h) be the second derivative of h**4/12 - 11*h**3/6 + 2*h**2 + 2*h. Let u be r(11). Factor 0 - 1/4*y + 0*y**3 + 1/4*y**5 - 1/2*y**u + 1/2*y**2.
y*(y - 1)**3*(y + 1)/4
Factor 12*w**2 + 16*w - 6*w**3 + 2*w**3 - 2*w**4 - 2*w**3.
-2*w*(w - 2)*(w + 1)*(w + 4)
Let x(g) be the third derivative of g**6/120 - g**5/15 - 23*g**2. Solve x(z) = 0.
0, 4
Let r = -2/251 + 255/502. What is w in 1/4*w**3 + 5/4*w - w**2 - r = 0?
1, 2
Let g be (-482)/(-12111)*(-18)/(-4). Let p = 1/367 + g. Find l such that p*l**2 + 2/11*l**4 + 0*l + 0 + 4/11*l**3 = 0.
-1, 0
Let j = -9 + 7. Let p be 9/12 - j/4. Factor 3/4*q + 1/2 - p*q**2.
-(q - 1)*(5*q + 2)/4
Let t = 1/84 + 53/252. Let 2/9*f**5 + 0*f - 2/9*f**4 + 2/9*f**2 - t*f**3 + 0 = 0. What is f?
-1, 0, 1
Let x(g) be the first derivative of g**6/30 - g**5/10 + g**4/12 + 3*g + 3. Let p(r) be the first derivative of x(r). Factor p(j).
j**2*(j - 1)**2
Find p, given that -15*p**2 + 0*p**2 - 43*p**3 - 10*p + 89*p**3 - 51*p**3 = 0.
-2, -1, 0
Let t(z) be the first derivative of 7 + 0*z + 2/39*z**3 - 1/13*z**2. What is v in t(v) = 0?
0, 1
Let g = 109 - 107. Let x(b) be the first derivative of -1/4*b**4 + 1/2*b**2 - g*b + 2/3*b**3 - 2. Suppose x(m) = 0. What is m?
-1, 1, 2
Let f be (-2 - 0)/(-2)*2. Factor -2*m**2 + 0*m**2 + 2*m**2 + 1 - m**f.
-(m - 1)*(m + 1)
Let t(s) = -s**3 - 6*s**2 + 2. Let k be t(-6). Solve -18 + k*l**2 + 18 + l**3 = 0 for l.
-2, 0
Suppose 3*l - 12 = 66. Let v = l + -23. Factor -1/4*u**v - 3*u + 2 + 3/2*u**2.
-(u - 2)**3/4
Let k = -44 + 65. Let a be 6*1*7/k. Factor 1/2*h**4 + 0 - 1/2*h**3 - 1/2*h**a + 1/2*h.
h*(h - 1)**2*(h + 1)/2
Let o(s) be the second derivative of 6*s**7/7 - 12*s**6/5 - 7*s**5/5 + 4*s**4 + 8*s**3/3 - 2*s. Find n such that o(n) = 0.
-2/3, -1/3, 0, 1, 2
Let q(p) = 2*p**3 + 11*p**2 + 12*p - 1. Let o be ((-6)/(-9))/(4/(-6)). Let a(w) = w**3 + w**2 + 1. Let b(j) = o*a(j) - q(j). What is u in b(u) = 0?
-2, 0
Let h(u) be the first derivative of -4*u**3/3 - 8*u**2 - 16*u + 11. Let h(f) = 0. Calculate f.
-2
Let v(f) be the first derivative of -2/3*f**3 + 0*f**2 + 0*f**5 + 1/180*f**6 + 0*f - 1/12*f**4 + 1. Let w(q) be the third derivative of v(q). Factor w(z).
2*(z - 1)*(z + 1)
Suppose 6 = -6*y + 18. Let h(z) be the third derivative of -1/120*z**6 + 0*z**3 + 2*z**y - 1/24*z**4 + 0*z - 1/30*z**5 + 0. Determine a so that h(a) = 0.
-1, 0
Let z(i) be the first derivative of -i**3/3 + i**2/2 - 15. Let z(s) = 0. Calculate s.
0, 1
Let l(o) be the first derivative of 2*o**3/51 - 6*o**2/17 + 18*o/17 + 31. Factor l(b).
2*(b - 3)**2/17
Let w be 4 + (-5 + 7)*-2. What is q in w - 4/7*q**4 + 0*q + 4/7*q**2 + 2/7*q**5 - 2/7*q**3 = 0?
-1, 0, 1, 2
Let a(u) be the third derivative of 0*u + 0*u**4 + 0*u**3 - 1/60*u**5 + 0 - 2*u**2. Factor a(m).
-m**2
Let m(y) be the first derivative of 2*y**6/3 + 4*y**5/5 - y**4 - 4*y**3/3 - 10. Let m(k) = 0. Calculate k.
-1, 0, 1
Let a be ((-21)/18 + 1)*-4. Find k such that 0 - a*k**3 + 2/3*k**2 + 0*k = 0.
0, 1
Find v, given that 7/2*v**2 - v + 0 - 2*v**4 + 5/2*v**3 = 0.
-1, 0, 1/4, 2
Let v be 2/5 - (-48)/30. Let z(g) be the first derivative of 8/5*g**5 + 5/2*g**4 + 0*g - 2*g**v - 14/3*g**3 - 2. Factor z(y).
2*y*(y - 1)*(y + 2)*(4*y + 1)
Let l be (0 - (0 - -1))*0. Factor 0 - 2/11*k**2 + 2/11*k**4 + 0*k + l*k**3.
2*k**2*(k - 1)*(k + 1)/11
Let s(q) = -2*q**3 + 10. Let t(a) = a**3 + a**2 - a + 1. Let v be t(-2). Let i(k) = -k + 1. Let b(h) = v*s(h) + 6*i(h). Factor b(c).
2*(c - 2)*(c + 1)**2
Let w(p) = -3*p**4 + 6*p**3 + 4*p**2 - 5*p + 5. Let g(l) = l**4 - 3*l**3 - 2*l**2 + 2*l - 2. Let f(q) = 5*g(q) + 2*w(q). Solve f(v) = 0.
-2, -1, 0
Let q(i) be the second derivative of i**4/4 - 3*i**2/2 + 11*i. Factor q(u).
3*(u - 1)*(u + 1)
Let v be 1/1*-1*-3. Factor 3*o - v*o**4 + 0*o + 9*o**3 - 9*o**2 + 0*o.
-3*o*(o - 1)**3
Suppose 2*z - 9 + 9 - 7*z**2 + 5*z**3 = 0. What is z?
0, 2/5, 1
Suppose -v**3 - 4/9*v**5 - 11/9*v**4 + 1/9*v + 0 - 1/9*v**2 = 0. Calculate v.
-1, 0, 1/4
Let m = 179269 - 34060829/190. Let x = m + 2/95. Suppose 0*b**4 - 9/4*b + 3/2*b**2 - 3/4*b**5 + 3*b**3 - x = 0. What is b?
-1, 1, 2
Let s(b) = -b - 1. Let c be s(-1). Let z(x) be the first derivative of 0*x + c*x**2 - 4/3*x**3 + 3 - 1/2*x**4. Determine v, given that z(v) = 0.
-2, 0
Let r(n) = -5*n**2 - 19. Let u(p) = -2*p**2 - 10. Let q(b) = -6*r(b) + 13*u(b). Factor q(v).
4*(v - 2)*(v + 2)
Factor -3*z**5 - 12*z**2 - 12*z**4 - 3*z + 83 - 18*z**3 - 83.
-3*z*(z + 1)**4
Let z = -218 + 218. Factor z + 1/2*v**2 - 1/2*v.
v*(v - 1)/2
Let r(a) = a**3 - 6*a**2 - 11*a. Let d(k) = -2*k**3 + 6*k**2 + 12*k. Let f(n) = -2*d(n) - 3*r(n). Factor f(v).
v*(v + 3)**2
Let z(p) be the third derivative of -2*p**5/5 + 7*p**4/6 - 2*p**3/3 - 14*p**2. Determine b so that z(b) = 0.
1/6, 1
Suppose -4*y + 10 = c, -4*y + 18 = -7*c + 12*c. Determine i so that 3/5*i**3 - 3/5*i**y - 3/5*i + 0 + 3/5*i**4 = 0.
-1, 0, 1
What is x in -2/5*x**3 + 8/5*x**2 + 4/5 - 2*x = 0?
1, 2
Let n be ((-3)/(-6))/((-5)/150). Let b = 18 + n. What is l in 0*l - 3/4*l**4 - 3/2*l**b - 3/4*l**2 + 0 = 0?
-1, 0
Let m(v) be the third derivative of -v**7/630 - v**6/180 - v**5/180 + 10*v**2. Factor m(t).
-t**2*(t + 1)**2/3
Let p(a) be the third derivative of -a**5/240 + a**4/96 - 73*a**2. Factor p(o).
-o*(o - 1)/4
Let v(i) be the second derivative of 0 + 6*i - 1/48*i**4 + 0*i**2 + 1/24*i**3. Let v(w) = 0. What is w?
0, 1
Let j = -7 + 7. Let v be j/(1 + (2 - 5)). Factor -3 - 9*g - 3*g**2 - 9 - 3*g + v*g.
-3*(g + 2)**2
Factor -1/2 - 2/3*c - 1/6*c**2.
-(c + 1)*(c + 3)/6
Let n = 25/76 + -3/38. Suppose 3*y - 3*x + 6 = 0, -x = -3*y - 1 - 1. Factor -1/4*c**2 + y + n*c**3 + 0*c.
c**2*(c - 1)/4
Factor -917*k**2 + 2*k - 3*k**3 + 916*k**2 + k**4 + k**3.
k*(k - 2)*(k - 1)*(k + 1)
Let y(o) = -o**5 - 8*o**4 - 9*o**3 - o**2 + 7*o + 3. Let m(h) = -6*h**5 - 47*h**4 - 53*h**3 - 5*h**2 + 42*h + 18. Let d(c) = 6*m(c) - 34*y(c). Factor d(u).
-2*(u - 1)*(u + 1)**3*(u + 3)
Factor -4*n**4 - 4/3 - 6*n - 32/3*n**2 - 2/3*n**5 - 28/3*n**3.
-2*(n + 1)**4*(n + 2)/3
Suppose 0 = -5*f - 7 - 23. Let a be f/(-21) + (-8)/(-21). Find u, given that 0*u + 2/3*u**3 + a*u**2 + 0 = 0.
-1, 0
Let n(k) be the first derivative of -7*k**4/10 + 46*k**3/15 - 6*k**2/5 + 7. Determine f, given that n(f) = 0.
0, 2/7, 3
Let x(t) be the second derivative of -5*t + 0*t**2 - 1/3*t**3 + 1/3*t**4 + 0 - 1/10*t**5. Factor x(r).
-2*r*(r - 1)**2
Let h(p) be the third derivative of p**9/756 - p**7/70 - p**6/45 - 5*p**3/3 - 7*p**2. Let q(s) be the first derivative of h(s). Factor q(f).
4*f**2*(f - 2)*(f + 1)**2
Let z(a) be the third derivative of -a**6/180 + a**5/30 - 4*a**3/9 + 12*a**2. Factor z(q).
-2*(q - 2)**2*(q + 1)/3
Factor 5/2*k**2 - 2 - 4*k.
(k - 2)*(5*k + 2)/2
Let u be 3/(-60)*25/(-10). Let p(f) be the first derivative of 0*f**3 - u*f**2 + 1 + 1/16*f**4 + 0*f. Factor p(a).
a*(a - 1)*(a + 1)/4
Suppose -l - 5*l = 0. Let y(k) be the second derivative of 1/10*k**5 + 1/6*k**4 + 0*k**3 + l + k + 0*k**2. Factor y(b).
2*b**2*(b + 1)
Suppose q - 4 = -q. Let n be (q/(-10))/((-4)/30). Factor n*i - 1/2*i**2 + 0.
-i*(i - 3)/2
Let z be 179/924 - 4/22. Let w(c) be the second derivative of 2*c + 0*c**2 + z*c**7 - 1/24*c**4 + 3/40*c**5 + 0*c**3 + 0 - 1/20*c**6. Factor w(d).
d**2*(d - 1)**3/2
Let u be (-1)/(-5)*(-9 - -10). Let w(l) be the second derivative of 0 + 4/75*l**6 + u*l**4 + 9/50*l**5 + 0*l**2 + 2*l + 1/15*l**3. Factor w(j).
2*j*(j + 1)**2*(4*j + 1)/5
Let g(w) = -56*w**2 - 144*w + 192. Let i(k) = -k**3 - 55*k**2 - 143*k + 193. Let o(r) = 3*g(r) - 4*i(r). Factor o(z).
4*(z - 1)*(z + 7)**2
Let i = 12 - 10. Let 21*h**5 + i*h**4 - 22*h**5 - 4*h**3 + 3*h**3 = 0. Calculate h.
0, 1
Factor -5*f + 6*f**4 + 5*f**3 + 9*f**2 - f**4 + 6*f**2 - 20*f**3.
5*f*(f - 1)**3
Solve 50*v**2 + 26*v**3 - 19*v**3 - 8*v**3 - 60*v**4 - 25*v**5 + 10 - 19*v**3 + 45*v = 0 for v.
-1, -2/5, 1
Let t(j) = 32*j**3 + 9*j**2 - 10*j + 8. Let x(m) = 129*m**3 + 36*m**2 - 39*m + 33. Let n be 18/9 - -19*1. Let k(u) = n*t(u) - 5*x(u). Factor k(y).
3*(y + 1)*(3*y - 1)**2
Let u(z) = z**2 - 16*z - 49. Let j(b) = 6*b**2 - 81*b - 245. Let x(l) = 4*j(l) - 22*u(l). Factor x(n).
2*(n + 7)**2
Solve 2/9*s**3 + 0*s**2 - 2/9*s + 0 = 0.
-1, 0, 1
Let x(v) be the second derivative of 0*v**2 + 0 + 3*v - 1/20*v**5 - 1/6*v**4 + 1/42*v**7 + 1/15*v**6 + 0*v**3. Find q such that x(q) = 0.
-2, -1, 0, 1
Suppose -3*i = -