- 1)
Let k(j) be the second derivative of j**8/672 - j**6/240 + 5*j**2/2 - 7*j. Let z(y) be the first derivative of k(y). Factor z(u).
u**3*(u - 1)*(u + 1)/2
Suppose 0 = 2*d + 3*d. Let b = d + 3. Factor 2*m**2 - m**3 + b*m**2 - 4*m**2.
-m**2*(m - 1)
Suppose -2*x**4 + 10*x**2 + x**4 - 9*x**2 = 0. Calculate x.
-1, 0, 1
Let q = 17 + -13. Let 0 + 2/5*o + 6/5*o**q - 2/5*o**3 - 6/5*o**2 = 0. What is o?
-1, 0, 1/3, 1
Let x be (-89)/10 + 10 - (1 - 0). Let r(u) be the second derivative of 5/4*u**4 - x*u**6 - 4*u + u**3 + 0*u**2 + 9/20*u**5 - 1/14*u**7 + 0. Factor r(j).
-3*j*(j - 2)*(j + 1)**3
Let w be ((-1)/6)/(-1)*(4 + -1). Let 1/2*p**2 + p + 0 - w*p**3 = 0. Calculate p.
-1, 0, 2
Suppose -3*g + 3*l + 80 = -184, 4*g - 307 = -5*l. Let a = g - 329/4. Factor -a*m**2 + 0 + 1/2*m + 1/4*m**3.
m*(m - 2)*(m - 1)/4
Let h(t) be the third derivative of t**6/120 + t**5/20 - t**4/4 - 4*t**3/3 - 45*t**2. Factor h(y).
(y - 2)*(y + 1)*(y + 4)
Let u(c) be the third derivative of -3*c**7/10 + 97*c**6/40 - 117*c**5/20 + 47*c**4/8 - 3*c**3 + 21*c**2. What is r in u(r) = 0?
2/7, 1/3, 1, 3
Let d(a) be the third derivative of 2/21*a**3 + 0 + 0*a + 5/84*a**4 + 7*a**2 + 2/105*a**5 + 1/420*a**6. Determine j, given that d(j) = 0.
-2, -1
Let 2/5*q**4 + 0 + 6/5*q**3 - 2*q**2 - 2/5*q**5 + 4/5*q = 0. Calculate q.
-2, 0, 1
Let v = 691/1332 + -11/148. Factor 16/9 - 8/9*p + 2/9*p**3 - v*p**2.
2*(p - 2)**2*(p + 2)/9
Let b = -1600 - -8001/5. Find k, given that b*k**2 + 0 + 1/5*k = 0.
-1, 0
Let s = 2/2954413 - -9968174360/22308772563. Let d = -2/839 + s. What is p in 2/9 + 2/9*p**4 - d*p**2 + 0*p**3 + 0*p = 0?
-1, 1
Let s(z) = 3*z**3 + 19*z**2 + 25*z + 9. Let h(d) = 6*d**3 + 39*d**2 + 51*d + 18. Let o(w) = 4*h(w) - 9*s(w). Factor o(g).
-3*(g + 1)**2*(g + 3)
Suppose 17*r**4 + 17*r**2 + 13*r**2 + 25*r**3 - 12*r**4 = 0. Calculate r.
-3, -2, 0
Suppose 5*f + 5*r = 2*r + 31, -2*f = r - 12. Factor -2*l**f - l**2 - l**2 + 4*l**4 - 2*l**2 + 2*l.
-2*l*(l - 1)**3*(l + 1)
Let l(s) = -8*s**3 + 2*s**2 - 2*s + 6. Let v(x) = -x**3 + x**2 + 1. Let m(d) = -l(d) + 6*v(d). Factor m(c).
2*c*(c + 1)**2
Suppose 7 = 4*x - 5. What is a in -2*a**3 + a**3 - 4*a**2 + x*a**2 + 0*a**2 = 0?
-1, 0
Solve 1/3*l - 1/6*l**2 + 1/2 = 0 for l.
-1, 3
Let r(f) = 10*f**2 - 4*f + 7. Suppose -20 = 4*y + d + 4, 15 = -5*y - 5*d. Let g(c) = -9*c**2 + 3*c - 6. Let j(q) = y*g(q) - 6*r(q). Factor j(x).
3*x*(x + 1)
Let l(v) be the second derivative of v**9/22680 + 5*v**4/6 - 7*v. Let z(d) be the third derivative of l(d). Solve z(x) = 0.
0
Suppose 0*v - 5*m = -v + 8, -4*m - 7 = -v. Suppose -2*z - v*z = -10. Factor -3*h + 5*h**2 - 4*h**2 + 3*h**3 + 2*h**z - 3*h**4.
-3*h*(h - 1)**2*(h + 1)
Let b(u) be the second derivative of u**7/21 + u**6/5 + 3*u**5/10 + u**4/6 + 8*u. Suppose b(z) = 0. What is z?
-1, 0
Solve 240/13*y - 450/13 - 32/13*y**2 = 0.
15/4
Let o = 806/63 + -88/7. Find z such that o + 0*z - 2/9*z**2 = 0.
-1, 1
Let t = -302 - -705. Let g = t + -2813/7. Let -8/7 - 2/7*z**2 + g*z = 0. What is z?
2
Let j(o) be the first derivative of o**4/2 + 10*o**3/3 + 3*o**2 - 18*o + 16. Factor j(y).
2*(y - 1)*(y + 3)**2
Let v(g) = 0*g + g + 0*g. Let w be v(3). Solve 8*i**2 - 2*i**w - 5 - 8*i + 5 = 0.
0, 2
Let a(t) = -5 + 1 + 5*t - t**2 + t**2 - t**2. Let p be a(3). Factor -2/3*g + 2/3*g**p + 0.
2*g*(g - 1)/3
Let k(m) be the first derivative of m**8/560 - m**6/120 - 2*m**3 - 1. Let x(c) be the third derivative of k(c). Factor x(u).
3*u**2*(u - 1)*(u + 1)
Suppose 13 = 3*x - 2*s - 12, 5*x - 5*s - 50 = 0. Suppose -3*v + 2*t = -10, 3*v - 1 = x*t + 15. Factor 2/3*k**4 + 0*k**v - 2/3 + 4/3*k**3 - 4/3*k.
2*(k - 1)*(k + 1)**3/3
Let j = -2 + 2. Let x(z) be the third derivative of -1/24*z**3 - 1/240*z**5 + 0*z + j - 1/48*z**4 + 2*z**2. Factor x(b).
-(b + 1)**2/4
Suppose 4*p + 2*d + 2*d = 32, -5*d + 8 = -3*p. Determine x, given that -x**2 - p + 2 + 6*x - 7 = 0.
3
Let w(c) = -10*c**5 - 2*c**4 + 10*c**3 - 7*c**2 - 9. Let q(t) = -t**5 + t**3 - t**2 - 1. Let l(s) = 36*q(s) - 4*w(s). Find a such that l(a) = 0.
-2, -1, 0, 1
Let r(w) be the first derivative of -w**7/140 - w**6/240 + w**5/15 - w**4/12 + w**2/2 - 3. Let u(a) be the second derivative of r(a). Find v such that u(v) = 0.
-2, 0, 2/3, 1
Suppose 0 = -0*y + 3*y. Let 2*g**5 + 2*g + 0*g**5 - 4*g**3 + y*g = 0. What is g?
-1, 0, 1
Let n = -19 - -6. Let d(u) = -15*u**3 + 2*u - 13. Let k(l) = -7*l**3 + l - 6. Let t = -2 + 8. Let p(b) = n*k(b) + t*d(b). Factor p(z).
z*(z - 1)*(z + 1)
Factor -3/4*y**4 + 0*y**3 - 6*y + 9/4 + 9/2*y**2.
-3*(y - 1)**3*(y + 3)/4
Let d(i) be the third derivative of i**6/40 + i**5/20 - i**4/4 - 11*i**2. Find u such that d(u) = 0.
-2, 0, 1
Let c = -464 - -5122/11. Factor 14/11*x + c*x**2 + 4/11 + 10/11*x**3 + 2/11*x**4.
2*(x + 1)**3*(x + 2)/11
Factor 0 + 0*y + 2/7*y**2 - 2/7*y**3.
-2*y**2*(y - 1)/7
Let x(q) be the first derivative of -q**6/3 + 3*q**5/5 - q**4/4 - 6. Factor x(v).
-v**3*(v - 1)*(2*v - 1)
Let w(x) = -15*x - 133. Let r be w(-9). Determine z so that 0 - 10/3*z**r - 2/3*z = 0.
-1/5, 0
Let l = -833123/13492 - 2/3373. Let z = l - -62. What is y in -1/2*y - z - 1/4*y**2 = 0?
-1
Factor 7*i**2 + 12*i + 2 - 11*i**2 + 14.
-4*(i - 4)*(i + 1)
Factor 0*m**2 - 2/5*m**3 + 0*m + 0 + 2/5*m**4.
2*m**3*(m - 1)/5
Let i(q) be the second derivative of q**5/2 + q**4/3 - 20*q**3/3 - 8*q**2 + 6*q. Suppose i(f) = 0. Calculate f.
-2, -2/5, 2
Suppose -89 + 17 = 3*z. Let c be (-16)/z*(1 - -2). Factor -5/2*x**3 + 2*x**4 + 0*x + 0 + x**c - 1/2*x**5.
-x**2*(x - 2)*(x - 1)**2/2
Factor -3*o + 0*o + 7*o**2 + o.
o*(7*o - 2)
Suppose 0 = -4*u + 2*v, 5*u + 5*v - 3*v = 0. Let m(w) be the second derivative of 0 - 1/18*w**4 + 0*w**5 + 0*w**3 + u*w**2 - 3*w + 1/45*w**6. Factor m(y).
2*y**2*(y - 1)*(y + 1)/3
Let s(o) = -4*o**5 - 20*o**4 - 48*o**3 - 46*o**2 - 20*o - 4. Let n(t) = -t**4 + t**3 - t. Let m(d) = 2*n(d) + s(d). Suppose m(j) = 0. Calculate j.
-2, -1, -1/2
Let v(q) = -10*q**2 + 26*q + 1. Let a(u) = -u**3 + u + 1. Let p(d) = -2*a(d) + 2*v(d). Factor p(g).
2*g*(g - 5)**2
Let i(s) be the first derivative of 1/4*s**4 - 1/6*s**6 + 1/5*s**5 + 0*s - 1/3*s**3 - 3 + 0*s**2. Factor i(h).
-h**2*(h - 1)**2*(h + 1)
Let n(q) be the second derivative of -27*q**5/4 + q**4/2 + 26*q**3/9 - 4*q**2/3 - 17*q. Factor n(j).
-(5*j + 2)*(9*j - 2)**2/3
Let c = 18 - -1. Suppose -6*b - 7 + c = 0. Find q such that 1/3*q**b - 1/3*q + 0 - 1/3*q**4 + 1/3*q**3 = 0.
-1, 0, 1
Let q be -4 - (-2 + (1 - 1)). Let v = 4 + q. Factor t**2 + t**2 + t**4 - 3*t**v.
t**2*(t - 1)*(t + 1)
Suppose -i + 7 = 4*o - 2*o, -5*o = -4*i - 37. Factor 6*b**2 + 0*b**o + 3*b**5 + 1 - 5*b + 2*b**3 + 0*b**3 - 7*b**4 + 0*b**5.
(b - 1)**3*(b + 1)*(3*b - 1)
Suppose -8 = -n + 3*n - 3*l, 22 = 3*n + 4*l. Factor 0*s**n + 3*s**3 - 4*s**3 - 3*s**2 + 4*s**3.
3*s**2*(s - 1)
Let s(o) be the third derivative of o**8/56 + o**7/30 + o**6/60 + 2*o**2. Factor s(z).
z**3*(2*z + 1)*(3*z + 2)
Suppose -2*n - 3*m + 8 = 0, 3*n - 4*m = -3*m + 12. Determine o, given that 0 - 2/9*o**2 + 0*o + 2/9*o**n + 2/9*o**5 - 2/9*o**3 = 0.
-1, 0, 1
Let m(a) be the first derivative of -3*a**2 + 10*a - 2. Let k(x) = x**2 - x - 1. Suppose -5*h + 10 = -0*h. Let i(d) = h*k(d) + m(d). Factor i(c).
2*(c - 2)**2
Let l(a) = -a**3 - a**2 - a. Let b(c) = -16*c**2 + 20*c - 10. Let x(k) = -b(k) + 2*l(k). Suppose x(i) = 0. Calculate i.
1, 5
Let v(s) = 2*s**4 - 12*s**2 + 12*s - 2. Let r(a) = a - 1. Let k(g) = -4*r(g) - v(g). Solve k(n) = 0 for n.
-3, 1
Let r(t) be the first derivative of t**4/48 - t**3/12 + t**2/8 - 2*t + 2. Let o(s) be the first derivative of r(s). Factor o(y).
(y - 1)**2/4
Let a(h) be the third derivative of -h**5/180 - h**4/9 - 8*h**3/9 - 15*h**2. Factor a(t).
-(t + 4)**2/3
Let x(g) be the first derivative of -4 + 0*g + 6*g**4 + 48/5*g**5 - 7*g**3 + 3/2*g**2. Factor x(b).
3*b*(b + 1)*(4*b - 1)**2
Suppose 1/4*w**3 + 1/4*w**2 - 1/4*w**5 + 0 + 0*w - 1/4*w**4 = 0. Calculate w.
-1, 0, 1
Suppose 1 + k + 3 - 7*k + k**2 + 10*k = 0. Calculate k.
-2
Suppose 3*k + 3*z - 18 = 0, 0 = 3*k - 2*k - z - 4. What is q in -2*q**5 - 2*q**5 + 2*q**k + q**5 + q**4 + q**3 - q**2 = 0?
-1, 0, 1
Let j(n) be the third derivative of -n**5/420 + n**4/168 + n**3/21 - 10*n**2. Factor j(f).
-(f - 2)*(f + 1)/7
Let u(a) = -a**2 - 5*a + 8. Let w be u(-6). Suppose w*t + t = 0. Determine i, given that 2/11*i**2 + 0*i + t = 0.
0
Suppose 4*