- 1)**2/7
Let o(w) = 13*w**4 - 9*w**3 + 4*w**2 - 8*w. Let u(r) = 24*r**4 - 18*r**3 + 9*r**2 - 15*r. Let g(n) = -9*o(n) + 5*u(n). Factor g(k).
3*k*(k - 1)**3
Let n(c) = -c + 1. Let f be ((-6)/4)/((-1)/2). Suppose 15 = -6*m + f*m, -4*v + 21 = -5*m. Let x(y) = -y**2 - 2*y + 3. Let i(h) = v*x(h) + 3*n(h). Factor i(g).
g*(g - 1)
Find k such that -25 + 25 - 28*k**3 + 1620*k**2 + 5*k**4 - 152*k**3 = 0.
0, 18
Factor 348*u**2 - 23*u**3 + 27*u**3 - 376*u**2.
4*u**2*(u - 7)
Let c be 1/(4 - (-60)/(-16)). Let a(f) be the first derivative of -1/22*f**c + 1/11*f**2 + 0*f**3 + 0*f - 2. Factor a(u).
-2*u*(u - 1)*(u + 1)/11
Let x(f) = f**2 + 8*f - 5. Let u be x(-9). Suppose -16 - 22*s**2 + 4*s**2 + u*s**3 + 32*s - 2*s**2 + 0 = 0. What is s?
1, 2
Suppose -2*x - 3*x + 27 = -4*a, 3*a + 24 = 5*x. Let o = x - 0. Find w, given that 7*w**4 - 6*w**o + 2*w + 4*w + 0 - 4*w**4 - 3 = 0.
-1, 1
Let q = 50/27 - 173/108. Factor -1/2*y**4 + 0 + 0*y**2 - q*y**3 - 1/4*y**5 + 0*y.
-y**3*(y + 1)**2/4
Let z(x) be the first derivative of -4/3*x**3 + 0*x + 1/4*x**4 + 2*x**2 - 7. What is p in z(p) = 0?
0, 2
Let c(d) be the second derivative of d**4/3 - 10*d**3 + d - 104. Factor c(k).
4*k*(k - 15)
Let p(w) = 2*w**4 + w**3 - w**2 - 1. Let u(j) = -15*j**4 + 3*j**3 + 21*j**2 - 9*j - 6. Let n(c) = -6*p(c) - u(c). Suppose n(f) = 0. What is f?
-1, 1, 4
Let a be 8/(-7)*7/14 + 703/777. Factor 5*s**2 + 0 - s**4 + 6*s + a*s**5 - 7/3*s**3.
s*(s - 3)**2*(s + 1)*(s + 2)/3
Let p(o) be the first derivative of o**7/420 + o**6/45 + 4*o**3 - 5. Let w(x) be the third derivative of p(x). Let w(y) = 0. What is y?
-4, 0
Let t be (-96 + 111 + 148/(-10))/((-1)/(-57)). Suppose t*n - 27/5 + 3/5*n**3 - 33/5*n**2 = 0. Calculate n.
1, 9
Let a be (4 - -2)/((-22 + 2)*-1). Let h(s) be the second derivative of 12*s + 0 + 1/20*s**4 - 6/5*s**2 + a*s**3. Factor h(j).
3*(j - 1)*(j + 4)/5
Let y(h) be the second derivative of -h**7/588 - h**6/105 - h**5/105 + 13*h**3/6 + 12*h. Let x(r) be the second derivative of y(r). Factor x(i).
-2*i*(i + 2)*(5*i + 2)/7
Let z = -55 - -82. Let w be (-30)/(-4)*18/z. What is k in 0*k + 0 + 0*k**4 - 2/9*k**3 + 0*k**2 + 2/9*k**w = 0?
-1, 0, 1
Let f be (-6 - (-28)/7) + 2. Suppose f = -10*d - 11*d. Factor -6*k**3 + d - 15/2*k**2 - 3/2*k.
-3*k*(k + 1)*(4*k + 1)/2
Let x = -26 - -63. Let o be x/5 - (7 + -5). Find h, given that -o*h**5 - 12/5*h**3 + 0 + 0*h + 0*h**2 - 36/5*h**4 = 0.
-2/3, 0
Let a(q) be the second derivative of 0 - 10*q + 5/3*q**4 + 1/5*q**5 + 2*q**3 - 18*q**2. Find b, given that a(b) = 0.
-3, 1
Let n = 12 - 9. Factor -2*a**4 - 2*a**4 + 4*a**n + 162*a**2 - 154*a**2.
-4*a**2*(a - 2)*(a + 1)
Let i(j) be the third derivative of j**6/60 - j**5/20 - j**4/2 - 7*j**3/6 - 58*j**2 - 2. Solve i(k) = 0.
-1, 7/2
Let o = -63 + 84. Let u be (18/o)/3*7. Factor 2/9*n**u - 4/9 + 2/9*n.
2*(n - 1)*(n + 2)/9
Let b be 1444/10*8/(-192)*-20. Let p = -120 + b. Solve p*s**2 + 0*s + 0 = 0.
0
Determine g, given that -263*g**2 + 290 - 28*g + 259*g**2 - 114 = 0.
-11, 4
Let t be 111/27 + 6/(-54). Let c(s) be the first derivative of -8 + 1/20*s**t + 1/15*s**3 + 0*s + 0*s**2. Let c(w) = 0. Calculate w.
-1, 0
Let d be 0*(2*(-3)/81 - 370/(-1350)). Solve -2/3*k**2 + 10/21*k**3 - 2/21*k**4 + 2/7*k + d = 0 for k.
0, 1, 3
Let j(o) = 2*o**2 + 54*o - 61. Let d(b) = b**2 + 27*b - 31. Let i(y) = 5*d(y) - 3*j(y). Let a be i(-28). Factor -6/5*g**2 + 4/5*g + a.
-2*g*(3*g - 2)/5
Let q(x) = 7*x**2 - 131*x - 34. Let u be q(19). Let z(d) be the second derivative of 1/36*d**3 + 1/12*d**2 - 1/120*d**5 - 4*d - 1/72*d**u + 0. Factor z(k).
-(k - 1)*(k + 1)**2/6
Let w(q) be the third derivative of q**6/60 - q**5/5 - q**4/12 + 2*q**3 + 60*q**2 - 4*q. Factor w(p).
2*(p - 6)*(p - 1)*(p + 1)
Let y(v) be the second derivative of 5*v**4/12 + 5*v**3/6 + 2*v - 8. Let y(x) = 0. Calculate x.
-1, 0
Suppose -5*w = -p + 27, -6*p + 4*w + 26 = -3*p. Let s(i) be the second derivative of 4*i + 0 + 1/6*i**4 - p*i**2 - 1/3*i**3. Factor s(a).
2*(a - 2)*(a + 1)
Let o(x) = x**3 + 10*x**2 - 10*x + 19. Let d be o(-11). Let w(n) = n**2 - 5*n - 24. Let j be w(d). Solve j + 4/9*h - 2/9*h**2 = 0 for h.
0, 2
Let d(q) = -2*q**4 + q**2 - q - 1. Let s(x) = -10*x**4 + 46*x**3 + 27*x**2 - 3*x - 3. Let n(k) = -3*d(k) + s(k). Suppose n(j) = 0. What is j?
-1/2, 0, 12
Let z = -10509 - -10509. Factor -2/3*v**2 + 2/3 + z*v.
-2*(v - 1)*(v + 1)/3
Let d(n) be the first derivative of n**6/39 + 14*n**5/65 - 20*n**4/13 + 88*n**3/39 - 753. What is q in d(q) = 0?
-11, 0, 2
Factor 1/4*k**5 - 1/2*k**2 + 5/4*k**4 - 3/4 + 3/2*k**3 - 7/4*k.
(k - 1)*(k + 1)**3*(k + 3)/4
Suppose 4 = g - 2*c, -5*g - 16 = 4*c + 6. Let q be (-1 - g)/(1/((-4)/(-2))). Find i such that 4/9*i + 0 - 2/9*i**q = 0.
0, 2
Let m(w) = w**3 + 212*w**2 + 425*w + 1052. Let i be m(-210). Factor -1/3*b + 1/2 - 1/6*b**i.
-(b - 1)*(b + 3)/6
Let v(p) be the third derivative of -p**5/330 + 3*p**4/22 - 27*p**3/11 - 245*p**2. Let v(l) = 0. What is l?
9
Let y(p) = -2*p + 18. Suppose 0 = 27*r - 21*r - 54. Let s be y(r). Factor 1/3*k**2 + s*k - 4/3.
(k - 2)*(k + 2)/3
Solve -14*p**4 - 344*p**2 - 279/2*p**3 + 45/2*p + 25 = 0.
-5, -1/4, 2/7
Let x be ((-4)/8)/(10/(-4)). Let a = 2536/5 + -507. Factor -1/5*j**5 + 0 + 0*j + a*j**3 + 1/5*j**2 - x*j**4.
-j**2*(j - 1)*(j + 1)**2/5
Suppose 0*y = -y. Suppose -174 = -25*o - 33*o. Factor -3/4*p**2 + y*p - 9/8*p**o - 3/8*p**4 + 0.
-3*p**2*(p + 1)*(p + 2)/8
What is p in 0*p**4 - 24/7*p**2 + 0 + 0*p + 76/7*p**3 - 100/7*p**5 = 0?
-1, 0, 2/5, 3/5
Let x(p) = -p**3 - 11*p**2 - 13*p + 7. Let q be x(-9). Let t = q + 38. Factor i - 3/2*i**2 + 0*i**3 + 1/2*i**4 + t.
i*(i - 1)**2*(i + 2)/2
Let b(f) = 2*f**2 - 3*f - 5. Let c = -4 - -2. Let r(a) = -a. Let y(n) = c*r(n) - b(n). Let j(w) = 6*w**2 - 14*w - 14. Let m(o) = 5*j(o) + 14*y(o). Factor m(d).
2*d**2
Let l(d) = d**5 - d**4 - d**3 - d - 1. Let g(q) = -10*q**5 + 115*q**4 + 600*q**3 + 810*q**2 + 15*q + 15. Let z(k) = g(k) + 15*l(k). Factor z(x).
5*x**2*(x + 2)*(x + 9)**2
Suppose -7*l = 9*l. Let o(v) be the first derivative of -4/3*v**3 - 1/2*v**4 + 0*v**2 + l*v + 1. Factor o(m).
-2*m**2*(m + 2)
Factor -117/2*a - 1/4*a**2 - 13689/4.
-(a + 117)**2/4
Let h(o) be the first derivative of -o**6/12 + 5*o**4/8 - o**2 + 167. Find x such that h(x) = 0.
-2, -1, 0, 1, 2
Factor 4*v**3 + 7*v**2 - 38*v + 13*v - 6 + 3*v**2 + 17*v.
2*(v - 1)*(v + 3)*(2*v + 1)
Let w(m) be the second derivative of 0*m**6 + 5/42*m**7 + 5/6*m**3 + 0*m**4 + 0*m**2 + 9*m + 0 - 1/2*m**5. Solve w(j) = 0 for j.
-1, 0, 1
Let s(j) be the first derivative of 2/5*j**3 + 6/5*j**2 - 6*j + 1/20*j**4 - 2. Let i(d) be the first derivative of s(d). Factor i(m).
3*(m + 2)**2/5
Let z(h) be the first derivative of -2/5*h**5 + 0*h**2 + 0*h + 0*h**4 + 2/3*h**3 - 18. Factor z(r).
-2*r**2*(r - 1)*(r + 1)
Let f(k) be the first derivative of k**5/5 + 3*k**4/2 + 13*k**3/3 + 6*k**2 + 4*k - 186. Factor f(q).
(q + 1)**2*(q + 2)**2
Suppose -2*q + 4*q + v + 8 = 0, 0 = 4*q + 4*v + 24. Let n be 2/6*((q - -3) + 0). Let 7/6*d**5 + 0*d + n*d**4 + 0*d**2 + 0 + 0*d**3 = 0. What is d?
-2/7, 0
Let j(x) = 11*x**3 - 11*x**2 - 30*x + 6. Let l(w) = -155*w**3 + 155*w**2 + 420*w - 85. Let o(r) = 85*j(r) + 6*l(r). Factor o(v).
5*v*(v - 3)*(v + 2)
Let x(r) be the second derivative of -r**4/12 + 2*r**3/3 + 63*r + 1. Suppose x(v) = 0. Calculate v.
0, 4
Let j(d) be the first derivative of d**4/8 + 8*d**3/3 + 16*d**2 + 48. Factor j(g).
g*(g + 8)**2/2
Factor 60 + 312/5*u + 3/5*u**3 + 87/5*u**2.
3*(u + 2)**2*(u + 25)/5
Factor 2/17*b**2 + 112/17*b + 1568/17.
2*(b + 28)**2/17
Solve 4475 - 12*j**2 - 4475 + 5*j**3 - 40*j - 23*j**2 = 0 for j.
-1, 0, 8
Suppose 0 = z + 4*w - 19, 3*z + 2*w - 5 = 4*z. Let q(p) be the second derivative of -p**z - p**2 - 1/10*p**5 - p - 1/2*p**4 + 0. Factor q(v).
-2*(v + 1)**3
Let q(n) be the second derivative of n**5/25 + 22*n**4/15 + 38*n**3/15 - 84*n**2/5 - 254*n. What is o in q(o) = 0?
-21, -2, 1
Let u(z) = 3*z**3 - 34*z**2 - 5*z - 225. Let c be u(12). Let -4/5*o + 2*o**c - 4/5*o**4 + 0 - 2/5*o**2 = 0. What is o?
-1/2, 0, 1, 2
Let s(n) be the first derivative of -n**5/20 - 3*n**4/16 + n**3/3 + 3*n**2/2 + 98. Factor s(o).
-o*(o - 2)*(o + 2)*(o + 3)/4
Let d(j) be the third derivative of 0*j - 5/3*j**3 + 0 + 1/30*j**5 + 1/3*j**4 - 10*j**2. Factor d(m).
2*(m - 1)*(m + 5)
Let w(s) be the third derivative of s**8/84 - 8*s**7