ative of 2*g**2 + 1/60*g**5 + 0 + 1/3*g**3 + 0*g + 1/8*g**z. Factor p(h).
(h + 1)*(h + 2)
Determine p, given that 2/5 + 2/15*p**3 - 2/15*p - 14/15*p**2 + 8/15*p**4 = 0.
-1, 3/4, 1
Determine s so that 0 - 8/7*s - 4/7*s**2 = 0.
-2, 0
Let u(o) be the second derivative of o**7/28 - o**6/20 - 3*o**5/40 + o**4/8 - 2*o - 6. Suppose u(c) = 0. Calculate c.
-1, 0, 1
Let q(f) be the first derivative of 2 + 0*f + 3/2*f**2 + 1/210*f**5 - 1/21*f**3 + 0*f**4. Let w(z) be the second derivative of q(z). Factor w(i).
2*(i - 1)*(i + 1)/7
Suppose 35 = 13*s - 8*s - 4*g, -2*s + g + 11 = 0. Factor 0*q + 0 + q**4 + 2/3*q**2 + 5/3*q**s.
q**2*(q + 1)*(3*q + 2)/3
Let u = -2133/5 + 427. Let d be (-2)/(-5) + -1 + 1. Factor 0*r**3 - 4/5*r**2 + u + d*r**4 + 0*r.
2*(r - 1)**2*(r + 1)**2/5
Factor -2*t**4 + 0*t + 0*t**2 + 3*t**3 + 1/3*t**5 + 0.
t**3*(t - 3)**2/3
Factor -4*k**2 + 2*k**2 + 11*k - 6 + 15*k - 18*k.
-2*(k - 3)*(k - 1)
Let s be (3 - 15/6)*4. Let g be (3/6*2)/1. Determine a so that a**3 - a**2 + 0*a - g + 1 - s*a = 0.
-1, 0, 2
Let k = 125/3 + -41. Factor k*o**2 + 0*o - 2/3.
2*(o - 1)*(o + 1)/3
Let n(x) be the second derivative of 2*x**7/21 + 2*x**6/5 - x**5/5 - 7*x**4/3 + 8*x**2 + 7*x. Find k such that n(k) = 0.
-2, -1, 1
Let q(s) be the first derivative of 1/7*s**2 + 4/35*s**5 + 0*s - 1/21*s**6 - 1 + 0*s**4 - 4/21*s**3. Factor q(m).
-2*m*(m - 1)**3*(m + 1)/7
Let a(i) be the second derivative of i**6/6 - 3*i**5/5 + 3*i**4/4 - i**3/3 - 12*i. Determine u so that a(u) = 0.
0, 2/5, 1
Let r be 15/(-12) - (-10)/5. Factor -3/4 + 9/4*v - 9/4*v**2 + r*v**3.
3*(v - 1)**3/4
Let s(c) be the first derivative of 4*c**5/5 - c**4 - 4*c**3 + 10*c**2 - 8*c + 5. Factor s(f).
4*(f - 1)**3*(f + 2)
Let m = 4 + -2. Solve -3 + 5*x**2 + x - x - 2*x**m = 0 for x.
-1, 1
Suppose 3*b**2 + 0*b**2 + 18*b**4 + 3*b**2 - 4*b**3 - 20*b**4 = 0. What is b?
-3, 0, 1
Let i(g) be the third derivative of 0*g**3 + 0*g**5 - 1/84*g**4 - g**2 + 0*g + 0 + 1/420*g**6. Factor i(h).
2*h*(h - 1)*(h + 1)/7
Let p(u) be the first derivative of u**5 - 2/3*u**6 + 0*u - 1/4*u**4 + 0*u**3 + 0*u**2 + 3. Factor p(i).
-i**3*(i - 1)*(4*i - 1)
Factor 0 - 2/3*t + 2*t**2 - 4/3*t**3.
-2*t*(t - 1)*(2*t - 1)/3
Suppose w + 2*w = 15. Let r(k) = -30*k**2 + 12*k + 8. Let c(z) = 20*z**2 - 8*z - 5. Let a(l) = w*r(l) + 8*c(l). Factor a(f).
2*f*(5*f - 2)
Let l(f) be the second derivative of f**7/63 - 2*f**6/45 + f**4/9 - f**3/9 + 24*f. Factor l(b).
2*b*(b - 1)**3*(b + 1)/3
Suppose -h - 26 = -5*t + h, 9 = 3*t + h. Find y, given that 6*y**t + 18*y**3 + 8*y**4 - 2*y**2 - y**2 + 7*y**2 = 0.
-1, -2/7, 0
Let k(v) = -v**3 - 9*v**2 + 8*v - 17. Let a be k(-10). Solve 0 - 1/4*h + 1/4*h**a + 1/4*h**4 - 1/4*h**2 = 0 for h.
-1, 0, 1
Let z(j) be the second derivative of -j**6/180 + j**3/6 - j. Let s(h) be the second derivative of z(h). Factor s(r).
-2*r**2
Let w(f) be the first derivative of 2*f**5/35 + 5*f**4/7 + 22*f**3/7 + 40*f**2/7 + 32*f/7 + 5. Determine b, given that w(b) = 0.
-4, -1
Let i(x) be the second derivative of x**7/84 + x**6/60 - x**5/10 - x**4/6 - 37*x. Let i(k) = 0. What is k?
-2, -1, 0, 2
Let f = -42 + 169/4. Factor -f*u**3 - 1/4 - 3/4*u**2 - 3/4*u.
-(u + 1)**3/4
Let t(l) be the first derivative of l**7/14 + l**6/5 - l**4/2 - l**3/2 + 5*l + 1. Let c(d) be the first derivative of t(d). Find o such that c(o) = 0.
-1, 0, 1
Let d(w) be the first derivative of -w**3/3 + w**2 - w - 8. Suppose d(q) = 0. Calculate q.
1
Let l(r) = r + 12. Let q be l(-5). Let z = 11 - q. Factor 4 + 5*h**2 - 6*h - z*h**2 + h**2.
2*(h - 2)*(h - 1)
Let w(s) = 2*s**2 + 6*s + 4. Let h be w(-3). Factor h*m**2 - 4 + 3*m**4 - 10*m**2 + 7.
3*(m - 1)**2*(m + 1)**2
Suppose 6 = h + 2. Let i(t) = -t**3 - t**2 - 3*t + 1. Let l(x) = x**3 + 2*x**2 + 3*x - 1. Let u(y) = h*l(y) + 5*i(y). Let u(w) = 0. Calculate w.
1
Let v(c) be the second derivative of -c**5/100 + c**4/60 - 2*c. Factor v(g).
-g**2*(g - 1)/5
Let z = -48/17 + 475/102. Factor -z*r**2 - 1/3*r - 5/2*r**3 + 0.
-r*(3*r + 1)*(5*r + 2)/6
Factor -5/8*w - 1/8*w**3 - 1/2*w**2 - 1/4.
-(w + 1)**2*(w + 2)/8
Let k(f) be the first derivative of f**6 + 51*f**5/10 + 9*f**4 + 13*f**3/2 + 3*f**2/2 - 5. Find x, given that k(x) = 0.
-2, -1, -1/4, 0
Suppose 166*p**2 + 106*p**2 - 580*p**3 - 20*p**5 - 72*p**2 + 208*p**4 = 0. Calculate p.
0, 2/5, 5
Let a(i) = 7*i**4 - 5*i**3 - 8*i**2. Let s(b) = -29*b**4 + 20*b**3 + 31*b**2. Let c(y) = -9*a(y) - 2*s(y). Factor c(r).
-5*r**2*(r - 2)*(r + 1)
Suppose -2*f = f. Let j(x) be the first derivative of -1/16*x**4 + 0*x**3 + 0*x**2 + f*x**5 - 1 + 1/24*x**6 + 0*x. What is s in j(s) = 0?
-1, 0, 1
Suppose 4*v - 3*f - 8 = 0, -v + 5*f + 0*f = -2. Factor c**3 - 7*c**v + 6*c**2 + 0*c**2 - 2*c.
c*(c - 2)*(c + 1)
Let s(q) be the first derivative of 4/15*q**3 - 4 + 3/2*q**4 + 0*q**2 + 0*q. Factor s(f).
2*f**2*(15*f + 2)/5
Factor -3*d**2 + 0*d + d**2 - 2*d.
-2*d*(d + 1)
Let l(k) = -5*k + 2. Let m(y) = -11*y + 4. Let j(q) = -13*l(q) + 6*m(q). Let d be j(-4). What is g in -2/3 - 2/3*g**d + 4/3*g = 0?
1
Factor a**2 + 6*a + 2*a**2 + a**2 - a**2 + 3.
3*(a + 1)**2
Let g(z) = z**2 + z. Let m(x) = -x**4 - 5*x**3 - 14*x**2 - 12*x - 2. Let c(q) = -15*g(q) - 3*m(q). What is d in c(d) = 0?
-2, -1
Let x(p) be the second derivative of p**4/4 + p**3/2 - 3*p**2 - 5*p. Let x(z) = 0. Calculate z.
-2, 1
Let f(l) be the first derivative of 1/3*l + 0*l**4 + 1/15*l**5 - 2/9*l**3 + 0*l**2 - 5. Factor f(b).
(b - 1)**2*(b + 1)**2/3
Let c(m) be the third derivative of m**7/7560 - m**6/1080 + m**5/360 - m**4/8 - 3*m**2. Let a(r) be the second derivative of c(r). Solve a(g) = 0.
1
Let j(y) = 4*y + y + 6*y**2 + 2 + 0*y + y**3. Let c be j(-5). Factor -2*p - 2*p**2 + 3*p**c + 3*p.
p*(p + 1)
Let g(j) be the second derivative of j**7/3780 + j**4/4 + 3*j. Let i(l) be the third derivative of g(l). Factor i(z).
2*z**2/3
Suppose x = -3*x + 6*x. Let j(s) be the first derivative of -s**2 - 2*s**3 - 2 - 3/2*s**4 - 2/5*s**5 + x*s. Determine q, given that j(q) = 0.
-1, 0
Let o(h) be the second derivative of h**4/6 - h**3/6 - 2*h**2 - 8*h. Let f be o(2). Solve 1 + 5/2*d - 7/2*d**f = 0.
-2/7, 1
Suppose -2/13*d**3 + 0 + 2/13*d**2 + 4/13*d = 0. What is d?
-1, 0, 2
Let x = -25 + 27. Suppose 2*h**5 - 2*h**3 + 5*h**2 - 2*h**x - 2*h**4 - h**2 = 0. What is h?
-1, 0, 1
Let v = 58/45 - 8/9. Factor 8/5*d**2 - 8/5*d + v.
2*(2*d - 1)**2/5
Let p be ((-4)/(-3))/(20/6). Suppose 0 + 2/5*k**3 + p*k - 4/5*k**2 = 0. Calculate k.
0, 1
Suppose -45*v + 38*v = -21. Find g, given that -2/5*g**v - 4/5*g + 6/5*g**2 + 0 = 0.
0, 1, 2
Let t(y) be the second derivative of -y**6/150 - 3*y**5/100 - y**4/60 + y**3/10 + y**2/5 + 11*y. Determine w so that t(w) = 0.
-2, -1, 1
Let l(n) = -5*n - 21. Let r be l(-5). Let c(u) be the first derivative of 2 + 1/8*u**r + 1/6*u**3 + 0*u - 1/2*u**2. Factor c(t).
t*(t - 1)*(t + 2)/2
Let d = 33 - 38. Let q be (7/70)/((-2)/d). Factor -q*t**2 + 1/4*t**4 + 0 + 1/2*t - 1/2*t**3.
t*(t - 2)*(t - 1)*(t + 1)/4
Suppose -6 = -2*w + 2*s, -2*s = -5*s + 3. Let q(l) be the first derivative of 0*l + 0*l**3 + 1/3*l**2 - 1/6*l**w + 4. Find c such that q(c) = 0.
-1, 0, 1
What is v in 3*v + 30*v**3 - 34*v**3 - 3*v + 4*v**4 = 0?
0, 1
Let i(n) = n**2 + n + 1. Let m(y) = 3*y**2 + 2*y + 1. Suppose -3*o + 2 = -8*v + 3*v, -3*v - 5 = 2*o. Let u(x) = o*m(x) + 2*i(x). Factor u(b).
-(b - 1)*(b + 1)
Suppose -11*t + 34*t**2 - 36*t**2 + 9*t = 0. Calculate t.
-1, 0
Let t(z) be the first derivative of 16*z**5/25 + 2*z**4 + 11*z**3/5 + z**2 + z/5 - 2. Solve t(i) = 0.
-1, -1/4
Let f be (-144)/(-42) + 12/(-28). Let t(p) = -3*p. Let w be t(-6). Factor -6*i**2 - 2/3*i**f - w*i - 18.
-2*(i + 3)**3/3
What is h in 1/5*h**2 + 1/5*h - 2/5 = 0?
-2, 1
Let q(n) = 3*n**3 - 7*n. Let r(p) = 12*p**3 + p**2 - 28*p + 1. Suppose 7 = 4*z - 1. Let a be 3/(z/((-8)/(-3))). Let m(b) = a*r(b) - 18*q(b). Factor m(h).
-2*(h - 2)*(h + 1)*(3*h + 1)
Let u(w) = 5*w**2 - w. Let z(i) = -24*i**2 + 4*i. Let r be 50/(-2)*(-4)/10. Suppose r + 2 = 4*v. Let h(t) = v*z(t) + 14*u(t). Factor h(d).
-2*d*(d + 1)
Suppose -2*p = -8, -2*t - 3*t + 2*p = -2. Let c(o) be the second derivative of 0 + 1/12*o**4 - o - 1/2*o**3 + 3/20*o**5 - 1/2*o**t. Solve c(s) = 0.
-1, -1/3, 1
Factor -2/5*n**4 - 4/5*n**3 + 0*n**2 + 4/5*n + 2/5.
-2*(n - 1)*(n + 1)**3/5
Let w = 4 - 1. Let o be 0 + 3/(-9) + w. Let 8/3 - o*s + 2/3*s**2 = 0. Calculate s