+ x**3 + 0*x**2 + 0 + 0*x**4. Let g(h) be the second derivative of y(h). Factor g(q).
-q**2/4
Solve 22/3*x**3 - 16/3 + 4*x**4 + 2/3*x**5 + 4/3*x**2 - 8*x = 0.
-2, -1, 1
Let q be (-4)/((-1)/((-6)/(-3) + -1)). Let b = 11 - 8. Suppose 0*d + 4/3*d**5 - 4*d**4 + q*d**b + 0 - 4/3*d**2 = 0. Calculate d.
0, 1
Let u = -3200/3 + 1082. Factor -50/9*p**4 - 56/9*p - 8/9 - 140/9*p**3 - u*p**2.
-2*(p + 1)**2*(5*p + 2)**2/9
Let w be 14/(-21)*18/((-18)/3). Let 0*b**3 - 2/3*b**w - 1/3*b**5 + 0 + 1/3*b + 2/3*b**4 = 0. What is b?
-1, 0, 1
Let w = -44770 + 44773. Find q such that 0*q + 0 + 3/5*q**2 - 3/5*q**w = 0.
0, 1
Let s(m) be the second derivative of -m**4/6 + 7*m**3/3 + 8*m**2 + m + 46. Let s(a) = 0. What is a?
-1, 8
Let l(i) be the second derivative of 4*i + 0*i**3 + 0 + 9/20*i**5 - 6*i**2 + 7/4*i**4. Let l(a) = 0. Calculate a.
-2, -1, 2/3
Let q(j) = j**4 + 5*j**3 + 3*j**2 + 3*j. Let g(u) = 2*u**4 + 10*u**3 + 7*u**2 + 6*u. Let n(a) = -4*g(a) + 7*q(a). Solve n(t) = 0.
-3, -1, 0
Let q(f) = 17*f**5 - 6*f**3 - 11*f**2 - 11*f + 22. Let p(x) = -3*x**5 + x**3 + 2*x**2 + 2*x - 4. Let y(i) = 11*p(i) + 2*q(i). Factor y(n).
n**3*(n - 1)*(n + 1)
Suppose -4*m + 63*k - 8 = 59*k, -m - 8*k = -34. Factor -6/5*y**m - 12*y - 54/5.
-6*(y + 1)*(y + 9)/5
Factor 32/7*d**2 - 24/7*d**3 + 0 + 0*d + 4/7*d**4.
4*d**2*(d - 4)*(d - 2)/7
Let r be 28/6 + 2/(-3). Suppose 2*b - 1 = -5*p, -8 = -0*b + r*b. Factor -g**2 + 0*g**3 + 0*g**3 + g**3 + p - g.
(g - 1)**2*(g + 1)
Let a = -110 + 294. Let d = a + -181. Find k, given that -9/4 - 3/2*k + 3/2*k**3 - 3/4*k**4 + d*k**2 = 0.
-1, 1, 3
Suppose -4 = o - 2. Let r(s) = s**3 - 6*s**2 - 5*s - 2. Let q(w) = w**3 + 3*w**2 - 4*w**2 - 13*w + 13*w. Let k(p) = o*r(p) + 4*q(p). Solve k(l) = 0 for l.
-2, -1
Let q be (-297)/(-13) - (-2)/13. Suppose -48*b**3 + q*b**3 + 20*b**3 - 15*b - 45 + 25*b**2 = 0. Calculate b.
-1, 3
Let b(y) = 24*y - 284. Let h be b(12). Let m = 79/10 + -32/5. Solve 12*x**2 + 33*x**3 + 27/2*x**5 + 0 + 36*x**h + m*x = 0 for x.
-1, -1/3, 0
Suppose -8*y + 135 = -3*y. Let w = -5 + y. Factor 3*n**4 + w*n**4 + 10*n + 35*n**2 + 0*n**4 + 5*n**5 + 48*n**3 - 3*n**3.
5*n*(n + 1)**3*(n + 2)
Let x = 205 + -205. Let h(m) be the third derivative of 0*m**3 - 1/28*m**4 + 0*m + x - m**2 - 1/210*m**5. Factor h(t).
-2*t*(t + 3)/7
Let l(f) be the third derivative of -f**5/8 + 7*f**4/12 + f**3/3 + 115*f**2. What is c in l(c) = 0?
-2/15, 2
Let q(g) be the first derivative of -3*g**4/4 + 305*g**3 - 35112*g**2 + 69312*g + 296. Factor q(t).
-3*(t - 152)**2*(t - 1)
Suppose v + v = -s - 3, 4*s - 9 = -v. Factor 518*x - 845 + 125*x**2 - 13*x**3 - 11*x**s + 29*x**3 + 197*x.
5*(x - 1)*(x + 13)**2
Let a(p) be the first derivative of -4/21*p**3 + 8/7*p**2 - 12/7*p + 3. Factor a(f).
-4*(f - 3)*(f - 1)/7
Find y, given that -1/3*y**2 - 1/9 + 4/9*y = 0.
1/3, 1
Let w(o) be the first derivative of 5*o**4/4 - 115*o**3/3 + 715*o**2/2 - 605*o + 127. Factor w(t).
5*(t - 11)**2*(t - 1)
Suppose 4*r = 4*p - 40, p - 2*r + 28 = 45. Let k = -726/5 - -146. Factor 2/5*b**p - 4/5*b**2 + k - 2/5*b.
2*(b - 2)*(b - 1)*(b + 1)/5
Let u(o) be the first derivative of 18 - 4*o**2 + 4*o**3 + 2*o + 2/5*o**5 - 2*o**4. Factor u(h).
2*(h - 1)**4
Let k(l) be the first derivative of l**6/15 - l**4/3 + l**2 - 56*l - 30. Let n(g) be the first derivative of k(g). Factor n(p).
2*(p - 1)**2*(p + 1)**2
Suppose 7*o - 25 - 10 = 0. Let n(w) be the third derivative of 0*w**o + 1/300*w**6 + 2/525*w**7 + 1/840*w**8 + 0*w**3 + 0*w**4 + 0 + 0*w + 4*w**2. Factor n(d).
2*d**3*(d + 1)**2/5
Let n(h) be the third derivative of -h**6/120 - 9*h**5/20 - 13*h**4/12 + h**2 - 52. Find b, given that n(b) = 0.
-26, -1, 0
Factor -66 + 0*k**2 + 2*k**2 - 4*k + 48*k + 20*k.
2*(k - 1)*(k + 33)
Suppose -4*j = -43 + 11. Suppose y - 5*h + j*h = 0, 5*h = -2*y. Factor y - 1/6*g - 1/6*g**2.
-g*(g + 1)/6
Let d(k) = -8*k - 4*k + 2*k + 24 - 4*k + 8*k**2. Let b(h) = 23*h**2 - 43*h + 71. Let n(o) = -6*b(o) + 17*d(o). Determine c so that n(c) = 0.
1, 9
Let v(i) = -i - 6. Let j be (2 + -7)*12/10. Let c be v(j). Factor -s**4 + c*s + 1/3*s**5 - 1/3*s**2 + 0 + s**3.
s**2*(s - 1)**3/3
Suppose 4*a + 3*q - 82 = 5*q, 0 = 4*a - q - 85. Let x = a - 19. Factor -197 + 12*u**2 + x*u**3 + 197 + 9*u.
3*u*(u + 1)*(u + 3)
Let m(l) be the first derivative of -4913*l**6/27 - 578*l**5 + 833*l**4/3 - 1208*l**3/27 + 8*l**2/3 - 130. Factor m(b).
-2*b*(b + 3)*(17*b - 2)**3/9
Suppose 0 = 128*k - 130*k + 138. Determine l so that -2*l**2 - 2*l**3 + 138*l + 2 - 67*l - k*l = 0.
-1, 1
Let w(v) = 2*v - 11*v - 3*v**3 + v**3 - 2*v + 13*v**2 + 3. Let m(a) = 2*a**3 - 14*a**2 + 10*a - 2. Let r(k) = 3*m(k) + 4*w(k). Factor r(n).
-2*(n - 3)*(n - 1)**2
Let x(z) = 7*z**5 - 26*z**4 + 38*z**3 - 2*z + 2. Let d(i) = -85*i**5 + 310*i**4 - 455*i**3 + 25*i - 25. Let c(a) = 2*d(a) + 25*x(a). Factor c(g).
5*g**3*(g - 4)*(g - 2)
Let p(g) be the first derivative of -3*g**5/5 + 8*g**4/3 - 14*g**3/3 + 4*g**2 + 37*g - 35. Let h(v) be the first derivative of p(v). Factor h(f).
-4*(f - 1)**2*(3*f - 2)
Solve -1352*k - 2/3*k**3 - 52*k**2 - 35152/3 = 0 for k.
-26
Let w(t) = 3*t**4 - t**3 + 4. Let y(h) = -5 - 107*h**4 + 104*h**4 + 2. Let r(v) = -3*w(v) - 4*y(v). Suppose r(j) = 0. What is j?
-1, 0
Let q = -8467 + 8470. Factor 0 - 23/8*h**2 - 5/4*h + 5/8*h**q.
h*(h - 5)*(5*h + 2)/8
Suppose 0 = -9*w - 29 + 50 + 6. Suppose 0 + 0*f**2 + 0*f - 3/4*f**w + 1/4*f**4 = 0. Calculate f.
0, 3
Let p(n) be the third derivative of 51/44*n**4 + 0*n - 4/11*n**5 + 0 - 9/11*n**3 - 5/11*n**6 + 19*n**2. Find h, given that p(h) = 0.
-1, 3/10
Let w = 176 + -172. Suppose -w*c + 0*q - 5*q = 7, 2*q = 2*c - 10. Let -5/2*u + 10*u**c + 0 = 0. What is u?
0, 1/4
Let p(q) be the second derivative of q**4/12 + 7*q**3/6 + 9*q**2/2 - 3*q. Let j be p(-6). Factor 2 + 7*r**3 + 6*r + 6*r**2 + 12*r**2 + r**j + 6*r.
2*(r + 1)**2*(4*r + 1)
Determine f, given that 1/3*f**3 + 0 - f**2 + 0*f = 0.
0, 3
Factor -6557*h**3 + 60 + 6560*h**3 - 4*h**2 - 16*h + 40*h - 29*h**2.
3*(h - 10)*(h - 2)*(h + 1)
Let h(j) = j**2 - 5*j + 21. Let b be (2 + 1)/((-3)/2). Let u = -422 - -417. Let w(x) = 2*x - 10. Let p(l) = b*h(l) + u*w(l). Find i, given that p(i) = 0.
-2, 2
Let u be 1/(-2) - (777/1540 - 1). Let n = u + 7483/660. Let -11*a**3 - n*a**2 - 8/3 + 15*a**4 + 12*a = 0. What is a?
-1, 2/5, 2/3
Suppose -2/13*h**3 + 46/13*h**2 - 2/13*h**4 - 6*h + 36/13 = 0. Calculate h.
-6, 1, 3
Let d(j) = -j**2 - 12*j - 16. Let r be d(-10). Find y such that -2*y**3 + r*y - 5*y**2 - 6*y + y**2 = 0.
-1, 0
Suppose 4*k - 2*k = -2. Let z be (-1)/1*1/k. Factor -1 + 2 - 2*f - z + 3*f**2.
f*(3*f - 2)
Let g(b) = -b**3 - 5*b**2 - 2*b - 10. Let o be g(-5). Let a be (-1 + 0)*o/(0 + -1). Determine d so that -d**4 + 1/3 - 8/3*d**3 - 2*d**2 + a*d = 0.
-1, 1/3
Let n be -2 - (0 + 1 + -14). What is w in 11*w**3 - n*w**2 - 5*w**3 + 0*w**3 - 10 - 11*w**2 - 38*w = 0?
-1, -1/3, 5
Let g(r) be the second derivative of -r**5/70 + 3*r**4/14 - 2*r**3/3 + 42*r + 2. Factor g(x).
-2*x*(x - 7)*(x - 2)/7
Factor 0 + 1/2*g + 1/2*g**2.
g*(g + 1)/2
Let s(d) be the third derivative of -2*d**7/105 + 2*d**6/15 - d**5/15 - d**4 + 2*d**2 + 56. Suppose s(i) = 0. What is i?
-1, 0, 2, 3
Let r(n) be the first derivative of 2/5*n**2 - 1/20*n**4 + 4/5*n - 10 - 1/15*n**3. Factor r(k).
-(k - 2)*(k + 1)*(k + 2)/5
Let m be (-120)/(-32) + (-8)/4. Let 1/2*o - o**4 - 5/4*o**3 + 0 + m*o**2 = 0. Calculate o.
-2, -1/4, 0, 1
Let t(v) = -v**3 + 5*v**2 - 3*v - 1. Let k be t(-5). Let d = -527/2 + k. Determine q so that d*q**4 + 1/2*q - q**2 - q**3 + 1/2 + 1/2*q**5 = 0.
-1, 1
Suppose -99*f**3 + 4*f**2 + 100*f**3 + 5*f + 2*f - 4*f = 0. What is f?
-3, -1, 0
Let b(x) be the first derivative of -x**6/4140 - x**5/138 + 11*x**4/276 + 28*x**3/3 + 39. Let d(m) be the third derivative of b(m). Factor d(a).
-2*(a - 1)*(a + 11)/23
Let x be (170/(-52) - -3)*(-84)/147. Let -4/13*w**4 + 0 + 6/13*w**3 - x*w**5 + 8/13*w**2 - 8/13*w = 0. What is w?
-2, 0, 1
Let n be (413/35 - 11)/(126/15). Let k(f) be the third derivative of -n*f**3 - 15*f**2 + 0*f + 1/21*f**4 - 1/105*f**5 + 0. Determine j, given that k(j) = 0.
1
Suppose -2*t - 4*w + 352 = 0, -2*w = -3*t + 514 + 30. Suppose -183*h = -t*h - 9. Determine n so that -2/7*n**h + 8/7*n + 2/7*n**2 - 8/7 = 0.
-2, 1, 2
Let q(r) be the second derivative of 0*r**3 - 1/6*r**6 - 1/2*r**5 - 5/12*r**4 + 0 + 15*r + 0*r*