(3/(-2))/(-3)*4. Let b = -8 + 11. Determine w, given that 14*w**2 + 4*w**2 - u*w**4 - 4*w**4 + 10*w**b - 8*w**4 - 4 - 10*w = 0.
-1, -2/7, 1
Factor -103*i**3 - 8*i**4 + 38*i**4 + 5*i**5 + 68*i**3.
5*i**3*(i - 1)*(i + 7)
Let p be (-6)/2 + 1 + 2. Let s(b) be the third derivative of b**2 + 1/240*b**6 + 0 + p*b**3 + 1/48*b**4 + 1/60*b**5 + 0*b. Factor s(y).
y*(y + 1)**2/2
Let s(k) be the second derivative of -13/20*k**5 - 1/6*k**3 + 0*k**2 + 1/10*k**6 - 7/12*k**4 + 0 + 3/7*k**7 + k. Determine o so that s(o) = 0.
-1/2, -1/3, 0, 1
Let k(n) be the first derivative of 3/14*n**2 - 3/28*n**4 + 1 + 3/35*n**5 + 6/7*n - 3/7*n**3. Solve k(x) = 0 for x.
-1, 1, 2
Factor -j**4 + 1/4*j + 0 - 3/2*j**2 + 9/4*j**3.
-j*(j - 1)**2*(4*j - 1)/4
Let g(o) = -o**2 + o + 1. Suppose 5 = 4*p + 25. Let a(k) = 0*k**3 - 2*k + 5 - 7*k**2 + 4*k + 3*k + 2*k**3. Let z(u) = p*g(u) + a(u). Solve z(d) = 0.
0, 1
Suppose -4*z + 6*z = 2*w + 8, -5*w - z - 20 = 0. Let q be (w - -1) + 29/9. Determine b, given that 4/9*b + 0 - q*b**2 = 0.
0, 2
Let u(z) be the third derivative of -1/150*z**5 + 0 - 1/30*z**4 - 3*z**2 + 0*z + 0*z**3. Factor u(w).
-2*w*(w + 2)/5
Let j(s) be the first derivative of 0*s - 1 + 1/3*s**3 + 1/4*s**2. Determine m so that j(m) = 0.
-1/2, 0
Suppose 0 = -3*b - 8 + 14. Let 1/2 - o + 1/2*o**b = 0. What is o?
1
Let c(f) = 2*f**5 - 8*f**4 + 14*f**3 - 6*f**2 + 2*f + 2. Let d(x) = 2*x**5 - 7*x**4 + 13*x**3 - 5*x**2 + 3*x + 3. Let z(j) = 3*c(j) - 2*d(j). Factor z(w).
2*w**2*(w - 2)**2*(w - 1)
Suppose 3*k - 3*t - 7 = -4, 4*k - 5*t - 2 = 0. Suppose 6*b - k = 3. Factor 3/2*i - 1/2*i**3 - b + 0*i**2.
-(i - 1)**2*(i + 2)/2
Suppose n - 3*s = 5*n - 31, -16 = n - 4*s. Factor 0 - 2*v**3 - 2*v**2 - 2/3*v - 2/3*v**n.
-2*v*(v + 1)**3/3
Let h(d) be the third derivative of -d**5/15 - d**4 - 6*d**3 - 7*d**2. Let h(a) = 0. What is a?
-3
Let p(f) be the first derivative of -2*f**5/3 + 17*f**4/6 - 32*f**3/9 + 4*f**2/3 - 1. Solve p(l) = 0 for l.
0, 2/5, 1, 2
Suppose -4 = 4*f + 2*d - 2, 2*d + 14 = 2*f. Factor 0*y - 2/15*y**4 + 0 + 4/15*y**f - 2/15*y**3.
-2*y**2*(y - 1)*(y + 2)/15
Let n = -59/8 + 61/8. Suppose n*v**2 - 1/4 + 0*v = 0. What is v?
-1, 1
Let l be (-18)/81 + (-1 - (-76)/18). Factor 3/2*m**5 + 7/2*m**l - 4*m**4 - m**2 + 0 + 0*m.
m**2*(m - 1)**2*(3*m - 2)/2
Let c be (17/102)/((-1)/(-3)). Factor -3/2*y + c*y**2 + 1.
(y - 2)*(y - 1)/2
Factor r**2 + 0 + 1/2*r**3 + 1/2*r.
r*(r + 1)**2/2
Let w(n) be the second derivative of n**4/4 + 7*n**3/2 - 12*n**2 - 30*n. Factor w(c).
3*(c - 1)*(c + 8)
Let h(y) = y**3 - 4*y**2 - 5*y + 4. Let m be h(4). Let a be (-4)/(-6)*(-12)/m. Suppose -1/2*g**4 - a - g**5 + g**2 - g + 2*g**3 = 0. Calculate g.
-1, -1/2, 1
Let x(h) be the third derivative of h**8/84 - 2*h**7/35 + h**6/15 - 4*h**2. Factor x(z).
4*z**3*(z - 2)*(z - 1)
Let l(a) = -3*a**5 + 9*a**4 + 15*a**3 - 12*a**2 - 15*a - 3. Let j(n) = n**2 + n + 1. Let i(c) = -3*j(c) - l(c). Find k, given that i(k) = 0.
-1, 0, 1, 4
Let i(c) = c**4. Let x(n) = n**4 - 15*n**3 + 27*n**2 - 21*n + 6. Let g(w) = -2*i(w) - x(w). Find a, given that g(a) = 0.
1, 2
Suppose -b = 3*r + 6, 2*b + 2*b = -5*r - 3. Let z = 265/3 + -87. What is o in -5/3*o + z*o**2 - 1/3*o**b + 2/3 = 0?
1, 2
Factor -2/3*u**3 + 0 - 4/3*u**2 - 2/3*u.
-2*u*(u + 1)**2/3
Let z(a) be the third derivative of -7/40*a**6 + 1/14*a**7 + 0*a + 0*a**3 + 1/10*a**5 - 4*a**2 + 0*a**4 + 0. Factor z(l).
3*l**2*(l - 1)*(5*l - 2)
Let z(x) = -x**3 - 4*x**2 + 3*x - 5. Suppose -10 = 6*v - 4*v. Let n be z(v). Find f such that -2/3*f**2 + 0 - 2/3*f**n + 0*f + 2/3*f**4 + 2/3*f**3 = 0.
-1, 0, 1
Suppose -25 = -0*w - 5*w. Factor -22*b**2 + w*b + 7*b**3 + 3*b**3 - 2*b**4 + 6*b**2 + 3*b.
-2*b*(b - 2)**2*(b - 1)
Let g(b) = -b + 4. Let a be g(3). Let u = 4 - a. Let 0 - 2/3*s**4 + 0*s + 0*s**u + 0*s**2 = 0. What is s?
0
Let x(b) be the first derivative of b**4/2 - 2*b**3/3 - 8*b**2 + 24*b + 15. Let x(q) = 0. What is q?
-3, 2
Let r(s) be the first derivative of -2*s**2 - 4*s - 1 - 1/3*s**3. Factor r(t).
-(t + 2)**2
Let x = -3 - -8. Let r be (294 - 0)*1/x. Factor 28/5*d**2 - 88/5*d + r*d**3 + 16/5.
2*(3*d + 2)*(7*d - 2)**2/5
Let p = 881/24 - 81319/2280. Let a = p + 3/19. What is x in -4/5*x**2 + 0*x + 0 + a*x**4 - 2/5*x**3 = 0?
-2/3, 0, 1
Let z(i) be the first derivative of i**3 + 3*i**2 - 9*i + 8. Factor z(v).
3*(v - 1)*(v + 3)
Suppose 0 = g + 2*b - 8, b + 2 = 2*g - 9. Suppose -6*y**5 + g*y**3 - 5*y**4 - y**4 + 5*y**2 - y**2 + 2*y**4 = 0. Calculate y.
-1, -2/3, 0, 1
Let n(y) be the third derivative of y**7/1050 - y**6/450 - y**5/150 + 5*y**4/24 + 9*y**2. Let b(z) be the second derivative of n(z). Let b(o) = 0. What is o?
-1/3, 1
Let f be -4*(-4)/(48/(-183)). Let h = 433/7 + f. Factor 4/7 - h*b - 2*b**3 - 24/7*b**2.
-2*(b + 1)**2*(7*b - 2)/7
Let v be 3*1*59/354. Factor -v*f**2 + f - 1/2.
-(f - 1)**2/2
Let z(l) = 2*l**2 + l - 5. Let n(g) = g**2 + g - 3. Let w(i) = 5*n(i) - 3*z(i). Factor w(k).
-k*(k - 2)
Let d(c) = -c + 7. Let g be d(5). Let i be (-1 + g)*(7 + -4). Let -i*t + 4*t**4 - 3*t**2 - 5*t**2 + 4*t**2 + 5*t - 2*t**5 = 0. Calculate t.
-1, 0, 1
Let q be (-4)/1 - 10/(-60)*32. Solve q*d**2 - 4/3 + 0*d = 0.
-1, 1
Factor -1/2*b**3 - 1/2*b**2 + b + 0.
-b*(b - 1)*(b + 2)/2
Let d(j) = 7*j**5 + j**4 - j**3 - 7*j**2 - 3. Let m(g) = 20*g**5 + 4*g**4 - 4*g**3 - 20*g**2 - 8. Let c(n) = -8*d(n) + 3*m(n). Let c(b) = 0. What is b?
-1, 0, 1
Factor -1/3*h + 4/3*h**3 - 4/3*h**2 + 1/3.
(h - 1)*(2*h - 1)*(2*h + 1)/3
Let u = 13529/80 - 1381/16. Factor -6*z**2 - 48/5*z + 278/5*z**3 + 162/5*z**5 + 8/5 + u*z**4.
2*(z + 1)**3*(9*z - 2)**2/5
Let z(c) = -2*c**3 - 6*c**2 - c. Let q be z(-3). Let l(k) be the first derivative of 0*k**3 + 0*k + 1/16*k**4 + 0*k**2 + 1/20*k**5 + q. Factor l(v).
v**3*(v + 1)/4
Determine l, given that -10/11*l**5 + 2/11*l**3 + 0*l + 8/11*l**4 + 0*l**2 + 0 = 0.
-1/5, 0, 1
Let y(x) be the second derivative of -x - 1/150*x**5 + 0 - 1/15*x**4 - x**2 - 4/15*x**3. Let o(m) be the first derivative of y(m). Determine s so that o(s) = 0.
-2
Let v be 9 - 2 - 660/100. Factor -v*c**2 - 2/5 + 4/5*c.
-2*(c - 1)**2/5
Let n(b) be the second derivative of -1/24*b**4 + 3*b - 1/40*b**5 + 1/12*b**3 + 1/4*b**2 + 0. Factor n(t).
-(t - 1)*(t + 1)**2/2
Let c be 8540/9 + (13 - 17). Let j = -944 + c. Determine m so that -j*m**2 + 2/9 - 2/3*m = 0.
-1, 1/4
Let c(t) be the first derivative of 0*t**2 - 1 + 4/3*t**3 + t**4 + 0*t. Solve c(k) = 0 for k.
-1, 0
Let g be (-5)/(-20) - 2/8. What is t in -4*t**2 - 3 + 4 + 5*t**2 - 2*t + g*t = 0?
1
Suppose -1 = g - 4. Let z(q) be the second derivative of -1/2*q**2 + 1/2*q**3 - 13/48*q**4 + 3/40*q**5 + 0 + g*q - 1/120*q**6. Suppose z(v) = 0. Calculate v.
1, 2
Let u(q) = 44*q**4 - 50*q**2 + 10*q**3 - 3*q + 20*q**2 - 7*q. Let c(o) = -9*o**4 - 2*o**3 + 6*o**2 + 2*o. Let w(m) = -14*c(m) - 3*u(m). What is g in w(g) = 0?
-1, -1/3, 0, 1
Let c(b) be the second derivative of b**6/180 + b**5/60 + 2*b**3/3 - 2*b. Let l(s) be the second derivative of c(s). Factor l(a).
2*a*(a + 1)
Suppose i - 3 = 1. Suppose -4*c - c**i + 2*c + 1 - 4 + 2*c**3 + 4 = 0. Calculate c.
-1, 1
Let a(q) be the third derivative of 1/18*q**3 + 0 + 0*q - 1/60*q**5 - 2*q**2 - 1/36*q**4. Suppose a(x) = 0. Calculate x.
-1, 1/3
Let f(l) be the first derivative of -l**5/300 + l**4/120 + 3*l**2/2 - 1. Let s(d) be the second derivative of f(d). Suppose s(w) = 0. Calculate w.
0, 1
Let m(q) = q**3 - 6*q**2 + q - 3. Let c be m(6). Suppose -n**3 + n**5 + 3*n - n**c + 2*n - 4*n = 0. What is n?
-1, 0, 1
Let q(f) be the first derivative of -f**5/60 + f**4/36 + f**3/18 - f**2/6 + 8*f + 3. Let j(p) be the first derivative of q(p). Factor j(z).
-(z - 1)**2*(z + 1)/3
Suppose -2*i - i = 12. Let m = -2 - i. Determine l so that 0*l**3 - 2/7*l**m + 0*l + 0 + 2/7*l**4 = 0.
-1, 0, 1
Let k(l) = 15*l**2 + l**3 - 5*l**2 + l + 8*l + 0*l**3. Let w be k(-9). What is f in w*f + 0 - 1/3*f**2 = 0?
0
Suppose p + 4*i - 4 = 2*p, 4 = 4*i. Let f(u) be the first derivative of 2 - 1/4*u + 1/12*u**3 + p*u**2. What is m in f(m) = 0?
-1, 1
Factor 0*n**2 + 0*n + 16/9*n**5 + 14/9*n**4 - 2/9*n**3 + 0.
2*n**3*(n + 1)*(8*n - 1)/9
Let s(r) be the first derivative of -2*r**3/27 + 4*r**2/9 - 2*r/3 + 15. Factor s(k).
-2*(k - 3)*(k - 1)/9
Solve 11*c**3 + 19*c**3 - 737*c**4 - 48*c + 60 - 87*c**2 + 746*c**4 = 0 for c.
-5, -1, 2/3, 2
Suppose 0 = -2*b + 4*b - 2. Suppos