1. Let w(y) = -6*y**2 - 10*y + 7. Let j(x) = -5*x**2 - 9*x + 6. Let t(a) = u*w(a) - 7*j(a). Factor t(n).
-n*(n - 3)
Let s(y) = y**3 - 23*y**2 + 3*y - 51. Let t be s(23). Let p = t + -15. Factor -3*m**2 - m**4 + 3*m**5 + 4*m**2 + 3*m**p - 6*m**3.
m**2*(m - 1)*(m + 1)*(3*m - 1)
Let s(i) = -3 - i**3 - i**2 + 0*i**2 - i**2. Let a be s(-3). Factor k**4 + 3*k - a*k**2 - 14*k**3 + 5*k**2 + 11*k**3.
k*(k - 3)*(k - 1)*(k + 1)
Factor -192*j**2 + 0 + 216*j + 16/3*j**4 + 1/6*j**5 + 92/3*j**3.
j*(j - 2)**2*(j + 18)**2/6
Let -70 - 1/10*g**3 + 51/2*g - 9/5*g**2 = 0. What is g?
-28, 5
Let o(p) be the third derivative of -p**6/180 + 5*p**5/9 + 169*p**4/36 - 530*p**3/9 + 5*p**2 + 6*p + 3. Factor o(r).
-2*(r - 53)*(r - 2)*(r + 5)/3
Let j = 235 - 1186/7. Let z = -1370/21 + j. Suppose -1/3 - z*y**2 - 2/3*y = 0. What is y?
-1
Suppose 0 = -3*r + 5*v + 97, -8*r + 11*r + 3*v - 57 = 0. Let 90*l - 4*l**4 + 5*l**5 - r*l**3 - 31*l**4 + 27*l**2 + 18*l**3 + 11*l**3 + 108*l**2 = 0. What is l?
-1, 0, 3, 6
Let t = -750 - -752. Let u be 9/t + (-325)/78. Find c, given that u*c**2 + 2 - 5/3*c = 0.
2, 3
Factor 0 + 2/11*h**2 - 520/11*h.
2*h*(h - 260)/11
Let d(a) be the second derivative of 0*a**2 + 8*a - 5/6*a**3 - 5/504*a**6 + 1/84*a**5 - 1/168*a**4 + 0. Let u(b) be the second derivative of d(b). Factor u(x).
-(5*x - 1)**2/7
Let i(z) be the second derivative of 0*z**2 - z - 14/9*z**3 - 1/18*z**4 + 69. Find t, given that i(t) = 0.
-14, 0
Let n(u) be the third derivative of u**6/720 + 73*u**5/180 + 374*u**4/9 + 11560*u**3/9 - 13*u**2 + 35*u - 3. Factor n(i).
(i + 10)*(i + 68)**2/6
Let u = -3/31 + 37/62. Let d(r) = -2*r**2 + 285*r + 432. Let h be d(144). Suppose 3*x**3 + 3*x + h - u*x**4 - 11/2*x**2 = 0. What is x?
0, 1, 2, 3
Let c = -552 + 554. Let -d**c + 7*d**2 - 3 - 9*d + 0 - 4*d + 5 = 0. What is d?
1/6, 2
Let h(j) = 6*j**4 + 117*j**2 - 63*j - 9. Let z(l) = 8*l**4 - l**3 + 236*l**2 - 125*l - 15. Let y(n) = 5*h(n) - 3*z(n). Factor y(q).
3*q*(q - 4)*(q + 5)*(2*q - 1)
Let i be (-5 + -3)*(-684)/7296. Determine f, given that -i*f**2 + 1/4*f**4 - 1/2*f**3 + 0*f + 0 = 0.
-1, 0, 3
Suppose -201*x + 312 = -26*x - 71*x. Factor -288/7*t - 4/7*t**x - 12*t**2 + 1728/7.
-4*(t - 3)*(t + 12)**2/7
Let j = -69 - -72. Factor -10 - 5*h**j - 2*h - h**2 + 7*h + 3*h**2 + 13*h**2 - 5*h**4.
-5*(h - 1)**2*(h + 1)*(h + 2)
Solve -3*o**2 + 0 + o**4 + 1/4*o**5 + 9/4*o - 1/2*o**3 = 0 for o.
-3, 0, 1
Let o(r) be the first derivative of r**2/2 - 8*r + 10. Let h be o(10). Let -21 + h - 65*v**2 + 80*v - 1 + 15*v**3 = 0. What is v?
1/3, 2
Let q(u) be the first derivative of -3*u**4/32 + 49*u**3/4 - 855*u**2/16 - 1323. Factor q(r).
-3*r*(r - 95)*(r - 3)/8
Suppose 8*r = 689 + 183. Factor 765 - 27*n - r*n - 3*n**2 + 7*n**2 + 391.
4*(n - 17)**2
Let b be 710/(-2154) - (-1)/3. Let d = b + 706/3231. Find k, given that -5/9*k**4 - k**3 + 0 - 1/9*k**5 - d*k - 7/9*k**2 = 0.
-2, -1, 0
Let p(y) = 6*y**4 - 30*y**3 - 33*y**2. Let q(z) = -z**4. Let j(u) = 2*u**2 + 17*u - 8. Let d be j(-9). Let k(m) = d*p(m) + 3*q(m). Factor k(w).
3*w**2*(w - 11)*(w + 1)
Let a(z) be the first derivative of -z**6/180 + 7*z**5/90 - 2*z**4/9 - 16*z**3/9 + z**2/2 + 53*z + 36. Let t(s) be the second derivative of a(s). Factor t(n).
-2*(n - 4)**2*(n + 1)/3
Suppose -5*f - 25 = 5*x, -389*x + 4*f + 38 = -387*x. Let 0 + 3/4*u**5 + 0*u - 3/2*u**2 - 13/4*u**x - u**4 = 0. Calculate u.
-1, -2/3, 0, 3
Let r(x) be the third derivative of x**5/180 - 71*x**4/72 + 224*x**3/9 + 215*x**2 - 2. Let r(l) = 0. Calculate l.
7, 64
Let b(l) be the first derivative of -5*l**6/6 + 31*l**5 - 440*l**4 + 8860*l**3/3 - 9440*l**2 + 14080*l - 3832. Find j, given that b(j) = 0.
2, 8, 11
Let a = -385 - -388. Factor -82*y**2 + y**4 - 105*y**2 + 247*y**2 - 5*y**a - 6*y**4.
-5*y**2*(y - 3)*(y + 4)
Let m = -1081 + 1131. Let j be 60/m*-3*6/(-54). Find h such that -4/5*h**3 - 2/5 + 2/5*h**5 + j*h - 2/5*h**4 + 4/5*h**2 = 0.
-1, 1
Factor -168*s**2 + 355*s**3 - 25*s**4 + 337*s**3 - 272*s + 21*s**4 - 160 - 736*s**3.
-4*(s + 2)**3*(s + 5)
Let w(s) be the third derivative of 9*s**5/8 + 1805*s**4/4 + 651605*s**3/9 + 18*s**2 - 8*s + 1. Factor w(a).
5*(9*a + 722)**2/6
Let m(c) = -c**3 - 15*c**2 - 15*c + 16. Let n be m(-14). Factor -27 + 37 - 5*t**2 - 20*t - n.
-5*(t + 2)**2
Let s(g) = -11*g**4 - 15*g**3 - 9*g**2 - 38*g + 2. Let z(y) = -5*y**4 - 8*y**3 - 7*y**2 - 19*y. Let b(h) = 3*s(h) - 7*z(h). Factor b(m).
(m + 1)**2*(m + 2)*(2*m + 3)
Let w(b) be the first derivative of 3*b**2 - b**3 - 18*b**2 + 36 - 10 + 42. Factor w(z).
-3*z*(z + 10)
Let g(j) = -2*j**2 - 2842*j - 5664. Let q(s) = 3*s**2 + 5685*s + 11328. Let c(u) = 5*g(u) + 2*q(u). Factor c(h).
-4*(h + 2)*(h + 708)
Let o(d) be the second derivative of 0*d**2 + 10*d + 4 - 5/12*d**4 - 7/20*d**5 + 2/3*d**3 + 1/15*d**6. Factor o(t).
t*(t - 4)*(t + 1)*(2*t - 1)
Let v(y) = -13*y**2 - 24*y - 25. Let n(b) be the first derivative of 2*b**3/3 + b**2/2 + b + 109. Let u(x) = -21*n(x) - 3*v(x). Solve u(d) = 0.
-1, 18
Let c(p) = p**2 + 27*p + 140. Let d be c(-19). Let y(i) = 3*i + 42. Let o be y(d). Let 2/3*r**3 + 18 + o*r**2 + 18*r = 0. Calculate r.
-3
Let g(a) be the second derivative of -a**5/190 - 65*a**4/114 - 64*a**3/57 + 5*a + 106. Solve g(k) = 0.
-64, -1, 0
Let p(x) be the first derivative of -4*x**6/3 + 36*x**5/5 - 21*x**4/2 + 19*x**3/3 - 3*x**2/2 + 747. Factor p(o).
-o*(o - 3)*(2*o - 1)**3
Let o = 391107/25340 + -21/3620. Find y such that -22/7*y**4 - 30/7 + 2/7*y**5 - 118/7*y - o*y**3 - 172/7*y**2 = 0.
-1, 15
Let z(f) be the first derivative of -30 + 5/3*f**3 + 500/3*f + 1/24*f**4 + 25*f**2. Solve z(r) = 0 for r.
-10
Let z(h) be the first derivative of h**6/1260 - h**5/420 - 2*h**3 + 35. Let g(l) be the third derivative of z(l). Factor g(x).
2*x*(x - 1)/7
Let v(j) be the first derivative of -j**8/1848 + j**6/330 - j**4/132 - 139*j**2/2 + 160. Let l(u) be the second derivative of v(u). Factor l(m).
-2*m*(m - 1)**2*(m + 1)**2/11
Let h(t) be the third derivative of t**6/60 + 2*t**5/15 - 7*t**4/3 + 32*t**3/3 + 6*t**2 + 51. Let h(z) = 0. Calculate z.
-8, 2
Suppose 4*i + g = -27, -i - 3*g + 9 = -8*g. Let n(j) = -2*j + 32. Let f be n(i). Solve -10 - f*u + 69*u + 11*u**2 + 4*u**2 = 0.
-2, 1/3
Let i(w) = -w**2 + 334*w - 35337. Let k(s) = -6*s + 1. Let m(r) = -4*i(r) + 28*k(r). Let m(p) = 0. What is p?
188
Let n = 6858019/5 + -1371599. Suppose -1/5*b**2 - 2/5*b + n = 0. Calculate b.
-6, 4
Let a = 55908 - 55905. Suppose 1/10*c + 1/5*c**2 + 0 + 1/10*c**a = 0. Calculate c.
-1, 0
Let -230 + 7*a**2 + 367 + 1178*a + 199 = 0. What is a?
-168, -2/7
Let n(w) be the third derivative of w**6/540 - 7*w**5/135 - 17*w**4/108 + 10*w**3/9 + 1847*w**2. Factor n(d).
2*(d - 15)*(d - 1)*(d + 2)/9
Solve 73/5*x**2 + 14*x - 3/5 = 0.
-1, 3/73
Let l be -9*(68/(-306))/(2/3). Let m be (-5 - (-7 - -2))/l. Find a such that 0*a**2 + m*a - 1/2*a**3 - 1/2*a**4 + 0 = 0.
-1, 0
Let g(i) be the first derivative of -i**5/10 + 3*i**4 + 59*i**3/6 - 93*i**2/2 + 52*i - 609. Let g(r) = 0. What is r?
-4, 1, 26
Suppose -474 = -7*q - 5. Suppose -72*b = -q*b. Factor 1/5 - 1/5*m**2 + b*m.
-(m - 1)*(m + 1)/5
Let m(b) be the third derivative of -b**8/168 - b**7/5 - 53*b**6/20 - 479*b**5/30 - 20*b**4 + 300*b**3 - 24*b**2 - 30*b. Determine l, given that m(l) = 0.
-6, -5, 1
Let x = 124 - 122. Determine g so that 5*g**2 - 7*g**3 + 21*g**3 + 11*g**2 + x*g**4 - 358*g + 326*g = 0.
-4, 0, 1
Let u = -2524 + 2524. Let c(y) be the second derivative of 2/3*y**3 + u - y + 0*y**2 - 1/2*y**4 - 1/2*y**5. Determine v so that c(v) = 0.
-1, 0, 2/5
Let o = -776194 - -3104785/4. Solve -3/4*k**3 + 0*k**2 + o*k + 3/2 = 0 for k.
-1, 2
Suppose -54 + 22 = -4*y. Suppose -18*z**4 - 10*z**3 + 15*z**2 - 3*z**5 - 10*z**3 + y*z**3 + 3*z**2 + 15*z = 0. What is z?
-5, -1, 0, 1
Suppose -6*y - y + 35 = 0. Suppose 4*v - v - 6 = 0, y*c + v - 32 = 0. Factor -20*u**2 - c*u**3 + 5*u**3 + 6*u**3.
5*u**2*(u - 4)
Let j(q) be the second derivative of -q**8/1400 - q**7/1400 + q**6/600 - q**3/2 - q**2 + 2*q + 14. Let g(z) be the second derivative of j(z). Factor g(r).
-3*r**2*(r + 1)*(2*r - 1)/5
Let f = -5462 + 5462. Let k(b) be the second derivative of 0*b**2 + 1/10*b**5 - 1/2*b**4 + f*b**3 + 10*b + 0. Suppose k(u) = 0. Calculate u.
0, 3
Suppose a + 2 = 0, 19 = 4*w + a - 47. Suppose 4*m = -c + 6*c - 30, -w = 4*c + 5*m. Factor -2/3 + 1/3*y**c + 1/3