 8
Let s be (-3)/31*(-2)/(-138)*2. Let q = 2842/3565 - s. Factor -8/5*x**2 - q + 12/5*x.
-4*(x - 1)*(2*x - 1)/5
Suppose -15 = -3*m + 2*f, 4*f = 5*m - 17 - 8. Factor -1/5*k**m - 3/5*k**3 - 1/5*k**2 - 3/5*k**4 + 0*k + 0.
-k**2*(k + 1)**3/5
Let a(k) be the third derivative of k**5/60 + 17*k**4/24 + 11*k**3 - 426*k**2. Factor a(m).
(m + 6)*(m + 11)
Let x = 7 + -7. Suppose x = -5*y + 15. Factor 2 + 2 - 8*h**3 - 18*h + 0 + 24*h**2 + 0*h**y.
-2*(h - 2)*(2*h - 1)**2
Let m(x) be the first derivative of -1/3*x**3 + x + 3 + 0*x**2 - 1/3*x**4 - 1/10*x**5. Let t(d) be the first derivative of m(d). Factor t(i).
-2*i*(i + 1)**2
Let o = 8 - 10. Let s be 0/1*(-1 + o/(-1)). Find f, given that 0*f**2 + s*f + 0*f**3 + 0 - 2/9*f**5 + 2/9*f**4 = 0.
0, 1
Let o(x) be the second derivative of x**6/10 - 9*x**5/10 + 5*x**4/4 + 12*x**3 - 54*x**2 + 22*x + 1. Factor o(q).
3*(q - 3)**2*(q - 2)*(q + 2)
Let i(l) be the second derivative of l**4/12 + 5*l**3/2 - 8*l**2 + 54*l. Factor i(c).
(c - 1)*(c + 16)
Let y(n) be the first derivative of n**6/6 + n**5/4 - 5*n**4/12 - 5*n**3/6 + 12*n - 28. Let z(k) be the first derivative of y(k). Solve z(j) = 0.
-1, 0, 1
Suppose 5*l - 10 = -0*l. Let r(o) = -2*o**3 + 6*o**2 + 6*o + 9. Let n be r(4). Factor h**l - 2 + 2*h + 2 - n - 2*h**2.
-(h - 1)**2
Suppose -12*a - 55 = -23*a. Let p(v) be the first derivative of -a + 0*v + 2/15*v**3 - 2/25*v**5 + 1/5*v**2 - 1/10*v**4. Factor p(n).
-2*n*(n - 1)*(n + 1)**2/5
Let w be 3 - (-2 + -1 + -84). Let t = 6 + -4. Solve v - v**t + w - 90 = 0.
0, 1
Let q(k) be the first derivative of -k**4/4 + 4*k**3 + 20*k - 26. Let a(u) be the first derivative of q(u). Solve a(l) = 0 for l.
0, 8
Factor -4/3*g + 2/3*g**2 - 10.
2*(g - 5)*(g + 3)/3
Let f(a) = 7*a**2 + 5*a - 18. Let u(j) = 20*j**2 + 14*j - 52. Let r(o) = -14*f(o) + 5*u(o). Determine c so that r(c) = 0.
-2, 2
Suppose 10*p - 17*p + 42 = 0. Suppose 3*l = p*l + 11*l. Let l*w + 1/3 - 1/3*w**2 = 0. What is w?
-1, 1
Let f(z) be the third derivative of 1/24*z**4 - 16*z**2 - 1/120*z**6 - 1/30*z**5 + 1/3*z**3 + 0*z + 0. Solve f(g) = 0.
-2, -1, 1
Let j(n) be the second derivative of 14*n + 0 - 1/18*n**4 - 1/9*n**3 + 0*n**2. Suppose j(o) = 0. Calculate o.
-1, 0
Let -9*k - 3/2*k**2 + 24 = 0. What is k?
-8, 2
What is c in 2/5*c + 0 - 1/5*c**2 = 0?
0, 2
Let f be (4 - (3 + 5)) + 2. Let k be (44/20 - 2)*(-1 - f). Suppose 0 + 0*h**3 - 1/5*h**2 + 0*h + k*h**4 = 0. What is h?
-1, 0, 1
Factor 1/2*m**2 + 1922 - 62*m.
(m - 62)**2/2
Suppose -71*j + 1132 = 280. Suppose -v + 12 = 2*z + v, -20 = -5*z - 3*v. Let -1 + z + 5 + 3 - j*p + 4*p**2 = 0. Calculate p.
1, 2
Find n such that -3 + 3/4*n**2 + 0*n = 0.
-2, 2
Let l(p) be the second derivative of 3*p**4 - 86*p**3/3 - 20*p**2 - 7*p - 1. Factor l(n).
4*(n - 5)*(9*n + 2)
Let s(f) = -6*f**4 + 9*f**3 + 15*f**2 - 21*f - 19. Let m(h) = h + 388 + h**4 - 389 - 2*h**2 + h**3 + 2*h**2. Let b(v) = m(v) + s(v). Factor b(p).
-5*(p - 2)**2*(p + 1)**2
Let m be (-63)/(-30) - (20 + 1591/(-74)). Factor 7/5*v**4 - 2*v**3 + 27/5*v - m*v**2 - 1/5*v**5 + 27/5.
-(v - 3)**3*(v + 1)**2/5
Let u(y) be the third derivative of -y**6/540 + y**5/90 + y**4/12 - y**3/6 + 4*y**2. Let s(w) be the first derivative of u(w). Factor s(n).
-2*(n - 3)*(n + 1)/3
Let w = 19756/5 + -3951. Let 0 + 0*q + w*q**5 + 0*q**3 + 0*q**2 + 2/5*q**4 = 0. What is q?
-2, 0
Let q be 11/(-22) - (-5)/2. Suppose 13 = b + q*b - r, -3 = b - 4*r. What is j in 5 + 10 - b*j**2 - 10 = 0?
-1, 1
Factor 16/9*d**4 - 4/9*d**5 + 0 + 20/9*d**3 + 0*d + 0*d**2.
-4*d**3*(d - 5)*(d + 1)/9
Let h be (1 - 0) + (1 - -2) + -4. Let v be (-26)/(-6) + (-32)/8. Factor 2/3*f + h - v*f**2.
-f*(f - 2)/3
Let 76*p + 73*p - 80 + 43*p - 6*p**3 - 82*p**2 - 2*p**3 + 22*p**2 = 0. What is p?
-10, 1/2, 2
Let b be ((-36)/(-16))/(6/(-80)). Let y be 20/b - (-38)/3. Suppose 147*k**4 - 66*k + 6*k - 9*k**2 + y + 0 + 210*k**3 = 0. Calculate k.
-1, 2/7
Let g(m) be the third derivative of m**8/60480 + m**7/5040 - 3*m**5/20 - 4*m**2. Let o(z) be the third derivative of g(z). Suppose o(s) = 0. What is s?
-3, 0
Let y(g) be the first derivative of -5*g**4/26 - 12*g**3/13 - 12*g**2/13 + 16*g/13 + 111. Factor y(l).
-2*(l + 2)**2*(5*l - 2)/13
Let o(j) = j**3 - 4*j**2 - j + 27. Let g be o(3). Let 45/2*w**2 + 5/2*w**4 + 0*w - g*w**3 + 0 = 0. Calculate w.
0, 3
Let y(u) be the first derivative of 1/6*u**4 + 1/30*u**5 + 0*u + 5/18*u**3 + 11 + 1/6*u**2. Suppose y(d) = 0. What is d?
-2, -1, 0
What is w in -6*w - 17*w**2 - 11*w**2 + 3*w - 9*w**3 = 0?
-3, -1/9, 0
Let v(q) be the third derivative of q**8/4480 - q**7/1120 - q**6/192 + 3*q**5/160 - 10*q**3/3 + 18*q**2. Let y(c) be the first derivative of v(c). Factor y(i).
3*i*(i - 3)*(i - 1)*(i + 2)/8
Let l = 9 - 5. Suppose 4*w - 17 = -3*v, 2*w + l*v - 14 = w. Factor 2*z**4 - 2*z**4 + 2*z**4 - 2*z**w.
2*z**2*(z - 1)*(z + 1)
Let h = 11 + -5. Suppose -4*n = 3*y + h, 4*n = 3*n - 4*y - 8. Find j, given that 1/5*j**3 + 0 + 0*j**2 + n*j = 0.
0
Suppose -7*z + 97 = -1478. Determine p so that z - 28*p - 233 - 3*p**3 - 28*p**2 - 5*p**3 = 0.
-2, -1, -1/2
Let f(h) be the second derivative of h**4/18 - 4*h**3/3 + 11*h**2/3 - 5*h + 9. Suppose f(n) = 0. What is n?
1, 11
Factor 3*n**4 + 14*n**3 + 6*n**3 - 4*n**4 - 406*n + n**2 + 386*n.
-n*(n - 20)*(n - 1)*(n + 1)
Let r = -85 - -86. Let y be (r/4)/((-7)/(-8)). Let 0*m**3 + 2/7*m**5 + 0 + 0*m**2 + y*m**4 + 0*m = 0. What is m?
-1, 0
Let k(w) = -122*w + 10616. Let x be k(87). Suppose -2/9*i + 2/9*i**x + 2/9*i**3 + 0 - 2/9*i**4 = 0. What is i?
-1, 0, 1
Let l = 65 - 62. Factor k**3 + 32 - l*k**3 - 48*k + 13*k**2 - 2*k**3 + 11*k**2.
-4*(k - 2)**3
Let b(p) be the second derivative of 1/9*p**4 + 1/12*p**3 + 4*p + 0*p**2 + 0 + 1/40*p**5 - 1/90*p**6. Factor b(a).
-a*(a - 3)*(a + 1)*(2*a + 1)/6
Let a(v) = 2*v**2 + 4*v. Let u(o) = -4*o + 5. Let c be u(2). Let r be a(c). Factor 18*l + 2/3*l**3 - 18 - r*l**2.
2*(l - 3)**3/3
Suppose 0 = 11*z - 9*z - 32. Let w = z + -13. Let -3*j**5 - 9*j**4 + 0*j + 5*j + 9*j**2 - j - 3*j**w + 2*j = 0. Calculate j.
-2, -1, 0, 1
Let n be 0/((-4)/(16/4)). Determine m so that n*m**2 + 7*m - 5*m**2 + 3*m = 0.
0, 2
Factor -4/3*u**3 + 0 + 0*u + 0*u**2 - 2/9*u**5 + 10/9*u**4.
-2*u**3*(u - 3)*(u - 2)/9
Let q be (-1044)/(-26) - -10*8/(-520). Suppose 20*n - n**4 + 25*n**3 + 0*n**4 + q*n**2 + 6*n**4 = 0. Calculate n.
-2, -1, 0
Let a(o) be the second derivative of 3*o**5/140 + 5*o**4/14 + 23*o**3/14 + 3*o**2 + 630*o. Factor a(z).
3*(z + 1)*(z + 2)*(z + 7)/7
Let b be -3 + (-3 - (-27)/1). Find k, given that -k**2 + 28*k**3 - b*k**2 + 2*k - k + 3*k = 0.
0, 2/7, 1/2
Factor -24*n + 3*n**2 + 4*n + 123*n + 99*n - 16*n + 183.
3*(n + 1)*(n + 61)
Let s(k) = 2*k**2 + 10*k - 12. Let o(b) = -4*b**2 - 9*b + 13. Let n(x) = 2*o(x) + 3*s(x). Factor n(a).
-2*(a - 5)*(a - 1)
Let u be (-16750)/(-500) + (1/1)/1. Suppose -21/2*p**5 + u*p**4 + 0 + 0*p + 6*p**2 - 30*p**3 = 0. Calculate p.
0, 2/7, 1, 2
Let x(j) be the second derivative of 1/72*j**4 + 7*j + 25/12*j**2 - 5/18*j**3 + 0. Find z such that x(z) = 0.
5
Let j(h) be the second derivative of h**6/30 - 3*h**5/20 - 7*h**4/12 + 5*h**3/2 + 9*h**2 - 39*h. Let j(b) = 0. Calculate b.
-2, -1, 3
Let d(u) be the second derivative of 0 + 11/30*u**4 + 1/3*u**3 + 2/25*u**5 - 10*u - 2/5*u**2. Factor d(z).
2*(z + 1)*(z + 2)*(4*z - 1)/5
Let u(h) be the second derivative of h**7/399 + 7*h**6/285 + 4*h**5/95 - 8*h**4/57 + 57*h. Factor u(m).
2*m**2*(m - 1)*(m + 4)**2/19
Let u(x) be the first derivative of -x**3 + 321*x**2/2 + 324*x - 697. Factor u(k).
-3*(k - 108)*(k + 1)
Let r = -1716 + 1718. Factor -2*o + 2/3*o**r + 4/3.
2*(o - 2)*(o - 1)/3
Let h = 295/18 + -89/6. Let f = h - 8/9. Factor -2/3*r**2 - 2/3*r**3 + 2/3*r + f*r**4 + 0.
2*r*(r - 1)**2*(r + 1)/3
Let c(v) be the second derivative of 1/6*v**6 + 5/4*v**4 + 0*v**2 + 26*v + 0 + 5/4*v**5 - 15/2*v**3. Let c(l) = 0. Calculate l.
-3, 0, 1
Let 580*t**2 -