+ 1)**2/2
Let z(i) = -10*i**2 - 15*i - 15. Let u(m) = -m**2 + m + 1. Suppose 5*f = -12 + 7. Let n(g) = f*z(g) + 5*u(g). Suppose n(s) = 0. What is s?
-2
Let r(i) be the third derivative of -i**7/735 - i**6/84 + 13*i**5/210 - i**4/12 + 282*i**2. Factor r(b).
-2*b*(b - 1)**2*(b + 7)/7
Let r(y) = 14*y**2. Let b be r(-1). Suppose 0 = -2*x - 4, 3*v = -2*x + 5*x + 18. Factor -18*t**2 + b*t**2 - 4*t + t**3 + v*t**4 + 3*t**3.
4*t*(t - 1)*(t + 1)**2
Let h be 38*9/798 - -9*2/56. Factor -h*j**2 + 3/4 + 0*j.
-3*(j - 1)*(j + 1)/4
Let 312*m + 4/5*m**2 + 30420 = 0. What is m?
-195
Suppose 4*d - 37*w + 2 = -32*w, d + 3*w - 8 = 0. Factor 3/4*k**4 + 0 + 3/2*k**d + 0*k - 9/4*k**3.
3*k**2*(k - 2)*(k - 1)/4
Suppose -2*p + 1090 = -664. Suppose 9*t**2 + p*t**4 + 15*t**3 - 21*t**2 - 880*t**4 = 0. What is t?
0, 1, 4
Let h(w) be the second derivative of -w**4/48 - 7*w**3/3 + 57*w**2/8 + 333*w. Factor h(l).
-(l - 1)*(l + 57)/4
Suppose 50/7*r**4 + 0 + 36/7*r + 40/7*r**3 - 102/7*r**2 = 0. What is r?
-2, 0, 3/5
Let i(l) = 3*l**4 + 6*l**3 - 6*l**2 - 3*l. Let s be (-4)/(-6)*(-12)/(-8). Let g(z) = -z**3 + z. Let d(t) = s*i(t) + 3*g(t). Determine y, given that d(y) = 0.
-2, 0, 1
Suppose x - 2 = -f + 6*f, 4*f - x = -2. Let r be 2 + f/((-4 - -4) + -2). Find n, given that -9*n**r - 9/5*n**4 + 27/5*n + 33/5*n**3 - 6/5 = 0.
2/3, 1
Let f(q) be the second derivative of -q**8/3080 - q**7/770 + 14*q**3/3 + 44*q. Let w(s) be the second derivative of f(s). Factor w(x).
-6*x**3*(x + 2)/11
Factor -2*x - 5/3 - 1/3*x**2.
-(x + 1)*(x + 5)/3
Let v = 11298/5 + -2253. Factor v*s**2 - 108/5 + 36/5*s - 3/5*s**4 - 6/5*s**3.
-3*(s - 2)**2*(s + 3)**2/5
Let g(f) be the third derivative of -9/13*f**3 + 10*f**2 + 1/780*f**6 + 0 + 9/52*f**4 - 3/130*f**5 + 0*f. Factor g(w).
2*(w - 3)**3/13
Let t(a) be the third derivative of -a**5/5 + 51*a**4/8 + 13*a**3/2 - 25*a**2 - 1. Factor t(b).
-3*(b - 13)*(4*b + 1)
Let x(k) be the third derivative of 3/160*k**5 + 0*k**3 + 0*k + 0 + 17*k**2 + 1/1680*k**7 + 0*k**4 - 1/160*k**6. Factor x(l).
l**2*(l - 3)**2/8
Find z such that -12/5*z**2 - 34/15*z - 2/15*z**3 + 0 = 0.
-17, -1, 0
Factor 4/3*o + 2/3*o**2 - 10.
2*(o - 3)*(o + 5)/3
Factor -88/3 + 92/3*a - 4/3*a**2.
-4*(a - 22)*(a - 1)/3
Let c(g) be the first derivative of -g**4/4 - 22*g**3/3 - 21*g**2/2 - 479. Factor c(t).
-t*(t + 1)*(t + 21)
Factor -1/4*h**2 - 3/4*h + 3/4*h**3 + 0 + 1/4*h**4.
h*(h - 1)*(h + 1)*(h + 3)/4
Let o(f) = 2*f**3 + 4*f**2 - 41*f - 40. Let p(q) = 4*q**3 + 8*q**2 - 81*q - 80. Let x(d) = -5*o(d) + 3*p(d). Factor x(i).
2*(i - 4)*(i + 1)*(i + 5)
Let y(i) = 12*i**2 + 20*i + 8. Let p(a) = a**2 + 2*a + 1. Let g(b) = -10*p(b) + y(b). Solve g(n) = 0 for n.
-1, 1
Let x(v) be the second derivative of 10*v + 6/7*v**3 - 1/21*v**5 + 9/2*v**2 + 0 + 1/14*v**4 + 1/210*v**6. Let i(p) be the first derivative of x(p). Factor i(z).
4*(z - 3)**2*(z + 1)/7
Factor 4232 + 3147*c + 650*c - 540*c**2 + 1974*c**2 + 2*c**4 + 100*c**3 + 803*c.
2*(c + 2)**2*(c + 23)**2
Factor -5*b**4 + 15*b**4 + 2*b**2 + 2*b**5 - 6*b**3 + 4*b - 12*b**4.
2*b*(b - 2)*(b - 1)*(b + 1)**2
Let r(v) = -v. Let q(w) = -2*w**2 + 16*w. Let y(b) = 2*q(b) + 28*r(b). Solve y(u) = 0 for u.
0, 1
Factor 16/11*i**2 + 0 + 10/11*i**5 - 36/11*i**4 + 24/11*i**3 + 0*i.
2*i**2*(i - 2)**2*(5*i + 2)/11
Let k(l) be the second derivative of 2*l**4/21 + 19*l**3/7 + 2*l**2 - 19*l. Factor k(t).
2*(t + 14)*(4*t + 1)/7
Suppose -12*r + 4 + 2*r**2 + 8 - 17 + 15 = 0. What is r?
1, 5
Factor -88/13*u - 2/13*u**3 + 56/13 + 34/13*u**2.
-2*(u - 14)*(u - 2)*(u - 1)/13
Let u(x) be the second derivative of -x**6/10 + 3*x**5/20 + 13*x. Determine b, given that u(b) = 0.
0, 1
Let z(g) = 6*g**3 + 352*g**2 + 3782*g - 968. Let u(f) = -23*f**3 - 1409*f**2 - 15127*f + 3872. Let d(n) = -2*u(n) - 9*z(n). Factor d(t).
-2*(t + 22)**2*(4*t - 1)
Let n(l) be the third derivative of -l**8/336 + l**7/90 - l**6/72 + l**5/180 - l**2 + 123. Suppose n(v) = 0. Calculate v.
0, 1/3, 1
Let b(x) be the second derivative of -x**4/3 - 4*x**3/3 + 65*x. Factor b(v).
-4*v*(v + 2)
Let r be -1 + (4*-2)/4. Let w be 1*-3 + (r - -19). Find i such that 8*i + 17*i**3 - w*i**3 + 4*i + 16*i**2 = 0.
-3, -1, 0
Let p = 42 + -33. Let t(s) = 11*s**3 + 4*s**2 - 7*s + 9. Let c(r) = -5*r**3 - 2*r**2 + 3*r - 4. Let h(o) = p*c(o) + 4*t(o). Let h(b) = 0. What is b?
-1, 0
Let w(q) be the second derivative of 35*q**7/6 - 91*q**6/2 + 36*q**5 - 25*q**4/3 + 44*q + 1. Factor w(l).
5*l**2*(l - 5)*(7*l - 2)**2
Let m(p) be the first derivative of -2*p**3/9 + 308*p**2/3 - 47432*p/3 - 916. Factor m(f).
-2*(f - 154)**2/3
Let j be 8/3*(-15)/(-70). Let g = -10/29 - -360/203. Find l, given that -g*l**3 - 2/7*l**5 + 0*l + 0 - 8/7*l**4 - j*l**2 = 0.
-2, -1, 0
Let u(r) be the third derivative of 4*r**2 + 0 - 4/27*r**3 - 1/540*r**6 + 1/90*r**5 + 0*r**4 + 0*r. Let u(b) = 0. Calculate b.
-1, 2
Let l = -735 - -740. Let k(o) be the third derivative of -l*o**2 + 1/180*o**5 + 2/9*o**3 + 0 - 1/18*o**4 + 0*o. Factor k(u).
(u - 2)**2/3
Factor -6*p + 1584*p**2 - 8*p - 1582*p**2.
2*p*(p - 7)
Let n(o) be the first derivative of -o**6/2 + 21*o**5/5 - 3*o**4 - 12*o**3 - 5. Solve n(m) = 0 for m.
-1, 0, 2, 6
Let d(i) = i**4 + 36*i**3 + 55*i**2 - 300*i - 500. Let y(g) = 2*g**4 + 107*g**3 + 165*g**2 - 900*g - 1500. Let s(h) = -17*d(h) + 6*y(h). Factor s(r).
-5*(r - 5)**2*(r + 2)**2
Let l = 2602/5 + -518. Factor -1/5*b**4 + 8/5*b - l*b**2 + 0 + 6/5*b**3.
-b*(b - 2)**3/5
Let s be 25/(-125)*-8*5/4. Suppose 8/3 + 2/3*f**s - 10/3*f = 0. What is f?
1, 4
Suppose -3*n + 4 = 1. Let c be (-3 - n)/(-1 + -1). Let 3*z + 2 - 4*z - 2*z**c + z**2 + 0*z**2 = 0. Calculate z.
-2, 1
Let h(i) be the third derivative of i**8/8960 - i**7/3360 - i**6/480 + 2*i**4/3 - 11*i**2. Let w(k) be the second derivative of h(k). Factor w(v).
3*v*(v - 2)*(v + 1)/4
Solve 0 + 1/3*c**2 + 0*c + 7/6*c**3 = 0 for c.
-2/7, 0
Let o(a) be the first derivative of 6/5*a**5 + 32/3*a - 20 + 64/3*a**2 + 8*a**4 + 176/9*a**3. Factor o(q).
2*(q + 2)**2*(3*q + 2)**2/3
Factor -14 + 1/3*q**2 + 19/3*q.
(q - 2)*(q + 21)/3
Let b(x) be the second derivative of 2*x**7/21 + 34*x**6/5 + 150*x**5 + 874*x**4/3 - 20938*x**3 + 123462*x**2 - 3*x - 2. Factor b(y).
4*(y - 3)**2*(y + 19)**3
Let n(i) be the second derivative of -i**5/80 + i**4/24 - i**3/24 + 2*i + 2. Factor n(w).
-w*(w - 1)**2/4
Let y(r) be the first derivative of 3*r**2/2 + 21*r + 21. Let u be y(-7). Factor 2/7*p**2 - 6/7*p**3 - 2/7*p**5 + 6/7*p**4 + 0*p + u.
-2*p**2*(p - 1)**3/7
Let p(m) = -m**3 + 2*m**2 + 2*m. Let a(n) = -136*n**3 - 924*n**2 + 524*n - 64. Let l(u) = a(u) - 10*p(u). What is o in l(o) = 0?
-8, 2/9, 2/7
Find b, given that 18/5*b**3 - 18/5*b + 4/5*b**2 - 4/5 = 0.
-1, -2/9, 1
Let w(i) = 2*i**3 - 17*i**2 - 19*i - 9. Let y(m) = -3*m**3 + 33*m**2 + 40*m + 19. Let l(c) = -10*w(c) - 6*y(c). Factor l(v).
-2*(v + 1)**2*(v + 12)
Let m(i) = -i + 3. Let z(b) = 6*b - 19. Let w(j) = 39*m(j) + 6*z(j). Let q be w(0). Find h, given that 2/3*h**q - 2/3*h + 4/3 - 4/3*h**2 = 0.
-1, 1, 2
Let n(c) be the third derivative of -c**6/240 - c**5/20 - 11*c**4/48 - c**3/2 + 7*c**2 + 10*c. Suppose n(b) = 0. Calculate b.
-3, -2, -1
Let z(x) = -18*x**2 - 133*x + 151. Let t(r) = 10*r**2 + 66*r - 76. Let f(n) = 11*t(n) + 6*z(n). Factor f(l).
2*(l - 35)*(l - 1)
Suppose 52*p + 13/3*p**3 - 24 - 1/6*p**4 - 193/6*p**2 = 0. What is p?
1, 12
Suppose -20*x**2 + 26 - 2*x**3 + 48 + 46*x - 98 = 0. Calculate x.
-12, 1
Solve 0*g + 0 - 4*g**3 + 28/5*g**4 - 12/5*g**5 + 4/5*g**2 = 0 for g.
0, 1/3, 1
Let g(c) be the third derivative of -16/21*c**5 - 25*c**2 - 16/35*c**6 - 8/21*c**4 + 0 + 0*c**3 + 8/147*c**7 + 0*c + 25/588*c**8. What is f in g(f) = 0?
-2, -2/5, 0, 2
Let d(s) = 14*s**3 + 59*s**2 + 57*s + 11. Suppose 4*z + 2 = -u + 1, z + 5*u + 24 = 0. Let t(r) = r**2 + r + 1. Let q(m) = z*d(m) + t(m). Factor q(y).
2*(y + 1)*(y + 3)*(7*y + 2)
Let p be -18*((-897)/(-182) - 5). Factor -3/7*a**2 + p*a - 6/7.
-3*(a - 2)*(a - 1)/7
Let a(q) be the first derivative of q**3/3 + 7*q**2/2 + 10*q + 32. Find c, given that a(c) = 0.
-5, -2
Factor 2/13*f**4 + 20/13*f - 2*f**2 + 0 + 4/13*f**3.
2*f*(f - 2)*(f - 1)*(f + 5)/13
Let p(y) = -14*y**5 + 10*y**4 + 22*y**3 + 2*y**2 - 28*y + 44. Let a(w) = -w**5 + w**4 + w**3 - w + 3. Let k(r) = 12*a(r) - p(r). Determine c so that k(c) = 0.
-2, 1
Suppose -36*a = 38*a - 148. Find o, given