(u) + 6*z(u). Factor b(j).
j*(j - 1)*(j + 1)**2
Let d(q) be the first derivative of q**6/15 + 6*q**5/25 + q**4/5 + 3. Factor d(t).
2*t**3*(t + 1)*(t + 2)/5
Let g(j) be the third derivative of 0*j + 1/48*j**4 + 0 - 2*j**2 + 1/240*j**5 + 1/24*j**3. Find s, given that g(s) = 0.
-1
Let q(p) = -p**3 + 16*p**2 - 15*p + 2. Let c be q(15). Let j(b) be the second derivative of 0*b**3 - 2*b - 1/6*b**4 + b**c + 0. Factor j(t).
-2*(t - 1)*(t + 1)
Let u(r) = 10*r**5 - 3*r**4 + 3*r**3 - 6*r**2 + r + 9. Let q(z) = 0 - 81*z**3 + 80*z**3 + z**4 - z**5 - 1. Let k(c) = 21*q(c) + 3*u(c). Factor k(l).
3*(l - 1)*(l + 1)**3*(3*l - 2)
Suppose s = -3*s - 32. Let i be 6/s - 6/(-8). Factor 1/3*k - 2/3*k**2 + 1/3*k**3 + i.
k*(k - 1)**2/3
Let c(i) = -i**2 + 22*i + 11. Let w be c(23). Let a = w + 14. Factor -2/5*v**a - 2/5*v + 0.
-2*v*(v + 1)/5
Let w(l) be the third derivative of -l**6/60 - l**5/5 - 11*l**4/12 - 2*l**3 - 38*l**2. Let w(z) = 0. Calculate z.
-3, -2, -1
Let v be 3/20 - 1/(-4). Let p be ((-3)/(-5))/(30/20). Suppose -v*y**3 - 4/5*y**4 + 0 - p*y**5 + 0*y + 0*y**2 = 0. What is y?
-1, 0
Suppose f - 8 = 5*f. Let x = 5 + f. Find v such that 0*v**3 - 3*v**2 + x*v + v**4 - 3*v**3 + 2*v**4 + 0*v**4 = 0.
-1, 0, 1
Let z(r) = -r**2 - 2*r + 5. Let b be z(-3). Factor 6*u**3 - 2/9 - 6*u**2 + b*u.
2*(3*u - 1)**3/9
Let t(v) be the third derivative of -v**6/180 + v**5/18 - 2*v**4/9 + 4*v**3/9 + 3*v**2. Suppose t(q) = 0. Calculate q.
1, 2
Factor -4/7*u**2 + 4/7*u**3 + 0 + 0*u + 8/7*u**4.
4*u**2*(u + 1)*(2*u - 1)/7
Let a(f) be the third derivative of f**7/2415 + f**6/230 + 3*f**5/230 - 10*f**2. Determine j, given that a(j) = 0.
-3, 0
Let q = -295 - -591/2. Let -1/2*b**3 + q - 3/2*b + 3/2*b**2 = 0. Calculate b.
1
Let c be (95/(-30) + 3)/(1/(-4)). Let h(x) be the first derivative of -c*x**3 + 2 - 18*x + 6*x**2. Let h(m) = 0. What is m?
3
Let n be (-13 - -14) + (1 - 2). Let t(y) be the third derivative of 0 + n*y**4 + 0*y**3 + 0*y - 3*y**2 + 1/90*y**5 + 1/180*y**6. Let t(g) = 0. Calculate g.
-1, 0
Suppose 13 = 8*l - 3. Factor -s**l + 0*s + 0 - 1/2*s**3.
-s**2*(s + 2)/2
Suppose 4*x = -5*z + 54, -5*z + z = 8. Factor 4*h - x*h**3 + 5 + 16*h**4 - 33*h**2 + 12*h**5 + 3 + 9*h**2.
4*(h - 1)*(h + 1)**3*(3*h - 2)
Let i = 1 - -1. Suppose -2*b - v = -9, -i*b - b + 16 = 2*v. Find r, given that 26*r**2 - 18*r**b + 4 + 41*r**2 - 28*r = 0.
2/7
Let b(z) = -5*z + 38. Let w be b(7). Let f(s) be the third derivative of -1/12*s**5 + 3*s**2 + 0 + 0*s + 7/24*s**4 - 1/3*s**w. Factor f(t).
-(t - 1)*(5*t - 2)
Let q be 1 - (-2 + -3*1). Suppose 0*o = 3*o - q. Solve o*m**4 + 2*m**4 + 3*m**4 + 2*m**5 - 5*m**4 = 0 for m.
-1, 0
Let c be 3/(-6)*1*-6. Let n(g) be the first derivative of 1/16*g**4 + 0*g**2 + 1/12*g**c + 4 + 0*g. Suppose n(u) = 0. Calculate u.
-1, 0
Let r(c) be the first derivative of -c**7/420 + c**6/90 - c**5/60 + 5*c**3/3 + 3. Let j(m) be the third derivative of r(m). Suppose j(q) = 0. What is q?
0, 1
Suppose 0 = -0*g - 4*g + 28. Suppose -2 = -p, 7*o = 4*o + p + g. Solve b**2 + 2*b**o - b**3 + b**3 + b**4 = 0 for b.
-1, 0
Suppose -30 = -5*k - 5. Factor -1/2 + l**3 - l**2 - 3/2*l + 3/2*l**4 + 1/2*l**k.
(l - 1)*(l + 1)**4/2
Let o(q) be the second derivative of 7*q - 1/7*q**3 + 1/7*q**2 - 1/70*q**5 + 1/14*q**4 + 0. Determine h, given that o(h) = 0.
1
Let a(b) = b**2 - 2*b**2 + b**3 - 1 - b**2 + b. Let i be a(2). Find r such that -6*r**2 + 3*r**2 + 5*r - 2*r**3 - i - 7*r**3 = 0.
-1, 1/3
Let c(y) be the second derivative of 7*y**8/80 + 11*y**7/40 + 4*y**6/15 + y**5/10 - 2*y**3/3 - 2*y. Let x(a) be the second derivative of c(a). Factor x(p).
3*p*(p + 1)*(7*p + 2)**2
Suppose -4*i - 29 = -2*h + i, -5*i - 35 = -5*h. Let 1/3*f**h + 1/3*f**3 + 0 + 0*f = 0. What is f?
-1, 0
Suppose x = -3*x, 5*t - 4*x = 0. Let r be (-104)/(-468) - -2*(-16)/(-18). Let t*y - 2/11 + 2/11*y**r = 0. What is y?
-1, 1
Let u(z) be the second derivative of z**7/420 - z**6/360 - z**5/60 + z**4/24 - 2*z**3/3 + 5*z. Let m(w) be the second derivative of u(w). What is b in m(b) = 0?
-1, 1/2, 1
Let f(b) = b**2 + 40 + b**4 - 40. Let j(l) = -3*l**4 + 6*l**3 + 9*l**2. Let d(u) = 6*f(u) - j(u). Factor d(k).
3*k**2*(k - 1)*(3*k + 1)
Let i(v) be the third derivative of v**5/150 + v**4/60 - 2*v**3/15 + 8*v**2. Solve i(n) = 0 for n.
-2, 1
Factor -w - 25/2*w**4 - 3/2*w**2 + 21/2*w**3 + 9/2*w**5 + 0.
w*(w - 1)**3*(9*w + 2)/2
Let u(i) = i**4 - i**3 - i**2 + i. Let y(f) = 4*f**4 - 2*f**3 - 6*f**2 + 2*f + 2. Let j(x) = 3*u(x) - y(x). Factor j(s).
-(s - 1)**2*(s + 1)*(s + 2)
Determine f so that -13*f**2 - 1331*f - 36 + 1271*f - 15*f**2 - 4*f**3 = 0.
-3, -1
Let z be ((-16)/60)/((-46)/(-3)). Let i = 48/115 + z. Suppose -1/5*x**2 - i + 3/5*x = 0. Calculate x.
1, 2
Let t(d) = 5*d**3 + 29*d**2 + 31*d - 64. Let c(n) = n**3 + n**2 - n. Let x(l) = c(l) - t(l). Find z, given that x(z) = 0.
-4, 1
Suppose 5*z = -z. Let z + 2/3*o**2 - 2/3*o**4 + 2/3*o**3 - 2/3*o = 0. What is o?
-1, 0, 1
Suppose -2*z + 24 = z + 4*k, 0 = -2*k + 6. Let r(t) = t**2 - 2*t - 5. Let i be r(z). Find v such that 2*v**3 - 6*v**3 + 6*v**i + 2*v**4 = 0.
-1, 0
Let n(i) be the third derivative of 15*i**8/112 - i**7/70 - 3*i**6/10 + i**5/5 + 12*i**2 - 1. Suppose n(a) = 0. Calculate a.
-1, 0, 2/5, 2/3
Let a(s) be the first derivative of 1 - 1/8*s**4 + 0*s**2 - 1/2*s**3 + 2*s. Factor a(m).
-(m - 1)*(m + 2)**2/2
Let i = -2 - -5. Factor 24*y - 50*y**i - 4 - 18*y**2 - 3*y**2 + y**3.
-(y + 1)*(7*y - 2)**2
Suppose 5*y + 6 = 26. Find p, given that p**4 - y*p**4 + 4*p**2 - 2 + p**4 = 0.
-1, 1
Let l(t) be the second derivative of 5*t**7/42 - t**6/6 - t**5/2 + 5*t**4/6 + 5*t**3/6 - 5*t**2/2 - 5*t. Solve l(h) = 0 for h.
-1, 1
Let t(w) = -w**3 - 7*w**2 - 8*w - 6. Let z be t(-5). Let n = 18 + z. Solve 0*m + 3/5 - 3/5*m**n = 0 for m.
-1, 1
Let r(o) be the second derivative of -o**5/10 - 2*o**4/9 + 17*o**3/9 + 2*o**2 + o - 19. Factor r(t).
-2*(t - 2)*(t + 3)*(3*t + 1)/3
Suppose 0*r - 6 = -2*r. Factor -2*h**3 + 3*h**4 + 4*h**2 - h**4 - 9*h**2 + 2*h**5 + r*h**2.
2*h**2*(h - 1)*(h + 1)**2
Let t(j) be the first derivative of -2/7*j**3 - 6 - 2/7*j - 1/14*j**4 - 3/7*j**2. Find l, given that t(l) = 0.
-1
Let d(k) be the third derivative of -k**9/6048 + k**8/1680 - k**6/360 + k**5/240 + k**3/6 - 4*k**2. Let a(q) be the first derivative of d(q). Factor a(u).
-u*(u - 1)**3*(u + 1)/2
Suppose 5*p - 2*d - 30 = 0, 8*p - 4*d - 12 = 4*p. Let j = -6 + p. Let 5 + a**j - 5 - 2*a = 0. Calculate a.
0, 2
Find u such that 3*u - 9/2*u**4 - 2*u**5 - u**3 + 1/2 + 4*u**2 = 0.
-1, -1/4, 1
Let r(q) be the second derivative of 3*q**5/40 - 3*q**4/8 - 9*q**3/4 - 15*q**2/4 + 9*q. Determine z, given that r(z) = 0.
-1, 5
Let g(u) be the second derivative of u**5/80 + 8*u. Factor g(k).
k**3/4
Let s be 11/7 - (-3 - -4). Let r = s + -1/14. Determine v, given that -3/2*v**2 + v + r = 0.
-1/3, 1
Suppose -5*y = -0*z - 4*z + 20, 8 = -2*y. Solve -2/7*g**2 + 0 + z*g + 2/7*g**5 - 6/7*g**4 + 6/7*g**3 = 0 for g.
0, 1
Factor 0 - 1/4*k**2 + 5/4*k.
-k*(k - 5)/4
Let k(p) = -p**2 + 11*p + 2. Let w be k(11). Factor 0 - 2/3*x + 2/3*x**w.
2*x*(x - 1)/3
Let r(b) be the third derivative of 5*b**7/168 + 11*b**6/24 + 47*b**5/20 + 11*b**4/3 + 8*b**3/3 - 3*b**2. Factor r(a).
(a + 4)**2*(5*a + 2)**2/4
Suppose -3*h = -1 - 5. Let 2*m**5 - m**4 - m**3 + m - h*m**3 + 0*m**3 + m**2 = 0. Calculate m.
-1, -1/2, 0, 1
Let q be (-28)/35 - 12/10. Let t(w) = -5*w**2 + 2. Let j(l) = 19*l**2 + l - 9. Let x(y) = q*j(y) - 9*t(y). Solve x(p) = 0 for p.
0, 2/7
Let v(q) be the first derivative of -q**6/18 + q**4/2 - 8*q**3/9 + q**2/2 - 11. Factor v(h).
-h*(h - 1)**3*(h + 3)/3
Factor 0*y**4 + 5*y**4 - 3*y**4 - 6 - 12*y**2 - 16*y.
2*(y - 3)*(y + 1)**3
Let r(s) be the third derivative of -s**6/30 + s**5/5 - s**4/3 - 4*s**2. Factor r(v).
-4*v*(v - 2)*(v - 1)
Let u be (-3)/(-2 - 3/(-3)). Suppose -3*w - 4*o = -18, -3*o + 9 = u*w - 2*o. Factor -j - 8*j**3 - 16*j**4 - 16*j**3 - 7*j**2 - w*j**2.
-j*(j + 1)*(4*j + 1)**2
Let w(m) be the second derivative of -m**7/84 - m**6/20 - m**5/40 + m**4/8 + m**3/6 + 17*m. What is h in w(h) = 0?
-2, -1, 0, 1
Suppose 16*j - 12 = 10*j. Determine i so that -2/11*i**4 + 0*i**j + 0 + 0*i + 2/11*i**3 = 0.
0, 1
Suppose -17 = 2*n + a, 4*n - 5*a = -0*n - 55. Let p = 10 + n. Factor 0*u**2 + 1/3*u**3 + p - 1/3*u.
u*(u - 1)*(u + 1)/3
Let r(w) be the first derivative of 4*