 Factor j(y).
-2*y*(y + 1)**2/9
Let r(k) be the second derivative of k**7/189 - 4*k**6/135 + k**5/18 - k**4/27 - 34*k. Factor r(t).
2*t**2*(t - 2)*(t - 1)**2/9
Factor -1/3*j**2 - 2/3*j - 1/3.
-(j + 1)**2/3
Suppose f**4 - 1/4*f + 0 - f**2 + 1/4*f**3 = 0. Calculate f.
-1, -1/4, 0, 1
Let h(j) be the first derivative of -j**4/10 + 4*j**3/5 - 11*j**2/5 + 12*j/5 + 2. Let h(m) = 0. What is m?
1, 2, 3
Let y(l) = l**3 + l**2 + l - 1. Let r(t) = 16*t**3 + 12*t**2 + 32*t - 20. Let k(m) = r(m) - 20*y(m). Factor k(d).
-4*d*(d - 1)*(d + 3)
Suppose 8/3*q**3 + 4/3 + 4/3*q**4 - 4/3*q - 8/3*q**2 - 4/3*q**5 = 0. Calculate q.
-1, 1
Let r(w) be the first derivative of w**3/3 + w**2/2 + w - 5. Let f(s) = 15*s**2 - 9*s + 6. Let v = -1 + 0. Let j(g) = v*f(g) + 3*r(g). Solve j(q) = 0.
1/2
Let q(i) be the first derivative of 0*i**2 + 3 - 2/3*i**3 + 2*i. Let q(j) = 0. Calculate j.
-1, 1
Suppose 4*s - 8 = -2*l, -s = 2*l + l + 8. Suppose -s = -4*m + 2*m. Determine o so that 0 + 1/2*o**m + 0*o + 1/2*o**4 - o**3 = 0.
0, 1
Let x = -423947/28 + 15153. Let g = x - 47/4. Factor 4/7*h**3 + 0*h**2 - 4/7*h - g*h**4 + 2/7.
-2*(h - 1)**3*(h + 1)/7
Let w = 7 + -4. Let r(a) be the first derivative of 5*a**2 + 5 + 2*a**3 + w*a + a + 0*a**2 - 3. Solve r(z) = 0 for z.
-1, -2/3
Let b = 9 + -14. Let v be (1*-2 - b) + 1. Factor -9*i - 3 - 1 - 5*i + 14*i**2 + v*i.
2*(i - 1)*(7*i + 2)
Suppose 2*f = -f. Suppose -8*i + 3*i + 3*w - 3 = f, i = 4*w - 4. Let -4*g**2 - 2*g**4 - g**5 + i*g**5 + 6*g**2 + g = 0. What is g?
-1, 0, 1
Let g(f) be the second derivative of -f**6/6 + 5*f**4/3 + 20*f. Determine n so that g(n) = 0.
-2, 0, 2
Let t be -1*(-8)/(-28) + 24/14. Factor -t*o - 2/7*o**3 - 8/7*o**2 - 4/7.
-2*(o + 1)**2*(o + 2)/7
Let l(t) be the second derivative of t**4/4 - 7*t**3/2 + 15*t**2 + 8*t + 2. Let l(j) = 0. What is j?
2, 5
Let f(s) = 7*s**3 + 3*s**2 - 15*s - 11. Let o(y) = -3*y**3 - y**2 + 7*y + 5. Let j be 2*-1 + (12 - 14). Let i(t) = j*f(t) - 9*o(t). Suppose i(c) = 0. What is c?
-1
Let x(t) be the third derivative of -t**7/420 + t**5/120 + 5*t**2. Factor x(z).
-z**2*(z - 1)*(z + 1)/2
Suppose 12*q**5 - 4*q**3 + 31*q**3 - 20*q**4 - 9*q**2 + 11*q**4 + q - 22*q**4 = 0. What is q?
0, 1/4, 1/3, 1
Factor 0*u**3 + 0*u + 1/5*u**4 + 0 + 1/5*u**5 + 0*u**2.
u**4*(u + 1)/5
Suppose 0 = -5*h + 3*h + 8. Let g = 7 - h. Factor -3 + 2*z**3 + 1 + 6*z**4 + 2*z**5 - 6*z - 4*z**2 + 2*z**g.
2*(z - 1)*(z + 1)**4
Factor -20/3*p - 4/3 - 23/3*p**2 - 7/3*p**3.
-(p + 1)*(p + 2)*(7*p + 2)/3
Factor -1/3*v + 0*v**2 + 0 + 1/3*v**3.
v*(v - 1)*(v + 1)/3
Let q(u) = -14*u + 5. Let t be q(0). Suppose 1/3*f**t - 2/3*f**2 + f**4 - f + 2/3*f**3 - 1/3 = 0. Calculate f.
-1, 1
Let a(h) be the third derivative of h**7/70 - h**6/20 + h**4/4 - h**3/2 + 11*h**2. Solve a(m) = 0.
-1, 1
Let s = -25 - -30. Let o(j) be the third derivative of -1/54*j**s - 3*j**2 + 0 + 2/27*j**3 - 1/36*j**4 + 0*j. Suppose o(l) = 0. Calculate l.
-1, 2/5
Determine k, given that -11 - k + k**3 + 11 = 0.
-1, 0, 1
Let x(u) be the first derivative of -u**5/180 - u**4/24 - u**3/9 - 3*u**2/2 + 2. Let s(g) be the second derivative of x(g). Let s(t) = 0. What is t?
-2, -1
Let n(g) be the third derivative of 0*g + 1/30*g**5 + 0 + 1/3*g**4 + 4/3*g**3 - g**2. Suppose n(i) = 0. Calculate i.
-2
Let p(m) = -m**3 - m - 1. Let j(l) = 11*l**3 - 10*l**2 + 23*l + 3. Let u(v) = -2*j(v) - 18*p(v). Factor u(w).
-4*(w - 3)*(w - 1)**2
Let c be 2 + 0 + 2 + -5. Let o = 1 - c. Factor 3*h + 2*h**3 + 0*h**3 + 2 - 5*h - 2*h**o.
2*(h - 1)**2*(h + 1)
Let n be (-24)/(-18) - (-4 + (-87)/(-18)). Suppose 1 - 1/2*l**2 + n*l = 0. Calculate l.
-1, 2
Suppose -4*d - c = -25 + 6, 0 = 5*d + c - 23. Factor 2*x**5 - 2*x**4 + 3*x**4 - 5*x**d.
2*x**4*(x - 2)
Let w(v) be the third derivative of v**8/5600 - v**7/1260 + v**6/900 + v**4/3 - 7*v**2. Let r(n) be the second derivative of w(n). Factor r(i).
2*i*(i - 1)*(3*i - 2)/5
Let d(g) = -g**2 + 7*g - 3. Let u be d(6). Find s, given that -10*s**4 + 6*s**5 - 2*s**5 - 2*s**5 + 3*s**3 - 16*s + 8*s**2 + 9*s**u = 0.
-1, 0, 2
Suppose 5*h - 4*y = -13, 0 = -3*h + 5*h - 4*y + 10. Let c be (h + 15/9)*3. Factor -2/5*b**c + 0*b**3 + 0 + 2/5*b**4 + 0*b.
2*b**2*(b - 1)*(b + 1)/5
Let 4 - 4*i + 2*i**2 + 0 + 10*i = 0. What is i?
-2, -1
Suppose 0 = 4*a - 5*g + 7, 2*g - 5 = 5*a - 3*g. Determine q, given that 3 + 1 + 4*q**2 + 0*q**2 + 8*q + 0*q**a = 0.
-1
Let v(r) = r**3 + 2*r**2 - 3*r + 2. Let h be v(-3). Let p = -2 - -4. Factor -2*n**h + n - p*n**2 + 3*n**2.
-n*(n - 1)
Let m be (4 + 8/(-4))*1. What is k in -5*k**4 - 5*k - 7*k - 15*k**4 + 12*k**3 - 8 + 28*k**m = 0?
-1, -2/5, 1
Let j(f) be the first derivative of -f**7/105 - f**6/30 + f**4/6 + 2*f**3/3 - 1. Let v(d) be the third derivative of j(d). Factor v(w).
-4*(w + 1)**2*(2*w - 1)
Factor 5/6*v**2 + 0*v + 0 - 5/3*v**3 + 5/6*v**4.
5*v**2*(v - 1)**2/6
Determine b so that -2/5*b**2 + 0*b + 0 - 2/5*b**5 + 2/5*b**4 + 2/5*b**3 = 0.
-1, 0, 1
Let d(z) be the third derivative of 0*z**4 + 10*z**2 + 1/20*z**6 - 1/70*z**7 + 0*z + 0 - 1/20*z**5 + 0*z**3. Factor d(p).
-3*p**2*(p - 1)**2
Let f(i) be the second derivative of 0*i**2 + 1/15*i**3 - 1/50*i**5 - 1/30*i**4 + 1/75*i**6 + 2*i + 0. Solve f(o) = 0.
-1, 0, 1
Let s(h) be the second derivative of -1/42*h**4 + 0*h**2 + 0*h**3 + 3*h + 0. Factor s(r).
-2*r**2/7
Determine j, given that -3/4*j**2 + 15/4 + 3*j = 0.
-1, 5
Let q(j) be the second derivative of -j**6/90 - j**5/60 + j**4/36 + j**3/18 - 3*j. Find x such that q(x) = 0.
-1, 0, 1
Let w = 435 + -1737/4. Factor 0 + 0*t + 1/4*t**4 + 1/2*t**2 + w*t**3.
t**2*(t + 1)*(t + 2)/4
Suppose 0 = -x + 3*n - 5 - 7, 5*x - 20 = -n. Determine t, given that -5 + 6*t**3 - 15*t - 1 - 3*t**x + 6*t = 0.
-1, 2
Let c(j) = -j**5 - 2*j**4 - 3*j**3 - 2. Let q(i) = 3*i**5 + 5*i**4 + 8*i**3 - i**2 + 7. Let x(t) = 14*c(t) + 4*q(t). Solve x(a) = 0 for a.
-2, -1, 0
Let m(w) = w**2 + 5*w - 4. Let t be m(-6). Factor 2*o + 0*o**2 - 5*o**t + o - 7*o**2 + 15*o**3 - 6*o**4.
-3*o*(o - 1)**2*(2*o - 1)
Let h be (14/(-4))/(1/2). Let q = h - -10. Factor 0*l**2 + q*l**2 + 2*l - 5*l**2.
-2*l*(l - 1)
Let o(t) be the second derivative of -t**6/105 + 3*t**5/70 - t**4/14 + t**3/21 - 13*t. Find r such that o(r) = 0.
0, 1
Factor -z**3 + 5*z**3 - 3*z**2 - 5*z**2.
4*z**2*(z - 2)
Let k = -36 + 39. Let -2/9*x**5 + 2/9*x**2 + 0 + 2/9*x**k - 2/9*x**4 + 0*x = 0. What is x?
-1, 0, 1
Factor -1/3*w + 0 + 4/3*w**2.
w*(4*w - 1)/3
Let f(u) be the first derivative of -2*u**5/5 - u**4/4 + u**3 + u**2/2 - u - 21. Factor f(i).
-(i - 1)*(i + 1)**2*(2*i - 1)
Suppose -3*f - 2*x - 3*x = -9, -5*f = -4*x - 15. Let q be -1 - 0 - (f - 6). Factor 0 + 1 - y**q + 0*y**2.
-(y - 1)*(y + 1)
Suppose 0 = 5*j - w - 3 - 5, 2*j = 4*w - 4. Solve -2*a**4 + 2*a**3 + 4*a**4 - a**2 - 2*a - a**j = 0 for a.
-1, 0, 1
Let b be 2 + (-1)/1 - 1. Suppose 5*f = -b*f. Determine l so that 2/5*l**2 + 2/5*l**4 + 0*l + f + 4/5*l**3 = 0.
-1, 0
Let v(w) be the second derivative of -2*w**6/3 - 2*w**5/5 + 20*w**4/3 + 16*w**3/3 - 42*w. Find k such that v(k) = 0.
-2, -2/5, 0, 2
Suppose 4*m + 165 = -59. Let p = 170/3 + m. Factor -p*l**4 + 4/3*l**3 - 2/3*l**2 + 0*l + 0.
-2*l**2*(l - 1)**2/3
Let h(y) = 7*y**2 + 12*y - 17. Let a(b) = 155*b**2 + 265*b - 375. Let x(t) = -2*a(t) + 45*h(t). Factor x(z).
5*(z - 1)*(z + 3)
Suppose 0*z - 6 = -z. Suppose 25 = -s + z*s. Factor 2*p**4 + p**3 - p**3 + p**3 + p**s.
p**3*(p + 1)**2
Let n(z) be the third derivative of -z**8/840 + z**7/175 - 2*z**5/75 - 4*z**2. Suppose n(v) = 0. Calculate v.
-1, 0, 2
Let h(a) = -a - 1. Let v be h(-3). Factor 0 - 2/5*g**v + 4/5*g.
-2*g*(g - 2)/5
Let v(l) = -2*l**2 + 6*l - 4. Let h(u) = 5*u**2 - 17*u + 12. Let o(a) = 6*h(a) + 17*v(a). Factor o(k).
-4*(k - 1)*(k + 1)
Suppose k - 6*k = -10, -k = -a. Let y be -14*3/24 - -2. Let 1/2*i + y*i**a - 1/2*i**3 - 1/4 = 0. Calculate i.
-1, 1/2, 1
Let s(o) be the second derivative of 0 + o + 41/5*o**5 - 4*o**3 + 35/12*o**7 - 4*o**2 - 231/20*o**6 + 23/3*o**4. Determine x so that s(x) = 0.
-2/7, 2/5, 1, 2
Suppose 5*u + 0*u = 0. Suppose -4*o + 20 = 0, 3*o = -2*s - u*o + 25. Solve 3/2*r**4 + 0 + 8*r**3 - 7*r**s - r - 3/2*r**2 = 0.
-1, -2/7, 0, 1/2, 1
Let y = 796/5 - 155. Factor -6/5*p**4 - 19/5*p**3 - 9/5*p - y*p**2 - 1/5.
-(p + 1)**3*(6*p + 1)/5
Let v(h) be the first derivative of h**8/1680 + h**7/420 + h**6/360 - h**3 + 1. Let f(r) be the third der