 Let r be (w + -9)/((-2)/4). Factor 18*a + 10 + 3*a**2 - 5 + r.
3*(a + 3)**2
Let v = -495 + 500. Let n(f) = f + 1. Let g(x) be the second derivative of 5*x**4/12 + 25*x**3/6 + 20*x**2 - x. Let i(r) = v*n(r) + g(r). Factor i(l).
5*(l + 3)**2
Let c be (-6)/(7 - 56/((-30)/(-15))). Factor -8/7*s - 8/7 - c*s**2.
-2*(s + 2)**2/7
Let n = -461 + 291. Let f = n + 341/2. Factor 3/2 - f*p**2 + p.
-(p - 3)*(p + 1)/2
Let v = -143 + 147. Factor 6*j**v - 452 - 4*j**4 + 454 - 4*j**2.
2*(j - 1)**2*(j + 1)**2
Let a(t) be the second derivative of t**4/42 - 47*t**3/21 + 46*t**2/7 - 180*t. Factor a(k).
2*(k - 46)*(k - 1)/7
Let i be ((-4)/(-20))/(1/5). Let u be (12/3)/(i + 1). Factor -17*v + 11*v - v**u + 8*v.
-v*(v - 2)
Let r(q) be the first derivative of -2*q**3/3 + q**2 + 4*q - 65. Suppose r(v) = 0. What is v?
-1, 2
Let f = 12147 + -1154006/95. Let o = f + 12/19. Factor 2/5*w**2 + o*w - 1/5.
(w + 1)*(2*w - 1)/5
Let w(r) = -26*r + 51*r + 22*r - 12 + 27*r**2. Let q(y) = -190*y**2 - 330*y + 85. Let z(t) = 2*q(t) + 15*w(t). Determine j so that z(j) = 0.
-2, 1/5
Let z(b) be the second derivative of -b**8/336 + b**7/210 + b**6/60 + 11*b**2/2 + 10*b. Let n(m) be the first derivative of z(m). Factor n(a).
-a**3*(a - 2)*(a + 1)
Let -2*u + 0 - 58/3*u**4 + 74/3*u**3 - 22/3*u**2 + 4*u**5 = 0. What is u?
-1/6, 0, 1, 3
Let 4*p**3 + 21*p + 31*p - 48*p - 16*p**2 + 24 = 0. What is p?
-1, 2, 3
Let m(y) be the third derivative of -1/96*y**4 + 0*y + 0 + 4*y**2 + 0*y**3 + 1/480*y**5. Factor m(d).
d*(d - 2)/8
Suppose -l = -4*d + 29 - 10, 3*d - 12 = 0. Let k = 6 + l. Factor 2*i**2 - i**2 - 15*i - 3*i**4 + 8*i**2 + 6 + k*i**3.
-3*(i - 1)**3*(i + 2)
Let b be (-66)/(30 - 8) - (-22)/6. Let -4/3*x + 0 - 2*x**2 - b*x**3 = 0. Calculate x.
-2, -1, 0
Let x be 20/(-16) + (-310)/(-248). Factor x*s + 4*s**3 + 0 + 8/5*s**2.
4*s**2*(5*s + 2)/5
Let v(q) = -11*q**3 - 11*q**2 - 4*q - 6. Let a(i) = 13*i**3 + 12*i**2 + 4*i + 5. Let g(t) = 6*a(t) + 7*v(t). Let s be g(6). Factor s*u - 1/3 + 1/3*u**2.
(u - 1)*(u + 1)/3
Let s(y) be the first derivative of y**4/24 + y**3/2 + 9*y**2/4 - 2*y - 6. Let n(t) be the first derivative of s(t). Factor n(f).
(f + 3)**2/2
Let u(c) be the third derivative of 11/16*c**4 + 0 + 0*c + 1/80*c**5 + 121/8*c**3 + 29*c**2. Factor u(f).
3*(f + 11)**2/4
Let u(m) = 7*m**4 + 6*m**3 + 199*m**2 - 648*m - 11672. Let s(r) = -r**4 + r**2 + 1. Let z(k) = -24*s(k) - 3*u(k). Solve z(o) = 0 for o.
-9, 12
Let s(r) = -r**2 - 10*r - 14. Suppose -46 + 14 = 4*j. Let u be s(j). Factor -33/4*q + 9/4*q**u + 9/2.
3*(q - 3)*(3*q - 2)/4
Let o be (-177)/360 - ((-66)/(-12) + -6). Let y(c) be the third derivative of 1/24*c**4 + o*c**5 + 0 + 1/12*c**3 + 7*c**2 + 0*c. Factor y(q).
(q + 1)**2/2
Let i(w) = 13*w**2 - 192*w + 1147. Let k(n) be the first derivative of 7*n**3/3 - 48*n**2 + 573*n + 5. Let f(m) = -3*i(m) + 5*k(m). Suppose f(p) = 0. What is p?
12
Let r = 717/4 + -179. Let i(u) be the first derivative of 3/2*u**2 - u + 4 - u**3 + r*u**4. Factor i(l).
(l - 1)**3
Let d be ((-8)/(-12))/(17 + (-517)/33). Let z be 1*-4*(-1)/2. Factor b + 0 - d*b**3 + 1/2*b**z.
-b*(b - 2)*(b + 1)/2
Determine d so that 0 + 1/5*d**2 + 4/5*d = 0.
-4, 0
Let m(v) be the second derivative of -v**5/80 - 5*v**4/48 + 13*v**3/24 - 7*v**2/8 - 191*v. Factor m(w).
-(w - 1)**2*(w + 7)/4
Suppose 0 = -0*u + 5*u - 15. Factor -48 - 3*v**2 - 10*v + u*v - 15*v - 2*v.
-3*(v + 4)**2
Let i(b) be the third derivative of -1/84*b**8 + 0*b**3 + 0 - 2/35*b**7 - 16*b**2 + 0*b**6 + 0*b**5 + 0*b + 0*b**4. Factor i(p).
-4*p**4*(p + 3)
Let h(a) be the second derivative of -2*a**6/105 + a**5/10 + a**4/21 - 13*a**3/21 - 6*a**2/7 + 2*a. Find q, given that h(q) = 0.
-1, -1/2, 2, 3
Let x(m) be the second derivative of -m**5/40 + 3*m**4/4 + 19*m**3/12 - 188*m. Factor x(f).
-f*(f - 19)*(f + 1)/2
Let r(x) = x**2 - 16*x + 30. Let q be r(14). Factor 0 - 5*b**q + 75 - 4*b**2 + 30*b + 12*b**2.
3*(b + 5)**2
Let j(d) be the first derivative of -3*d**4/16 - 3*d**3 + 81*d**2/8 - 21*d/2 - 332. Factor j(s).
-3*(s - 1)**2*(s + 14)/4
Solve 77/3*w - 1/3*w**2 + 0 = 0.
0, 77
Let v be 2/(((-36)/90)/(8/(-10))). Let c(k) be the third derivative of 0 + 0*k + 0*k**v + 1/600*k**6 + 0*k**3 + 0*k**5 + 4*k**2. What is m in c(m) = 0?
0
Let t(l) = 42*l**3 + 34*l**2 + 2*l + 12. Let z(w) = w**2 + w - 4. Let d(p) = -5*t(p) - 15*z(p). Find b such that d(b) = 0.
-5/7, -1/6, 0
Let q = 6493/8 - 6475/8. Suppose 3/4*p**3 - 15/4*p**2 + q*p + 27/4 = 0. Calculate p.
-1, 3
Let v(q) be the first derivative of 0*q**2 - 1/9*q**6 + 0*q**3 + 0*q + 7 + 0*q**4 + 2/15*q**5. Suppose v(s) = 0. What is s?
0, 1
Let h(y) be the first derivative of y**6/15 + 2*y**5/5 + 4*y**4/5 + 8*y**3/15 + 59. Factor h(v).
2*v**2*(v + 1)*(v + 2)**2/5
Suppose 0 = 27*k - 23*k - 12. Factor -3*y**4 + 28*y**3 - 2*y**4 + y**4 + 4*y**k.
-4*y**3*(y - 8)
Let k = 4/15 - -29/60. Suppose -6*d - 21 = -5*r - 3*d, -2*r + 5*d = -16. Suppose k*g**r + 0 - 1/4*g + 1/2*g**2 = 0. What is g?
-1, 0, 1/3
Suppose 2689*x**3 + 116*x - 48*x**2 - 1352*x**3 - 1357*x**3 - 48 = 0. Calculate x.
-4, 3/5, 1
Let j(h) be the second derivative of -h**6/6 + 15*h**5/4 + 5*h**4/12 - 25*h**3/2 - 108*h. Factor j(x).
-5*x*(x - 15)*(x - 1)*(x + 1)
Let y be ((-33)/(-44))/((-6)/(-24)). Find h, given that 0 - 1/2*h**2 - 1/2*h**5 - 3/2*h**y + 0*h - 3/2*h**4 = 0.
-1, 0
Let l be (-2)/(8/(-5) + 2). Let p(h) = -8*h**4 + 5*h**3 - 5*h**2 + 5*h. Let o(u) = u**4 - u**3 + u**2 - u. Let b(w) = l*o(w) - p(w). What is q in b(q) = 0?
0
Let h(r) be the first derivative of 18/7*r**4 + 16/7*r**2 + 2/21*r**6 + 16 + 0*r + 80/21*r**3 + 4/5*r**5. Let h(l) = 0. What is l?
-2, -1, 0
Let f(q) be the second derivative of -q**7/3360 + q**6/180 - q**5/30 - 8*q**3/3 + 15*q. Let t(j) be the second derivative of f(j). Factor t(i).
-i*(i - 4)**2/4
Suppose 0 = 5*u - 4*s - 175 + 145, 7 = u - s. Let y(k) = -k**2 + 6*k + 2. Let v be y(6). Find c such that -6*c - u*c**4 - 4/3 - 22/3*c**3 - 10*c**v = 0.
-1, -2/3
Let j = 455 + -455. Let r(k) be the second derivative of 1/12*k**3 + j + 1/24*k**4 + 4*k - 1/2*k**2. Factor r(y).
(y - 1)*(y + 2)/2
Let w(i) be the first derivative of -i**3/3 + 13*i**2 - 106*i - 15. Let j(q) = -q + 1. Let v(p) = -30*j(p) - 5*w(p). Solve v(t) = 0 for t.
10
Let n be (-3 + -5 + 8)/(-1). Let x(l) be the third derivative of 0*l**4 - 1/360*l**5 - 3*l**2 + 0 - 1/720*l**6 + 0*l + n*l**3. What is p in x(p) = 0?
-1, 0
Suppose t - 3 = -3*i, -3*t + 5 = 5*i - 4. Find d such that -3 + 0*d - 9*d**2 + 189*d**t + 324*d**4 + 0*d - 21*d = 0.
-1/3, -1/4, 1/3
Let w(r) be the first derivative of r**9/27216 + r**8/7560 + r**7/7560 - 2*r**3 + 42. Let q(f) be the third derivative of w(f). Factor q(o).
o**3*(o + 1)**2/9
Let r(p) be the third derivative of p**5/30 + 5*p**4/4 - 18*p**3 + 519*p**2. Factor r(w).
2*(w - 3)*(w + 18)
Let w(n) be the second derivative of -n**7/294 - n**6/35 + n**5/70 + n**4/7 - n**3/42 - 3*n**2/7 + 6*n + 1. Solve w(m) = 0.
-6, -1, 1
Let t(j) be the first derivative of -1/3*j**4 + 0*j - 8/3*j**2 - 12 + 16/9*j**3. Find d such that t(d) = 0.
0, 2
Let g = 15 + 0. What is q in -9*q**3 - 12*q**3 - g*q**2 + 15 + 16*q**3 + 5*q = 0?
-3, -1, 1
Factor 32*s**2 + 0*s**3 + 7 + 4*s**3 + 52*s - 1 + 33 - 15.
4*(s + 1)**2*(s + 6)
Let h(a) = -34*a**2 + 1. Let m be h(-1). Let i = m + 64. Factor -2*w**2 - 2*w**5 - 6*w**3 - 6*w**4 + 31 - i.
-2*w**2*(w + 1)**3
Factor -8*l**3 + 118 + 3*l**5 - 12*l - l**3 - 118 - 6*l**4 + 24*l**2.
3*l*(l - 2)*(l - 1)**2*(l + 2)
Let o = 6/35 + -11/105. Let g(a) be the first derivative of -o*a**3 - 1/5*a**2 + 0*a - 4 + 1/20*a**4. Factor g(n).
n*(n - 2)*(n + 1)/5
Let y = 10 - 8. Suppose 4*k - 6 = -5*s, -s = 2*s + y*k - 4. Determine w so that 2*w**2 - 2*w + s*w**3 - 2 + 2*w - 3*w + w = 0.
-1, 1
Let a = 58 + -54. Suppose -4 + 2 + a*g**2 + 7*g - 8*g**2 + 4 = 0. What is g?
-1/4, 2
Suppose -4*g + 22 + 24 = -c, -5*c - 26 = -3*g. Let h(w) be the second derivative of 4/35*w**5 + 0*w**3 + 1/7*w**4 + 0 + 1/35*w**6 - g*w - 1/7*w**2. Factor h(i).
2*(i + 1)**3*(3*i - 1)/7
Let s be (-35)/(-20) - (-3)/12. Let -3*n + 2 + n + 3*n**3 + 0*n - 2*n**s - n**3 = 0. Calculate n.
-1, 1
Suppose -2/3*z**3 - 4/3*z**2 - 2/3*z + 0 = 0. What is z?
-1, 0
Let g(v) = -2*v**2 - 19*v - 16. Let p be g(-8). Suppose 3*n = i - 5*i + 12, -3*i + 9 = -n. Let -13*a**4 - 4*a**4 - 6*a**3 + i*a**2 + p*a**4 = 0. What is a?
