4. Let y(x) be the second derivative of 2*x + 0 + 0*x**2 - 1/105*x**6 + 1/42*x**4 - 1/70*x**5 + m*x**3. Solve y(p) = 0.
-1, 0, 1
Let t(i) = i - 9. Let q be t(11). Factor 5*d - 3*d + 13*d + 2*d**q + 32 + d.
2*(d + 4)**2
Let -7*r**3 - 14 - 3*r**5 - 6*r + 20 - 6*r**2 + 19*r**3 - 3*r = 0. Calculate r.
-2, -1, 1
Let d(w) = -w**2 - 4*w + 2. Let m(b) = -b + 4. Let x be m(8). Let q be d(x). Factor -3*j**2 + j - 3*j - j + 0*j**q.
-3*j*(j + 1)
Let u(l) be the first derivative of -6 - 2*l + 0*l**2 + 2/3*l**3. What is z in u(z) = 0?
-1, 1
Let u(k) be the third derivative of -1/30*k**5 + 0*k**4 + 1/3*k**3 + 0*k + 3*k**2 + 0. Factor u(v).
-2*(v - 1)*(v + 1)
Suppose -5*z + 0 = -4*v + 12, v = 3. Let k(w) be the first derivative of -1/2*w**4 - 1/3*w**3 + z*w - 1/5*w**5 + 0*w**2 + 2. Factor k(d).
-d**2*(d + 1)**2
Let m = -2009/50 - -201/5. Let g(b) be the second derivative of 0*b**2 - 1/30*b**4 - m*b**5 + 2*b + 0 + 2/15*b**3. Factor g(k).
-2*k*(k - 1)*(k + 2)/5
Let z(h) be the second derivative of -h**4/18 + 10*h**3/9 + 11*h**2/3 - 8*h. Factor z(b).
-2*(b - 11)*(b + 1)/3
Let z be 2/(-4) + 0 + 1. Let s be 10/(-55) - ((-24)/(-33))/(-4). Factor 2*t**4 + 0*t**2 + s + z*t**5 + 2*t**3 + 0*t.
t**3*(t + 2)**2/2
What is g in 2/7*g**3 + 10/7*g**4 + 0*g**2 + 8/7*g**5 + 0*g + 0 = 0?
-1, -1/4, 0
Suppose -y + 6*o = 2*o, 5*o - 25 = 0. Let l be (y/15)/((-2)/(-3)). Factor 1/5*q**l + 0*q + 1/5*q**3 + 0.
q**2*(q + 1)/5
Let f(a) be the first derivative of -a**3/7 + 17. Suppose f(l) = 0. Calculate l.
0
Let z(g) = -g**3 - 6*g**2 + g + 6. Let l be z(-6). Suppose 0 = -5*c - l*o - 5*o + 5, 0 = -o - 2. Suppose 2 - 2*q**2 + 4*q + c*q**2 + 0*q + 2 = 0. What is q?
-2
Suppose 4 = 29*j - 83. Factor j*b**3 + 1 - 19/4*b**2 - 3*b.
(b - 2)*(3*b + 2)*(4*b - 1)/4
Let s(w) = -w**3 + 7*w**2 - w + 8. Let u be s(7). What is n in -2 - n**2 + u + 1 - n = 0?
-1, 0
Factor -2*m**4 - 37*m**2 - 3*m**5 + m**2 + 12*m**2 - 36*m**3 - 16*m**4.
-3*m**2*(m + 2)**3
Suppose 0 = 8*s - 3*s - 10. Solve -2 + 10 - 2*a**s + 8*a + 4*a**2 = 0 for a.
-2
Find q, given that -2/13*q**2 + 2/13*q + 4/13 = 0.
-1, 2
Let b(w) be the second derivative of w**6/6 + 8*w**5 + 160*w**4 + 5120*w**3/3 + 10240*w**2 + 46*w. Factor b(d).
5*(d + 8)**4
Let l(a) be the second derivative of 0 + 0*a**2 + 1/36*a**4 - 1/60*a**5 + a + 0*a**3. Suppose l(r) = 0. Calculate r.
0, 1
Let i(p) be the second derivative of 0*p**2 - 1/3*p**3 - 1/10*p**5 + 0 + 2*p - 1/6*p**4 - 1/40*p**6. Let y(t) be the second derivative of i(t). Factor y(j).
-(3*j + 2)**2
Let r(w) be the third derivative of -w**2 - 1/30*w**5 + 1/336*w**8 + 1/210*w**7 + 0*w + 1/24*w**4 - 1/60*w**6 + 1/6*w**3 + 0. Solve r(f) = 0.
-1, 1
Let x(n) be the second derivative of -n**6/10 + 3*n**5/5 - 5*n**4/4 + n**3 + 23*n. Suppose x(t) = 0. What is t?
0, 1, 2
Suppose -2*h = -14 + 2. Suppose 18*n + h*n**2 + n**2 - 4*n**2 + 27 = 0. Calculate n.
-3
Let u(a) be the third derivative of 0*a + 0 - 1/42*a**5 + 5*a**2 - 2/21*a**4 + 4/21*a**3. Determine p so that u(p) = 0.
-2, 2/5
Let x(k) be the third derivative of -4/525*k**7 - 3*k**2 + 1/840*k**8 + 0*k**3 - 1/75*k**5 + 0*k**4 + 0*k + 1/60*k**6 + 0. Let x(q) = 0. Calculate q.
0, 1, 2
Let l(w) be the second derivative of -w**6/15 - 3*w**5/10 - 11*w. Factor l(m).
-2*m**3*(m + 3)
Let s(i) be the third derivative of -i**7/350 + 10*i**2. Factor s(h).
-3*h**4/5
Let a(f) be the second derivative of f**4/36 + f**3/18 - f**2/3 - 5*f. Factor a(x).
(x - 1)*(x + 2)/3
Solve -3/5*h**2 + 1/5*h**4 + 0 - 2/5*h**3 + 0*h = 0 for h.
-1, 0, 3
Suppose -4*r + 3*x + 8 = -x, 3*x = -r - 6. Suppose r = -v + 2. Let 1/3*g**v + 0 + 1/3*g = 0. Calculate g.
-1, 0
Let i(y) be the first derivative of 1 - 2*y**2 - y - 5/12*y**3 + 7/16*y**4. Factor i(v).
(v - 2)*(v + 1)*(7*v + 2)/4
Find y, given that 18/7*y**3 - 4/7*y**2 + 0 + 0*y = 0.
0, 2/9
Let n(m) be the first derivative of -m**6/21 + m**4/7 - m**2/7 - 13. Determine s so that n(s) = 0.
-1, 0, 1
Let g(p) be the first derivative of -p**2 - 2/3*p**4 + 2*p - 4/3*p**3 + 3. Let q(n) be the first derivative of g(n). Factor q(u).
-2*(2*u + 1)**2
Let v(t) = 4*t**3 - 4*t**2 + 8*t + 4. Suppose 3*u + 24 = -u. Let d(i) = -9*i**3 + 8*i**2 - 17*i - 8. Let h(g) = u*d(g) - 13*v(g). Determine m so that h(m) = 0.
-2, -1, 1
Let n(s) = 9*s + 416. Let r be n(-46). Determine g so that -10/3*g - r*g**2 - 4/3 = 0.
-1, -2/3
Let n(w) = -w**2 + 8*w - 9. Let v(d) = d**2 - 10*d - 5. Let m be v(11). Let a be n(m). Factor 0*r - 1/2*r**2 + 0 - 1/2*r**4 - r**a.
-r**2*(r + 1)**2/2
Let y(q) be the third derivative of q**2 + 1/6*q**4 + 1/10*q**5 - 1/105*q**7 + 0*q**6 + 0 + 0*q + 0*q**3. Factor y(l).
-2*l*(l - 2)*(l + 1)**2
Let f(d) be the third derivative of -d**6/240 + d**5/60 + d**4/48 - d**3/6 - 2*d**2. Solve f(i) = 0.
-1, 1, 2
Let f(g) be the second derivative of -1/2*g**4 - 1/15*g**6 + 1/3*g**3 + g + 0 + 3/10*g**5 + 0*g**2. Factor f(o).
-2*o*(o - 1)**3
Suppose m = 5*m. Determine h so that 2/7*h - 10/7*h**3 + 6/7*h**4 + 2/7*h**2 + m = 0.
-1/3, 0, 1
Let h(s) be the third derivative of -1/36*s**5 + 0 - 1/90*s**6 + 2*s**2 - 1/630*s**7 + 0*s**3 + 0*s - 1/36*s**4. Factor h(j).
-j*(j + 1)**2*(j + 2)/3
Let o(q) be the first derivative of -q**4/6 + 4*q**3/9 - q**2/3 - 11. What is k in o(k) = 0?
0, 1
Let h be 9/21 + 4/((-28)/(-11)). Let d(g) be the first derivative of -1/15*g**5 + 0*g**h + 1 + 1/12*g**4 + 0*g**3 + 0*g. Let d(b) = 0. Calculate b.
0, 1
Suppose 0 = 2*k + 1 - 7. Suppose 0*c + 6 = -k*d + 3*c, 3*d + 2*c - 14 = 0. Factor 24/7*r + 8/7 - d*r**2.
-2*(r - 2)*(7*r + 2)/7
Let d(h) be the third derivative of -h**7/1050 - h**6/300 - h**5/300 - 4*h**2. Find o such that d(o) = 0.
-1, 0
Let l(u) be the second derivative of -u**6/6 + 3*u**5/4 - 5*u**4/4 + 5*u**3/6 + 25*u. Factor l(p).
-5*p*(p - 1)**3
Let t(l) = l**2 - 4*l + 11. Let v(i) = i**2 - 3*i + 12. Let r(m) = 3*t(m) - 2*v(m). Factor r(a).
(a - 3)**2
Let f = 0 - -2. Factor -2*w**3 + 2*w + 3*w**2 - 4*w**f - 2 + 4 - 1.
-(w - 1)*(w + 1)*(2*w + 1)
Let n be -4 + (-18)/(-3) - -2. Factor -45 + 4*a**2 + 45 - 4*a**n + 6*a**3.
-2*a**2*(a - 2)*(2*a + 1)
Let j(y) be the second derivative of -7*y**7/3 - 7*y**6/5 + 12*y**5/5 - 2*y**4/3 - 13*y. Factor j(v).
-2*v**2*(v + 1)*(7*v - 2)**2
Let -236 - 2*a**3 - 2*a**2 + 14*a + 248 + 2*a**2 = 0. What is a?
-2, -1, 3
Let t(v) be the second derivative of 5*v**4/12 + 5*v**3/6 - 5*v**2 - 2*v + 12. Factor t(s).
5*(s - 1)*(s + 2)
Let u(r) = -6*r - 1. Let b be u(-1). Let t(m) = -m**2 + 5*m + 4. Let v be t(b). Factor -1/3*a**v + 1/3*a**3 - 1/3*a + 0 + 1/3*a**2.
-a*(a - 1)**2*(a + 1)/3
Let x(m) be the third derivative of -1/1050*m**7 - 1/600*m**6 + 0*m + 0 + 1/120*m**4 - 3*m**2 - 1/15*m**3 + 1/100*m**5. Factor x(a).
-(a - 1)**2*(a + 1)*(a + 2)/5
Suppose 1/3*i**3 - 4/3*i + 0 - i**2 = 0. Calculate i.
-1, 0, 4
Let g(s) be the first derivative of 2/5*s**5 - s**4 + s**2 + 1/3*s**6 - 3 + 2*s - 4/3*s**3. Factor g(o).
2*(o - 1)**2*(o + 1)**3
Let s(l) be the third derivative of 0*l**3 + 0*l + 0*l**4 - 1/40*l**5 + 2*l**2 + 0 - 1/140*l**7 - 1/40*l**6. Determine a, given that s(a) = 0.
-1, 0
Let p be (-2964)/(-171) - (-1 - -2). Let 14/3*h + 1/3 + p*h**2 = 0. Calculate h.
-1/7
Let 4/7*j + 2/7*j**2 + 2/7 = 0. What is j?
-1
Let g = -2 + 5. Let b(w) be the second derivative of -1/3*w**3 + 1/6*w**4 - 1/15*w**6 + 0*w**2 + 0 + 1/10*w**5 + g*w. Factor b(s).
-2*s*(s - 1)**2*(s + 1)
Let m = 9 + -6. Solve 3*y**2 + 4*y**m - 2*y**2 - 5*y**2 = 0 for y.
0, 1
Let l(c) be the second derivative of -c**4/12 + c**2/2 + 7*c. What is i in l(i) = 0?
-1, 1
Suppose -3*o - 126*h = -123*h - 12, -2*o - 3*h = -12. Factor o - 18/5*l**2 - 14/5*l**3 - 4/5*l.
-2*l*(l + 1)*(7*l + 2)/5
Let h be (9/25)/(69/230). Factor -9/5 - 1/5*o**2 + h*o.
-(o - 3)**2/5
Suppose 5*a + 5*n + 5 = 0, -5*a + n - 1 = -14. Factor -4 - 46/3*p - 14/3*p**a.
-2*(p + 3)*(7*p + 2)/3
Factor 2/3*y**3 + 1/3*y**5 - y**4 + 2/3*y**2 - y + 1/3.
(y - 1)**4*(y + 1)/3
Solve -a - 5*a - 4*a**2 + 0*a**3 + 2*a**3 = 0 for a.
-1, 0, 3
Let l(d) be the second derivative of -d**4/3 + 4*d**3/3 + 4*d**2 - 7*d. Let g(x) = x**2. Let t(f) = 6*g(f) + l(f). Suppose t(w) = 0. What is w?
-2
Factor 2/3 - 17/9*m + 5/9*m**2.
(m - 3)*(5*m - 2)/9
Determine q, given that 0 + 2/7*q + 2/7*q**2 = 0.
-1, 0
Let t = -26 - -31. Let r(a) be the second derivative of 0 + 1/30*a**6 + 1/6*a**3 + a - 1/30*a**t - 1/6*a**2 - 1/