t x(l) = l**5 + 2*l**4 - l**2 + l. Let z(r) = -4*r**4 + 3*r - 2*r**4 + r**2 + 5*r**4 - 4*r. Let d(m) = -2*x(m) - 2*z(m). Factor d(j).
-2*j**4*(j + 1)
Let f(q) = 2*q**3 + 11*q**2 - 4*q. Let v(d) = d**2. Let r(u) = -2*f(u) + 18*v(u). Find l, given that r(l) = 0.
-2, 0, 1
Let f(i) = i**3 - 5*i**2 + 4*i - 4. Let h be f(4). Let z be (-10)/(-3)*(-6)/h. What is v in 0 + 2/5*v**z + 2/5*v**3 - 4/5*v**4 + 0*v**2 + 0*v = 0?
0, 1
Factor 36/7*x**2 - 8/7 + 4/7*x - 52/7*x**3 + 20/7*x**4.
4*(x - 1)**3*(5*x + 2)/7
Let b = 16 - 12. Find y, given that -2*y**b - 4*y**5 - y**5 - 17*y**2 + 4 - 35*y**3 + 0*y**4 - 21*y**4 + 4*y = 0.
-2, -1, 2/5
Factor -2 + 2/3*t**2 + 4/3*t.
2*(t - 1)*(t + 3)/3
Let -15*a**2 - 2 + 13*a**2 + 10 = 0. Calculate a.
-2, 2
Find v, given that 2/7*v**4 + 2/7 - 5/7*v**5 - 5/7*v + 10/7*v**3 - 4/7*v**2 = 0.
-1, 2/5, 1
Determine c so that 2/13*c**2 + 0*c - 2/13*c**3 + 0 = 0.
0, 1
Let l(y) = 17*y**2 - 23*y + 15. Let d(s) = 4*s**2 - 6*s + 4. Let w(p) = 18*d(p) - 4*l(p). Factor w(v).
4*(v - 3)*(v - 1)
Find m such that 4*m**4 - 4*m**5 + 7*m**3 - 7*m**3 + 4*m**3 + 0*m**4 - 4*m**2 = 0.
-1, 0, 1
Suppose 0*q**3 + 0 - 1/3*q**4 + 1/3*q**2 + 0*q = 0. Calculate q.
-1, 0, 1
Let i = -9 + 13. Factor -6*c + 32*c**2 + 3*c**4 + 6*c**3 - c**i - 34*c**2.
2*c*(c - 1)*(c + 1)*(c + 3)
Solve -4 + 0*l**3 - 5*l**2 - l**3 + 8*l**2 = 0.
-1, 2
Find v, given that -8/9*v + 10/9 - 2/9*v**2 = 0.
-5, 1
Let x(q) = -2*q**3 - 8*q**2 - 6*q. Let b(o) = -8*o**3 - 33*o**2 - 25*o. Let z(l) = -4*b(l) + 18*x(l). Find g such that z(g) = 0.
-2, -1, 0
Let s(j) = j**2 + 5*j - 4. Let d be s(-6). Factor i**2 + 4*i**d + 2 - 3*i**2 - 4*i + 0*i**2.
2*(i - 1)**2
Let m = 464513/108 + -4301. Let l(s) be the third derivative of 0 - 7/270*s**5 + 1/180*s**6 + 0*s - 1/27*s**3 + m*s**4 + 4*s**2. Find k such that l(k) = 0.
1/3, 1
Let a(y) be the first derivative of 2*y**3/15 - 2*y**2/5 - 6*y/5 + 2. Suppose a(i) = 0. Calculate i.
-1, 3
Let u(j) be the first derivative of 0*j + 4*j**2 + 1 + 4/3*j**3. Let u(x) = 0. Calculate x.
-2, 0
Let h(y) be the first derivative of -y**4/14 + 8*y**3/21 - 5*y**2/7 + 4*y/7 - 5. Suppose h(a) = 0. Calculate a.
1, 2
Let m(v) be the third derivative of 0 + 0*v**5 + 0*v - 3*v**2 + 0*v**6 + 0*v**4 - 1/525*v**7 + 1/840*v**8 + 0*v**3. Factor m(z).
2*z**4*(z - 1)/5
Let h be (-52)/(-5) + (-6)/(-10). Factor 8*a**3 + 3*a**4 - h*a**2 - 19*a**4 - 34*a**3 - a - 10*a**3 + 64*a**5.
a*(a - 1)*(4*a + 1)**3
Let k(m) = 4*m**2 + 439*m + 3375. Let b(t) = -t**2 - 146*t - 1125. Let f(p) = -11*b(p) - 4*k(p). Let f(v) = 0. Calculate v.
-15
Let v(o) be the third derivative of -5*o**2 - 1/270*o**5 + 0*o + 1/27*o**4 + 1/27*o**3 + 0 - 1/135*o**6. Determine j, given that v(j) = 0.
-1, -1/4, 1
Let c(l) = -10*l**3 - 6*l**2 - 8*l + 6. Let f(k) = -k**3 + k**2 + 1. Let j(b) = -c(b) + 6*f(b). Factor j(g).
4*g*(g + 1)*(g + 2)
Let g(q) = 5*q**4 - 9*q**3 - 25*q**2 - 3*q + 3. Let p(h) = 3*h**4 - 4*h**3 - 13*h**2 - 2*h + 2. Let a(u) = -2*g(u) + 5*p(u). Determine i so that a(i) = 0.
-1, 2/5, 2
Let t(b) = -4*b**2 + 2*b + 5. Let r(l) = -5*l**2 + 2*l + 6. Let k(n) = 5*r(n) - 6*t(n). Solve k(y) = 0 for y.
-2, 0
What is o in 15/4*o**3 - 25/2*o**2 + 15/4*o + 0 = 0?
0, 1/3, 3
Let q(y) be the second derivative of -1/540*y**6 + 1/90*y**5 - 1/36*y**4 + 1/6*y**3 - 2*y + 0 + 0*y**2. Let t(l) be the second derivative of q(l). Factor t(d).
-2*(d - 1)**2/3
Let j(r) be the first derivative of -6 + 2*r + 27/2*r**3 + 9*r**2. Determine c, given that j(c) = 0.
-2/9
Let x(w) = w**2 + 18*w - 19. Let o be x(-19). Determine p so that 0 + 1/7*p**5 + 4/7*p**4 + o*p**2 + 4/7*p**3 + 0*p = 0.
-2, 0
Suppose p + 2*p - 29 = -5*x, -x + p = -1. Let 0*m**2 + x*m**2 - 21*m**5 + 12*m**4 + 10*m**5 + 7*m**5 - 12*m**3 = 0. What is m?
0, 1
Let j(i) = i - 6. Let a be j(8). Factor n - 5*n**2 + 4*n**a - 3*n - 1.
-(n + 1)**2
Let t(u) be the third derivative of u**6/160 + u**5/40 - 7*u**4/32 + u**3/2 + 4*u**2 - 3. Find q, given that t(q) = 0.
-4, 1
Let j(w) = 3*w**2 + 2 - w**3 + w**2 - 2*w + 0. Let i be j(3). Factor -2 + 7 + 7*r**2 + 9*r**3 + 5*r**4 + 2*r + r**i - 5.
r*(r + 1)**3*(r + 2)
Let i(x) = 1. Let o(j) = -j + 4. Let z(k) = -6*i(k) - o(k). Let b be z(10). Solve -c**5 - 7/3*c**3 + 0 - 8/3*c**4 - 2/3*c**2 + b*c = 0.
-1, -2/3, 0
Let v(x) = -14*x**2 - 32*x + 18. Let w(p) = -42*p**2 - 97*p + 53. Let o(u) = 17*v(u) - 6*w(u). Factor o(k).
2*(k + 3)*(7*k - 2)
Let x(z) = -7*z**2 + z. Let k(n) = 2*n**2 + 23*n**2 - 3*n + 2*n**2. Let a(r) = 4*k(r) + 15*x(r). Factor a(u).
3*u*(u + 1)
Let d be (20/(-25))/(4/(-10)). Suppose d*j + 3*l = 16, -l - 2 = -4. Factor 1 + m + j*m + 2 + 1 + 2*m**2.
2*(m + 1)*(m + 2)
Let b be 6/(-9) - (-2)/3. Suppose b*z + 3*z = 6. Factor 1/3*j**z + 0*j + 0 + 1/3*j**4 + 2/3*j**3.
j**2*(j + 1)**2/3
Suppose -2*r + 12 = r. Suppose 0 = -g - r + 12. Find d such that d + g - 4 - 2*d**2 + d = 0.
-1, 2
Let b(h) = -6*h**4 - 10*h**3 - 14*h**2 - 18*h. Let d = -3 + -1. Let j(q) = -7*q**4 - 10*q**3 - 13*q**2 - 19*q + 1. Let p(l) = d*j(l) + 5*b(l). Factor p(u).
-2*(u + 1)**3*(u + 2)
Suppose 0 = -8*h + 3*h + 10. Let -a**2 - 4 + h*a**2 + 4 - 4 = 0. What is a?
-2, 2
Let u(c) = c**2 + 2*c - 5. Let d = -6 - -2. Let m be u(d). Factor 0 + 12/5*q**2 - 18/5*q**m - 2/5*q.
-2*q*(3*q - 1)**2/5
Suppose 5*a - 2*p = 2, -a - p + 14 = 2*p. Suppose -3*c + 15 = a*o - o, -c - 5*o = -19. Factor 8*z + 4 + 3*z**2 + c - z**2.
2*(z + 2)**2
Suppose 2*f = 6*f - 32. Suppose -8 = -2*i + 4*c, 0 = 4*i - c - f - 1. Let 2*u**4 - u - i*u**2 + u + 0*u**4 = 0. What is u?
-1, 0, 1
Factor 0 - 8/7*u + 20/7*u**2 - 8/7*u**3.
-4*u*(u - 2)*(2*u - 1)/7
Let t(w) be the second derivative of w**7/49 + 11*w**6/105 + 4*w**5/35 - 2*w**4/21 - 4*w. Determine x so that t(x) = 0.
-2, 0, 1/3
Let t(a) be the first derivative of -a**4/24 - a**3/12 + a**2/2 - a - 2. Let f(y) be the first derivative of t(y). Factor f(q).
-(q - 1)*(q + 2)/2
Factor -4/9*q + 0 - 10/9*q**2 - 4/9*q**3.
-2*q*(q + 2)*(2*q + 1)/9
Let q(j) = -2*j**2 + 6*j - 2. Let o(c) = c. Let r(t) = -4*o(t) + 2*q(t). Factor r(x).
-4*(x - 1)**2
Find i, given that 4/13*i + 2/13 + 2/13*i**2 = 0.
-1
Let a(v) = -v**2. Let q be -1*((-6)/(-3))/(-1). Let j(u) = -u**2 + 3*u + 2. Let i(b) = q*a(b) - j(b). Determine x, given that i(x) = 0.
-2, -1
Let x(b) = -b**2 - 9*b - 8. Let c(g) = g**3 - 4*g**2 - 2*g. Let a be c(4). Let d be x(a). Let -2*u + u - u**4 + u**2 + u**3 + d*u**4 = 0. Calculate u.
-1, 0, 1
Let c(k) = 18*k**3 + 6*k**2 - 12*k. Let b(a) = -a**3 + a. Let u(g) = 10*b(g) + c(g). Factor u(z).
2*z*(z + 1)*(4*z - 1)
Let n(k) be the third derivative of k**8/252 - 4*k**7/315 - 3*k**6/40 - 19*k**5/180 - k**4/18 + 3*k**2 - 2. What is y in n(y) = 0?
-1, -1/2, 0, 4
Let l be (-6)/(-2)*15/3. Let n = l - 11. Factor -4*o**n + o**2 + 6*o**3 - o**2 - 2*o.
-2*o*(o - 1)**2*(2*o + 1)
Let n be 805/700 - 6/(-10). Factor 3/4*u**4 - n*u**3 + 3/4*u**2 + 3/4*u - 1/2.
(u - 1)**3*(3*u + 2)/4
Let i = 62 - 60. Let l(b) be the third derivative of 1/3*b**3 + 1/60*b**5 - i*b**2 - 1/8*b**4 + 0 + 0*b. Factor l(x).
(x - 2)*(x - 1)
Let g(j) be the first derivative of -4*j**3/15 + 4*j**2/5 - 1. Let g(q) = 0. Calculate q.
0, 2
Let k(l) be the second derivative of -4*l + 1/15*l**6 + 1/6*l**4 + 7/30*l**5 - 2*l**2 + 0 - 1/3*l**3. Let s(w) be the first derivative of k(w). Factor s(j).
2*(j + 1)**2*(4*j - 1)
Let t(m) be the first derivative of -5*m**6/24 + 4*m**5/5 - 13*m**4/16 + m**3/6 + 2. Suppose t(n) = 0. What is n?
0, 1/5, 1, 2
Let k(w) = -2*w**2 - 2*w. Let y be k(0). Solve y - 3/2*q**2 - 3/2*q**3 + 0*q = 0.
-1, 0
Let u(v) be the third derivative of -8*v**2 + 0*v - 3/5*v**3 + 0 + 1/10*v**4 - 1/150*v**5. Factor u(k).
-2*(k - 3)**2/5
Factor -i + 52 - 2*i + i**2 + 0*i - 50.
(i - 2)*(i - 1)
Let v be ((-4)/66)/(3/21). Let n = v + 202/165. Factor n*b**2 + 2/5 - 6/5*b.
2*(b - 1)*(2*b - 1)/5
Suppose -7*p + 6 = -4*p. Let q(c) be the third derivative of -4/9*c**3 + c**p - 1/90*c**5 + 0*c + 0 + 1/9*c**4. Factor q(d).
-2*(d - 2)**2/3
Let g(q) be the third derivative of -q**6/150 - q**5/60 + 7*q**4/120 + q**3/15 + 3*q**2. Factor g(d).
-(d - 1)*(d + 2)*(4*d + 1)/5
Let c(f) be the first derivative of -f**4/4 - 5*f**3/3 - 4*f**2 - 4*f - 12. Factor c(o).
-(o + 1)*(o + 2)**2
Let w = 9 - 5. Suppose w*n + 20 = 5*r, 0 = 5*r - 6*n + 3*n - 20. Let r - l**3 - 10*l + l**3 - 2*l**3 + 8*l**2 = 0. What is l?
1, 2
Let a(s) 