4. Let p(w) = -w**2 + w + 6. Let c(y) = l*p(y) - 5*n(y). Factor c(g).
(g + 2)**2
Let q(p) = -8*p + 19. Let j be q(2). Factor -4*c**2 - 5*c - 151*c**3 + 156*c**j + c**4 - 2 - 3*c**2 + 8.
(c - 1)**2*(c + 1)*(c + 6)
Let w(d) be the second derivative of -55*d**4/14 - 46*d**3/21 + 3*d**2/7 - 2*d + 333. Suppose w(v) = 0. Calculate v.
-1/3, 3/55
Let i be (1 + 3)/(-4) - (-3 - 0). Solve -23*s - 3*s**3 - 10*s + 5*s**2 + 15*s + 10*s**i = 0 for s.
0, 2, 3
Let m(h) be the second derivative of h**4/6 + 1616*h**3/3 + 652864*h**2 - 21*h - 54. Let m(r) = 0. What is r?
-808
Suppose -39*w + 64 = -23*w. Solve -8*t**3 - 10*t + 2*t**4 - 1042 - t**w + 17*t**2 + 1042 = 0 for t.
0, 1, 2, 5
Factor 23/5*o**2 + 14/5 - 33/5*o - 1/5*o**4 - 3/5*o**3.
-(o - 2)*(o - 1)**2*(o + 7)/5
Suppose -5*x - 3 = -13. Suppose 20*h - 31*h = 15*h. Determine u so that 0 + h*u + 2/15*u**x = 0.
0
Let x(z) be the second derivative of -9*z**5/10 - 28*z**4/3 + 44*z**3 + 32*z**2 + 27*z. Factor x(t).
-2*(t - 2)*(t + 8)*(9*t + 2)
Let n = -136708 - -136710. Factor 56/9*f - 32/3 - 4/9*f**n.
-4*(f - 12)*(f - 2)/9
Factor 1/2*u**4 + 58561/2*u**2 - 243*u**3 + 59292*u + 29768.
(u - 244)**2*(u + 1)**2/2
Determine u, given that 0*u**3 + 128267*u**2 + 5*u**3 - 128212*u**2 + 50*u = 0.
-10, -1, 0
Let s(g) be the first derivative of -g**4/22 - 94*g**3/33 - 46*g**2/11 - 4987. Factor s(j).
-2*j*(j + 1)*(j + 46)/11
Let p = 150/32323 + 7869027/38658308. Let t = p - 5/92. Factor 512/13 - 64/13*r + t*r**2.
2*(r - 16)**2/13
Let x(k) = -k**3 + 5*k**2 + 9*k - 15. Suppose -31*n + 37*n - 36 = 0. Let u be x(n). Factor -2/13*f**u + 0 - 2/13*f - 4/13*f**2.
-2*f*(f + 1)**2/13
Factor 896 + 3*t**2 - 1816 + 2765 - 624*t.
3*(t - 205)*(t - 3)
Let f(m) = 7*m**4 + 21*m**3 + 5*m**2 - 76*m + 48. Let v(b) = b**4 + b**3 - b**2. Let p(s) = f(s) - 5*v(s). Factor p(y).
2*(y - 1)**2*(y + 4)*(y + 6)
Let p(g) be the first derivative of -g**3 + 33/2*g**2 - 54*g - 79. Factor p(a).
-3*(a - 9)*(a - 2)
Let u = -3317 + 3319. Let h(c) be the first derivative of 1/6*c**3 + 1/4*c**4 + 1/10*c**5 + 0*c - 3 + 0*c**u. What is w in h(w) = 0?
-1, 0
Let f(h) be the first derivative of h**4/3 + 200*h**3/3 + 586*h**2/3 - 592*h - 3811. Factor f(x).
4*(x - 1)*(x + 3)*(x + 148)/3
Let l(p) be the second derivative of p**6/6 - 12*p**5 + 1555*p**4/6 - 920*p**3 + 2645*p**2/2 - 27*p + 7. Factor l(v).
5*(v - 23)**2*(v - 1)**2
Suppose -24 - 11*d + 1/2*d**2 = 0. Calculate d.
-2, 24
Let q(t) be the third derivative of -t**8/336 + 299*t**7/210 - 22499*t**6/120 + 22201*t**5/60 - 4*t**2 - 324. Factor q(f).
-f**2*(f - 149)**2*(f - 1)
Let g(n) be the third derivative of 0*n - 1/2*n**6 + 1/3*n**5 + 0*n**3 + 3*n**2 - 37/42*n**7 + 0*n**4 - 20 + 75/112*n**8. Solve g(x) = 0.
-2/5, 0, 2/9, 1
Let o(q) be the second derivative of -q**5/110 - 41*q**4/22 - 1240*q**3/11 + 3844*q**2/11 + 289*q. Factor o(x).
-2*(x - 1)*(x + 62)**2/11
Let h = -111986 + 111986. Let 0 + h*y**3 + 0*y + 1/2*y**5 - 1/2*y**4 + 0*y**2 = 0. What is y?
0, 1
Solve -685 + 22*g**5 + 504 + 75*g - 20*g**5 + 92*g**3 + 377 - 425*g - 28*g**4 + 88*g**2 = 0.
-2, 1, 7
Let k(g) be the third derivative of -g**7/280 + g**6/60 + 7*g**5/40 + g**4/2 - 95*g**3/3 - 166*g**2. Let z(i) be the first derivative of k(i). Factor z(w).
-3*(w - 4)*(w + 1)**2
Let k be (1945/12)/((-11)/(-88)). Let i = 1297 - k. Factor -1/9*y**2 - i*y**3 + 0*y - 1/3*y**4 + 0 - 1/9*y**5.
-y**2*(y + 1)**3/9
Let t(x) be the first derivative of -7*x**6/48 - 41*x**5/20 - 179*x**4/32 + 44*x**3/3 - 21*x**2/4 - 1204. What is q in t(q) = 0?
-7, -6, 0, 2/7, 1
Factor 0 - 32/5*c**3 - 34/5*c**2 + 0*c + 2/5*c**4.
2*c**2*(c - 17)*(c + 1)/5
Let b(s) = -32 - 28 + 0*s**2 + 28*s + 5*s**2 - 13*s**2. Let a(h) = h**2 + h - 1. Let x(c) = -4*a(c) - b(c). What is w in x(w) = 0?
4
Suppose 0 = -111*i + 489 - 267. Let t(j) be the second derivative of 1/50*j**5 + 0*j**3 + 0*j**4 - 2/75*j**6 + 29*j + 0 + 1/105*j**7 + 0*j**i. Factor t(r).
2*r**3*(r - 1)**2/5
Let j(d) be the third derivative of -d**6/80 + d**5/4 + d**4 - 40*d**3 - 9*d**2 - 54*d. Factor j(c).
-3*(c - 10)*(c - 4)*(c + 4)/2
Let s(i) be the second derivative of -22*i + 0*i**2 + 11/90*i**6 + 0*i**3 - 5/126*i**7 - 7/60*i**5 + 0 + 1/36*i**4. Factor s(m).
-m**2*(m - 1)**2*(5*m - 1)/3
Let b(y) be the first derivative of 0*y - 1/120*y**6 + 0*y**4 + 0*y**3 + 13 - 6*y**2 + 1/15*y**5. Let l(o) be the second derivative of b(o). Factor l(c).
-c**2*(c - 4)
Let 864*g - 24822 + 24822 + 4*g**2 = 0. What is g?
-216, 0
Let t be ((-80)/(-256))/((-80)/(-768)). Factor -4590/13*q - 324/13 - 50820/13*q**t + 29282/13*q**5 - 23760/13*q**2 - 26620/13*q**4.
2*(q - 2)*(11*q + 3)**4/13
Let m(n) = -n**2 + 12*n - 62. Let y be m(9). Let b be (4 - (-130)/y) + 70/441. What is u in 64/9*u - b*u**2 - 256/9 = 0?
8
Let -276*h - 3/2*h**2 + 555/2 = 0. What is h?
-185, 1
Let q be 2/6 + 1320/792. Let c(o) be the third derivative of -o**q + 0*o - 1/14*o**4 - 1/420*o**5 - 6/7*o**3 + 0. Factor c(j).
-(j + 6)**2/7
Let j(s) = s**2 + 27*s - 26. Let n be j(1). Let o(f) be the second derivative of -1/3*f**3 + 0 + 24*f - 3/4*f**n - 1/24*f**4. Suppose o(c) = 0. What is c?
-3, -1
Suppose 0 = 10*k - 15*k + 45. Suppose -2*l - 2 = 0, -t = 2*l - k - 2. Factor -u + t*u**3 - 4*u**3 + 4 - 11*u**3 + 7*u.
-2*(u - 2)*(u + 1)**2
Let q(l) be the second derivative of -5*l**5 + 280*l**4/3 + 1024*l**3 - 36864*l**2 + 2896*l. Factor q(x).
-4*(x + 8)*(5*x - 48)**2
Let k(c) = -19 + 44 + c**4 - 13*c - 20*c**2 + 49*c - 30*c**3. Let u(a) = a**4 + a. Let i(v) = k(v) - 6*u(v). Factor i(b).
-5*(b - 1)*(b + 1)**2*(b + 5)
Let w(b) = 2*b**5 - 2*b**3. Let f(t) = 3*t**5 - 16*t**4 + 68*t**3 - 4*t**2 - 287*t - 196. Let m(i) = 5*f(i) - 5*w(i). Suppose m(q) = 0. Calculate q.
-1, 4, 7
Suppose -7 = 2407*f + 21*f - 7. Factor 0 + 2/3*c**5 + f*c**2 + 0*c**3 - 122/3*c**4 + 0*c.
2*c**4*(c - 61)/3
Suppose -4*g - 4*i + 7564 = 0, 5669 = -g + 4*g - i. Factor -597*y**4 + 1895*y + 3*y**5 - 8100*y**2 - 12020*y - 3 + 465*y**4 + 3 + g*y**3.
3*y*(y - 15)**3*(y + 1)
Let t(v) be the first derivative of 2*v**5/35 + 10*v**4/7 + 10*v**3/3 - 20*v**2/7 - 72*v/7 - 1226. Let t(x) = 0. What is x?
-18, -2, -1, 1
Let w be ((-1)/2)/(-2*(-5)/(-80)). What is t in 120*t + w*t**2 + 17*t**2 - 22*t**3 + 72 - 2*t**5 + 17*t**2 - 14*t**4 = 0?
-3, -2, -1, 2
Let q(g) be the first derivative of -49*g**6 - 2282*g**5/5 - 979*g**4 - 104*g**3 + 680*g**2 - 256*g + 598. Suppose q(n) = 0. What is n?
-16/3, -2, -1, 2/7
Let z be -2 + ((-1256)/(-616) - 0). Let f = 169/385 - z. Factor -2/5*r**4 - f*r**2 - 4/5*r**3 + 0*r + 0.
-2*r**2*(r + 1)**2/5
Let w(f) = -9*f**3 + 23*f**2 + 160*f - 47. Let y(s) = 3*s**3 - 8*s**2 - 53*s + 16. Suppose u + 524 - 510 = 0. Let l(n) = u*y(n) - 4*w(n). Solve l(z) = 0.
-3, 1/3, 6
Let f(o) be the third derivative of o**5/150 - 14*o**4/15 + 784*o**3/15 - 16*o**2 - 22. Let f(g) = 0. Calculate g.
28
Let o(p) be the first derivative of 4*p**5/5 - 4*p**4 - 4*p**3/3 + 32*p**2 - 48*p - 222. Let o(f) = 0. Calculate f.
-2, 1, 2, 3
Let j(a) be the first derivative of a**4 - 800*a**3/3 + 794*a**2 - 792*a + 2400. Suppose j(c) = 0. What is c?
1, 198
Let u(o) be the second derivative of -1/50*o**5 + o - 96 - 1/15*o**3 - 6/5*o**2 + 2/15*o**4. What is r in u(r) = 0?
-1, 2, 3
Let n(u) = -344*u**3 + 1880*u**2 + 76*u - 24. Let a(z) = -207*z**3 + 1128*z**2 + 46*z - 14. Let h(r) = -12*a(r) + 7*n(r). Determine s, given that h(s) = 0.
-1/19, 0, 5
Let l(a) = 37*a - 259. Let z be l(10). Factor 4*b**3 - b - 10*b - 97*b - 105 - z.
4*(b - 6)*(b + 3)**2
Let v(r) be the first derivative of -34/3*r**3 + 18*r**2 + 16 + 0*r - 1/2*r**4. Factor v(f).
-2*f*(f - 1)*(f + 18)
Let i be (-3312)/(-2944) - 5/8. Find d, given that 0*d + 0 + 3/2*d**3 - 1/6*d**5 + 5/6*d**2 + i*d**4 = 0.
-1, 0, 5
Let j(q) be the third derivative of -1/24*q**3 + 2*q + 1/40*q**5 - q**2 + 5/96*q**4 + 0. Find f such that j(f) = 0.
-1, 1/6
Let r be (2/(-7))/(8 + ((-159)/14 - -3)). Find u, given that -372/5*u**2 - 1352/5 - r*u**4 + 364*u - 92/5*u**3 = 0.
-13, 1, 2
Factor 16928/5 + 192/5*n**2 - 4968/5*n - 2/5*n**3.
-2*(n - 46)**2*(n - 4)/5
Let b(q) = -2*q - 9. Let n(v) = v. Let c(p) = -b(p) + 2*n(p). Let s be c(-2). Solve 2*i**2 + s - 2*i - 2 - 3 = 0.
-1, 2
Suppose 5*x = -g + 33, g = -3*x - g + 17. Let b = 16 - x. Factor -6*j**4 + 12*j**3 + 4*j**5 - b*j**3 - j**5.
3*j**3*(j - 1)**2
Let x(f) be the first de