tor -6*v + 0*v + 2 + 2*v**3 - 4*v**2 + 4*v + 2.
2*(v - 2)*(v - 1)*(v + 1)
Let x = 2/305 - -364/305. Let q = -64 + 66. Let 2/5*z**q + 4/5 + x*z = 0. What is z?
-2, -1
Suppose -2*z + 7*z - 20 = 0. Suppose -w = -z*w. Solve -1/2*a - 3*a**3 - 1/2*a**5 + 2*a**2 + w + 2*a**4 = 0.
0, 1
Factor 0*h + 2*h**2 + 0*h - 3*h**2.
-h**2
Let i(n) be the first derivative of 2 + 1/10*n**2 + 2*n - 2/15*n**3 + 1/20*n**4. Let h(o) be the first derivative of i(o). Factor h(p).
(p - 1)*(3*p - 1)/5
Let y(l) = 5*l**4 + 2*l**2 - 7. Let z(u) = 2*u**4 + u**2 - 3. Let h(m) = -3*y(m) + 7*z(m). Determine f so that h(f) = 0.
-1, 0, 1
Let x(s) = -10*s**3 - s - 2. Let w be x(-2). Factor w*k + 3 - 3*k**2 - 80*k.
-3*(k - 1)*(k + 1)
Let z be (-49)/(-42) + 20/(-24). Factor 0 - 1/3*k**2 - z*k.
-k*(k + 1)/3
Let s(t) be the first derivative of t**5/420 - t**4/168 - t**2 - 6. Let j(q) be the second derivative of s(q). Let j(z) = 0. Calculate z.
0, 1
Let h(i) = -9*i + 345. Let g be h(38). Factor 2/7*q**g + 1/7*q**2 + 0 + 1/7*q**4 + 0*q.
q**2*(q + 1)**2/7
Suppose 24 = 3*d + d. Let s(f) be the third derivative of 17/180*f**5 - 7/180*f**d - 2*f**2 + 0 + 0*f - 1/9*f**3 - 1/72*f**4. Solve s(z) = 0 for z.
-2/7, 1/2, 1
Let h(i) be the first derivative of 6 + 2/3*i - 2/3*i**5 + 5/6*i**2 + 0*i**3 - 1/6*i**6 - 5/6*i**4. Find m, given that h(m) = 0.
-1, 2/3
Suppose 10*j - 9*j = 4. Let c(y) be the third derivative of -1/105*y**7 + 1/30*y**5 + 0*y + 3*y**2 + 0 - 1/60*y**6 + 1/168*y**8 + 0*y**j + 0*y**3. Factor c(w).
2*w**2*(w - 1)**2*(w + 1)
Let 33/7*s - 10/7*s**2 - 36/7 + 1/7*s**3 = 0. Calculate s.
3, 4
Let d be 33/6 - 4/8. Let y(z) be the third derivative of -1/12*z**d + 0 + z**2 + 2/9*z**3 - 1/20*z**6 + 0*z + 1/18*z**4. Solve y(r) = 0.
-2/3, 1/2
Let g(j) = -9*j**3 + 21*j**2 - 15*j + 13. Let k(u) = -5*u**3 + 11*u**2 - 7*u + 7. Let m(f) = -3*g(f) + 5*k(f). Factor m(c).
2*(c - 2)*(c - 1)**2
Let r(u) = 25*u**4 + 102*u**3 - 36*u**2 - 68*u - 23. Let f(k) = k**3 - 1. Let j(d) = 21*f(d) - 3*r(d). Suppose j(y) = 0. Calculate y.
-4, -2/5, 1
Suppose 42*r**3 + 36*r**3 - 80*r**3 + 2*r = 0. What is r?
-1, 0, 1
Let y = 23 - 21. Factor -o**y - 7*o + 5*o - 2 - o.
-(o + 1)*(o + 2)
Let m be ((-12)/(-36))/(2/(-18)). Let h be (0/m)/(-4 - -2). Determine i, given that 2/9*i**3 + 0 - 2/9*i**5 - 2/9*i**2 + 2/9*i**4 + h*i = 0.
-1, 0, 1
Let n(y) = -5*y**2 + 5*y - 4. Suppose 2*w = -3 + 9. Let m(i) = i**2 - i + 1. Let h(p) = w*n(p) + 12*m(p). Factor h(q).
-3*q*(q - 1)
Let l(s) be the first derivative of -4*s**3/9 - 1. Factor l(c).
-4*c**2/3
Factor 49*r**2 + r**3 + 3*r**3 - 53*r**2.
4*r**2*(r - 1)
Suppose -3*y - 1 = 5*a - 2, -y + 7 = 5*a. Let w be -9*(-2 - 10/(-6)). Factor n + w*n**2 - 2*n**2 - 2*n**a.
-n*(n - 1)
Let u(l) be the first derivative of -l**5/5 - l**4/4 + 10. Suppose u(x) = 0. What is x?
-1, 0
Solve 25/4 - 5/2*i + 1/4*i**2 = 0 for i.
5
Let q(h) be the first derivative of 7*h**9/48 - h**8/40 - 83*h**7/840 + h**6/90 + h**5/30 - 4*h**3/3 + 1. Let w(n) be the third derivative of q(n). Factor w(b).
b*(3*b - 1)**2*(7*b + 2)**2
Let u(q) be the third derivative of q**6/120 - q**5/30 + q**4/24 - 28*q**2. Suppose u(k) = 0. What is k?
0, 1
Factor 6*h - 4*h**2 - 2*h + 4*h + 60.
-4*(h - 5)*(h + 3)
Let j be ((-12)/(-9))/(8/12). Let f(n) be the second derivative of j*n + 0 + 1/6*n**2 + 1/36*n**4 - 1/9*n**3. Find r, given that f(r) = 0.
1
Let n(i) = i**3 + i**2 - i - 1. Suppose 0*t + 60 = -5*t. Let z(d) = d**5 + d**4 + 3*d**3 + 3*d**2 - 4*d - 4. Let k(j) = t*n(j) + 3*z(j). Factor k(g).
3*g**2*(g - 1)*(g + 1)**2
Solve 0 - 3*u**2 - 3/2*u**4 + 9/2*u**3 + 0*u = 0 for u.
0, 1, 2
Let o(q) = q**2 + 3*q - 4. Let u be o(-4). Suppose u*c - 3*c = -15. Factor 20*p**2 + c*p - 11*p + p**2.
3*p*(7*p - 2)
Factor 1/3*y**4 - 4/3*y - 5/3*y**3 + 0 + 8/3*y**2.
y*(y - 2)**2*(y - 1)/3
Let j(v) be the second derivative of v**6/105 - v**5/14 + v**4/42 + v**3 - 18*v**2/7 - v. Factor j(q).
2*(q - 3)**2*(q - 1)*(q + 2)/7
Factor 10*s**3 + 7*s**3 - 23*s**3 - 3*s**4.
-3*s**3*(s + 2)
Let n(x) = 5*x**3 - 3*x - 2. Let f(v) = -6*v**3 + 3*v + 3. Let w(y) = 4*f(y) + 5*n(y). Let p(r) be the first derivative of w(r). Factor p(h).
3*(h - 1)*(h + 1)
Let m(q) be the second derivative of -8*q - 1/4*q**4 + 0 + 1/30*q**6 + 5/6*q**3 - q**2 - 1/20*q**5. What is o in m(o) = 0?
-2, 1
Factor 1/4*w**2 + 0*w - 1/4.
(w - 1)*(w + 1)/4
Let z(x) = -12*x**3 - 15*x + 8. Let b(f) = 8*f**3 + 10*f - 5. Let m(l) = -8*b(l) - 5*z(l). Let i(p) = -5*p**3 - 6*p. Let a(r) = 5*i(r) - 6*m(r). Factor a(n).
-n**3
Let q(i) be the third derivative of i**6/40 - i**5/5 + i**4/2 - 29*i**2. Suppose q(m) = 0. What is m?
0, 2
Factor -5/4*n**5 + 5/4*n**4 + 0 + 0*n - 5/4*n**2 + 5/4*n**3.
-5*n**2*(n - 1)**2*(n + 1)/4
Let k = 6 + -3. Suppose k*c - 12 = -c. Factor c*n**3 + 2*n - 4*n - n**3.
2*n*(n - 1)*(n + 1)
Let l(m) be the third derivative of 1/60*m**6 + 1/15*m**5 - 3*m**2 - 2/3*m**3 + 0 + 0*m - 1/12*m**4. Determine v, given that l(v) = 0.
-2, -1, 1
Let g(v) be the first derivative of -3*v**6/80 - v**5/40 + 5*v**4/48 - v**3/12 - 3*v**2/2 - 3. Let w(d) be the second derivative of g(d). Solve w(q) = 0.
-1, 1/3
What is s in 7/2*s**2 - 2*s**3 + 0 + s = 0?
-1/4, 0, 2
Let a = -10 - -12. Determine v so that -v**3 - 3*v**3 + 0*v**3 + a*v**3 = 0.
0
Let l(p) be the third derivative of -p**6/600 - p**5/150 + p**4/40 - 10*p**2. Factor l(g).
-g*(g - 1)*(g + 3)/5
Find b, given that -17 + 15*b**3 - 10*b - 12*b**2 + 7*b**3 + 20*b**4 + 37 - 16 = 0.
-1, 2/5, 1/2
Factor 4/7 - 8/7*g**3 - 4/7*g**5 - 12/7*g**4 + 8/7*g**2 + 12/7*g.
-4*(g - 1)*(g + 1)**4/7
Let c(u) = -u + 3*u + 0*u + u + 1. Let k be c(1). Let 1/4*t**k - 1/4 + 0*t**2 + 1/2*t - 1/2*t**3 = 0. What is t?
-1, 1
Let 4/5*l + 4/5*l**2 + 0 - 4/5*l**3 - 4/5*l**4 = 0. Calculate l.
-1, 0, 1
Suppose 3*n + 0*n = 12. Suppose -n*a + 2*a**4 + 2 + a**3 + 0*a**3 + 3*a**3 - 4 = 0. What is a?
-1, 1
Let b be -4 - 0 - 1*-3. Let l = b + 3. Factor -4*a**2 + 3*a**2 - l*a - 4*a**2 - a**2.
-2*a*(3*a + 1)
Let q be 1 + 1/105 - 1. Let l(i) be the third derivative of 0*i + 0*i**3 + 0*i**4 + i**2 + 0*i**5 + 0 + q*i**7 - 1/60*i**6. Factor l(y).
2*y**3*(y - 1)
Suppose -3*s = -12 - 0. Let w(h) be the second derivative of -h + 2/21*h**3 + 1/42*h**s + 1/7*h**2 + 0. Factor w(l).
2*(l + 1)**2/7
Let p(s) be the second derivative of s**4/4 - 9*s. Factor p(k).
3*k**2
Let l(q) = 68*q**5 - 204*q**4 + 40*q**3 + 288*q**2 - 56*q - 64. Let k(f) = f**5 - f**4 + f**3 + f. Let r(m) = -8*k(m) + l(m). Solve r(i) = 0 for i.
-1, -2/5, 2/3, 2
Let c(r) be the first derivative of -2*r**3/9 + 16*r**2/3 - 128*r/3 - 38. What is m in c(m) = 0?
8
Suppose -x + 3*l = 7, -4*l + 1 = -x - 2*x. Find a, given that a**x + 5*a**3 - 2*a**3 - 3*a**4 - a**3 = 0.
0, 1, 2
Let z(g) be the second derivative of 3/10*g**6 - 3*g + 0*g**3 + 0 + 0*g**2 - 3/10*g**5 + 5/14*g**7 + 0*g**4. Factor z(q).
3*q**3*(q + 1)*(5*q - 2)
Let u(o) = -6*o**2 + 22*o - 34. Let s(f) = f**2 + f + 1. Let v(z) = 3*z**2 + 3*z + 2. Let l(n) = -5*s(n) + 2*v(n). Let c(i) = -2*l(i) - u(i). Factor c(b).
4*(b - 3)**2
Let x(c) be the first derivative of 0*c - 1/48*c**4 - 1/120*c**5 - c**2 + 2 + 0*c**3. Let s(q) be the second derivative of x(q). What is z in s(z) = 0?
-1, 0
Suppose -n**3 + 0*n + 2*n - 4*n + 4 + 5*n**2 - 6*n = 0. Calculate n.
1, 2
Let v(q) be the second derivative of -q**6/195 - q**5/26 - q**4/26 + 3*q**3/13 - 24*q. Factor v(n).
-2*n*(n - 1)*(n + 3)**2/13
Let v(z) be the third derivative of z**6/24 - z**5/12 - 5*z**4/24 + 5*z**3/6 - 3*z**2. Factor v(n).
5*(n - 1)**2*(n + 1)
Find w, given that 30*w**3 + 5*w**5 - 17*w**4 + 38*w**2 - 35*w + 2*w**2 - 23*w**4 = 0.
-1, 0, 1, 7
Let i(s) be the second derivative of s**9/5040 - s**8/1120 + s**6/120 - s**5/40 - s**4/4 - 6*s. Let h(p) be the third derivative of i(p). Factor h(q).
3*(q - 1)**3*(q + 1)
Let h(o) be the first derivative of o**3/6 - 3*o**2/4 + o + 1. Factor h(u).
(u - 2)*(u - 1)/2
Suppose -b = -3*y, 0 = 4*y + b + 3*b. Let y*a - 2/3*a**4 - 2/3*a**2 + 0 - 4/3*a**3 = 0. What is a?
-1, 0
Let s(u) be the third derivative of 4*u**5/15 + 13*u**4/6 + 2*u**3 - 31*u**2. Suppose s(w) = 0. Calculate w.
-3, -1/4
Let q(g) = 5*g + 12 - 4*g - 2*g. Let s be q(0). Suppose s*m + 12*m**4 + 24*m**2 + 4*m - 2*m**4 - 36*m**3 = 0. What is m?
-2/5, 0, 2
Suppose -j - 5*f - 3 = -2*j, -j = -3*f - 3. Factor 9 - 13 + u**2 + u**3 - u + j.
(u 