Let n = -43 + 37. Let f(d) = 9*d**3 - 3*d**2 - 36*d + 18. Let j(q) = -8*q**3 + 2*q**2 + 35*q - 19. Let c(s) = n*j(s) - 5*f(s). Factor c(g).
3*(g - 2)*(g - 1)*(g + 4)
Let x(w) = 7*w**2 + 14*w - 17. Let t be x(-8). Factor -t*n**4 + 222*n**4 + 172*n**4 + 48*n**2 + 120*n**3.
3*n**2*(5*n + 4)**2
What is a in 99/2*a**2 - 15/4*a**3 + 45/4*a**5 - 6 + 3*a - 33*a**4 = 0?
-1, -2/5, 1/3, 2
Let o be ((-1098)/(-2835) - (-24)/(-54))/(3/(-60)). Factor -o + 4/7*s + 4/7*s**2.
4*(s - 1)*(s + 2)/7
Let s = -2330 - -2340. Let p(f) be the first derivative of 3/2*f**5 + 5/2*f**3 - 5*f + 15/4*f**2 + s - 35/8*f**4. Let p(o) = 0. What is o?
-2/3, 1
Let j = -397/12 + 133/4. Let c(q) be the first derivative of 0*q - 1/16*q**4 - 1/8*q**2 - 5 - j*q**3. Suppose c(f) = 0. What is f?
-1, 0
Let g be 30/1 + (6 - 9). Let b be 315/g - 2/(-6). Solve -n - 8*n**4 + b*n**3 + 5*n - 12*n**2 + 4*n**4 = 0 for n.
0, 1
Let v(h) = -h**2 - 14*h + 5. Let d be v(-14). Let i be (-2)/d*(-2 - 3). Factor c**3 - 27 - c**i + 23 + 4*c**2.
(c - 1)*(c + 2)**2
Suppose -1990 = -7*h - 3*h. Let v = h + -1789/9. Factor 0 + 0*s**4 + 0*s**2 + 0*s + v*s**5 - 2/9*s**3.
2*s**3*(s - 1)*(s + 1)/9
Let n(d) = -2*d**2 - 1. Let a(q) = -12*q**2 + 372*q - 372. Let w(x) = a(x) - 4*n(x). Determine j so that w(j) = 0.
1, 92
Suppose 0 = 2*o - 2 + 4. Let v be (-6)/(-5 + o) - (-2)/(-4). Solve -1/2*y**3 + y + 0 - v*y**2 = 0 for y.
-2, 0, 1
Let t be 2 - (-2 - (2 - 3)). Let p(m) = 2*m**2 + 3*m - 2. Let x(i) = -25*i**2 - 40*i + 25. Let f(y) = t*x(y) + 40*p(y). Suppose f(o) = 0. Calculate o.
-1, 1
Let g(p) be the first derivative of -p**4/4 + 44*p**3/3 - 242*p**2 - 32. Solve g(n) = 0 for n.
0, 22
Factor 1/3*n**2 + 61/3 - 62/3*n.
(n - 61)*(n - 1)/3
Let d(p) be the third derivative of 0*p + 1/63*p**4 + 1/63*p**3 + 0 + 20*p**2 + 1/315*p**6 + 1/105*p**5 + 1/2205*p**7. Factor d(j).
2*(j + 1)**4/21
Let u(l) = 20*l**3 + 1308*l**2 + 1300*l + 328. Let k(b) = -21*b**3 - 1307*b**2 - 1300*b - 329. Let a(q) = 4*k(q) + 5*u(q). Find j such that a(j) = 0.
-81, -1/2
Let k = 1302 - 1302. Let n(a) be the third derivative of 1/60*a**4 + k*a + 0*a**5 + 0 - 2/45*a**3 - 1/900*a**6 - 11*a**2. Determine i, given that n(i) = 0.
-2, 1
Factor -5*u + 4*u - 2*u**2 + 21*u + 14*u.
-2*u*(u - 17)
Solve 1/8*q**3 + 1/2*q**2 - 5/4 - 7/8*q = 0 for q.
-5, -1, 2
Factor -39/4*t**3 + 39/8 + 1/8*t**5 + 77/8*t - 37/8*t**4 - 1/4*t**2.
(t - 39)*(t - 1)*(t + 1)**3/8
Let v(p) = p**2 - 1. Suppose 7 = 3*y + 22. Let c(q) = -10*q**2 + 5. Let h(t) = y*v(t) - c(t). Solve h(d) = 0 for d.
0
Let b be 7/21*9 - 2. Let l = b + 1. Let 2/9*a**l + 0*a - 2/9 = 0. What is a?
-1, 1
Let d(v) = -v**3 + 2*v**2 + 2*v - 2. Let u be d(2). Let o be 2*(10/4)/((-2280)/(-96) - 15). Factor -2/7*a**3 + 0*a + o*a**u + 0.
-2*a**2*(a - 2)/7
Let s = -7 + 127/18. Let f(z) be the third derivative of 0 - 1/180*z**5 + s*z**3 + 0*z + 0*z**4 - 4*z**2. Determine r so that f(r) = 0.
-1, 1
Let z be 8/28 + 13/((-546)/(-72)). Find d, given that -5/9*d**z + 4/9*d**3 + 0 + 2/9*d - 1/9*d**4 = 0.
0, 1, 2
Let n = 2 - -2. Suppose 6*q + w = n*q, 0 = -3*q - w + 2. Find c, given that -1 + c**2 + 2*c**q - 1 + 4*c - 5*c**2 = 0.
1
Solve -6/5 - 1/5*z**2 - z = 0 for z.
-3, -2
Let i = 1365 - 4094/3. Find f, given that -1/3*f + i*f**2 + 0 = 0.
0, 1
Suppose -8/3*a**2 - 2/9*a**3 - 64/9 - 8*a = 0. What is a?
-8, -2
Factor 296 - 196 - 28*x**2 - 17*x**2 - 3*x**3 + 60*x - 2*x**3.
-5*(x - 2)*(x + 1)*(x + 10)
Suppose 5*x = 3*x - 88. Let d be 2/8 + (-55)/x. Factor -d*l + l**3 + 3/2*l**4 - l**2 + 1/2*l**5 - 1/2.
(l - 1)*(l + 1)**4/2
Let n(p) be the first derivative of -1/10*p**5 - 1/2*p**3 + 1/4*p**2 + 3/8*p**4 + 8 + 0*p. Suppose n(w) = 0. What is w?
0, 1
Let j(h) be the first derivative of 3*h**5/80 + 3*h**4/16 + h**3/4 - 8*h - 6. Let s(t) be the first derivative of j(t). Factor s(d).
3*d*(d + 1)*(d + 2)/4
Let y(h) be the second derivative of 5*h - 1/360*h**6 + 0*h**3 + 0 - 3/2*h**2 + 0*h**4 - 1/60*h**5. Let t(n) be the first derivative of y(n). Factor t(s).
-s**2*(s + 3)/3
Let q be ((-2)/(-4))/(305/732). Determine r, given that 2/5*r**3 + 2/5 + 6/5*r + q*r**2 = 0.
-1
Suppose 4*o - 36 = -0*o - 4*x, -2*x - 22 = -3*o. Let q = -6 + o. Factor b**q - 2*b - 2*b**2 + 2*b**3 + 2 - b**2.
2*(b - 1)**2*(b + 1)
Let c be 2/(-6)*(-162)/6. Suppose -4 = 4*a - 16. Let -a - v**2 - c*v - 5*v**2 - 3*v**2 - 3*v**3 = 0. Calculate v.
-1
Suppose 534 = -0*b + 5*b - s, 0 = 2*b - 4*s - 210. Let x = -207/2 + b. Factor 13/2*m - 2 - 15/2*m**2 + x*m**3 - 1/2*m**4.
-(m - 4)*(m - 1)**3/2
Factor -9*o + 23*o**3 - 5*o**4 - 25*o**2 + 0*o**2 + 7*o**3 + 9*o.
-5*o**2*(o - 5)*(o - 1)
Factor 0 - 36*b + 0*b**3 + 18*b**2 - 2/3*b**4.
-2*b*(b - 3)**2*(b + 6)/3
Suppose -28 = 5*a - 6*a. Let b be (8/(-44) - 0)/((-4)/a). Find u such that -6/11*u + 0 + b*u**2 + 2/11*u**4 - 10/11*u**3 = 0.
0, 1, 3
Let k(c) be the third derivative of 0*c + 17*c**2 + 0 + 11/60*c**5 - 13/24*c**4 + 1/3*c**3. Factor k(r).
(r - 1)*(11*r - 2)
Let y(t) be the first derivative of 1/20*t**4 + 4/25*t**5 + 0*t**2 - 1/10*t**6 + 0*t - 2/15*t**3 - 8. Factor y(k).
-k**2*(k - 1)**2*(3*k + 2)/5
Let t(x) be the third derivative of 10/3*x**3 + 1/4*x**6 + 0 + 13/12*x**5 + 11*x**2 + 0*x + 5/2*x**4 + 1/42*x**7. Determine r so that t(r) = 0.
-2, -1
Let p(y) be the third derivative of y**6/720 - y**5/90 - 7*y**4/144 + 5*y**3/18 - 2*y**2 + 42*y. Factor p(i).
(i - 5)*(i - 1)*(i + 2)/6
Suppose 2*v + 5*y + 524 = 0, 422 = -3*v - 3*y - 346. Let z = v - -1767/7. Find p such that -z - 2/7*p**2 - p = 0.
-3, -1/2
Suppose -2817 = q + 2*q. Let s = 7521/8 + q. Determine x, given that -9/8*x**3 - 3/8*x + 0 + 3/8*x**4 + s*x**2 = 0.
0, 1
Let -105 - 12*y + 33*y - 31*y + 5*y**2 - 10*y = 0. What is y?
-3, 7
Suppose -2*z - 18 = n - 30, -2*n - 1 = -z. Factor 2/3 - 1/3*d - 1/3*d**n.
-(d - 1)*(d + 2)/3
Let l(y) be the first derivative of -5 + 3/5*y**5 - y**4 - 25/3*y**3 - 8*y - 13*y**2. Find s such that l(s) = 0.
-1, -2/3, 4
Let l(o) = -8*o**5 - 83*o**4 - 477*o**3 - 1280*o**2 - 1283*o - 3. Let h(s) = s**5 + s**4 - s**3 + s + 1. Let p(q) = -3*h(q) - l(q). Factor p(y).
5*y*(y + 4)**4
Let j be (3 - 7)*((-106)/(-36) - 3). Let y = -43 - -47. Find m, given that 0 - 4/3*m**y + 8/3*m**3 - 16/9*m**2 + 0*m + j*m**5 = 0.
0, 2
Let k(i) = 4*i**2 + 5*i + 1. Let g(f) = -f**2 + f. Let a(j) = -3*g(j) + k(j). Let r be a(-1). Factor -r*l + 0 - 37*l**2 + 40*l**2 + 0.
3*l*(l - 2)
Let u(h) be the first derivative of -h**3/3 - 9. Let k(j) = -8*j**2 - 2. Let c(o) = k(o) - 10*u(o). Factor c(s).
2*(s - 1)*(s + 1)
Let i = 742 - 14839/20. Let z(m) be the third derivative of 3/20*m**5 + 0*m - 3/8*m**4 - m**3 + i*m**6 - 7*m**2 + 0. Find d such that z(d) = 0.
-2, -1/2, 1
Let h(r) = -15*r**3 - 194*r**2 - 1529*r - 2304. Let o(m) = -8*m**3 - 96*m**2 - 764*m - 1152. Let g(f) = -4*h(f) + 7*o(f). Factor g(x).
4*(x + 2)*(x + 12)**2
Let v(z) be the first derivative of 0*z - 5/4*z**2 + 5/8*z**4 + 0*z**3 + 1. Factor v(d).
5*d*(d - 1)*(d + 1)/2
Let w(d) be the second derivative of -d**7/4200 - 13*d**6/1200 - 3*d**5/50 - d**4/4 + d**2/2 - 2*d - 46. Let k(g) be the third derivative of w(g). Factor k(p).
-3*(p + 1)*(p + 12)/5
Let l(s) be the first derivative of s**6/63 + 68*s**5/105 - 7*s**4/2 + 376*s**3/63 - 76*s**2/21 - 57. Let l(d) = 0. What is d?
-38, 0, 1, 2
Let n(h) = 8*h**4 - h**3 + 4*h**2 + 8*h + 2. Let o(g) = -g**4 - g**2 - g. Let v(m) = 5*n(m) + 35*o(m). Factor v(w).
5*(w - 2)*(w - 1)*(w + 1)**2
Let q = 1529 + -1026. Factor -110*r - 5 - q*r**2 - 550*r**3 + 35*r + 625*r**5 + 133*r**2 + 375*r**4.
5*(r - 1)*(r + 1)*(5*r + 1)**3
Let t = -1034 - -1036. Let s(k) be the first derivative of 0*k**t - 9/4*k**4 + 4 + 2*k**3 + 0*k + 3/5*k**5. Factor s(x).
3*x**2*(x - 2)*(x - 1)
Let w(v) = 20*v**3 + 228*v**2 + 210*v + 76. Let h(r) = r**3 + r**2 + 2. Let p(m) = 12*h(m) - w(m). Solve p(i) = 0 for i.
-26, -1/2
Let f(m) be the second derivative of -m**4/6 - 4*m**3/3 + 32*m**2 + m - 721. Let f(g) = 0. Calculate g.
-8, 4
Let q(j) be the third derivative of -2/3*j**4 - 1/210*j**7 + 0 + 0*j**3 + 7/120*j**6 - 2/15*j**5 - 35*j**2 + 0*j. Factor q(m).
-m*(m - 4)**2*(m + 1)
Let k(v) be the first derivative of -3/4*v + 39/32*v**4 - 13 + 9/8*v**3 + 3/8*v**5 - 3/16*v**2. Let k(d) = 0. Calculate d.
-1, 2/5
Let o(j) be the second derivative of j**8/560 - j**7/140 + j**6/120 + 2*j**3 - 13*j. Let h(w) be the second derivati