 such that -2/11 + 16/11*b**2 + 9/11*b**3 + 5/11*b = 0.
-1, 2/9
Let w(i) be the second derivative of i**4/8 - 9*i**3/2 + 24*i**2 + 47*i + 3. Factor w(p).
3*(p - 16)*(p - 2)/2
Let i(w) = -w**4 + w**3 - 11*w**2 + 5*w. Let d(f) = 3*f**3 + 10*f - 2*f**4 + 26*f**2 - f**4 - 49*f**2. Let c(n) = 6*d(n) - 13*i(n). Let c(q) = 0. What is q?
-1, 0, 1
Let a(i) be the third derivative of -i**6/1020 + 8*i**5/255 - 5*i**4/51 - 400*i**3/51 - 339*i**2. Suppose a(k) = 0. Calculate k.
-4, 10
Factor -270*v**2 + 160/3*v**4 + 1000/3*v**3 - 35/6 + 415/6*v.
5*(v + 7)*(4*v - 1)**3/6
Suppose 9 - 3 = -x. Let l = x + 8. Factor 9*a**3 - 2*a**5 + 5*a**3 - 12*a**3 - l*a**2 + 2*a**4.
-2*a**2*(a - 1)**2*(a + 1)
Let h(c) be the third derivative of 5*c**8/112 - 8*c**7/21 - c**6/2 + 39*c**2. Determine l, given that h(l) = 0.
-2/3, 0, 6
Let q(m) = -4*m**3 - 64*m**2 + 142*m - 72. Let s(w) = 20*w**3 + 320*w**2 - 711*w + 360. Let a(n) = -11*q(n) - 2*s(n). Factor a(p).
4*(p - 1)**2*(p + 18)
Solve -6/5 - 4/5*h**3 + 8/5*h**2 + 4/5*h - 2/5*h**4 = 0 for h.
-3, -1, 1
Suppose -6*b + b = -4*l - 632, b - 3*l = 122. Let g = b - 255/2. Determine v so that 1/4*v**2 + 1/4*v - g = 0.
-2, 1
Let h be ((-2)/(-6))/(0 - (-5)/45). Let j(f) be the second derivative of 0 + 4*f - f**2 + 4/3*f**h - 7/24*f**4. Factor j(q).
-(q - 2)*(7*q - 2)/2
Let j(k) be the first derivative of 0*k**2 + 0*k**3 - 1/4*k**6 - 14 + 3/4*k**4 + 3/10*k**5 + 0*k. Factor j(p).
-3*p**3*(p - 2)*(p + 1)/2
Factor -52*z + 64*z**2 - 38*z**3 - 5/4*z**5 + 16 + 11*z**4.
-(z - 2)**4*(5*z - 4)/4
Let r(w) be the third derivative of -w**7/11340 + w**6/810 - w**5/135 + w**4/8 + 4*w**2. Let p(i) be the second derivative of r(i). Factor p(x).
-2*(x - 2)**2/9
Let y(o) be the third derivative of -o**5/20 - o**4/8 + 11*o**3/6 - 20*o**2. Let f(i) = -3*i**2 - 3*i + 10. Let j(d) = -5*f(d) + 4*y(d). Factor j(k).
3*(k - 1)*(k + 2)
Let h(y) be the third derivative of -y**8/1008 + y**7/315 + y**6/72 - y**5/18 - y**4/18 + 4*y**3/9 - 2*y**2 - 46*y. Solve h(k) = 0 for k.
-2, -1, 1, 2
Suppose 52*g**3 + 3338/3*g**2 + 3848*g + 2/3*g**4 + 10952/3 = 0. What is g?
-37, -2
Let i(l) = -84*l**4 - 292*l**3 - 52*l**2 + 1060*l + 904. Let t(d) = 13*d**4 + 45*d**3 + 8*d**2 - 163*d - 139. Let x(m) = -5*i(m) - 32*t(m). Factor x(j).
4*(j - 2)*(j + 1)*(j + 3)**2
Solve 4/3*v**2 + 1/3*v**3 - 6 - 5*v = 0.
-6, -1, 3
Let l(x) be the third derivative of -x**7/420 - x**6/48 - x**5/40 + 5*x**4/48 + x**3/3 - 184*x**2 + 2. Factor l(z).
-(z - 1)*(z + 1)**2*(z + 4)/2
Let a(c) be the second derivative of -24*c + 0 + 1/36*c**6 - 1/84*c**7 - 1/120*c**5 + 0*c**2 + 0*c**3 - 1/72*c**4. Find q such that a(q) = 0.
-1/3, 0, 1
Let h(q) be the third derivative of -4*q**7/525 - q**6/12 - q**5/25 + 77*q**2. Factor h(k).
-2*k**2*(k + 6)*(4*k + 1)/5
Let u(i) be the second derivative of i**4/18 - 3*i**2 + 167*i. Determine z so that u(z) = 0.
-3, 3
Factor 8/11*a**2 - 30/11 - 118/11*a.
2*(a - 15)*(4*a + 1)/11
Let s(i) be the first derivative of -2*i**3/51 - i**2/17 + 40*i/17 - 284. Factor s(v).
-2*(v - 4)*(v + 5)/17
Let d be (250/45)/((-280)/(-336)). Solve 4/3*q**2 + 16/3 - d*q = 0.
1, 4
Let h = -11524 + 11526. Suppose -1/2*b**h + b - 1/2 = 0. Calculate b.
1
Let d(n) be the first derivative of n**4/4 + 2*n**3 - 27*n**2/2 - 144. Solve d(m) = 0 for m.
-9, 0, 3
Factor -7/2*q**3 + 8*q + 0 - 1/2*q**4 + 5*q**2.
-q*(q - 2)*(q + 1)*(q + 8)/2
Let b(i) be the first derivative of i**6/3 + 11*i**5/8 + 15*i**4/8 + 5*i**3/12 - 5*i**2/4 - 9*i - 6. Let m(d) be the first derivative of b(d). Factor m(r).
5*(r + 1)**3*(4*r - 1)/2
Let j(t) be the third derivative of -29*t**2 + 0*t - 6/7*t**3 - 1/280*t**6 + 1/140*t**5 + 1/7*t**4 + 0. Solve j(m) = 0.
-3, 2
Suppose 0 = 30*i - 35*i + 25. Let s be 10/(-25) + 92/i. Factor -3*m + m + m**2 + s - 21.
(m - 3)*(m + 1)
Let k be (9 - 13) + (6 - 1)*1. Let c(q) be the first derivative of -9/2*q + 3/2*q**2 - 1/6*q**3 + k. Suppose c(w) = 0. Calculate w.
3
Let y(x) be the second derivative of x**5/110 + x**4/66 - 2*x**3/33 + 2*x. Factor y(p).
2*p*(p - 1)*(p + 2)/11
Let z be (((-10)/4)/5)/((-1)/(-2)). Let g be (-5 + 1)*z/3. Suppose -i - g + 1/3*i**2 = 0. Calculate i.
-1, 4
Let m(v) = v**5 + 2*v**4 - v**3 + v**2 + 2. Let h(z) = 16*z**5 + 32*z**4 - 50*z**3 - 2*z**2 + 82*z + 88. Let o(l) = -2*h(l) + 28*m(l). Solve o(y) = 0.
-5, -1, 2, 3
Let f(s) be the third derivative of s**8/112 + 2*s**7/35 + s**6/10 - s**5/10 - 5*s**4/8 - s**3 - 4*s**2 + 5*s. Solve f(n) = 0.
-2, -1, 1
Let y(j) = -55*j**3 + 110*j**2 - 55*j - 40. Let s(g) = -8*g**3 + 16*g**2 - 8*g - 6. Let q(i) = -20*s(i) + 3*y(i). Determine h, given that q(h) = 0.
0, 1
Let z = -9127 + 27382/3. Factor -z*x**2 + 0 + 1/3*x - 2/3*x**3.
-x*(x + 1)*(2*x - 1)/3
Let c(k) be the second derivative of -k**5/10 + k**4/6 + 20*k**3/3 + 158*k. Solve c(d) = 0 for d.
-4, 0, 5
Let r(y) = -5*y**4 + 11*y**3 + 10*y**2 - 3*y. Let b(f) = 6*f**4 - 12*f**3 - 10*f**2 + 4*f. Let j(u) = -3*b(u) - 4*r(u). Factor j(a).
2*a**2*(a - 5)*(a + 1)
Let c(k) be the third derivative of -k**6/150 + 4*k**5/75 - k**4/6 + 4*k**3/15 - 2*k**2 - 56*k. Let c(y) = 0. What is y?
1, 2
Let o(v) be the second derivative of 5*v**7/6 + 11*v**6/2 - 157*v**5/4 + 1015*v**4/12 - 85*v**3 + 40*v**2 + 65*v. Factor o(p).
5*(p - 1)**3*(p + 8)*(7*p - 2)
Let g(a) be the second derivative of -a**6/135 - 7*a**5/90 - 7*a**4/27 - 8*a**3/27 + 2*a + 4. Let g(d) = 0. What is d?
-4, -2, -1, 0
Let p(r) = -12 + 22 - 8 - 5 + 2*r**2 + 10*r. Let v(g) = -3*g**2 - 10*g + 1. Let j(l) = -4*p(l) - 3*v(l). Suppose j(f) = 0. What is f?
1, 9
Suppose -4 = -5*p - 2*m + 5, 4*m = -3*p + 11. Suppose k = -k - 8, -v - p = 3*k. Factor c + v*c + 8 + 0*c + 4*c**2.
4*(c + 1)*(c + 2)
Let l(x) be the first derivative of 5*x**3/6 - 70*x**2 + 1960*x - 23. Suppose l(u) = 0. Calculate u.
28
Let z be (-154)/(-8) + 2/(-8). Suppose 0 = y + 4*n - 14, 2*y - 4*n = -11 + 3. Factor -9*l**2 + 4 + 2*l**4 - 7*l**3 - 4*l**3 + z*l**y + 11*l**2 - 16*l.
(l - 2)**2*(l - 1)*(2*l - 1)
Suppose 9/2*f**2 + 1/2*f**3 + 12*f + 8 = 0. Calculate f.
-4, -1
Let m = 21 - 19. Suppose -3*l = m - 8. Let -9*y**3 - 10*y**4 + 9 - 11*y**3 - 11*y**l - 10*y - 9*y**2 - 2*y**5 - 11 = 0. What is y?
-1
Let -44/9*f**3 - 322/3*f**2 - 8/9 + 176/9*f + 242/9*f**4 = 0. Calculate f.
-2, 1/11, 2
Let v(b) = -231*b - 229. Let a be v(-1). Suppose 1/9 + 2/9*t + 1/9*t**a = 0. What is t?
-1
Let z(d) = 11*d**2 + 7. Let n(w) = 5*w**2 + 3. Let b(u) = -9*n(u) + 4*z(u). Let s(c) = 5*c**3 - c**2 - 25*c - 19. Let l(j) = 4*b(j) + s(j). Factor l(f).
5*(f - 3)*(f + 1)**2
Let p = 34 + -14. Suppose 5*d + 2*z = p, -3*z + z = -10. Let d*u**2 - 3*u**3 - 2*u**2 - 4*u**2 + 7*u**2 = 0. Calculate u.
0, 1
Let -32/23*c - 34/23 + 2/23*c**2 = 0. What is c?
-1, 17
Let h(q) be the third derivative of 0*q + 0 - 7/64*q**4 - 12*q**2 + 3/160*q**5 - 3/8*q**3. Factor h(x).
3*(x - 3)*(3*x + 2)/8
Let q(a) = -40*a**2 + 24*a. Let i(s) = -38*s**2 + 25*s. Let n(h) = 4*i(h) - 3*q(h). Factor n(w).
-4*w*(8*w - 7)
Let b(h) = 10*h**3 - 2*h**2 - h + 4. Let j be b(-2). Let r be j/(-12) + (-4)/(-6). Find m, given that -3/2*m**2 - r*m - 9/2 + 3/2*m**3 = 0.
-1, 3
Let l(f) be the third derivative of -16*f**2 + 0*f**4 - 1/15*f**5 + 0 + 0*f + 8/3*f**3. Factor l(g).
-4*(g - 2)*(g + 2)
Let d be ((-3 - -3)/(-2))/(-1). Suppose 2*r + 4 = d, -3 = a - 2*r - 7. Factor 3*b + a*b**3 - 2 - 4*b**3 + 3*b**3.
-(b - 1)**2*(b + 2)
Suppose -3*j + 3*y = -18, -j + y - 2 = -4*j. Let p = 78 + -74. Determine g, given that -13 + p*g + 13 + 2*g**j = 0.
-2, 0
Let j(c) = -2*c**2 - 288*c - 13032. Let t(a) = 2*a + 5. Let z(m) = j(m) - 18*t(m). Suppose z(f) = 0. Calculate f.
-81
Let x(g) be the second derivative of 0 + 0*g**3 + 3/16*g**4 - 3/160*g**5 + 8*g - 6*g**2. Let x(l) = 0. Calculate l.
-2, 4
Let u(x) be the second derivative of 0 - 1/75*x**6 + 0*x**5 + 19*x + 0*x**2 + 1/30*x**4 + 0*x**3. What is k in u(k) = 0?
-1, 0, 1
Suppose 0 - 26/7*p**3 + 0*p - 10/7*p**4 + 12/7*p**2 = 0. Calculate p.
-3, 0, 2/5
Let r be (-777)/112 - (-6 + -1). Let k(a) be the second derivative of 1/32*a**4 - 1/24*a**3 + 5*a + 0 - r*a**2. Factor k(t).
(t - 1)*(3*t + 1)/8
Let t(o) be the third derivative of -o**5/150 + o**4/4 - 10*o**3/3 + 236*o**2. Find f such that t(f) = 0.
5, 10
Let u(l) = 47*l**2 - 660*l + 297. Let m(k) = -12*k**2 + 166*k - 74. Let a(h) = -18*m(h) - 4*u(h). Factor a(y).
4*(y - 12