*4 = 0.
-2, -2/7
Let s(t) = -t**2 + 2. Let y be s(2). Let n = y + 4. Determine h, given that -h**n - 9 - 2*h + 5 + 6*h = 0.
2
Let t(f) = 7*f**4 - 3*f**3 - 11*f**2 - 7*f + 9. Let y(r) = 22*r**4 - 10*r**3 - 34*r**2 - 22*r + 28. Let n(x) = -16*t(x) + 5*y(x). Factor n(a).
-2*(a - 1)**2*(a + 1)*(a + 2)
Suppose 9 = k + 17. Let b(z) = -z**3 - 9*z**2 - 9*z - 6. Let s be b(k). Suppose t - 1 - 1/4*t**s = 0. Calculate t.
2
Let v(b) be the second derivative of -4/7*b**2 - b - 20/21*b**3 - 25/42*b**4 + 0. Factor v(f).
-2*(5*f + 2)**2/7
Let q be (-3 + 0)*4/(-20)*5. Factor 1/4 - 1/4*l**q + 1/4*l - 1/4*l**2.
-(l - 1)*(l + 1)**2/4
Let d(j) = 2*j**2 - 16*j + 19. Let v be d(7). Determine h so that -2/9*h**2 + 0*h + 2/9*h**4 - 2/9*h**v + 2/9*h**3 + 0 = 0.
-1, 0, 1
Let x(y) = y - 1. Let b be x(8). Let g be b/14*(4 - 0). Factor 0*a**g - 2/9 - 4/9*a**3 + 4/9*a + 2/9*a**4.
2*(a - 1)**3*(a + 1)/9
Let q(s) be the first derivative of 1/4*s**4 + 2*s + 0*s**3 - 3/2*s**2 + 4. Determine i so that q(i) = 0.
-2, 1
Let h = 13 - 11. Let 1 + 13*v + 80*v**2 + 135*v**3 - 17*v**h + 108*v**4 - 1 + 1 = 0. Calculate v.
-1/3, -1/4
Suppose 0 = 3*i - 15. Find k, given that -k**2 + 8*k + 5 + 2*k**3 - i - 9*k = 0.
-1/2, 0, 1
Suppose 3/8*m**2 + 3/8 - 3/4*m = 0. Calculate m.
1
Let k(q) be the third derivative of q**7/2520 - q**6/1080 - q**5/180 - 5*q**3/6 + 5*q**2. Let y(v) be the first derivative of k(v). Factor y(d).
d*(d - 2)*(d + 1)/3
Let r(n) be the first derivative of -n**3/9 + n**2/3 + n - 20. Find i such that r(i) = 0.
-1, 3
Let m be 1/(-2*(-1)/4). Suppose 4*w = 4*f + 20, 0 = m*f - f + 3*w - 15. Determine j so that 0*j**4 + 0*j**2 + f + 1/3*j**5 + 0*j**3 + 0*j = 0.
0
Let a be (-2)/12 - (7/(-2) + -2). Let q(u) be the first derivative of 32/3*u + a*u**3 - 40/3*u**4 + 10/3*u**5 + 2 + 64/3*u**2. Factor q(m).
2*(m - 2)**2*(5*m + 2)**2/3
Let j be (-84)/(-22) - -3*10/165. Let o(h) be the first derivative of 1/3*h**3 - h + 5/8*h**4 - j - 5/4*h**2. Let o(t) = 0. Calculate t.
-1, -2/5, 1
Let f(m) = m - 4. Let t be f(6). What is j in 3*j**2 + j**2 - 6*j**t + 2*j**3 = 0?
0, 1
Let a be (-1)/(-4) - 63/(-36). Let k(u) be the second derivative of 0*u**a + u + 1/21*u**3 + 1/42*u**4 + 0. Factor k(y).
2*y*(y + 1)/7
Let n be (-5)/(-3) - (-1)/3. Solve 4 - 6*q**2 + 0*q**4 + 2*q**3 - 4*q**3 + 2*q**4 + n*q = 0 for q.
-1, 1, 2
Let t(y) be the first derivative of 12*y**4 - 44*y**3/3 + 4*y**2 + 11. Solve t(x) = 0.
0, 1/4, 2/3
Let g(k) = 4*k**2 - 10*k - 4*k**4 + 6*k**4 + 4*k - 8*k**2 + 2*k**3. Let r(s) = -2*s**4 - s**3 + 3*s**2 + 5*s. Let h(u) = 5*g(u) + 6*r(u). Factor h(o).
-2*o**2*(o - 1)**2
Let j(r) = -6*r**3 - 5*r + 5. Let c(o) = -5*o**3 - 4*o + 5. Let f(v) = 5*c(v) - 4*j(v). Let k(d) be the first derivative of f(d). Find g such that k(g) = 0.
0
Let o be 1/(-4) - 69/12. Let c be o*(-1)/(4/2). Let 6*s**c - 6*s + 3 + 4*s**4 - 2*s**3 + 2*s**3 - 7*s**4 = 0. What is s?
-1, 1
Suppose 4 = 4*d + 4. Factor 0 - 1/4*x**3 - 1/4*x**2 + d*x.
-x**2*(x + 1)/4
Suppose -39/4*c**4 - 9/2*c**5 - 6*c**3 - 3/4*c**2 + 0*c + 0 = 0. Calculate c.
-1, -1/6, 0
Solve 0 - 1/3*a + 2/3*a**2 - 1/3*a**3 = 0.
0, 1
Let v(o) be the first derivative of o**8/168 - o**7/35 + o**6/20 - o**5/30 - o**2/2 + 4. Let g(n) be the second derivative of v(n). Factor g(i).
2*i**2*(i - 1)**3
Factor 0 + k + 1/2*k**2 - 1/2*k**3.
-k*(k - 2)*(k + 1)/2
Let g(z) = 3 + z - 4 + 0. Let j(v) be the first derivative of -2*v**3/3 + v**2 - 2*v + 4. Let b(o) = -2*g(o) + j(o). Let b(i) = 0. What is i?
0
Let r(s) be the first derivative of s**7/21 - s**6/10 - s**5/20 + s**4/4 - s**3/6 - 2*s + 1. Let m(w) be the first derivative of r(w). Factor m(v).
v*(v - 1)**2*(v + 1)*(2*v - 1)
Let u(j) be the first derivative of 2 + 0*j + 3/2*j**2 - 4/3*j**3. Factor u(a).
-a*(4*a - 3)
Let h(g) be the second derivative of g**6/180 + g**5/30 - g**3/2 + 3*g. Let t(n) be the second derivative of h(n). Factor t(j).
2*j*(j + 2)
Let y(z) be the first derivative of 7 + 9/11*z**2 - 4/11*z - 14/33*z**3. Factor y(l).
-2*(l - 1)*(7*l - 2)/11
Let t be 86/18 - (-4)/18. Suppose -3*o = t*y - 9, -5*o - 4 = y + y. Factor -5 + y + b - 2*b**2 + 3*b.
-2*(b - 1)**2
Suppose -5*o - 5 = 5*g, o + 2*g = 3*g + 5. What is p in 0*p + 4/3*p**o + 2/3*p**4 - 2*p**3 + 0 = 0?
0, 1, 2
Let m(k) = 3*k**4 - k**3 - 9*k**2 - 11*k + 2. Let t(i) = -i**4 - i**3 + i - 1. Let n(p) = -m(p) - 4*t(p). Determine z so that n(z) = 0.
-2, -1
Let c(t) be the first derivative of -t**6/9 - 2*t**5/15 + t**4/2 + 2*t**3/9 - 2*t**2/3 + 1. Determine w so that c(w) = 0.
-2, -1, 0, 1
Suppose 123*q + 4 = 124*q. Solve 5/2*m**3 + 7/2*m - 1 - 9/2*m**2 - 1/2*m**q = 0 for m.
1, 2
Let x(v) be the third derivative of 0*v + v**2 - 1/1260*v**6 - 1/210*v**5 - 1/2*v**3 + 0 + 0*v**4. Let s(f) be the first derivative of x(f). Factor s(w).
-2*w*(w + 2)/7
Factor 0*q**2 + 0 + 2/9*q**3 + 2/9*q**4 + 0*q.
2*q**3*(q + 1)/9
Let c(y) be the third derivative of 0*y**4 + 0*y**5 + 0 + 0*y + 0*y**3 + 1/315*y**7 + 1/180*y**6 - 3*y**2. Factor c(f).
2*f**3*(f + 1)/3
Solve 19/3*v - 14/3 + 5/3*v**3 + 38/3*v**2 = 0.
-7, -1, 2/5
Find r such that -4/7*r**4 + 0*r + 4/7*r**3 + 0 + 8/7*r**2 = 0.
-1, 0, 2
Factor 2/5*x**2 + 32/5 - 16/5*x.
2*(x - 4)**2/5
Let w(z) = -z**5 - 5*z**4 + 2*z**2 - 2. Let s(n) = n**5 + 6*n**4 - n**3 - 3*n**2 + 3. Let d be -3*(2 - 1) + 0. Let p(q) = d*w(q) - 2*s(q). Factor p(y).
y**3*(y + 1)*(y + 2)
Let c be (-10)/35 - 74/(-14). Suppose -c = 5*m + 5*x, -3*m - 4*x = 2*m + 4. Find k, given that 4/7*k**3 + m*k**2 + 2/7 - 2/7*k**4 - 4/7*k = 0.
-1, 1
Let t(b) be the first derivative of 0*b + 1/9*b**3 - 6 + 0*b**2 + 1/24*b**4. Find h, given that t(h) = 0.
-2, 0
Let h = 11/3 + -7/6. What is p in 1/4*p**4 + 3*p**2 + 3/4 + 3/2*p**3 + h*p = 0?
-3, -1
Determine i, given that -12*i**3 - 4*i - 2*i**4 - 640 - 12*i**2 + 640 - 2*i**4 = 0.
-1, 0
Let k = 120/427 - -2/427. Determine f so that 2/7*f**2 - 2/7*f**4 - 2/7*f**3 + 0 + k*f = 0.
-1, 0, 1
Let k = -8 - -12. Factor -8 + 3*n**3 + 6*n**2 + k*n**3 - 5*n**3.
2*(n - 1)*(n + 2)**2
Let r(x) be the second derivative of -x**5/10 + x**4 - 3*x**3 + 5*x. Factor r(p).
-2*p*(p - 3)**2
Let z(a) = -15*a**2 - 27*a + 30. Let o(g) = 6*g**2 + 11*g - 12. Let b(n) = -12*o(n) - 5*z(n). Find m such that b(m) = 0.
-2, 1
Let f(x) = -x - 1. Let u be f(-6). Factor -u + 9*d**3 + 5 - 8*d**2 + 2*d - 3*d**3.
2*d*(d - 1)*(3*d - 1)
Suppose 3/2*d**2 - 3/2 + 0*d = 0. What is d?
-1, 1
Let p = 14 - 12. Let c be 5/2*p/10. Factor 0*t + 1/2*t**5 - 1/2*t**4 - 1/2*t**3 + c*t**2 + 0.
t**2*(t - 1)**2*(t + 1)/2
Find p such that -1/4*p - 3/4*p**2 - 1/4*p**4 + 0 - 3/4*p**3 = 0.
-1, 0
Let s(n) be the first derivative of n**7/84 - n**6/20 + n**5/20 + n**4/12 - n**3/4 + n**2/4 - 5*n + 1. Let h(d) be the first derivative of s(d). Factor h(k).
(k - 1)**4*(k + 1)/2
Let -4*l**3 - 8*l**2 + 2*l**5 - 6*l**2 + 3 - 1 + 2*l**4 + 10*l**2 + 2*l = 0. Calculate l.
-1, 1
Suppose -9/5*h**3 - 6/5*h**4 + 3/5*h**5 + 0 + 24/5*h**2 - 12/5*h = 0. Calculate h.
-2, 0, 1, 2
Suppose 0 = 5*h - 12*h. Let s(g) be the third derivative of h + 1/24*g**4 + 0*g**5 + 2*g**2 + 0*g + 0*g**3 - 1/120*g**6. Factor s(x).
-x*(x - 1)*(x + 1)
Let n(f) be the third derivative of -f**7/105 - f**6/40 - f**5/60 + 6*f**2. Factor n(c).
-c**2*(c + 1)*(2*c + 1)
Let k(d) = -9*d**2 + 11*d - 2. Let f(w) = 9*w**2 - 11*w + 2. Let y(x) = -3*f(x) - 4*k(x). Factor y(i).
(i - 1)*(9*i - 2)
Let k be (-47)/(-7) + (-10)/(-35). Let y(d) = d**2 - 7*d. Let s be y(k). Factor s*g - 2/9*g**4 + 0 - 2/9*g**2 + 4/9*g**3.
-2*g**2*(g - 1)**2/9
Let t(i) be the second derivative of -1/12*i**4 + 0*i**2 - 3/20*i**5 + 1/3*i**3 + 4*i + 0 + 1/30*i**6 + 1/42*i**7. Factor t(u).
u*(u - 1)**2*(u + 1)*(u + 2)
Suppose 4*y - 78 = 3*x, -y - 107 = -6*y - x. Let i(b) = 51*b**2 - 9*b. Let v(h) = 5*h**2 - h. Let l(w) = y*v(w) - 2*i(w). Factor l(o).
3*o*(o - 1)
Let j be (-4)/3*((-30)/(-12) + -4). Factor -11*v - 121/4*v**j - 1.
-(11*v + 2)**2/4
Factor -2/5*h**4 - 2/5 + 0*h**3 + 4/5*h**2 + 0*h.
-2*(h - 1)**2*(h + 1)**2/5
Suppose 0 = c - 5*y + 21, c = 2*y - 8 + 2. Find b, given that 0*b**c - 3*b**3 + 3*b + 2 - 3*b**2 + 4*b**3 - 4*b + b**4 = 0.
-2, -1, 1
Suppose -2*k + 9 - 3 = 0. Let z be 6*(1/(-6) + 5/10). Factor -2/5*g**k - 6/5*g - 2/5 - 6/5*g**z.
-2*(g + 1)**3/5
Let 0 + 4/7*a + 2/7*a**2 = 0. What is a?
-2, 0
Suppose -2*x + 28 = 5*a, 44 - 8 = 5*a + 4*x. Factor -2 + 0 + 2