 + 162*q**2 + 4*q - 162. Let w(t) = -t**3 - 81*t**2 - t + 81. Let f(n) = -2*c(n) - 5*w(n). Factor f(b).
3*(b - 1)*(b + 1)*(b + 27)
Suppose 19 = 3*o + 5*w - 3*w, 3*o = -3*w + 18. Find t such that 5*t**4 - 3*t + o*t**2 - t**5 + 5*t**3 + 6*t**3 + t - 20*t**3 = 0.
0, 1, 2
Let m be (-6)/9 - 70/21. Let s be (640/45)/m - -4. Determine p, given that -s*p + 2/9 + 2/9*p**2 = 0.
1
Let p(s) be the first derivative of 10*s**3 - 8/3*s**2 - 8/3*s + 14. Factor p(x).
2*(5*x - 2)*(9*x + 2)/3
Let x be -1 - 0 - -6 - (-308)/(-66). Factor 1/3 - 1/3*v**2 + 1/3*v - x*v**3.
-(v - 1)*(v + 1)**2/3
Let j(v) be the third derivative of -8*v**2 - 1/6*v**3 + 1/40*v**5 - 1/48*v**4 + 0 + 1/240*v**6 - 1/420*v**7 + 0*v. Determine d, given that j(d) = 0.
-1, 1, 2
Let k be 3 + -1 + (0 - 0). Let q be 12 + -12 - 2*-3. Factor -v**2 + 2*v**3 + 5*v**2 - 2*v - q*v**k + 2.
2*(v - 1)**2*(v + 1)
Let w(x) be the first derivative of 2*x**3/33 - 32*x**2/11 + 246. Factor w(l).
2*l*(l - 32)/11
Let y(c) be the second derivative of -1/12*c**4 + 1/2*c**2 - 32*c + 0 + 0*c**3. Suppose y(t) = 0. Calculate t.
-1, 1
Let d = 37/120 - -1/40. Let x be (-69)/345*(-1 + 1). Factor x - d*t**2 + 0*t.
-t**2/3
Let p(v) be the first derivative of -5*v**3/3 - 245*v**2/2 + 119. Find o such that p(o) = 0.
-49, 0
Let h(s) be the third derivative of s**7/1400 - s**6/600 - s**5/100 + 4*s**3/3 - 25*s**2. Let x(v) be the first derivative of h(v). Let x(c) = 0. Calculate c.
-1, 0, 2
Factor 7/2 + 3*q - 1/2*q**2.
-(q - 7)*(q + 1)/2
Let m(f) = -f**2 - 7*f + 10. Let t be m(-8). Let j be 3/(-2) + 7/t. Determine o so that -o + 4*o + 0*o**j - 4*o + 9*o**2 + 5*o**4 + 13*o**3 - 2 = 0.
-1, 2/5
Suppose -175*h = -176*h - 5*d - 5, -5*d = -4*h + 5. Find r, given that 0*r**3 + h*r - 1/5 + 2/5*r**2 - 1/5*r**4 = 0.
-1, 1
Let g(j) be the first derivative of j**8/840 - j**7/420 - j**6/180 + j**5/60 - 8*j**3/3 + 6. Let x(r) be the third derivative of g(r). Factor x(q).
2*q*(q - 1)**2*(q + 1)
Factor 1/4*w**2 + 18769/4 - 137/2*w.
(w - 137)**2/4
Factor 2/15*g**4 + 0*g**2 + 4/15*g - 2/15 - 4/15*g**3.
2*(g - 1)**3*(g + 1)/15
Let r = -72 - -227. Suppose 135*t**4 - 53 + 203*t**5 - 63*t**5 + 63 - 145*t**2 - r*t**3 + 15*t = 0. What is t?
-1, -1/4, 2/7, 1
Let b(y) be the second derivative of y**6/30 - 7*y**5/20 - 3*y**4/4 + 7*y**3/6 + 4*y**2 - 128*y - 1. Find q such that b(q) = 0.
-1, 1, 8
Let i(h) be the third derivative of -h**8/112 + 3*h**7/70 + h**6/40 - 3*h**5/20 - 19*h**2 + 1. Let i(g) = 0. What is g?
-1, 0, 1, 3
Let c(n) = 55*n**4 + 435*n**3 + 960*n**2 + 145*n - 15. Let l(m) = m**3 + m + 1. Let j(q) = c(q) + 15*l(q). Factor j(k).
5*k*(k + 4)**2*(11*k + 2)
Let r(a) be the first derivative of a**5/105 + a**4/42 + 3*a**2/2 - 3. Let c(n) be the second derivative of r(n). Factor c(y).
4*y*(y + 1)/7
Let i be 9/34*3840/2160. Find z, given that 6/17*z**2 + 2/17*z**4 + i*z**3 - 8/17 - 8/17*z = 0.
-2, -1, 1
Let x(i) be the first derivative of i**3/7 + 111*i**2/7 + 4107*i/7 + 27. Factor x(r).
3*(r + 37)**2/7
Determine p, given that 2/7*p**4 + 90/7 + 4/7*p**2 - 44/7*p**3 + 2/7*p**5 + 138/7*p = 0.
-5, -1, 3
Suppose 0 = -u + 5 + 10. Factor -30*g**4 + 10*g**4 + u*g**5 - 2 + 5*g**3 + 2.
5*g**3*(g - 1)*(3*g - 1)
Let q(w) be the second derivative of w**4/12 + 25*w**3/6 - 13*w**2 + 87*w. Find l, given that q(l) = 0.
-26, 1
Let g = 2415 + -9659/4. Let v(w) = -w**2 - 5*w. Let p be v(-5). Suppose g + 0*j**3 + 1/4*j**4 - 1/2*j**2 + p*j = 0. What is j?
-1, 1
Suppose -309*r + 296*r = -52. Let f(b) be the third derivative of -2/35*b**5 + 2/21*b**r + 0*b - 3/70*b**6 + 0 + 0*b**3 - 1/147*b**7 - 8*b**2. Factor f(u).
-2*u*(u + 2)**2*(5*u - 2)/7
Factor -5*z**4 - 5*z**4 - 10*z**4 - 40*z - 3*z**4 + 21*z**4 + 10*z**3 + 8*z**2.
-2*z*(z - 5)*(z - 2)*(z + 2)
Suppose 0 - 14/3*t**3 - 4*t**2 - 2/3*t**4 + 0*t = 0. Calculate t.
-6, -1, 0
Let g(w) = 4*w**2 - w - 3. Let k(t) = -5*t**2 + t + 4. Let l(x) = -4*g(x) - 3*k(x). Let h(c) = -6*c**2 + 18*c. Let a(v) = -h(v) + 3*l(v). Factor a(n).
3*n*(n - 5)
Let q(l) be the first derivative of 7 - 1/210*l**7 + 0*l**3 + 0*l**6 + 1/60*l**5 + 0*l**4 + 0*l - l**2. Let s(o) be the second derivative of q(o). Factor s(g).
-g**2*(g - 1)*(g + 1)
Let b(a) be the second derivative of a**5/50 - a**4/30 + 22*a + 4. Solve b(j) = 0.
0, 1
Let a = 109 - 43. Let u = 68 - a. Factor -z + 1/3*z**u + 0.
z*(z - 3)/3
Let m(o) be the third derivative of -o**7/280 - 7*o**6/80 - 69*o**5/80 - 35*o**4/8 - 25*o**3/2 + 187*o**2. Determine c so that m(c) = 0.
-5, -2
Let s(u) be the second derivative of u**5/4 + 5*u**4/2 - 10*u**3/3 - 60*u**2 - 4*u. Find b such that s(b) = 0.
-6, -2, 2
Find g, given that -2*g + 0 - 8/3*g**2 = 0.
-3/4, 0
Solve 1/3*u + 1/3*u**2 - 1/3 - 1/3*u**3 = 0.
-1, 1
Let i(z) = 4*z**2 - 33*z + 24. Let g(j) = -2*j**2 + 16*j - 12. Let b(r) = -r - 3. Let n be b(2). Let d(s) = n*g(s) - 2*i(s). Suppose d(q) = 0. Calculate q.
1, 6
Let s(r) be the third derivative of r**7/3780 - 7*r**6/1080 + r**5/15 - 7*r**4/24 + r**3/2 - 2*r**2 + 9. Let y(i) be the second derivative of s(i). Factor y(z).
2*(z - 4)*(z - 3)/3
Factor 25/2 + 5*q + 1/2*q**2.
(q + 5)**2/2
Find j, given that 24/11*j**4 + 72/11 - 108/11*j**3 + 224/11*j**2 - 210/11*j - 2/11*j**5 = 0.
1, 3, 4
Let x(r) be the first derivative of -r**4/6 - 152*r**3/27 - 223*r**2/9 - 44*r/3 + 545. What is q in x(q) = 0?
-22, -3, -1/3
Let n be -3 + -2 - -9 - (1 - -3). Let u(z) be the first derivative of -1/6*z**3 + 3/4*z**2 + n*z + 5. Factor u(w).
-w*(w - 3)/2
Let b(o) be the second derivative of -25*o**4/12 - 95*o**3/6 + 10*o**2 - 92*o. Determine i, given that b(i) = 0.
-4, 1/5
Let w(g) be the first derivative of g**7/1960 + g**6/180 + 17*g**5/840 + g**4/28 + 17*g**3/3 + 13. Let i(l) be the third derivative of w(l). Factor i(c).
(c + 1)*(c + 3)*(3*c + 2)/7
Determine v, given that 38/3*v - 1/6*v**2 + 77/6 = 0.
-1, 77
Suppose 55*s + 150 = 130*s. Let h be (-2)/5 - (-48)/45. Factor -h - 1/3*k**s - k.
-(k + 1)*(k + 2)/3
Solve -21/4 - 1/4*x**2 + 5/2*x = 0 for x.
3, 7
Let y(o) be the third derivative of 1/30*o**5 + 0*o - 1/84*o**8 - 19/525*o**7 + 0 - 1/50*o**6 + 1/30*o**4 - 12*o**2 + 0*o**3. Find q, given that y(q) = 0.
-1, -2/5, 0, 1/2
Let n(y) = 5*y**3 - 18*y**2 + 13*y + 12. Let r(b) = 4*b**3 - 15*b**2 + 13*b + 12. Let o(l) = -5*n(l) + 6*r(l). Let o(w) = 0. What is w?
-3, -1, 4
Determine y, given that -9/7*y - 12/7 + 9/7*y**3 + 15/7*y**2 - 3/7*y**4 = 0.
-1, 1, 4
Let d(p) be the second derivative of 2*p**6/15 - 3*p**5/5 - 4*p**4/3 - 241*p. Factor d(m).
4*m**2*(m - 4)*(m + 1)
Factor -4*m**2 + 43*m**3 + 38*m**3 - 8*m - 121*m**3 + 44*m**3.
4*m*(m - 2)*(m + 1)
Let q be 1/(-3)*9 - -8. Let t(f) be the second derivative of 0 + 7*f - 1/10*f**q + 1/6*f**4 + 0*f**2 + 2/3*f**3. Let t(k) = 0. Calculate k.
-1, 0, 2
Let f(c) be the third derivative of c**6/420 - c**5/210 - 3*c**4/28 + 3*c**3/7 - 105*c**2. Factor f(g).
2*(g - 3)*(g - 1)*(g + 3)/7
Let p be (-6)/(-9) + 185/15 - -3. Let o = -7 + 13. Factor -15 + 31 - p - o*f + 3*f**2 - 9.
3*(f - 3)*(f + 1)
Find u such that 11*u + 2*u**3 + u + 14 + 10*u + 2*u**2 - 8*u**3 = 0.
-1, 7/3
Let p(m) be the third derivative of 35*m**2 + 0 + 1/8*m**6 - 3/8*m**5 - 1/84*m**7 + 0*m**3 + 5/12*m**4 + 0*m. Solve p(r) = 0 for r.
0, 1, 4
Let o be (-1)/(-4)*4*-3. Let g be (-4 - -4)/4 - o. Factor 0*t**2 + 2*t**5 + 2*t**2 - t**4 - t**4 + 0*t**3 - 2*t**g.
2*t**2*(t - 1)**2*(t + 1)
Let g(k) be the second derivative of -k**6/240 - k**5/36 - k**4/36 - 5*k**3/3 - k. Let q(u) be the second derivative of g(u). Find z, given that q(z) = 0.
-2, -2/9
Suppose 7*d + 16 - 44 = 0. Factor d*t - 25 - 5*t**2 - 17*t - 17*t.
-5*(t + 1)*(t + 5)
Let l(s) be the third derivative of 1/90*s**5 + 0 - 1/9*s**4 - 4/3*s**3 - 7*s**2 + 0*s - 1/2160*s**6. Let x(u) be the first derivative of l(u). Factor x(t).
-(t - 4)**2/6
Let f(d) be the second derivative of d**6/20 - 11*d**5/40 - 7*d**4/8 + 33*d**3/4 - 27*d**2/2 - 79*d. Factor f(l).
(l - 3)**2*(l + 3)*(3*l - 2)/2
Factor 96/5 + 93/5*w - 3/5*w**2.
-3*(w - 32)*(w + 1)/5
Let q(y) be the first derivative of y**5/10 + y**4/6 - 16*y + 41. Let i(o) be the first derivative of q(o). Let i(w) = 0. Calculate w.
-1, 0
Let t(z) = -z**3 - z**2 - 1. Let s(q) = -5*q**2 - 8*q**3 - 8*q + 5*q - 5 + 4*q**2 + 2*q**2. Let c(b) = s(b) - 5*t(b). Factor c(i).
-3*i*(i - 1)**2
Let r(j) be the second derivative of -j**6/15