 given that x(f) = 0.
-1, 0, 5
Let j = -23 + 25. Let f(r) be the second derivative of 0*r**2 + 0 - 1/5*r**6 - 1/10*r**5 + j*r + 5/24*r**4 + 1/6*r**3. Determine p, given that f(p) = 0.
-1/2, 0, 2/3
Let z(w) = w**2 + 1. Let q(m) = -105*m**2 + 50*m + 15. Let a(u) = -q(u) + 20*z(u). Factor a(j).
5*(5*j - 1)**2
Suppose 3*v - 3 = -0*v. Let -1/3*x**2 + v + 2/3*x = 0. Calculate x.
-1, 3
Let o(z) be the second derivative of 1/20*z**4 + 0 - 1/10*z**3 + 3/100*z**5 + 9*z - 1/50*z**6 + 0*z**2. Factor o(y).
-3*y*(y - 1)**2*(y + 1)/5
Suppose 26 = 4*r + 2*b, -r + 5*b = -5*r + 35. What is y in -8/3*y**4 + 16/3*y**r - 1/3*y - 5*y**3 + 0 + 8/3*y**2 = 0?
-1, 0, 1/4, 1
Suppose -72*s + 73*s - 12 = -4*f, 14 = 3*f + 2*s. Suppose 0 + 1/3*c + 1/3*c**f = 0. Calculate c.
-1, 0
Let j be -1*3 + ((-2090)/(-50))/11. Factor -6/5*s**2 + 2/5 - j*s**3 + 0*s.
-2*(s + 1)**2*(2*s - 1)/5
Let w(d) = -22*d**2 - 100*d - 10. Let i(q) = -2*q**2 - 9*q - 1. Let x(l) = -68*i(l) + 6*w(l). Suppose x(o) = 0. Calculate o.
-2, -1
Let g be ((-20)/(1 + -3))/2. Suppose -b + 0 + 3 = 0, 2*f - 19 = -g*b. Suppose 1/4*r**3 + 0*r**f + 0 - 1/4*r = 0. What is r?
-1, 0, 1
Let d(j) = 0*j**3 + 2*j**3 - 4*j**2 - 8*j + 4*j - 7*j. Let u(w) = -2*w**2 + w**3 - 1 + 1 - 5*w. Let y(z) = -6*d(z) + 13*u(z). Factor y(b).
b*(b - 1)**2
Factor -5/4*c**2 + 0 - 3/4*c.
-c*(5*c + 3)/4
Let d(x) = -2*x**2 + x. Suppose 5*u + 5*m - m - 1 = 0, 3*u - 2*m + 17 = 0. Let c(o) = -3*o**2 + 2*o. Let n(h) = u*c(h) + 5*d(h). Factor n(k).
-k*(k + 1)
Suppose 92/7*s**3 - 250/7 + 900/7*s - 480/7*s**2 - 6/7*s**4 = 0. What is s?
1/3, 5
Let j(m) be the second derivative of m**7/168 - m**6/60 + m**4/24 - m**3/24 + 2*m. Determine u, given that j(u) = 0.
-1, 0, 1
Let k(l) be the third derivative of l**7/210 - l**6/30 + l**5/12 - l**4/12 - 13*l**2. Suppose k(m) = 0. Calculate m.
0, 1, 2
Factor -9*w**2 - 2*w**2 + 6*w**2 + 4*w**2.
-w**2
Let -5/2*o**2 - 45/2*o + 5/2*o**3 + 45/2 = 0. What is o?
-3, 1, 3
Suppose -17*z = -21*z - 2*n - 10, 5*z = -3*n - 15. Factor -1/3*k + z + 1/3*k**2.
k*(k - 1)/3
Suppose 1 + 3 + 2 + 12*s**2 + 16*s - 2 = 0. Calculate s.
-1, -1/3
Factor -72*v + 27/2*v**4 + 72*v**3 + 27/2 + 69*v**2.
3*(v + 3)**2*(3*v - 1)**2/2
Let v(u) be the second derivative of 0 - 1/24*u**3 - u**2 - 1/240*u**5 - u + 1/48*u**4. Let k(d) be the first derivative of v(d). Factor k(z).
-(z - 1)**2/4
Find j such that -2/3 + 2/3*j**2 + 0*j = 0.
-1, 1
Suppose -1/2*t**4 + 1/2*t**3 + 0 + 0*t + 0*t**2 = 0. Calculate t.
0, 1
Suppose -3*k - 2*k = -20. Factor 5*a**3 + 4*a**k - a**4 - a**3 + 5*a**3 - 12*a.
3*a*(a - 1)*(a + 2)**2
Let h(i) = 0*i**3 - 2*i**3 + 6*i**2 - 4 + i**3 + 2*i**2. Let x(l) = -l**2 - l + 1. Let f(w) = -h(w) - 4*x(w). Factor f(z).
z*(z - 2)**2
Let l = -4 - -6. Suppose -2*b - l + 4 = -g, -4*b = -4*g. Factor 5*u - 5*u - 1 + u**b.
(u - 1)*(u + 1)
Let l be ((-4)/6)/((-16)/(-24)). Let a be l/2 + (-1)/(-1). Suppose z**2 - 1/2*z**4 - a + 0*z**3 + 0*z = 0. Calculate z.
-1, 1
Let s(z) = 3*z + 3. Let q be s(-2). Let k be 1/q*6*-1. Find n such that n**2 + 0*n**k + 3*n - n + 1 = 0.
-1
Let k = 5 + -3. Suppose -1 = k*o - 5. Solve -2*y**o - y + 3*y**2 + 0*y**2 = 0 for y.
0, 1
Suppose 2*b = 5*u - 345, u = -2*b - 2*u - 369. Let t be b/(-385) + (-4)/22. What is z in t*z**2 + 2/7*z + 0 = 0?
-1, 0
Suppose 0*s + 2*s = 2. Let b(t) be the first derivative of -t + 0*t**2 + s + 1/3*t**3. Factor b(q).
(q - 1)*(q + 1)
Let 1/5*m + 0 + 2/5*m**2 = 0. Calculate m.
-1/2, 0
Let s(k) be the second derivative of 5*k**4/12 - 10*k**2 + 6*k. Suppose s(w) = 0. Calculate w.
-2, 2
Let p(k) be the third derivative of k**6/24 + k**5/4 + 5*k**4/12 - 5*k**2. Let p(x) = 0. Calculate x.
-2, -1, 0
Let c(m) = -8*m**5 + 17*m**4 + 41*m**3 + 33*m**2 - 17*m. Let a(h) = -h**5 + 2*h**4 + 5*h**3 + 4*h**2 - 2*h. Let f(k) = 51*a(k) - 6*c(k). Factor f(x).
-3*x**2*(x - 2)*(x + 1)**2
Let z(r) be the third derivative of -r**5/60 - 5*r**4/24 + r**3 + 3*r**2. Let k be z(-6). Find c, given that k - 2/3*c + 2/3*c**2 = 0.
0, 1
Let o be (6/20*-4)/((-12)/30). What is v in 1/2 - 1/2*v**2 + 1/2*v - 1/2*v**o = 0?
-1, 1
Factor 0*n**2 + n**2 - 6*n + 7*n.
n*(n + 1)
Determine g so that 3/4*g**2 + 3/4*g + 0 = 0.
-1, 0
Let x(y) = y**2 + 5*y + 4. Let r be x(-1). Let r*k**2 + 0*k + 0 + 2/7*k**3 = 0. What is k?
0
Let n(o) be the second derivative of -o**6/60 - o**5/20 + o**3/6 + o**2/4 + 5*o. Let n(a) = 0. Calculate a.
-1, 1
Let f(q) be the second derivative of -q**7/14 + 9*q**6/10 - 9*q**5/2 + 23*q**4/2 - 33*q**3/2 + 27*q**2/2 - 7*q. Factor f(i).
-3*(i - 3)**2*(i - 1)**3
Suppose -4*r = -2*r - 6. Factor -t**r - 4*t**3 - t + 3*t**3 + 3*t**2.
-t*(t - 1)*(2*t - 1)
Let k = 22 - 18. Let v(q) be the first derivative of 1/3*q**3 + 0*q - 1/5*q**5 - 2 + 0*q**k + 0*q**2. Factor v(h).
-h**2*(h - 1)*(h + 1)
Let q(d) = 3*d**5 - 6*d**4 + 3*d**3 - 4*d**2 - 4*d. Let b(z) = -z**5 + z**4 - z**3 + z**2 + z. Let u(n) = -4*b(n) - q(n). Find x such that u(x) = 0.
-1, 0
Let t(x) be the second derivative of -x + 0*x**4 - 3/40*x**5 + 0 + 0*x**3 + 0*x**2. Factor t(i).
-3*i**3/2
Let c(h) be the first derivative of -h**4 - 4*h**3/3 + 8*h**2 + 16*h - 12. Let c(a) = 0. What is a?
-2, -1, 2
Let s be 40/(-25)*2/(-8). Factor s*f**2 + 8/5 - 8/5*f.
2*(f - 2)**2/5
Let d be ((-8)/6)/(34/(-153)). Let c(q) be the second derivative of 1/12*q**4 - 1/30*q**d + 0 + 0*q**2 + 0*q**3 + 0*q**5 + 3*q. Factor c(o).
-o**2*(o - 1)*(o + 1)
Suppose s + 5*a = -0*s + 80, -4*a = -16. Let g be -3 - (s/(-8) - -4). Find n such that -1/2*n**2 + 1 + g*n = 0.
-1, 2
Factor 1/3*h**2 + 4/3 + 4/3*h.
(h + 2)**2/3
Let b(q) = -2*q**3 - 6*q**2 + 3*q + 2. Let l = 35 + -7. Suppose -7*t + 3*t = -l. Let m(y) = 5*y**3 + 13*y**2 - 6*y - 5. Let u(v) = t*b(v) + 3*m(v). Factor u(f).
(f - 1)**3
Let x(z) be the third derivative of -9*z**2 + 0*z + 1/480*z**5 + 1/32*z**4 + 0 + 3/16*z**3. Factor x(d).
(d + 3)**2/8
Let s(l) be the first derivative of 7 + 2*l**2 + 0*l + 2/3*l**3 - l**4 - 2/5*l**5. Factor s(a).
-2*a*(a - 1)*(a + 1)*(a + 2)
Let f(w) be the first derivative of -w**6/3 - 2*w**5/5 + w**4 + 4*w**3/3 - w**2 - 2*w + 9. Factor f(k).
-2*(k - 1)**2*(k + 1)**3
Suppose -5*m - 2*y - 1 = -y, 2*y = 3*m - 2. Let q(z) be the second derivative of -8/3*z**3 - z - 6/5*z**5 + m - z**2 - 19/6*z**4. Find a such that q(a) = 0.
-1, -1/3, -1/4
Suppose -4*c + 1 = -3. Let g = 7 - c. Let -1 - 1 - g*q**2 - 4*q + 4 = 0. Calculate q.
-1, 1/3
Let p = 109/285 + 1/57. Solve -p*r - 2/5*r**2 + 4/5 = 0 for r.
-2, 1
Factor -4/7*f**2 + 8/7*f + 1/7*f**4 - 2/7*f**3 + 0.
f*(f - 2)**2*(f + 2)/7
Let l(t) = -t**3 + 60. Let c be l(0). Let r be (32/c)/((-4)/(-6)). Suppose -2/5*o**2 - r*o + 0 = 0. What is o?
-2, 0
Factor -18/7 + 12/7*m - 2/7*m**2.
-2*(m - 3)**2/7
Let g(h) be the second derivative of h**5/40 - h**4/24 - 5*h**3/12 - 3*h**2/4 - 25*h. Suppose g(w) = 0. Calculate w.
-1, 3
Suppose 3*w + 462 = 10*w. Let o be 4/3*9/w. Factor -4/11*d**3 + o*d**5 + 0 + 0*d**2 + 0*d - 2/11*d**4.
2*d**3*(d - 2)*(d + 1)/11
Let j(u) = -u + 4. Let h be j(2). Suppose h*x + 1 - 2 + 1 - x**2 = 0. Calculate x.
0, 2
Let w = -10987/4 + 2727. Let n = w - -20. Suppose -n*j + 3/4*j**2 - 1/2 = 0. Calculate j.
-2/3, 1
Let c(y) = y**3 + y**2 - y + 1. Let o(g) = -2*g**5 + 5*g**4 - 10*g**3 - 5*g**2 + 6*g - 6. Let x(n) = 6*c(n) + o(n). Let x(l) = 0. What is l?
0, 1/2, 1
Suppose -2*c = -2, 2*c = -2*x + c - 1. Let u be 27/(-9) - 5*x. Factor 2/3*k**u + 1/3*k**3 + 1/3*k + 0.
k*(k + 1)**2/3
Let g(l) = 5*l**4 + l**3 - 3*l**2 - 3*l. Let p(t) = -14*t**4 - 4*t**3 + 8*t**2 + 8*t. Let h(b) = -8*g(b) - 3*p(b). Solve h(i) = 0.
-2, 0
Let y = 12 + -7. Let f = y - 3. Find a, given that 8*a - 16/3 + 2/3*a**3 - 4*a**f = 0.
2
Find d, given that -2/17*d + 4/17 + 2/17*d**3 - 4/17*d**2 = 0.
-1, 1, 2
Let x = 17 - 17. Let b(p) be the third derivative of -1/210*p**5 + 1/420*p**6 - 1/84*p**4 + 4*p**2 + 0*p**3 + 0*p + 1/735*p**7 + x. Factor b(v).
2*v*(v - 1)*(v + 1)**2/7
Suppose 0*l = l - 4. Let p be ((-1)/4)/((-4)/48). Find z such that 0 - 2/9*z**l + 2/9*z**2 + 0*z**p + 0*z = 0.
-1, 0, 1
Let l(d) be the third derivative of d**10/10080 - d**8/1120 + d**6/240 + 5*d**4/24 + 5*d**2. Let t(n) be the second derivative of l(n). Factor t(k).
3*k*(k - 1)**2*(k + 1)**2
Let b(d) be the first derivative of d**3/9 + d**2/3 + 18. Factor b(j).
j*(j + 2)/3
Let y(c) = 3*c**3 - 16*c**2 + 15*c - 10. Let i(d) = -d**2 -