6/135 - g**5/90 + g**4/27 - 15*g. Factor p(q).
-2*q**2*(q - 1)*(q + 2)/9
Suppose 5*v = 6*v - 3, 4*h = v - 3. Factor h*z - 7/4*z**3 + 1/2*z**2 - 3/4*z**5 + 0 + 2*z**4.
-z**2*(z - 1)**2*(3*z - 2)/4
Let v be -1 + 2 + (-3)/(-1). Suppose 0*a - v*a = -8. Factor -1 + k**5 - 5*k**4 - 2*k**3 + 2*k**a + 2*k + 0*k - k + 4*k**4.
(k - 1)**3*(k + 1)**2
Suppose 8 = 2*o + 2*h - 0*h, 3*o + 4*h - 12 = 0. Let k be ((-25)/(-4))/5*o. Determine n so that -8/5*n**3 + 3/5*n**k - 4/5*n**2 + 0*n + 0 - 1/5*n**4 = 0.
-1, -2/3, 0, 2
Find r, given that 8/7 + 450/7*r**2 + 120/7*r = 0.
-2/15
Let i(u) = -u**2 + 7*u + 10. Suppose -6*a + 3*y = -2*a - 23, -2*y - 2 = -a. Let g be i(a). Factor -7*z**g + 4*z**5 + 1 + 3*z**4 - 2*z - 2*z**3 - z**2 + 4*z**4.
(z - 1)*(z + 1)**3*(4*z - 1)
Factor 0*s + 0*s**2 + 0*s**3 - 2/15*s**4 + 0 + 2/15*s**5.
2*s**4*(s - 1)/15
Solve -3/7*k**2 - 6/7 + 9/7*k = 0.
1, 2
Suppose -24*p + 120 = -0*p. Factor -3/4*m**3 + 1/2*m**2 + 0 + 0*m + 0*m**4 + 1/4*m**p.
m**2*(m - 1)**2*(m + 2)/4
Let c be 2/(-18) + (1 - (-4)/18). Solve -2/9*q**3 + 4/9 + 8/9*q**2 - c*q = 0.
1, 2
Let m(t) be the third derivative of t**6/300 - t**2. What is g in m(g) = 0?
0
Let c(h) be the first derivative of 0*h + 1/20*h**4 - 2/15*h**3 + 7 + 1/10*h**2. Factor c(b).
b*(b - 1)**2/5
Factor -4/7*z - 5/7*z**4 + 1/7 + 2/7*z**3 + 2/7*z**5 + 4/7*z**2.
(z - 1)**3*(z + 1)*(2*z - 1)/7
Suppose 10 = 8*h - 3*h. Let l be (-3)/h*(-64)/120. Factor 6/5*d**3 - l*d**2 + 0 - 8/5*d**5 - 2/5*d + 8/5*d**4.
-2*d*(d - 1)**2*(2*d + 1)**2/5
Let k(j) be the first derivative of 0*j**2 + 3 - 3/10*j**5 + 3/8*j**4 + 1/12*j**6 - 1/6*j**3 + 0*j. Factor k(d).
d**2*(d - 1)**3/2
Determine f, given that 57/7*f**2 - 6/7*f**5 + 45/7*f**3 - 3/7*f**4 - 18/7 - 3/7*f = 0.
-2, -1, 1/2, 3
Let d(g) be the third derivative of -7*g**6/360 - g**5/90 + 11*g**2. Factor d(q).
-q**2*(7*q + 2)/3
Factor -2/9*d**3 - 2/9*d**4 + 2/9*d + 2/9*d**2 + 0.
-2*d*(d - 1)*(d + 1)**2/9
Let o(t) = -6*t**2 - 3*t - 5. Let q(d) = d**2 + d + 1. Let w(v) = -o(v) - 5*q(v). Factor w(x).
x*(x - 2)
Let j(o) = -o**3 + 2*o**2 + 10*o - 6. Let s be j(4). Suppose -2/5 + 12/5*y - 18/5*y**s = 0. What is y?
1/3
Let s(g) = g**3 + g**2 + g + 1. Let y(a) = 2*a**4 + 2*a**3 + 6*a**2 + 2*a - 4. Let o(x) = -6*s(x) - y(x). Factor o(z).
-2*(z + 1)**4
Suppose 4*w - 32 = -0*w. Suppose -2 = 2*x - w. Suppose -10/3*a**2 - 1/3 + 10/3*a**x + 5/3*a - 5/3*a**4 + 1/3*a**5 = 0. Calculate a.
1
Let y = -4370/9 + 486. Solve 0 - y*i + 2/9*i**2 = 0 for i.
0, 2
Let f(c) be the second derivative of -2*c**7/21 + c**5/5 + 25*c. Suppose f(y) = 0. Calculate y.
-1, 0, 1
Let n(f) = 15*f**5 + 10*f**4 - 12*f**2. Let u(y) = 30*y**5 + 20*y**4 - 26*y**2. Let j(a) = -13*n(a) + 6*u(a). Find p, given that j(p) = 0.
-2/3, 0
Let x = 4 - 2. Suppose -4*i = -x - 10. What is d in 0 + 0*d**2 - 1/2*d**i + 1/2*d = 0?
-1, 0, 1
Let x(i) be the second derivative of -i**7/105 + i**6/15 - i**5/6 + i**4/6 + i**2/2 + 5*i. Let o(s) be the first derivative of x(s). Solve o(k) = 0 for k.
0, 1, 2
Factor 2*l**4 + 0*l**3 + 3*l**3 - l**3 - 4*l**4.
-2*l**3*(l - 1)
Let f = 1506 - 10540/7. Determine s so that -4/7*s**2 - f + 1/7*s**3 + 5/7*s = 0.
1, 2
Let f(i) = -3*i - 2. Let l be f(-2). Suppose 3*a - l = a. Determine s so that 0*s**2 - 3*s**2 + s**a + 4*s = 0.
0, 2
Determine j, given that 2*j**3 - 8/5*j - 12/5*j**2 + 16/5 - 2/5*j**4 = 0.
-1, 2
Find p such that -p - p - 48 - 3*p**2 - 22*p = 0.
-4
Let h(b) be the third derivative of 0*b - 1/48*b**4 + 1/360*b**5 + 1/18*b**3 + 2*b**2 + 0. Factor h(a).
(a - 2)*(a - 1)/6
Suppose 0 = -2*o + 6. Let 5/3*t**2 + 1/3*t + t**o - 1/3 = 0. What is t?
-1, 1/3
Let x = 908/84315 + -1/803. Let a(t) be the second derivative of 1/70*t**5 - 1/147*t**7 + 0*t**2 + 1/42*t**4 - 3*t + 0 - x*t**6 + 0*t**3. Factor a(j).
-2*j**2*(j - 1)*(j + 1)**2/7
Let g(z) be the first derivative of 8/39*z**3 - 2 + 2/13*z**2 - 2/13*z - 1/13*z**4 - 6/65*z**5. Find x such that g(x) = 0.
-1, 1/3, 1
Let x(t) be the second derivative of t**6/15 + 4*t**5/5 + 7*t**4/2 + 6*t**3 + 15*t. Suppose x(v) = 0. What is v?
-3, -2, 0
Let x(o) = o**3 + 7*o**2 - 11*o - 12. Let n be x(-8). Factor 7*k + k + 28*k**2 + 4*k + n*k - 4.
4*(k + 1)*(7*k - 1)
Solve 1/5*g**2 - 8/5 - 2/5*g = 0.
-2, 4
Let b(i) be the second derivative of i**4/66 - 10*i**3/11 + 225*i**2/11 + 61*i. Find d, given that b(d) = 0.
15
Solve -3/4*l**2 - 12 + 6*l = 0.
4
Let s(k) = -5*k**2 - 7. Let q(c) = c**2 + 1. Let n(i) = 6*q(i) + s(i). Let p(r) = 2 - 6*r**2 - 1 + r**4 + 4*r**2. Let t(j) = 2*n(j) + 2*p(j). Factor t(o).
2*o**2*(o - 1)*(o + 1)
Let k be ((-18)/(-60))/(6/16). Let r(f) = f**3 + 7*f**2 - 7*f + 8. Let b be r(-8). Let -k*y - 2/5*y**2 + 2/5*y**3 + b = 0. Calculate y.
-1, 0, 2
Factor 2*b**2 - 4 + 6 + 4*b - b + b.
2*(b + 1)**2
Let t(r) be the third derivative of r**6/540 - 4*r**2. Suppose t(q) = 0. Calculate q.
0
Let u(a) = 7*a**3 + 11*a**2 + 9*a + 9. Let n(x) = -3*x**3 - 5*x**2 - 4*x - 4. Let l = 5 - 14. Let y(d) = l*n(d) - 4*u(d). Factor y(k).
-k**2*(k - 1)
Factor 6 - 4*p**2 - 5*p**3 + 2*p**3 + 14*p + p**3 - 14.
-2*(p - 1)**2*(p + 4)
Suppose -4*t + 7 = -3*x - 12, 0 = -3*t - 3*x + 9. Let z(f) be the second derivative of 2*f**2 + f**3 + 0 - f + 1/6*f**t. Factor z(k).
2*(k + 1)*(k + 2)
Let m = 450 + -3148/7. Suppose -m*v**3 - 6/7*v - 8/7*v**2 + 0 = 0. What is v?
-3, -1, 0
Factor -1/6*z**3 + 0 - 1/6*z**4 + 0*z + 1/6*z**5 + 1/6*z**2.
z**2*(z - 1)**2*(z + 1)/6
Let t(c) = c**3 + 13*c**2 + 6. Let q be t(-13). Let v = -3 + q. Let -1/4*n**4 + 0*n + 1/2*n**v - 1/4*n**2 + 0 = 0. What is n?
0, 1
Let n = 6 - 2. Let 2*b + 16*b**5 - 6*b**3 - 12*b**n - 2*b + 2*b**2 = 0. What is b?
-1/2, 0, 1/4, 1
Let s(b) = b + 4. Let w be s(-2). Factor -4*z + w*z**2 - 72 + 72.
2*z*(z - 2)
Suppose -3/5*w**2 + 3/5*w + 0 = 0. Calculate w.
0, 1
Let a(j) be the first derivative of -j**6/15 - 2*j**5/25 + 9. Determine h, given that a(h) = 0.
-1, 0
Let n(g) be the first derivative of g**5/60 + g**4/12 + g**3/6 + 5*g**2/2 + 1. Let a(r) be the second derivative of n(r). Suppose a(w) = 0. Calculate w.
-1
Let p(m) be the second derivative of -5*m**6/6 - 9*m**5/4 + 13*m**4/6 + 6*m**3 + 4*m**2 - 8*m. Factor p(d).
-(d - 1)*(d + 2)*(5*d + 2)**2
Let y(b) be the first derivative of 4*b**3/27 - 2*b**2/9 + 16. Factor y(n).
4*n*(n - 1)/9
Suppose -15 = 4*p - 5*r, r + r = p + 6. Let b(o) be the first derivative of -2/45*o**5 + p*o**3 + 0*o**2 - 1/18*o**4 + 0*o - 1. Determine w so that b(w) = 0.
-1, 0
Let h = -5 - -7. Suppose 10 = 2*v + v + h*u, 2*v + 2*u = 8. What is q in 2*q**4 - q**4 - 2*q**4 + 0*q**4 + q**2 + v*q - 3*q**3 + q**5 = 0?
-1, 0, 1, 2
Let r = 5/98 - -141/1078. Let k = 17 - 17. Factor 2/11*g - r*g**3 + k*g**2 + 0.
-2*g*(g - 1)*(g + 1)/11
Let t(m) = 2*m**2 - 3*m**2 + 7*m + 0 - 2. Let i be t(6). Factor -2*y**4 - 4*y**i + 0*y**4 - 4*y**5 + 2*y**2.
-2*y**2*(y + 1)**2*(2*y - 1)
Let c be (-135)/42 + 3 + 1. Let d = c + -93/154. Factor -4/11*o**3 - d*o**2 - 2/11*o**4 + 0 + 0*o.
-2*o**2*(o + 1)**2/11
Let d(h) = -2*h**5 + h**2 - 5 - 7*h**4 + h - 6*h + 7*h**3 + h**2. Let y(g) = -g**5 - 4*g**4 + 4*g**3 + g**2 - 3*g - 3. Let r(q) = 3*d(q) - 5*y(q). Factor r(k).
-k**2*(k - 1)*(k + 1)**2
Factor 24*i**3 - 28*i**3 + i**2 + 3*i**2 - 8*i**4.
-4*i**2*(i + 1)*(2*i - 1)
Suppose 1 = -2*f + 9. Let s(q) be the second derivative of -3*q + 1/2*q**f - 2/3*q**3 + 1/30*q**6 + 1/2*q**2 + 0 - 1/5*q**5. Suppose s(d) = 0. What is d?
1
Let z = 15 - 15. Let x(s) be the second derivative of -2*s + 0*s**3 + z*s**4 + 0*s**2 - 1/90*s**5 + 0. Suppose x(r) = 0. Calculate r.
0
Suppose 2*j - 211 = 5*s, -5*j + s + 539 = -0*s. Let t be 5/(-2)*j/(-225). Find p, given that 2/5 - 4/5*p - t*p**2 = 0.
-1, 1/3
Let m(c) be the second derivative of c**4/120 + c**3/20 - c**2/2 - 19*c. Factor m(n).
(n - 2)*(n + 5)/10
Let h(q) = -2*q - 18. Let s be h(-9). Let d(a) be the second derivative of -1/2*a**2 + 3*a + 0 + s*a**3 + 1/12*a**4. Factor d(f).
(f - 1)*(f + 1)
Let n(r) be the third derivative of -r**5/450 + r**4/180 - 7*r**2. Factor n(a).
-2*a*(a - 1)/15
Determine n, given that -5*n**2 + 3*n**2 - 44 + 20*n + 7*n**2 + 64 = 0.
-2
Let o = -4 + 3. Let p(r) = -r**5 + r**4 - r**3 - r**2 + r. Let l(k) = -12*k**5 - 2*k**4 - 2*k**3 + 2*k**2 + 8*k. Let z(i) = o*l(i) + 6*p(i). Solve z(m) = 0.
-1, -1/3, 0, 1
Suppose -s + 5*i - 31 = 0, 3*s + 13 = -2*i - 12. Let z be 17/33 - (-2)/s. Let