 0, 1
Let o(y) be the second derivative of -y**7/42 + y**5/20 + 6*y. Factor o(z).
-z**3*(z - 1)*(z + 1)
Let d(b) = -2*b**3 + 2*b**2 - b + 4. Let m(h) = -11*h**3 + 11*h**2 - 6*h + 23. Suppose 3*q = -q + 32. Let x = q - 14. Let n(g) = x*m(g) + 34*d(g). Factor n(c).
-2*(c - 1)**2*(c + 1)
Find w such that -19*w**2 - 15*w + 18 + 31*w**3 + 4*w**2 - 16*w**3 - 3*w**4 = 0.
-1, 1, 2, 3
Let w be (1*-6 + 2)/(7 - 17). Factor 4/5*s**2 - 2/5*s**4 - 2/5*s**5 - w + 4/5*s**3 - 2/5*s.
-2*(s - 1)**2*(s + 1)**3/5
Find u such that -375*u**5 - 237*u**4 + 180*u + 24 - 123*u**4 - 90*u**4 + 195*u**3 + 426*u**2 = 0.
-1, -2/5, 1
Let i(k) be the third derivative of -k**7/105 - k**6/12 - 4*k**5/15 - k**4/3 + 18*k**2. Find v, given that i(v) = 0.
-2, -1, 0
Solve -23*r**3 + 38*r**2 + 12*r**2 - 42*r + 8 - 8*r**2 + 15*r**3 = 0.
1/4, 1, 4
Suppose 0 = 4*t - 4*p - 0*p - 56, 4*t - 2*p = 50. Let h = -8 + t. Factor 5*q**4 + 5*q + q**5 + q**3 + 3*q**2 + 9*q**h + 1 + 7*q**2.
(q + 1)**5
Let w(l) be the first derivative of -l**3/6 - 3*l**2/4 + 2*l + 1. Factor w(h).
-(h - 1)*(h + 4)/2
Let l(i) = i**4 + 9*i**3 - 15*i**2 - 5*i + 6. Let u(p) = 2*p**4 + 8*p**3 - 15*p**2 - 5*p + 7. Let h(z) = 3*l(z) - 4*u(z). Let h(r) = 0. Calculate r.
-2, -1, 1
Let y(w) be the first derivative of 3*w**5/20 + 3*w**4/16 - 5*w**3/4 + 9*w**2/8 + 5. Factor y(c).
3*c*(c - 1)**2*(c + 3)/4
Let j(g) be the first derivative of -g**5/90 - g**4/36 + 2*g**3/9 + 3*g**2/2 + 1. Let z(m) be the second derivative of j(m). Determine l so that z(l) = 0.
-2, 1
Suppose 14*g - 15 - 13 = 0. Suppose 3/2*k**g - 5/6*k + 5/6*k**3 - 1/3 - 7/6*k**4 = 0. Calculate k.
-1, -2/7, 1
Let d be 2 - 1*(6 - 4). Let z(o) be the third derivative of 0*o**3 + 0*o - 1/24*o**4 + 2*o**2 + d + 1/60*o**5. What is f in z(f) = 0?
0, 1
Let s be (0 + 2/8)*8. Suppose 4*b - s*p = -8, -b + 2*p - 3 = 5. Factor 0*j - 2/5*j**2 + b.
-2*j**2/5
Factor 0 + 0*u + 1/3*u**4 - 1/3*u**3 - 2/3*u**2.
u**2*(u - 2)*(u + 1)/3
Let r(l) be the second derivative of l**6/105 + 3*l**5/70 + l**4/14 + l**3/21 + 9*l. Factor r(q).
2*q*(q + 1)**3/7
Let j(b) = b**2 - 6*b + 7. Let n be j(5). Let o be (-6)/6 - (-2)/2. Factor o*l - 1/3*l**n + 1/3.
-(l - 1)*(l + 1)/3
Let o(b) = -b**4 - b**3 + b**2 + b - 1. Let l(a) = 5*a**4 + 6*a**3 - 4*a**2 - 6*a + 1. Let j(c) = -l(c) - 2*o(c). What is n in j(n) = 0?
-1, -1/3, 1
Suppose 0 = 3*k - 4*k. Let b(y) be the third derivative of 4*y**2 + 1/48*y**4 + 1/120*y**5 + 0*y**3 + k + 0*y. Factor b(c).
c*(c + 1)/2
Let d(h) = h**2 + 7*h + 16. Let z be d(-4). Factor 1/2*w**5 + 0 + 0*w**3 - w**2 - 1/2*w + w**z.
w*(w - 1)*(w + 1)**3/2
Let m(d) = d + 21. Let f be m(0). Let a(t) = t**2 - t. Let i(y) = y**3 + 6*y**2 - 7*y. Let l(v) = f*a(v) - 3*i(v). Find g such that l(g) = 0.
0, 1
Let i be 3 + (-1)/2*-2. Factor -x**5 + 0*x**2 + i*x**4 - x**4 + 0*x**5 - 3*x**3 + x**2.
-x**2*(x - 1)**3
Let v be 2 + 17 - 3/(-1). Let g be 12/66 + (-4)/v. Factor g*k + 0 + 1/4*k**2.
k**2/4
Factor 0 + 0*y + 6/5*y**3 - 2/5*y**2 - 4/5*y**4.
-2*y**2*(y - 1)*(2*y - 1)/5
Let o(k) be the third derivative of k**8/1680 - k**6/600 - 2*k**2. Solve o(m) = 0.
-1, 0, 1
Let b(o) = -4*o**4 + 2*o**3 + 2*o. Let u(y) = y**4 + y**3 - y**2 - y. Suppose 4 = -4*z - 12. Let r = z - -6. Let j(g) = r*u(g) + b(g). Factor j(s).
-2*s**2*(s - 1)**2
Let p(h) = 6*h**2 - h. Let n(b) be the third derivative of b**5/20 - 3*b**2. Let z(c) = -5*n(c) + 3*p(c). Solve z(g) = 0 for g.
0, 1
Let o = 478 + -2386/5. Let l be (-4)/25*(-30)/12. Factor l*p + o - 2/5*p**2.
-2*(p - 2)*(p + 1)/5
Let j(g) = 4*g**3 + 2*g**2 - 4*g - 5. Let n = -6 + 4. Let q(a) = -a**3 + a + 1. Let t(f) = n*j(f) - 6*q(f). Factor t(w).
-2*(w - 1)*(w + 1)*(w + 2)
Factor -6/5*z**5 + 0*z**4 + 0*z**2 + 0 + 0*z + 6/5*z**3.
-6*z**3*(z - 1)*(z + 1)/5
Let q(u) = -u**2 + 3*u - 4. Let t(w) = -3 - 8 - 3*w**2 + 8*w + 0*w**2. Let o = -43 - -39. Let b(y) = o*t(y) + 11*q(y). Suppose b(r) = 0. What is r?
-1, 0
Let g(v) = 65*v**4 + 65*v**3 - 200*v**2 + 95*v. Let a(s) = 8*s**4 + 8*s**3 - 25*s**2 + 12*s. Let q(z) = 25*a(z) - 3*g(z). Factor q(i).
5*i*(i - 1)**2*(i + 3)
Let a = -5 + 8. Let w(r) be the second derivative of 0*r**a + 0*r**2 + 1/168*r**7 - 1/48*r**4 + 3/80*r**5 + 2*r + 0 - 1/40*r**6. Factor w(v).
v**2*(v - 1)**3/4
Let x be 3*(-27)/(-20) - 4. Let u(l) be the third derivative of -2*l**2 + 0*l + 0 - 1/2*l**4 + x*l**5 + 2*l**3. Factor u(t).
3*(t - 2)**2
Suppose 5*z + 5*r - 40 = 0, 3*z = -z - 3*r + 27. Let d = 1 + z. Factor -8/5*t**3 - 8/5*t + 12/5*t**2 + 2/5*t**d + 2/5.
2*(t - 1)**4/5
Let a(n) be the first derivative of -9*n**5/20 - 3*n**4/2 + 3*n**3/4 + 9*n**2/2 - 3*n + 10. Solve a(f) = 0 for f.
-2, 1/3, 1
Let f(q) be the third derivative of -3*q**7/560 + q**6/30 - 7*q**5/80 + q**4/8 + 2*q**3/3 + 5*q**2. Let p(x) be the first derivative of f(x). Factor p(g).
-3*(g - 1)**2*(3*g - 2)/2
What is v in 2*v + 2*v**5 + 2*v + 3*v**5 - 20*v**2 + 20*v**4 - 19*v + 10*v**3 = 0?
-3, -1, 0, 1
Let m(z) = 4*z**4 - 5*z**3 + 4*z**2 - 3. Let l(w) = -15*w**4 + 19*w**3 - 15*w**2 + 11. Let d(b) = -6*l(b) - 22*m(b). Factor d(v).
2*v**2*(v - 1)**2
Factor 0 - 4/5*h**2 + 2/5*h**3 + 0*h.
2*h**2*(h - 2)/5
Let g = -35 - -37. Factor 2/3*m + 0*m**4 + 2/3*m**5 - 4/3*m**3 + 0 + 0*m**g.
2*m*(m - 1)**2*(m + 1)**2/3
Let y(k) = -4*k**3 + 2*k**2 + 3. Let u = -8 + 4. Let d(w) = 5*w**3 - 3*w**2 - 4. Let l(r) = u*y(r) - 3*d(r). Factor l(s).
s**2*(s + 1)
Suppose 2*v = -10, 4*j = -3*v - 2 - 5. Determine c, given that 5*c**j - 3*c**2 + 0*c**2 + 0*c**3 - c**3 - c = 0.
0, 1
Let j(c) = 6*c**2 + 12*c + 5. Let u(f) = -3*f**2 - 6*f - 2. Let l(n) = -2*j(n) - 5*u(n). Let l(m) = 0. Calculate m.
-2, 0
Let x(i) be the third derivative of i**8/84 - i**6/30 - 5*i**2. Factor x(f).
4*f**3*(f - 1)*(f + 1)
Factor 2 - 18*i**2 - 2*i**4 + 4*i + 18*i**2 - 4*i**3.
-2*(i - 1)*(i + 1)**3
Let b be (6/4 + -2)*-6. Let a(q) be the second derivative of 0 + 4*q**2 + 121/6*q**4 - 2*q - 44/3*q**b. Factor a(f).
2*(11*f - 2)**2
Let k(g) be the second derivative of 1/45*g**4 + 0 + 1/315*g**7 + 0*g**2 - 2/225*g**6 - 1/150*g**5 + 0*g**3 - 4*g. Find c such that k(c) = 0.
-1, 0, 1, 2
Let b = 5 - 3. Factor -4*v**2 - 2*v - v**4 - b*v**5 + 2 + 2*v**4 + v**4 + 4*v**3.
-2*(v - 1)**3*(v + 1)**2
Factor -4*y**3 + 3*y**3 + y**2 + 13*y**4 + y**5 - 14*y**4.
y**2*(y - 1)**2*(y + 1)
Let o(j) be the third derivative of -j**8/60480 + j**7/7560 - j**5/12 - 6*j**2. Let k(y) be the third derivative of o(y). Suppose k(a) = 0. What is a?
0, 2
Factor k**2 - 6 + 4 + 2.
k**2
Let f = -3/29 - -83/522. Let q(m) be the second derivative of m + 4/9*m**3 + f*m**4 + 4/3*m**2 + 0. Solve q(i) = 0 for i.
-2
Let f be 1/(-4) + (-34)/(-8). Let b(a) be the first derivative of 1/9*a**6 + 2 + 4/15*a**5 + 0*a - 4/9*a**3 + 0*a**f - 1/3*a**2. Find g, given that b(g) = 0.
-1, 0, 1
Let q(n) be the first derivative of 4*n**3/69 - 5*n**2/23 - 6*n/23 + 29. Solve q(l) = 0 for l.
-1/2, 3
Determine r, given that -2/15*r + 0*r**4 + 0 + 4/15*r**3 - 2/15*r**5 + 0*r**2 = 0.
-1, 0, 1
Let g be (-2)/((-8)/(-10)*(-2)/4). Let l(c) be the first derivative of 1/3*c**2 - 2/15*c**g + 1/2*c**4 + 1 - 2/3*c**3 + 0*c. Determine f so that l(f) = 0.
0, 1
Let f(x) be the first derivative of -x**5/20 - x**4/12 + x**3/6 + x**2/2 - 5*x - 1. Let y(d) be the first derivative of f(d). Factor y(o).
-(o - 1)*(o + 1)**2
Factor -31*a**3 + 12*a**2 + 6 + 28*a**3 + 0*a**2 - 15*a.
-3*(a - 2)*(a - 1)**2
Let s(i) be the first derivative of 3*i**5/10 + 15*i**4/16 + i**3 + 3*i**2/8 - 1. Factor s(w).
3*w*(w + 1)**2*(2*w + 1)/4
Let o = 20 - 14. Suppose o*i - 2*i**4 - 6*i**2 + 2*i + 8 - 5*i**3 - 3*i**3 = 0. Calculate i.
-2, -1, 1
Let f(n) = 17*n**2 + 27*n + 10. Let p(v) = 6*v**2 + 9*v + 3. Let l(q) = 3*f(q) - 8*p(q). Factor l(r).
3*(r + 1)*(r + 2)
Let d(y) be the first derivative of y**2 - 3 + 1/2*y**3 + 1/2*y. Factor d(m).
(m + 1)*(3*m + 1)/2
Let k(g) = 147*g**3 - 226*g**2 + 91*g - 17. Let a(i) = i**2 - i - 1. Let j(v) = -5*a(v) + k(v). Factor j(b).
3*(b - 1)*(7*b - 2)**2
Let l(p) = p**2 + 5 + 11*p + 2 - 4 + 4. Let a be l(-11). Solve 8*y**3 + 0*y**2 + 2*y**2 - 2*y**4 - y**5 - a*y**5 = 0.
-1, -1/4, 0, 1
Let d be 2*(84/8)/7. Let z be (d/(-15))/(9/(-30)). Factor 2*t + 2*t**2 + z + 2/3*t**3.
2*(t + 1)**3/3
Suppose -2*h + 9 = -5*h + 5*u, 2*h - u = 1. Find v, given that 3 - 8*v - 2*v**2 + 3*v**2 + 1 + 3*v**h = 0.
1
Let s be -1 + 4 + 5 + (-114)/