 + 3*z**3. Let r(h) = b*a(h) - 3*t(h). Suppose r(x) = 0. What is x?
0, 1/4
Let v(g) be the second derivative of -g**5/80 - 5*g**4/48 - g**3/3 - g**2/2 + 6*g. Factor v(h).
-(h + 1)*(h + 2)**2/4
Let q(c) be the first derivative of c**4/46 + 26*c**3/23 + 507*c**2/23 + 4394*c/23 + 16. Factor q(p).
2*(p + 13)**3/23
Let l(y) be the first derivative of -y**3/3 - 2*y**2 - 36. Factor l(d).
-d*(d + 4)
Factor -2*h + 1 + 5/4*h**2 - 1/4*h**3.
-(h - 2)**2*(h - 1)/4
Suppose -5 = 2*m + 2*q - 1, -m + 23 = -4*q. Suppose 0*l - 6 = -m*l. Let 2/7*b**3 - 2/7*b**l - 2/7*b + 2/7 = 0. What is b?
-1, 1
Factor -2/13*f**3 + 2/13*f - 2/13 + 2/13*f**2.
-2*(f - 1)**2*(f + 1)/13
Let u be 30/7 - 6/21. Suppose -u*i + 0*i = 0. Solve q**2 + 1 + q**4 - 2*q**3 + i*q**4 - 1 = 0 for q.
0, 1
Suppose 0 = 2*j - 0*j - 4. Factor -5*r + r**3 + 5*r - j*r**2 + r.
r*(r - 1)**2
Let d(t) = -t**3 - t**2 - t + 5. Let n be d(0). Factor a**3 + a + n*a + 3*a**2 - 4*a.
a*(a + 1)*(a + 2)
Let y = -6 + 5. Let v be y/((-3)/(-6))*-7. Factor i + 15*i**3 + v*i**2 - 5*i**3 + 3*i.
2*i*(i + 1)*(5*i + 2)
Let n(p) be the third derivative of p**5/450 + p**4/180 - 2*p**3/45 - 35*p**2. Factor n(x).
2*(x - 1)*(x + 2)/15
Let l = 403/5 - 80. Solve 0 - 6/5*o + 3/5*o**2 - l*o**4 - 3/5*o**5 + 9/5*o**3 = 0 for o.
-2, -1, 0, 1
Let c = 305/8 + -18299/480. Let h(a) be the third derivative of 4*a**2 + c*a**6 + 0*a + 1/120*a**5 + 1/96*a**4 + 0*a**3 + 0. Factor h(n).
n*(n + 1)**2/4
Let s(t) be the first derivative of -2*t**3/27 + 4*t**2/3 - 8*t + 12. Factor s(a).
-2*(a - 6)**2/9
Suppose 0 = 5*c + 2*c + c. Let b(x) be the second derivative of c*x**4 + 1/21*x**7 - 2*x + 0 + 0*x**2 + 0*x**3 + 2/15*x**6 + 1/10*x**5. Factor b(h).
2*h**3*(h + 1)**2
Let f(h) be the second derivative of -h**6/225 - h**5/50 + 4*h**3/45 - 8*h. Factor f(c).
-2*c*(c - 1)*(c + 2)**2/15
Let a = 1/12 + 2/3. Let c(o) be the first derivative of -15/8*o**4 + 0*o + 3 + 21/10*o**5 + 0*o**2 + 1/2*o**3 - a*o**6. Factor c(g).
-3*g**2*(g - 1)**2*(3*g - 1)/2
Suppose 10*q + 70 = 8*q. Let h be 3/(q/(-10) - 2). Factor 0 + 4/11*m - 2/11*m**h.
-2*m*(m - 2)/11
Let f(q) be the second derivative of q**5/220 - q**4/11 + 8*q**3/11 - 32*q**2/11 - 14*q. Suppose f(o) = 0. What is o?
4
Let z(s) be the second derivative of s**7/1260 + s**6/360 - s**5/30 + 3*s**4/4 - 7*s. Let a(n) be the third derivative of z(n). Factor a(t).
2*(t - 1)*(t + 2)
Factor -12*q - 3*q**3 - q**3 - 4 + 4*q**2 + 16*q.
-4*(q - 1)**2*(q + 1)
Suppose u - 8 + 3 = 0. What is o in -3*o**3 - 3*o**4 - 2*o**2 + 5*o**2 - 14*o**u + 17*o**5 = 0?
-1, 0, 1
Let i = -81/2 + 41. Solve i*l - 1/2*l**2 + 1 = 0 for l.
-1, 2
Determine l, given that -5*l**2 - 427*l + 427*l + 5 = 0.
-1, 1
Let k(t) be the third derivative of t**5/4 - 7*t**4/24 - t**3/3 + 5*t**2. Solve k(z) = 0.
-1/5, 2/3
Let k(v) be the third derivative of -v**6/720 - v**5/120 - v**4/48 + v**3/6 + 2*v**2. Let q(b) be the first derivative of k(b). Find d such that q(d) = 0.
-1
Suppose -180 = 2*p + 3*p. Let f be p/8*4/(-6). Factor -3*h**4 - 2*h**4 - 4*h**3 + f*h**4.
-2*h**3*(h + 2)
Let z = -8 - -2. Let x(c) = c + 8. Let j be x(z). Solve -1/2*p**j - 1/2 + p = 0.
1
Let v(w) be the first derivative of w**5/80 + 5*w**4/96 + w**3/12 - w**2/2 - 4. Let q(a) be the second derivative of v(a). Suppose q(f) = 0. Calculate f.
-1, -2/3
Determine h so that -1/4*h**2 + 1/2 + 1/4*h = 0.
-1, 2
Suppose 4*s + 3*s**2 - 2*s**2 - 8 + 0*s**2 - 6*s = 0. What is s?
-2, 4
Factor -2/15*g + 0 + 2/15*g**2.
2*g*(g - 1)/15
Factor 5/4*f**2 + 2*f + 1/4*f**3 + 1.
(f + 1)*(f + 2)**2/4
Let w(u) be the second derivative of -7*u**4/60 - u**3/15 + u. Factor w(n).
-n*(7*n + 2)/5
Let z(u) be the second derivative of -u**6/240 + u**5/40 - u**4/16 + u**3/12 + 5*u**2/2 + u. Let r(h) be the first derivative of z(h). What is n in r(n) = 0?
1
Let s(w) be the third derivative of -2/105*w**7 + 2/15*w**6 + 3*w**2 - 2*w**4 + 0 + 0*w - 6*w**3 + 2/15*w**5. Factor s(h).
-4*(h - 3)**2*(h + 1)**2
Let w(t) = -7*t + 1. Let f be w(-1). Factor 8*p**3 + 90*p**3 + 49*p - f + 15*p - 154*p**2.
2*(p - 1)*(7*p - 2)**2
Let z be (-29)/144 - (-8)/180*5. Let d(o) be the second derivative of 1/4*o**3 - 1/8*o**2 - 2/15*o**6 - z*o**4 - 2*o + 0 - 3/10*o**5. Factor d(b).
-(b + 1)**2*(4*b - 1)**2/4
Let f(k) be the second derivative of k**6/24 + k**5/16 - 5*k**4/4 - 35*k**3/6 - 10*k**2 - 31*k. Determine v, given that f(v) = 0.
-2, -1, 4
Let d = 11 - 4. Find q such that 3*q**3 + 0*q**4 + d*q**4 - 10*q**4 = 0.
0, 1
Factor 5/2*s**3 + s**2 + 0 - 3/2*s.
s*(s + 1)*(5*s - 3)/2
Let j(p) = p**3 - p. Let t(i) = -6*i**3 - 20*i**2 + 26*i. Let q(x) = -10*j(x) - t(x). Factor q(b).
-4*b*(b - 4)*(b - 1)
Let i(v) be the second derivative of v**4/8 + 3*v**3/4 + 3*v**2/2 - 7*v. Solve i(j) = 0 for j.
-2, -1
Let d(r) be the first derivative of r**3 + 3. Solve d(s) = 0.
0
Let b = 51814/5 + -10302. Let p = -60 + b. Factor -6/5*l**2 - p + 2*l.
-2*(l - 1)*(3*l - 2)/5
Let g = 2 - -2. Factor -j**3 - 2*j**g + j**4 + j**2 + j**3.
-j**2*(j - 1)*(j + 1)
Let v(d) be the third derivative of -d**6/180 + d**5/18 - 7*d**4/36 + d**3/3 + 8*d**2. Solve v(o) = 0.
1, 3
Let c(k) be the first derivative of k**8/4200 + k**7/2100 - k**6/900 - k**5/300 + 2*k**3/3 + 1. Let l(b) be the third derivative of c(b). Factor l(j).
2*j*(j - 1)*(j + 1)**2/5
Factor 69*s**2 + 12 - 16*s + s**3 - 4*s**3 + 64*s + 9*s**4 + 45*s**3.
3*(s + 1)**2*(s + 2)*(3*s + 2)
Let u(z) = 7*z**2 - 3*z + 5. Let t be u(2). Let b = 27 - t. Factor 0 + b*k + 2/11*k**2.
2*k**2/11
Let c(h) be the second derivative of -h**6/900 + h**5/150 + h**3/3 + 3*h. Let a(y) be the second derivative of c(y). Factor a(z).
-2*z*(z - 2)/5
Let g(x) be the second derivative of -6*x - 2/5*x**5 + 2/21*x**7 - 4/15*x**6 + 8/3*x**4 + 4*x**2 + 0 - 14/3*x**3. Factor g(q).
4*(q - 1)**4*(q + 2)
Let m = 248/5 - 481/10. Suppose -m*k + 1/2*k**3 + 0*k**2 + 1 = 0. What is k?
-2, 1
Let i(s) be the third derivative of -s**2 + 0*s - 1/6*s**3 - 7/60*s**5 + 1/40*s**6 + 5/24*s**4 + 0. Factor i(y).
(y - 1)**2*(3*y - 1)
Let p(f) be the first derivative of 0*f**2 - 2/3*f**3 + 0*f - 5. Factor p(d).
-2*d**2
Let o(g) be the third derivative of -g**7/1050 - g**6/600 - 4*g**2. Factor o(q).
-q**3*(q + 1)/5
Let m(j) = 8*j**4 - 9*j**3 + 2*j**2 + 14*j - 5. Let u(h) = 7*h**4 - 9*h**3 + h**2 + 13*h - 4. Let y(g) = 4*m(g) - 5*u(g). Factor y(l).
-3*l*(l - 3)*(l - 1)*(l + 1)
Let 5/2*n**4 - n + n**3 + 0 - 5/2*n**2 = 0. Calculate n.
-1, -2/5, 0, 1
Let d(b) be the second derivative of b**5/20 + 5*b**4/12 - b**3/6 - 5*b**2/2 + 3*b + 2. Suppose d(f) = 0. What is f?
-5, -1, 1
Factor -4*y + 7*y**2 - 3*y**2 - 5 - 3.
4*(y - 2)*(y + 1)
Let 5/2*t + 1/2*t**3 - 2*t**2 - 1 = 0. Calculate t.
1, 2
Let x(f) = -f**3 + f**2 + 2*f - 3. Let b be x(2). Let s(u) = 4*u**3 - 3*u**2 + 3. Let d(w) = 7*w**3 - 5*w**2 + 5. Let j(o) = b*d(o) + 5*s(o). Factor j(p).
-p**3
Let o(c) be the third derivative of 0*c**3 - 2*c**2 + 0*c - 1/300*c**5 + 0 + 1/120*c**4. Solve o(m) = 0 for m.
0, 1
Let q(g) be the third derivative of -g**5/60 - 5*g**4/24 - g**3 + 7*g**2. Find v, given that q(v) = 0.
-3, -2
Let m(l) be the second derivative of l**6/780 - l**4/156 + 2*l**2 + 5*l. Let r(s) be the first derivative of m(s). Determine g, given that r(g) = 0.
-1, 0, 1
Suppose 2*g + 2*g - 216 = 0. Solve -f**2 + 54 - 2*f + f**3 - g = 0 for f.
-1, 0, 2
Let k(p) be the second derivative of 0*p**3 + p**2 + 0 + 1/32*p**4 + 1/80*p**5 - 3*p. Let j(q) be the first derivative of k(q). Determine x so that j(x) = 0.
-1, 0
Let o(k) be the first derivative of 0*k**2 + 0*k**3 - 1/20*k**4 - 1 + 0*k - 1/25*k**5. Determine r, given that o(r) = 0.
-1, 0
Let l(b) = b**2 - 23*b + 2. Let w be l(23). Factor 0*o**w + 0 + 2/5*o**3 - 2/5*o.
2*o*(o - 1)*(o + 1)/5
Suppose -2*q = -3*p - q + 17, -5*q - 20 = -2*p. Suppose -3*a - 5 - 4 = -p*h, a + 3*h - 11 = 0. What is i in -i + i + 2*i**a = 0?
0
Let y(h) be the third derivative of 2*h**7/315 - 13*h**6/360 + h**5/12 - 7*h**4/72 + h**3/18 + 29*h**2. Factor y(w).
(w - 1)**3*(4*w - 1)/3
Solve 2/3*q - 2/9*q**3 - 4/9 + 0*q**2 = 0 for q.
-2, 1
What is n in 0*n**2 - 1/2*n**3 + 0*n + 0 + 1/2*n**4 = 0?
0, 1
Determine v, given that 6*v**3 + 7*v**4 - 12 + 19*v**4 - 35*v**4 + 27*v**2 = 0.
-1, 2/3, 2
Let m(d) = -11*d**2 - 1. Let c be m(-2). Let z be (-4)/(-15)*c/(-15). Factor -z*o**2 - 7/5*o + 2/5.
-(o + 2)*(4*o - 1)/5
Let 