11/412. Factor -1/4*g**k + 0 - 3/4*g**3 - o*g - 3/4*g**2.
-g*(g + 1)**3/4
Let c = -5/11 + 37/33. Let s(d) be the first derivative of -c*d**3 + 0*d**2 + 0*d + 2 + 3/4*d**4 - 1/5*d**5. Suppose s(m) = 0. What is m?
0, 1, 2
Factor 54*y + 80 - 16*y + 5*y**2 + 2*y.
5*(y + 4)**2
Let a(i) be the first derivative of -2*i**5/5 + 3*i**4/8 + 3*i**3/2 + i**2/2 + 8. Solve a(l) = 0 for l.
-1, -1/4, 0, 2
Let w = -1/3 - -5/6. Let l = w - -1/4. Factor -l - 3/4*r + 3/4*r**2 + 3/4*r**3.
3*(r - 1)*(r + 1)**2/4
Factor -2/3*f + 2/3 + 2/3*f**3 - 2/3*f**2.
2*(f - 1)**2*(f + 1)/3
Let a(x) = -10 - 3*x**2 + 12*x + x**2 - 5. Let l be (-38)/10 + 34/(-170). Let m(q) = 2*q**2 - 12*q + 14. Let j(d) = l*a(d) - 3*m(d). Factor j(g).
2*(g - 3)**2
Factor -9/8 + 1/8*u**3 + 5/8*u**2 + 3/8*u.
(u - 1)*(u + 3)**2/8
Suppose -r + 2*r - 160 = -4*v, -4*v + 4*r + 160 = 0. Let h be (-6)/15 - (-26)/v. Factor 1/4*j**2 + 0*j + 1/4*j**3 + 0 - h*j**4 - 1/4*j**5.
-j**2*(j - 1)*(j + 1)**2/4
Let j be (3 - (-30)/5) + -4. Factor -9/2*g - j*g**2 - 3/2*g**3 - 1.
-(g + 1)*(g + 2)*(3*g + 1)/2
Suppose -z - 1 = 4*j, -5*z + 0 + 14 = j. Let p(q) be the second derivative of q**2 + 3*q - 2/3*q**z + 0 + 1/6*q**4. Factor p(i).
2*(i - 1)**2
What is n in -24*n**2 - 4*n - 22*n**4 + 6*n**2 - 127*n**3 + 97*n**3 - 6*n**5 = 0?
-1, -2/3, 0
Factor 19/11*d**2 - 1/11*d**3 - 80/11*d - 100/11.
-(d - 10)**2*(d + 1)/11
Suppose 2*u + 3*u = 10. Factor -3*v**3 - 6*v + 6*v - 6*v**u.
-3*v**2*(v + 2)
Let f(l) be the first derivative of -l**9/9072 + l**8/5040 + l**7/2520 - l**6/1080 - l**3 + 2. Let p(r) be the third derivative of f(r). Factor p(m).
-m**2*(m - 1)**2*(m + 1)/3
Let l(p) be the third derivative of -p**5/20 - p**2. Solve l(j) = 0.
0
Let c(j) be the second derivative of 3/2*j**2 - 3/2*j**3 + 3/4*j**4 + 0 - 3/20*j**5 + 7*j. Suppose c(f) = 0. What is f?
1
Let r(j) be the third derivative of j**8/560 + 3*j**7/175 + 3*j**6/50 + 2*j**5/25 - 6*j**2. Find w such that r(w) = 0.
-2, 0
Factor -1/7*j**2 + 0*j + 4/7.
-(j - 2)*(j + 2)/7
What is r in -1 + 4*r**2 + 38*r**3 + 1 - 34*r**3 = 0?
-1, 0
Let k(j) = -3*j**4 + 4*j**3 + 2*j**2 - 2*j + 1. Let n(i) = -86 + 86 + i. Let o(s) = -2*k(s) + 4*n(s). Solve o(v) = 0.
-1, 1/3, 1
Factor 4 - 8*s**3 + 8*s + s**4 + s**4 - 6*s**4 + 0*s**4.
-4*(s - 1)*(s + 1)**3
Let s be -7 + (7 - -6) + -2. What is k in 6/5*k**3 + 0 - 4/5*k**s + 1/5*k - 4/5*k**2 + 1/5*k**5 = 0?
0, 1
Let m be 181/4 + 2/(-8). Suppose 2*n = 2*f - 1 - 19, -5*f + m = -4*n. Determine l, given that -10*l**5 + 11*l**f - 4*l**3 + 3*l**3 = 0.
-1, 0, 1
Let j(f) be the second derivative of f**9/3024 + f**8/1680 + 2*f**3/3 + 2*f. Let v(x) be the second derivative of j(x). Determine y, given that v(y) = 0.
-1, 0
Let f(c) be the second derivative of c**5/20 - c**4/4 - 2*c**3/3 - 2*c - 4. Factor f(d).
d*(d - 4)*(d + 1)
Factor 0 + 2/3*t**4 + 16/3*t**2 - 10/3*t**3 - 8/3*t.
2*t*(t - 2)**2*(t - 1)/3
Determine z so that 6*z**2 + 4*z - 4 + 0*z**2 + 2*z**2 = 0.
-1, 1/2
Let a(y) be the first derivative of -5*y**4/6 - 4*y**3/3 + y**2 + 4*y + 3. Let z(k) be the first derivative of a(k). Factor z(r).
-2*(r + 1)*(5*r - 1)
Let w = -8 - 73. Let j be (2/3)/((-18)/w). Determine o, given that -2/9*o**4 + 2/9*o**2 - 2/9*o**j + 2/9*o + 0 = 0.
-1, 0, 1
Let i(v) = -8*v**2 + 78*v - 48. Let z(u) = u**2 - 11*u + 7. Let j(a) = 6*i(a) + 44*z(a). Factor j(p).
-4*(p - 1)*(p + 5)
Let m(a) be the third derivative of -4/3*a**3 + 1/10*a**5 + 0 - 4*a**2 + 1/15*a**6 + 0*a - 1/3*a**4 + 1/105*a**7. Suppose m(p) = 0. What is p?
-2, -1, 1
Let -2/5 + 2/15*y**2 + 4/15*y = 0. Calculate y.
-3, 1
Factor 10*o**2 - 10*o**2 + 6*o**2 + 55 + 60*o - o**2.
5*(o + 1)*(o + 11)
Factor 3/7*s**2 + 9/7*s + 6/7.
3*(s + 1)*(s + 2)/7
Factor 0 - 3/8*t**3 - 3/8*t - 3/4*t**2.
-3*t*(t + 1)**2/8
Let a(s) be the first derivative of 2*s**5/5 + 5*s**4/2 + 6*s**3 + 7*s**2 + 4*s - 3. Factor a(m).
2*(m + 1)**3*(m + 2)
Let j(m) be the third derivative of -4/3*m**3 + 0*m - 13/30*m**5 + 2*m**2 - 1/10*m**6 + 0 - 1/105*m**7 - m**4. Solve j(f) = 0.
-2, -1
Suppose i = -4*m - 3*i - 20, 5 = m - i. Factor 0*w + 0 + m*w**2 + 2/5*w**3.
2*w**3/5
Let i(s) be the first derivative of s**6/15 - 2*s**5/5 + s**4 - 4*s**3/3 + s**2 + 5*s - 5. Let h(w) be the first derivative of i(w). Let h(g) = 0. What is g?
1
Let t(o) = o**2 + o + 1. Let b(y) = 7*y**2 + 23*y + 3. Let g(l) = -b(l) + 3*t(l). Factor g(m).
-4*m*(m + 5)
Let f(y) = -6*y**3 - 6*y**2 + 2*y. Let v(p) = 7*p**3 + 7*p**2 - 2*p. Let k be 3 + 2*(-3)/(-3). Let l(i) = k*v(i) + 6*f(i). Factor l(x).
-x*(x - 1)*(x + 2)
Let r(o) = 2*o + 10. Let a be r(-5). Suppose 10/7*u**2 + 6/7*u**4 + a - 2/7*u - 2*u**3 = 0. Calculate u.
0, 1/3, 1
Let y(p) be the first derivative of 3 + p + 1/5*p**5 + 0*p**4 + 0*p**2 - 2/3*p**3. Solve y(r) = 0.
-1, 1
Let q = -5539/52 + 1386/13. Let i = 2/13 + q. Let a**3 + i*a**4 + 0 + 5/4*a**2 + 1/2*a = 0. What is a?
-2, -1, 0
Let h = -1/94 - -195/658. Suppose -2 - 4 = -3*r. Suppose -h*s - 2/7*s**r + 0 = 0. Calculate s.
-1, 0
Let z(y) = -y**4 - y**2 + y - 1. Let n(k) = -4*k**4 - 6*k**3 - 15*k**2 - 7*k - 6. Let i(q) = -n(q) + 3*z(q). Let i(t) = 0. What is t?
-3, -1
Let g be (-8)/(-14) - 190/(-35). Suppose 0 = -35*x + 33*x + g. Factor 0*r**2 + 0 - 2/11*r**x + 2/11*r.
-2*r*(r - 1)*(r + 1)/11
Let g(z) be the first derivative of z**3/3 + 18*z**2 + 324*z + 69. Factor g(c).
(c + 18)**2
Suppose 1 = -2*m + j, 26 = 5*m + 3*j + 1. Suppose 0 = m*h - 5 + 1. What is s in 0 + 0*s**h - 2/11*s**3 + 0*s = 0?
0
Suppose -3 = -q - z + 3, -2*z = -5*q + 2. Let k(r) be the second derivative of r + 0 - q*r**2 - 1/6*r**4 - r**3. Let k(j) = 0. What is j?
-2, -1
Let s = 70 + -68. Factor 1/4*z**3 + 0*z + 1/2*z**s + 0.
z**2*(z + 2)/4
Let a(g) be the second derivative of g**5/4 + 5*g**4/4 - 10*g**3/3 - 37*g. Factor a(l).
5*l*(l - 1)*(l + 4)
Let j(y) = -6*y**3 - 2*y**2 - y. Let m be j(-1). Suppose 5*u + 5*c + m = 0, u - 2*c = 4*u. Factor 4*t**2 + 2*t**3 - 4*t**u - 2*t.
2*t*(t - 1)*(t + 1)
Let f(w) be the second derivative of w**7/210 + w**6/50 + w**5/100 - w**4/20 - w**3/15 + 10*w. Solve f(d) = 0 for d.
-2, -1, 0, 1
Let s(t) be the first derivative of -t**5/80 + t**4/24 + 5*t + 7. Let z(i) be the first derivative of s(i). Factor z(h).
-h**2*(h - 2)/4
Factor 4/5*t + 2/5 + 2/5*t**2.
2*(t + 1)**2/5
Factor 1/4*d**2 + 0 - d.
d*(d - 4)/4
Factor 0 + 4*i + 1 + 11 - 16*i + 3*i**2.
3*(i - 2)**2
Let s be 4/46 - (-122)/184. Factor -s*n**2 + 1/4*n**3 + 0 + 1/2*n.
n*(n - 2)*(n - 1)/4
Let z(l) = l**2 - 2*l + 7. Suppose 5 = 4*h - 3. Let w(v) = 0*v**2 + h*v + v**2 - 2*v**2 - 8 + 0*v**2. Let o(q) = 6*w(q) + 7*z(q). Find y, given that o(y) = 0.
1
Let g be 1 - 2*2 - (-940)/282. Factor g*t**3 + 0 - 2/3*t + 1/3*t**2.
t*(t - 1)*(t + 2)/3
Let z be ((-1)/2)/(34/(-12)). Let g = 11/34 + z. Factor i**2 + g + 7/4*i - i**3.
-(i - 2)*(2*i + 1)**2/4
Let w(i) be the first derivative of i**6/120 + i**5/20 - 2*i**3/3 + 3*i**2/2 + 3. Let j(p) be the second derivative of w(p). Find f, given that j(f) = 0.
-2, 1
Let l(v) = 9*v**2 + 4*v + 9. Let h(p) = -4*p**2 - 2*p - 4. Let b(k) = -7*h(k) - 3*l(k). Suppose b(u) = 0. What is u?
-1
Let p(w) be the first derivative of 2*w**3/5 - 2*w**2/5 + 8. Suppose p(x) = 0. What is x?
0, 2/3
Let p = 2569/2145 - -1/429. Suppose 3/5*t**2 + 3/5*t - p = 0. What is t?
-2, 1
Suppose 0*m - m = 72. Let b = 218/3 + m. Find c, given that 0 - 2/3*c**5 + b*c**3 + 0*c - 2/3*c**2 + 2/3*c**4 = 0.
-1, 0, 1
Let a(c) be the second derivative of -2*c**5/65 - 3*c**4/26 - 2*c**3/13 - c**2/13 - 11*c. Suppose a(g) = 0. What is g?
-1, -1/4
Factor 1/2*d + 3/2*d**3 + 1/2*d**4 + 3/2*d**2 + 0.
d*(d + 1)**3/2
Determine z, given that -5*z**3 + 3*z**4 - 14*z**3 + 2*z**2 + 13*z**3 + z**2 = 0.
0, 1
Suppose 0 = -2*h + i - 3*i, 5*h = -3*i. Let t(c) be the third derivative of -3*c**2 + 1/3*c**4 - 1/30*c**5 - 4/3*c**3 + h + 0*c. Factor t(r).
-2*(r - 2)**2
Let j(s) = 5*s**2 - 8*s + 3. Let y(g) = g**2 - g. Let q(r) = -j(r) + 2*y(r). Factor q(x).
-3*(x - 1)**2
Let u = -5 + 7. Let i(z) = -z**3 + 3*z**2 - 2*z + 2. Let y be i(u). Factor s**5 + s + y*s**4 - s - 2*s**5 - s**3.
-s**3*(s - 1)**2
Let l(q) be the second derivative of -q**5/40 - 7*q**4/48 - q**3/6 + q**2/2 - 14*q. Find n, given that l(n) = 0.
-2, 1/2
Let x(w) = -11*w**3 + 69*w**2 + 189*w + 91. Let p(v) = -3*v**3 + 17*v**2 + 47*v + 23. Let h(a) = -9*p(a) + 2*x(a). Solve h(m) = 0.
-1,