- 1)**2*(i + 1)**2/3
Let x(d) = d**4 + 3*d**3 - d**2 - 3*d. Let l(k) = -2*k**4 - 7*k**3 + 2*k**2 + 7*k. Let z(b) = 4*l(b) + 9*x(b). Factor z(i).
i*(i - 1)**2*(i + 1)
Let s be (3 - 10/4)*6. Let f(l) = l**4 - 5*l**3 + 6*l**2 - 10*l - 1. Let w(a) = a**2 + a + 1. Let c(i) = s*w(i) + f(i). What is r in c(r) = 0?
1, 2
Suppose -3*v - 4*f + 29 = 7, 0 = -5*v - f + 31. Suppose -2*n - 2*r = -v, 3 = 2*n - r - 0*r. Factor 2*m**2 + n*m**3 - 2*m**3 - 2*m**4.
-2*m**2*(m - 1)*(m + 1)
Let b(d) = -d**3 + 3*d**2 + d + 3. Let m be b(3). Let k be 20/24 + (-2)/m. What is a in 0*a + k*a**2 - 1/2 = 0?
-1, 1
Let g(b) be the third derivative of b**6/280 - 3*b**5/70 + 3*b**4/14 - 4*b**3/7 - 5*b**2. Factor g(r).
3*(r - 2)**3/7
Suppose -20 = -4*q - 0*q. Factor 2*p + p**4 + p**4 + q*p**2 + 4*p**3 - p**4.
p*(p + 1)**2*(p + 2)
Let h(g) be the third derivative of -g**3 - 2*g**2 + 1/6*g**4 - 1/90*g**5 + 0 + 0*g. Solve h(t) = 0 for t.
3
Let z(c) = c**3 + 3*c**2 + c + 3. Let i be z(-3). Suppose i = l + l - 6. Find g, given that 2 - 32*g**l + 32*g**4 - 2*g**2 - 2 + 2*g = 0.
-1/4, 0, 1/4, 1
Let d(r) = r**2 + r + 1. Let s(w) = 10*w**2 + 2*w + 5. Let c(q) = 21*d(q) - 3*s(q). Factor c(o).
-3*(o - 2)*(3*o + 1)
Let h(t) be the first derivative of t**3/3 + 5*t**2/2 + 3*t - 2. Let p be h(-5). Factor z**p + z**4 + 1 - 1.
z**3*(z + 1)
Let o(v) be the first derivative of 4*v**5/35 - 4*v**3/7 - 4*v**2/7 - 57. Determine s so that o(s) = 0.
-1, 0, 2
Let g(p) be the first derivative of -p**3/5 + p**2/5 + p/5 + 17. Suppose g(o) = 0. Calculate o.
-1/3, 1
Let y(f) = f + 11. Let a be 12/42 + (-79)/7. Let u be y(a). Factor -2/3*d**2 + 0 + u*d.
-2*d**2/3
Suppose 11 = 4*s - 5, 0 = a - 4*s + 14. Factor 2/3 - 7/6*z**2 - a*z.
-(z + 2)*(7*z - 2)/6
Let v be (-55)/(-15) - 1/(-3). Let 2*i + 5*i**v + 0*i**4 - 7*i + 5*i**3 - 5*i**2 - 2*i**4 + 2 = 0. Calculate i.
-2, -1, 1/3, 1
Let y(s) be the first derivative of 3*s**4 - 8*s**3/3 - 24*s**2 + 32*s - 10. Find d, given that y(d) = 0.
-2, 2/3, 2
Let s(c) be the third derivative of c**7/385 + c**6/132 + c**5/330 - c**4/132 + 2*c**2. Factor s(b).
2*b*(b + 1)**2*(3*b - 1)/11
Let b(x) = 2*x - 12. Let r be b(7). Find p such that 0 + 2/3*p**3 + 2/3*p**4 + 0*p**r + 0*p = 0.
-1, 0
Let w be -7 + (-3 - -6) + -1. Let p = w - -11/2. Factor 0 + 0*c**3 + 1/2*c**4 + 0*c - p*c**2.
c**2*(c - 1)*(c + 1)/2
Let t be (1 - 0) + 2*(-58)/120. Let g(y) be the third derivative of y**2 + t*y**5 + 0 + 0*y + 1/3*y**4 + 4/3*y**3. Solve g(w) = 0.
-2
Suppose 5 + 1 = -c. Let z be ((-8)/6 + 1)*c. Let -w**z - w + w + 1 = 0. What is w?
-1, 1
Let i = 5 + -3. Solve 2*z + 1 + 3*z**2 + 0*z**3 - 4*z**i - z - z**3 = 0.
-1, 1
Let d(a) = 8*a**2 - a - 10*a**2 + 3*a**2 - a**4. Let p(q) = 4*q**4 + 12*q**3 + 11*q**2 + q. Let s(h) = d(h) + p(h). Factor s(o).
3*o**2*(o + 2)**2
Let a(h) = 2*h**2 - 84*h - 83. Let r be a(43). Find m such that -147/4*m**3 + r + 63/4*m**2 + 18*m = 0.
-2/7, 1
Let l be -3 - -1*724/240. Let x(j) be the third derivative of 0*j + 0 - 1/84*j**4 - l*j**6 - 1/245*j**7 + 0*j**3 - 2*j**2 - 1/42*j**5. Factor x(k).
-2*k*(k + 1)**2*(3*k + 1)/7
Let c = -677/3 + 232. Let v = 41/6 - c. Factor v*m**3 + 1/2*m + 0 + m**2.
m*(m + 1)**2/2
Let y(c) be the first derivative of -c**3/3 + 3*c**2 - 4*c - 1. Let a be y(4). Let d**2 + 2*d - 13*d - 27 - 7*d - a*d**2 = 0. Calculate d.
-3
Let y(l) be the first derivative of l**6/3 + 23*l**5/10 + 23*l**4/4 + 35*l**3/6 + l**2 - 2*l + 9. Solve y(c) = 0 for c.
-2, -1, 1/4
Find y such that y**2 - 6*y - y + 8*y + 0*y**2 = 0.
-1, 0
Let a(y) be the second derivative of 3*y**5/10 + y**4/4 - y**3/2 + 3*y. Factor a(s).
3*s*(s + 1)*(2*s - 1)
Solve -5*w + 2*w - w**2 + 2*w**2 = 0 for w.
0, 3
Let a(g) be the third derivative of g**7/210 - 17*g**6/360 + g**5/6 - g**4/6 - 4*g**3/9 - g**2. Factor a(m).
(m - 2)**3*(3*m + 1)/3
Suppose 10 = k - 2*w, -w - 8 = -4. Factor 0*j**k - 1/3*j**5 + 0*j + 1/3*j**4 + 0 + 0*j**3.
-j**4*(j - 1)/3
Let v = 4294 - 77261/18. Let p = v + -2/9. Solve -1/4 - 3/4*x**5 + p*x**2 - 5/4*x**4 + 1/2*x**3 + 1/4*x = 0 for x.
-1, 1/3, 1
Let -54*f**5 - 72*f + 141*f**3 + 51*f**2 + 12 - 93*f**5 - 63*f**4 + 57*f**3 + 21*f**3 = 0. Calculate f.
-1, 2/7, 1
Let u = 7 + -4. Factor -3*a**4 - u*a**3 + 2*a**3 - 2*a**3.
-3*a**3*(a + 1)
Let i(h) be the third derivative of -h**2 - 3/5*h**5 + 0*h - 1/40*h**6 - 6*h**4 - 32*h**3 + 0. Factor i(y).
-3*(y + 4)**3
Determine o, given that 2/3*o**3 - 16*o**2 - 1024/3 + 128*o = 0.
8
Suppose -10 = 2*u - 2*x, -2*u = -3*u + 3*x - 1. Let f = u + 7. Factor -4*h**2 + h**3 + f*h**3 + 3*h**4 + 2*h**2.
h**2*(h + 1)*(3*h - 2)
Let h = -3 + 6. Determine j, given that -h*j**5 + j**4 - 2*j**2 + 2*j**2 + 2*j**2 - 3*j**2 - 2*j + 5*j**3 = 0.
-1, -2/3, 0, 1
Let n(c) = 10*c**5 + 12*c**4 - 11*c**3 - 6*c**2 + 5*c + 2. Let d(v) = 39*v**5 + 48*v**4 - 45*v**3 - 24*v**2 + 21*v + 9. Let z(s) = 2*d(s) - 9*n(s). Factor z(r).
-3*r*(r + 1)**2*(2*r - 1)**2
Let c(m) be the first derivative of -m**6/7 + 12*m**5/35 - 3*m**4/14 + 13. Suppose c(o) = 0. What is o?
0, 1
Determine o, given that 4*o**3 + 0 + 6 + 11*o**2 - 2 + 12*o + o**2 = 0.
-1
Factor -125*l - 12*l**4 - 20 - 28*l**4 - 270*l**2 - 168*l**3 - 52*l**3.
-5*(l + 4)*(2*l + 1)**3
Let v = 131 + -1177/9. Factor -2/9*h - v*h**2 + 0.
-2*h*(h + 1)/9
Suppose -5*w + 12 - 2 = 0. Factor 4*z - 3 - 2 + 3 - w*z**2 + 0.
-2*(z - 1)**2
Let o(u) be the second derivative of -u**8/168 - 2*u**7/105 + u**5/15 + u**4/12 + 7*u**2/2 + 2*u. Let q(n) be the first derivative of o(n). Factor q(g).
-2*g*(g - 1)*(g + 1)**3
Let i = -1/57 + 22/171. Let w(y) be the first derivative of 3 + 4/27*y**3 - i*y**2 - 2/9*y. Factor w(a).
2*(a - 1)*(2*a + 1)/9
Let k(b) be the third derivative of b**8/112 - b**7/175 - b**6/20 + b**5/25 + b**4/8 - b**3/5 + 6*b**2. Suppose k(m) = 0. Calculate m.
-1, 2/5, 1
Let y(u) be the second derivative of u**6/90 - u**5/60 - u**4/36 + u**3/18 + 6*u. Factor y(k).
k*(k - 1)**2*(k + 1)/3
Let j(m) be the first derivative of 4*m**3/21 - 2*m**2/7 - 8*m/7 - 6. Factor j(x).
4*(x - 2)*(x + 1)/7
Let m(w) be the third derivative of -1/90*w**5 + 0*w - 1/360*w**6 - 6*w**2 + 0*w**3 + 1/24*w**4 + 0. Factor m(x).
-x*(x - 1)*(x + 3)/3
Let l(p) be the second derivative of 1/2*p**3 - 1/20*p**5 + 3/80*p**6 + 1/2*p**2 + 0 - 3/16*p**4 + 4*p. Let q(k) be the first derivative of l(k). Factor q(w).
3*(w - 1)*(w + 1)*(3*w - 2)/2
Let l(r) be the second derivative of -r**7/273 - 4*r**6/39 - 16*r**5/13 - 320*r**4/39 - 1280*r**3/39 - 1024*r**2/13 - 45*r - 2. Factor l(m).
-2*(m + 4)**5/13
Factor -8/9 - 4*c + 448/9*c**3 + 32/3*c**2.
4*(4*c + 1)**2*(7*c - 2)/9
Let z(k) = k - 1. Let r be z(3). Let p = r + 0. Determine j, given that -j + 1/3*j**p + 2/3 = 0.
1, 2
Let s(g) be the first derivative of 2 - 1/24*g**6 + 0*g**2 + 1/16*g**4 + 0*g - 1/12*g**3 + 1/20*g**5. Let s(k) = 0. What is k?
-1, 0, 1
Let z(q) be the third derivative of q**9/272160 - q**7/22680 - q**5/10 + 6*q**2. Let j(l) be the third derivative of z(l). Factor j(a).
2*a*(a - 1)*(a + 1)/9
Let x(h) be the first derivative of -h**6/150 + h**5/100 - 6*h - 1. Let b(f) be the first derivative of x(f). Factor b(n).
-n**3*(n - 1)/5
Let k be (3/(-12)*1)/(15/(-12)). Factor 8/5*b + k*b**3 + b**2 + 4/5.
(b + 1)*(b + 2)**2/5
Let h = -1 - 1. Let x be (h/4)/(5/(-30)). What is a in 4 - 1 + a**x - 3 + a**4 = 0?
-1, 0
Let h(y) = -y**2 + 2. Let z be h(0). Let w(j) = j**3 + 5*j**2 + 4*j. Let t be w(-4). Let 0*l**2 + t*l - 4*l + z*l - l**2 = 0. What is l?
-2, 0
Let c(h) be the third derivative of -h**5/80 - h**4/16 - h**3/8 - 37*h**2. Factor c(l).
-3*(l + 1)**2/4
Let g(v) be the first derivative of 0*v + 7/27*v**6 + 0*v**3 + 0*v**2 + 1 - 1/9*v**4 - 2/9*v**5. Factor g(f).
2*f**3*(f - 1)*(7*f + 2)/9
Let -14/3*i**4 + 4/3*i + 0 - 4/3*i**5 - 4*i**3 + 2/3*i**2 = 0. Calculate i.
-2, -1, 0, 1/2
Let u(m) be the third derivative of m**6/24 + m**5/3 + 5*m**4/8 - 2*m**2. Solve u(l) = 0.
-3, -1, 0
Let h(c) = 2*c**3 - 10*c**2 + 8*c - 4. Let m(b) = -10*b**3 + 51*b**2 - 39*b + 20. Let s(j) = 22*h(j) + 4*m(j). Factor s(x).
4*(x - 2)*(x - 1)**2
Suppose -5*s - 30 = 3*f, -3*s + 2*f = -s - 4. Let h be 3/(-4)*s/9. Suppose 0 + 1/2*l**2 - h*l**3 - 1/4*l = 0. What is l?
0, 1
Let k(n) be the second derivative of 7*n**6/80 + 141*n**5/160 + 21*n**4/16 - 8*n**3 + 6*n**2 + 3*n. Let k(h) = 0. Calculate h.
-4, 2/7, 1
Suppose 0 = 3*w - 17 + 2. Fact