b**4 + b**3 + b**2. Let w(a) be the first derivative of -2*a**6/3 + 3*a**4 + 4*a**3/3 - 38. Let g(d) = 12*v(d) - 2*w(d). Factor g(y).
-4*y**2*(y - 1)**3
Let u(c) be the second derivative of -7*c**5/30 - 4*c**4/9 + 11*c**3/3 - 6*c**2 + 8*c + 10. Factor u(s).
-2*(s - 1)*(s + 3)*(7*s - 6)/3
Let j(f) = f**4 - f**3 - f - 1. Let q(c) = 9*c**4 + 18*c**3 + 60*c**2 + 42*c - 6. Let l(o) = 6*j(o) - q(o). Determine n, given that l(n) = 0.
-4, -2, 0
Factor 365*g**3 + 45*g**5 - 280*g**2 - 15045 + 80*g - 210*g**4 + 15045.
5*g*(g - 1)**2*(3*g - 4)**2
Suppose -6 = -11*t + 5. Let x be (32/(-24))/(-3 + t). What is k in 2*k**2 + 2/3*k - 4/3*k**4 - x - 2/3*k**3 = 0?
-1, 1/2, 1
Suppose 429*o - 421*o = 0. Let m(n) be the second derivative of 1/100*n**5 + 0*n**3 - 3*n + 0*n**2 - 1/150*n**6 + o + 1/30*n**4. Let m(c) = 0. Calculate c.
-1, 0, 2
Let r be (6/(-8) - (-12)/16)/(-1). Let u(d) be the third derivative of r*d + 1/30*d**5 + 2/9*d**3 - 5*d**2 + 0 + 5/36*d**4. Suppose u(s) = 0. What is s?
-1, -2/3
Suppose -2*g + 29 = 5*a, -a - 5*g + 30 = 3*a. Factor 0*n**5 + 36*n**3 - 21*n**3 + n**a - 17*n**3 + n.
n*(n - 1)**2*(n + 1)**2
Suppose -3*p - 10 = -5*o, 1 = p - 4*o + 16. Let t(j) be the first derivative of j**4 + 2*j**2 - 2*j**3 - 1/5*j**5 - p - j. Factor t(n).
-(n - 1)**4
Let o be ((-5)/3)/(-3 - 8/4). What is w in -2/3 + o*w**2 - 1/3*w = 0?
-1, 2
Factor -3*x**3 - 2*x**3 + 3*x**3 + 4*x**3 + 2*x**2 + 3 - 5 - 2*x.
2*(x - 1)*(x + 1)**2
Let d(j) = 66*j - 2. Let p be d(-1). Let z = 68 + p. Factor 1/6*h + z - 1/6*h**2.
-h*(h - 1)/6
Let o be (-204)/(-17)*(-2)/(-6). Let l(q) be the first derivative of 5 + 5/6*q**2 - 2/9*q**3 + 4/15*q**5 - 2/3*q - 1/3*q**o - 1/18*q**6. Factor l(g).
-(g - 2)*(g - 1)**3*(g + 1)/3
Determine o, given that o**5 - 18*o + 31*o - 13*o - 2*o**3 + o**5 = 0.
-1, 0, 1
Let h(u) = 1. Let a(t) = -t + 20. Let d(z) = a(z) - 5*h(z). Let j be d(13). Factor -18*l**3 - 30*l - 3*l**j - l**2 - 9 - 32*l**2 - 3*l**4.
-3*(l + 1)**3*(l + 3)
Suppose 0 = 2*o + 10, 15 = 5*t - 2*o + o. Let u be 3/((-1)/t - -2). Solve -2*g**2 + 4*g + 4*g**2 + 0*g**2 - u*g**3 = 0 for g.
-1, 0, 2
Let g = -172 - -170. Let i be (-2)/(-2) + (g - 2) + 8. Factor 1/5*z + 0 - 1/5*z**i + 2/5*z**2 + 0*z**3 - 2/5*z**4.
-z*(z - 1)*(z + 1)**3/5
Let g = 18 - 9. Suppose 2*t - 1 - 5 = 2*y, 2*y + t = g. Factor -1/2*x**y + 0 - x.
-x*(x + 2)/2
Let j(p) = 3*p**3 - 2*p**2 - 2*p + 3. Let z be j(1). Factor -x**3 - 4*x**3 - 35*x**z - 13*x**3 - 2*x**3 + 10*x.
-5*x*(x + 2)*(4*x - 1)
Factor 0*j**4 + 0*j - 1/5*j**3 + 1/5*j**5 + 0*j**2 + 0.
j**3*(j - 1)*(j + 1)/5
Let h be (-20)/(-8)*408/20*-3. Let g = h + 153. Determine x, given that -2/9*x**2 + 4/9*x + g - 2/9*x**3 = 0.
-2, 0, 1
Let -5139*y**4 + 121*y**5 + 21660*y**3 - 144 - 11524*y**2 - 4557*y**4 + 196*y**5 + 183*y**5 + 3396*y**4 + 2208*y = 0. What is y?
1/5, 6
Let h(s) = s**3 - 9*s**2 + 8*s + 2. Let u be h(8). Determine r so that 3*r**2 + 6*r + 7*r**u - 32*r**3 - 21*r + 37*r**3 = 0.
-3, 0, 1
Let x(f) be the third derivative of 0*f**5 + 0*f + 0*f**3 + 16*f**2 + 0 + 0*f**4 - 1/30*f**6. Factor x(k).
-4*k**3
Let x(k) be the second derivative of 1/6*k**4 - 2/3*k**3 + 1/20*k**5 - 4*k**2 + 0 + 17*k. Determine o so that x(o) = 0.
-2, 2
Factor -48*k**4 - 64*k**2 - 9*k**5 + 64*k**2 + 13*k**5.
4*k**4*(k - 12)
Let m(r) = -r**2 - 1753*r + 7031. Let o be m(4). Find s, given that 1/3*s + 1/3*s**2 - 1/3 - 1/3*s**o = 0.
-1, 1
Solve -27*y**5 - 3*y**3 + 4*y**2 + 4*y - 3*y**4 - 25*y**5 + 51*y**5 - y**4 = 0 for y.
-2, -1, 0, 1
Let z be 10/15 - 2/(-6)*46. Solve -6 - 116*k**2 + 84*k - 224*k**3 - z*k**2 + 3 - 5 = 0.
-1, 1/8, 2/7
What is n in -2/11*n**4 - 24/11*n**3 + 0*n + 0 + 26/11*n**2 = 0?
-13, 0, 1
Suppose -2*x - 2*x = -3*o - 15, 4*o + 12 = 4*x. Suppose -2*p + x*p = -4*d + 8, 0 = 4*p - 4*d - 32. Factor 5*k - 3*k**2 - p*k + 4*k**2.
k**2
Let d(m) be the first derivative of -15*m**4/4 - 164*m**3 - 966*m**2/5 - 384*m/5 + 23. Factor d(j).
-3*(j + 32)*(5*j + 2)**2/5
Let f = 1911 + -1906. Let b(h) be the third derivative of 0*h**3 + 1/20*h**f + 1/24*h**4 + 0*h + 1/40*h**6 + 0 + 1/210*h**7 + 6*h**2. Factor b(w).
w*(w + 1)**3
Let j(w) be the second derivative of w**8/57120 - w**7/10710 - w**6/2040 - 5*w**4/3 + 3*w. Let s(u) be the third derivative of j(u). Factor s(t).
2*t*(t - 3)*(t + 1)/17
Let f(h) = -2*h**2 - 7*h + 39. Let n be f(-6). Let a(t) be the second derivative of n*t**2 - 2*t + 2*t**3 + 0 + 1/6*t**4. Solve a(u) = 0.
-3
Let l(j) be the third derivative of -j**6/300 - 4*j**5/25 - 63*j**4/20 - 162*j**3/5 - 32*j**2 - 2. Factor l(b).
-2*(b + 6)*(b + 9)**2/5
Suppose -20*j + 20 = -30*j. Let k be j/21*(-5 + -7). Factor k*s + 10/7*s**2 - 2/7.
2*(s + 1)*(5*s - 1)/7
Let p(b) = 3*b**2. Let t(c) = -40*c**2 + 16*c. Let j(u) = -12*p(u) - t(u). Determine g, given that j(g) = 0.
0, 4
Let j(i) be the first derivative of i**4/2 - 8*i**3/3 + 474. Factor j(a).
2*a**2*(a - 4)
Suppose -3*c - s - 1317 = 0, c - s + 455 = 4*s. Let u = -4836/11 - c. Factor -u*g - 2/11 - 2/11*g**2.
-2*(g + 1)**2/11
Let q = 3/701 + 1369/7711. Factor 0*m + q - 2/11*m**2.
-2*(m - 1)*(m + 1)/11
Let p(i) = -i**4 + i**3 + i**2 - 2*i - 1. Let d(v) = 9*v**4 - 5*v**3 - 21*v**2 + 10*v + 5. Let t(b) = d(b) + 5*p(b). Factor t(m).
4*m**2*(m - 2)*(m + 2)
Suppose -x - 4*h = -28, 5*x - 4*x - 13 = -h. Let y be (3/(-9))/(2/(-47 + -1)). Determine p, given that -p**3 + x*p - y*p + p**4 = 0.
0, 1
Factor -2/5*k**4 + 0 - 36/5*k + 8/5*k**3 + 6*k**2.
-2*k*(k - 6)*(k - 1)*(k + 3)/5
Suppose 0 = -i - 5 + 8. Suppose i*l + 0*l - 6 = 0. Factor 0*g - g**2 - l*g**2 - 4*g - 2*g.
-3*g*(g + 2)
Let b(s) be the second derivative of -s**6/80 - 159*s**5/160 - 459*s**4/16 - 1215*s**3/4 + 2187*s**2/2 - 17*s. Suppose b(o) = 0. What is o?
-18, 1
Suppose -6 = 5*h - 4*s, -h + 3*s = -s + 14. Suppose 5*v + 10 = 0, -2*v - 2 = -h*r + 6. Factor -4*m**2 - r*m + m**3 + 0*m**3 - 3*m**3.
-2*m*(m + 1)**2
Determine v, given that -57*v**3 + 33*v**3 + 15*v + 70*v**2 + 79*v**3 = 0.
-1, -3/11, 0
Let b = 1605/52 - 658/13. Let c = b + 20. Factor -c*w + 1/2 - 1/4*w**2.
-(w - 1)*(w + 2)/4
Let h be (9 - 468/54)*6/4. Factor -1/2*c**2 - h*c**4 + 0 + c**3 + 0*c.
-c**2*(c - 1)**2/2
Suppose 25 = 3*y - 4*x, 5*y - 6*x - 65 = -11*x. Let p(h) be the second derivative of -1/8*h**3 + 0 + 1/48*h**4 - y*h + 0*h**2. Find z, given that p(z) = 0.
0, 3
Factor -1/10*p**5 + 1/5*p**2 + 0*p**3 - 1/5*p**4 + 0 + 1/10*p.
-p*(p - 1)*(p + 1)**3/10
Let p = -45 - -34. Let w(r) = -7*r**2 + 19*r**2 - 3*r**2 + 3*r. Let o(f) = 17*f**2 + 7*f. Let h(m) = p*w(m) + 6*o(m). Factor h(x).
3*x*(x + 3)
Let y(o) = 0*o**2 - 1 + 4*o**4 + 0 - 3*o**4 - 2*o**2 - 2*o. Let f(v) = 2*v**4 - 4*v**2 - 5*v - 3. Let p(g) = 2*f(g) - 5*y(g). Factor p(u).
-(u - 1)**2*(u + 1)**2
Let g be (-5 - -2) + -288 + -1. Let t = g + 2632/9. Let -10/9*f**3 - 14/9*f - 2*f**2 - t - 2/9*f**4 = 0. What is f?
-2, -1
Let p(o) be the second derivative of o**5/10 + 7*o**4/12 - 5*o**3/6 - 2*o**2 - 131*o. Factor p(t).
(t - 1)*(t + 4)*(2*t + 1)
Factor 0 + 0*s + 14/5*s**4 + 6*s**3 + 2/5*s**5 + 18/5*s**2.
2*s**2*(s + 1)*(s + 3)**2/5
Let d(i) = 8*i**2 + 19*i + 26. Let s(v) = 4*v**2 + 10*v + 12. Let n(a) = 2*d(a) - 5*s(a). Suppose n(z) = 0. What is z?
-2, -1
Let g be 8/((-64)/(-20))*(-8)/(-10). Factor -12/7*s**g - 8/7*s**5 + 0 + 22/7*s**3 - 18/7*s + 8/7*s**4.
-2*s*(s + 1)**2*(2*s - 3)**2/7
Let g(h) be the second derivative of -5*h**7/14 + 10*h**6/3 - 47*h**5/4 + 35*h**4/2 - 10*h**3/3 - 20*h**2 - 687*h. Let g(t) = 0. What is t?
-1/3, 1, 2
Let w(i) = i**2 - 33*i - 277. Let h be w(40). Let m(a) be the first derivative of 10 - h*a + 1/3*a**3 - a**2. What is z in m(z) = 0?
-1, 3
Let r(x) = -8*x**2 + 20*x - 4. Let i(l) = l**3 + l**2 + l - 1. Let m(f) = 4*i(f) - r(f). Factor m(j).
4*j*(j - 1)*(j + 4)
Let n(p) be the first derivative of -19 + 9/2*p**3 + 729/2*p - 243/4*p**2 - 1/8*p**4. Determine c so that n(c) = 0.
9
Let o be -2 - -3 - (-6)/(15/5). Suppose 3*v**4 + o*v**4 - v**4 - v**4 - 4*v**3 = 0. Calculate v.
0, 1
Let w be 4/(-10) - 8/(-10). Let v = 3511/4395 - -1/879. Factor -v - w*z + 2/5*z**2.
2*(z - 2)*(z + 1)/5
Let r(b) be the third derivative of 27/2*b**3 + 5 - 1/112*b**8 - 1/4*b**6 + 0*b + 1/10*b**7 + 27/8*b**4 + 3*b**2 - 9/10*b**5. Factor r(a).
-3*(a - 3)**3*(a + 1)**2
Let l(h) be the second derivative of h**4/6 + h - 67. Let d(m) = -5*m**3 - 10*m**2 + 4*m**3 - m**2. Let n(