2
What is a in 16/7*a - 136/7*a**4 + 16/7*a**2 + 0 - 76/7*a**3 - 60/7*a**5 = 0?
-1, -2/3, 0, 2/5
Suppose r - i - 2*i - 7 = 0, 4*r - 14 = -2*i. Factor q + 0*q**2 - 6*q + 3*q**4 + 5*q**3 + r - q**2 - 6.
(q - 1)*(q + 1)**2*(3*q + 2)
Let n(z) = z**2 - 8*z - 6. Let c be n(9). Suppose -h + c*h = 6. Determine d, given that -6*d**h - 7*d + 6*d**5 + 7*d + 2*d**4 - 2*d**2 = 0.
-1, -1/3, 0, 1
Let w(a) = 35*a - 489. Let r be w(14). Factor 0*q + 3/4*q**2 - 1/4*q**3 - r.
-(q - 2)**2*(q + 1)/4
Let b(h) = h**3 + 5*h**2 - h - 3. Let y be b(-5). Suppose 10 = -3*n + n, 2*n + 20 = 5*s. Factor -u - s + 2*u**3 - u + y.
2*u*(u - 1)*(u + 1)
Factor 8/5 - 2*d**3 - 32/5*d - 38/5*d**2.
-2*(d + 2)**2*(5*d - 1)/5
Let r(h) be the first derivative of 2*h**3/51 + 2*h**2/17 + 34. Suppose r(v) = 0. What is v?
-2, 0
Let w = -11 - -34/3. Let s = 6/7 - 4/21. Let s*q**2 + 0 + 1/3*q + w*q**3 = 0. Calculate q.
-1, 0
Let x(g) = 4*g**2 - 1. Suppose 0 = 5*f + 2*c - 5, -5*f = -f + 4*c - 4. Let q be x(f). Suppose 5/3*m**q + 0 + 4*m**2 + 4/3*m = 0. Calculate m.
-2, -2/5, 0
Let w(h) be the first derivative of -3*h**5/5 - h**4 + 29. Factor w(o).
-o**3*(3*o + 4)
Let w = -83 + 251/3. Let m(l) be the first derivative of -1 - 2*l**2 + w*l**3 + 0*l. Factor m(c).
2*c*(c - 2)
Suppose 4*y = -k, 0 = -3*y - 2*y - k. Suppose 0 = c - 0 + 5, y = -x - c - 3. Solve 52*u**3 + 12*u + 48*u**2 + 10*u + 6*u**5 - x + 28*u**4 + 6 = 0.
-1, -2/3
Factor 2/5*s**3 + 0*s**2 + 0 + 2/5*s**4 + 0*s.
2*s**3*(s + 1)/5
Let q(b) be the first derivative of -b**6/9 - 14*b**5/15 - 3*b**4 - 40*b**3/9 - 8*b**2/3 + 21. Factor q(p).
-2*p*(p + 1)*(p + 2)**3/3
Let g(q) = q - 1. Let c be g(5). Factor 2*d**2 + d**4 - 9*d**5 - c*d**4 - d**3 - 3*d**2 + 6*d**3.
-d**2*(d + 1)*(3*d - 1)**2
Let p be 12/(-16)*2/(-3). Let j(x) be the first derivative of -3/8*x**2 + 1/12*x**3 + p*x + 1. Factor j(n).
(n - 2)*(n - 1)/4
Suppose 3*c = 5*p - 16, -3 = 3*c + 3. Solve -6/13*x**p + 4/13*x**5 + 6/13*x**4 - 2/13*x + 0 - 2/13*x**3 = 0 for x.
-1, -1/2, 0, 1
Let f(l) be the second derivative of l**5/85 + l**4/102 - 5*l**3/51 + 2*l**2/17 - 22*l. Find h such that f(h) = 0.
-2, 1/2, 1
Let t be 15/27 + (-4)/18. Factor 1/3 - t*k**4 + 2/3*k**3 - 2/3*k + 0*k**2.
-(k - 1)**3*(k + 1)/3
Let d(v) = -37*v**2 - 29*v + 2. Let n(t) = t**2 + t - 1. Let r(w) = 3*d(w) + 12*n(w). Factor r(c).
-3*(3*c + 2)*(11*c + 1)
Let u(h) = 2*h**3 + 6*h**2 + 7*h. Let i(k) = 22*k**3 + 66*k**2 + 78*k. Let l(x) = -6*i(x) + 68*u(x). Let l(j) = 0. Calculate j.
-2, -1, 0
Factor -3/5*t**2 + 0*t + 3/5.
-3*(t - 1)*(t + 1)/5
Factor 0*s**2 + 1/2*s**4 + 0 + 1/2*s**5 + 0*s - s**3.
s**3*(s - 1)*(s + 2)/2
Let h = 0 - -12. Suppose 4*n + h = 7*n. Find x such that 0 - 4/5*x**n - 6/5*x**5 + 8/5*x**3 + 4/5*x**2 - 2/5*x = 0.
-1, 0, 1/3, 1
Let l(n) be the second derivative of -n**5/80 - n**4/12 - 5*n**3/24 - n**2/4 - 12*n. Factor l(i).
-(i + 1)**2*(i + 2)/4
Let c = 6061/30 - 202. Let q(t) be the second derivative of 0*t**2 + 2*t - 1/25*t**5 - 1/75*t**6 + 0*t**3 - c*t**4 + 0. Factor q(f).
-2*f**2*(f + 1)**2/5
Solve 2*v + 3*v**3 + 11*v**2 + v - 17*v**2 = 0 for v.
0, 1
Let p(u) = u**2 + u. Let x be p(1). Suppose -32*w**3 - 26 - 4*w + 22*w**x + 26 + 14*w**4 = 0. What is w?
0, 2/7, 1
Let u(l) be the third derivative of -l**7/210 + 7*l**6/120 - l**5/10 + 11*l**2. Factor u(a).
-a**2*(a - 6)*(a - 1)
Let r(t) = -t**5 - t**4 + t**3 - 1. Let o(q) = 5*q**5 + 3*q**4 - 5*q**3 + q**2 + 4. Let m(x) = -o(x) - 4*r(x). Determine j, given that m(j) = 0.
-1, 0, 1
Factor 12/7 + 2/7*p**3 + 8/7*p**2 - 22/7*p.
2*(p - 1)**2*(p + 6)/7
Let r(s) be the first derivative of -s**8/1680 + s**6/200 + s**5/150 - 7*s**2/2 + 2. Let x(c) be the second derivative of r(c). Factor x(m).
-m**2*(m - 2)*(m + 1)**2/5
Factor -3*h + 6*h**2 - 8*h**3 + h + 4*h**2.
-2*h*(h - 1)*(4*h - 1)
Let l be 7/5 + (-57)/(-95). Let c = 108 + -754/7. Determine o, given that c*o - 2/7*o**l + 0 = 0.
0, 1
Let k = -154/3 - -52. Let l(p) be the second derivative of 0 - 1/4*p**4 - 1/30*p**5 + 0*p**3 + 3*p + k*p**2 + 1/30*p**6. Suppose l(s) = 0. What is s?
-1, 2/3, 2
Suppose 1 = -5*t + 6. Factor t - 20*z - 1 + 20*z**3 + 21*z**2 + 4 - 25*z**4.
-(z - 1)*(z + 1)*(5*z - 2)**2
Let w(i) be the second derivative of i**7/105 - i**5/15 + i**3/3 + i**2/2 - 7*i. Let d(c) be the first derivative of w(c). What is o in d(o) = 0?
-1, 1
Let h(v) = 6*v**3 + 36*v**2 + 65*v + 55. Let c(z) = 2*z**3 + 12*z**2 + 22*z + 18. Let t(f) = 7*c(f) - 2*h(f). Factor t(r).
2*(r + 2)**3
Find w such that -1/4*w**5 + 3/4*w**4 + 3/4*w - 1/2*w**3 - 1/4 - 1/2*w**2 = 0.
-1, 1
Let r(s) be the first derivative of 0*s + 7 + 1/2*s**4 + 3/10*s**5 - 1/2*s**2 - 1/6*s**3. What is k in r(k) = 0?
-1, 0, 2/3
Let z(q) be the third derivative of -1/90*q**6 + 1/18*q**4 + 0 + 1/105*q**7 + 1/9*q**3 + 0*q + 7*q**2 - 2/45*q**5. Find n such that z(n) = 0.
-1, -1/3, 1
Let c = -41 - -985/24. Let k(h) be the third derivative of c*h**4 - 1/60*h**5 + 0 + 2*h**2 + 0*h + 0*h**3. Find x, given that k(x) = 0.
0, 1
Let k = 60 - 57. Let r(o) be the second derivative of -1/45*o**6 - 5/18*o**k + 2*o - 7/60*o**5 + 0 - 1/4*o**4 - 1/6*o**2. Factor r(b).
-(b + 1)**3*(2*b + 1)/3
Let d be (4/5)/((-4)/(-10)). Let 2*t + 3*t**2 + 2*t - 3*t - 2*t**d = 0. What is t?
-1, 0
Let u(n) be the first derivative of 3*n**5/20 + 3*n**4/16 + 3. Solve u(c) = 0.
-1, 0
Let t(o) = o**2 - 1. Let r(u) = 4*u**2 - u - 3. Let k = 7 - 5. Suppose 0 = 3*p, k*m + 6 - 2 = -4*p. Let z(a) = m*r(a) + 7*t(a). Determine q so that z(q) = 0.
1
Let r(p) be the first derivative of -4*p**2 - 4*p**3 - 3 - 2/5*p**5 - 2*p - 2*p**4. Suppose r(q) = 0. Calculate q.
-1
Let b(o) = 5*o**2 + o. Let p(k) = 11*k**2 + k. Let m(g) = 13*b(g) - 6*p(g). Factor m(u).
-u*(u - 7)
Let r(x) be the second derivative of 0*x**5 + 0 - 2*x - 1/180*x**6 + 0*x**2 + 0*x**4 - 1/6*x**3. Let q(t) be the second derivative of r(t). Factor q(s).
-2*s**2
Let v(s) be the first derivative of -3*s**4/32 + s**3/8 + 3*s**2/16 - 3*s/8 - 22. Solve v(c) = 0 for c.
-1, 1
Let 0*r**2 - 2/7*r**3 + 0 + 2/7*r = 0. Calculate r.
-1, 0, 1
Let z(s) be the first derivative of s**5 - 15*s**4/4 + 5*s**3 - 5*s**2/2 + 20. Suppose z(j) = 0. Calculate j.
0, 1
Suppose 3*t - 4 = 2*r - 1, -5*r = 2*t - 21. Suppose -r*y - y = -4. Solve 7*b + 0*b**2 + y - 3 - 5*b**2 = 0.
2/5, 1
Let b(i) = -12*i**5 + 32*i**4 - 16*i**3 - 24*i**2 + 30*i - 10. Let a(z) = -z + 1. Let q(n) = -2*a(n) - b(n). Factor q(r).
4*(r - 1)**3*(r + 1)*(3*r - 2)
Let w be (-80)/(-36) + 4/(-18). Factor 17*c**4 + 46*c**3 + 13*c + 0*c**4 + 5*c**4 + 5*c**5 + w + 32*c**2 - 8*c**3.
(c + 1)**4*(5*c + 2)
Let v(l) be the second derivative of l**5/4 + 5*l**4/6 - 14*l. Factor v(c).
5*c**2*(c + 2)
Factor 7/4*k**4 + 1/4*k**5 + 15/4*k**3 + 0*k + 0 + 9/4*k**2.
k**2*(k + 1)*(k + 3)**2/4
Let g = -8 + 13. Suppose 0 = -4*z + g*z. What is a in 1/2*a + 1/2*a**2 + z = 0?
-1, 0
Let r = 17 - 11. Factor -9*s + r*s**2 + 24*s - 4*s**3 - 11*s.
-2*s*(s - 2)*(2*s + 1)
Suppose 0 = -3*q + 5*q - 34. Suppose -2*f = 2*f - 5*b + 13, 4*f = -b + q. Solve -2/9*h**f - 4/9*h**2 + 0 - 2/9*h = 0 for h.
-1, 0
Let w(y) = -2*y**3 - 6*y**2 + 15. Let a(d) = -d**3 - 3*d**2 + 8. Suppose 3*v + v - 16 = 0. Let s(c) = v*w(c) - 7*a(c). Find t such that s(t) = 0.
-2, 1
Let u = -1/12 - -5/12. Let k(q) be the third derivative of 1/30*q**5 + 1/12*q**4 + 0 + q**2 - u*q**3 - 1/60*q**6 + 0*q. Factor k(o).
-2*(o - 1)**2*(o + 1)
Let x = -8 - -10. Factor -a + 3*a**3 + a**4 + 1 - 1 - 2 - 2*a + a**x.
(a - 1)*(a + 1)**2*(a + 2)
Let u(m) be the second derivative of 2/3*m**3 + 0*m**2 - 3*m + 1/2*m**4 + 1/10*m**5 + 0. Solve u(l) = 0.
-2, -1, 0
Let k be (-1)/2*(-14)/28. Suppose 1/4*o**2 - 1/4 - 1/4*o**3 + k*o = 0. Calculate o.
-1, 1
Let u be (14 + 2)/(-5 + -3 - -19). Determine s so that 0 - 2/11*s + 32/11*s**5 - 16/11*s**2 - 30/11*s**3 + u*s**4 = 0.
-1, -1/4, 0, 1
Let g be 1 + 1 - (-683)/(-300). Let f = -2/75 - g. Determine k so that 1/4*k**2 + 0 + f*k = 0.
-1, 0
Let s(a) be the second derivative of -1/48*a**4 + 1/8*a**3 - 1/4*a**2 + 0 - 2*a. Factor s(x).
-(x - 2)*(x - 1)/4
Suppose -6*l + 5*n + 10 = -5*l, 0 = -l + 2*n + 4. Let 0 + 2/3*d**4 - 4/3*d**3 + 0*d**2 + l*d + 2/3*d**5 = 0. What is d?
-2, 0, 1
Let u(i) be the third derivative of -i**6/30 + 2*i**5/15 + i**4/6 - 4*i**3/3 - 6*i**2. Solve u(j) = 0.
-1, 1, 2
Let i(j) be the second derivative of -j**7/1260 + j**6/