- 7. Factor p(k).
-4*(k - 1)*(k + 1)**2/7
Suppose 0*r = 3*r. Suppose 2*v**3 - 4*v**3 + 8*v**2 + r*v**2 = 0. What is v?
0, 4
Let g(n) be the second derivative of -n**4/32 - n**3/16 + 8*n. Factor g(h).
-3*h*(h + 1)/8
Let i = -2 - -2. Solve i*s**3 + s**5 + 6*s**4 + s**5 + 6*s**3 + 2*s**2 + 0*s**5 = 0 for s.
-1, 0
Let u(w) be the third derivative of w**8/784 + 3*w**7/490 + w**6/140 - w**5/70 - 3*w**4/56 - w**3/14 + 4*w**2. Solve u(h) = 0 for h.
-1, 1
Suppose 0*j - 5*j - 184 = -4*q, 2*j + 3*q = -69. Let r be (0 + -3)*8/j. Factor r*v**2 + 1/6*v**3 + 1/3 + 5/6*v.
(v + 1)**2*(v + 2)/6
Let o(v) be the second derivative of v**6/1440 + v**5/480 - v**4/48 + v**3/6 - 2*v. Let m(w) be the second derivative of o(w). Find q, given that m(q) = 0.
-2, 1
Let q be 2/(-1) + (-312)/(-160). Let o = q - -17/20. Determine a so that -2/5*a**2 - o*a - 2/5 = 0.
-1
Let k(q) = 3*q**4 + q**3 - 9*q**2 - 4*q + 8. Let r(u) = -3*u**4 - 2*u**3 + 8*u**2 + 4*u - 9. Let w(c) = 6*k(c) + 5*r(c). Factor w(j).
(j - 3)*(j + 1)**2*(3*j - 1)
Let q(i) = i**5 - i**2 + i - 1. Let z(o) = -4*o**5 - 3*o**4 + 7*o**2 - 6*o + 6. Let a(k) = -6*q(k) - z(k). Suppose a(y) = 0. Calculate y.
-1/2, 0, 1
Find x, given that 0*x - 1/3*x**4 - 1/3*x**3 + 0*x**2 + 0 = 0.
-1, 0
Let k(q) be the first derivative of q**6/135 - q**5/90 - q**4/54 + q**3/27 + 7*q - 4. Let u(n) be the first derivative of k(n). Suppose u(x) = 0. What is x?
-1, 0, 1
Let h(v) be the second derivative of 0*v**4 - 1/9*v**3 + 2*v + 0*v**2 + 1/30*v**5 + 0. Factor h(g).
2*g*(g - 1)*(g + 1)/3
Factor -4*o**2 + 3*o**3 - 6*o**3 - 2*o**2 - 3*o.
-3*o*(o + 1)**2
Let x = 13 + -9. Let y(h) be the third derivative of 0*h**3 + 11/360*h**6 - 1/90*h**5 + 0*h + 0*h**x + 0 - h**2 - 8/315*h**7 + 1/144*h**8. Solve y(u) = 0 for u.
0, 2/7, 1
Let s(o) = o - 1. Let u be s(7). Solve -8*q**5 - 63*q**3 + 0*q**5 - 33*q**2 - 7*q**5 - u*q - 51*q**4 = 0 for q.
-1, -2/5, 0
Let q(y) be the second derivative of -y**5/100 - 7*y**4/20 - 49*y**3/10 - 343*y**2/10 - 27*y. Factor q(d).
-(d + 7)**3/5
Let n(v) be the third derivative of -v**7/1120 + v**5/160 + v**3/3 - 4*v**2. Let d(m) be the first derivative of n(m). Solve d(o) = 0.
-1, 0, 1
Suppose 4*a = -8, 0 = -3*n - a - 2 + 6. Suppose 5 + 1 = 2*b. Solve -2*m - b*m**2 + 1 - m**3 - n - m = 0.
-1
Suppose 0 = 15*c - 13*c - 26. Suppose -6*j**2 - j - c - 7*j + 11 = 0. What is j?
-1, -1/3
Let f(k) = -k**2 - k. Let i(x) = -17*x**2 - 21*x - 4. Let n(j) = -6*f(j) + 2*i(j). Factor n(r).
-4*(r + 1)*(7*r + 2)
Suppose 5*y - 3*y = 0. Suppose -c - 4*j + 1 = -3, y = 4*j. What is a in -1/3*a**c + 1/3 + 0*a**2 - 2/3*a + 2/3*a**3 = 0?
-1, 1
Let s(m) be the first derivative of -m**6/15 - 7*m**5/30 - m**4/6 + m**3/3 - 3*m**2 + 6. Let i(c) be the second derivative of s(c). What is l in i(l) = 0?
-1, 1/4
Let c(x) be the first derivative of -x**5/30 + x**4/18 + x**3/9 - x**2/3 + 2*x + 3. Let n(h) be the first derivative of c(h). Factor n(d).
-2*(d - 1)**2*(d + 1)/3
Let o(p) = -5*p**3 - 3*p**2 + 5*p + 1. Let s = 22 - 37. Let y(b) = 36*b**3 + 21*b**2 - 36*b - 6. Let z(h) = s*o(h) - 2*y(h). Factor z(a).
3*(a - 1)*(a + 1)**2
Let y(h) = 8*h**2 - 6*h. Let g(v) = 3*v**2 - 2*v. Let i(d) = 11*g(d) - 4*y(d). Find c such that i(c) = 0.
-2, 0
Factor 11/3*n + 1/6*n**2 + 121/6.
(n + 11)**2/6
Let r(y) = -5*y**5 - 9*y**4 - 2*y + 2. Let g(q) = q**4 - q**3 + q - 1. Let j(p) = -4*g(p) - 2*r(p). Suppose j(t) = 0. What is t?
-1, -2/5, 0
Let m = -423/208 - -35/16. Determine l, given that 10/13*l**2 - 14/13*l + 6/13 - m*l**3 = 0.
1, 3
Factor 0 + 2/7*p**4 + 6/7*p**2 - 2/7*p - 6/7*p**3.
2*p*(p - 1)**3/7
Let a(c) = 0 - c**2 + 5 + 3 - 1 + 10*c. Let d(z) = 2*z**2 - 11*z - 8. Let s(q) = -5*a(q) - 4*d(q). Factor s(k).
-3*(k + 1)**2
Let w(h) be the first derivative of -h**3/3 - 3*h**2/2 + 9. Factor w(j).
-j*(j + 3)
Let i = 378 - 376. Determine u, given that -8/3*u**i + 14/9*u**3 + 2/3*u + 4/9 = 0.
-2/7, 1
Let s(h) = h**2 + 2*h. Let u(l) = l**2 + l + 10. Let r(k) = 2*s(k) - u(k). Factor r(y).
(y - 2)*(y + 5)
Let a be (-3)/((-12)/(-4)) + 1. Suppose 8 = 3*f + 4*h - 10, a = -f - h + 5. Let -6/5*z**f + 4/5*z + 0 = 0. What is z?
0, 2/3
Let g(o) be the first derivative of -o**3 + 4*o**2 + 3*o - 5. Find i, given that g(i) = 0.
-1/3, 3
Suppose -4*d = -7*d + 9. Let f(b) be the first derivative of -1/7*b**2 - 2/7*b + 1 + 1/14*b**4 + 2/21*b**d. Find n such that f(n) = 0.
-1, 1
Suppose -5 = -2*o + o. Suppose -3*k - 4*b = -16, o*k = 4*b - 2*b + 18. Factor 0*f**2 + k*f + 2*f - 6*f**2 + 2*f**3 - 2.
2*(f - 1)**3
Find w, given that -6/5*w**3 - 4/5*w**2 - 1/5*w**5 - 1/5*w + 0 - 4/5*w**4 = 0.
-1, 0
Let f = 127/6 - 41/2. Factor 0*r**2 + 0 + f*r - 2*r**3 - 4/3*r**4.
-2*r*(r + 1)**2*(2*r - 1)/3
Let z(s) = -4*s**3 + 5*s**2 + 28*s + 24. Let c(n) = 2*n**3 - 2*n**2 - 14*n - 12. Let a(t) = 5*c(t) + 2*z(t). Factor a(u).
2*(u - 3)*(u + 1)*(u + 2)
Let g = 15 - 11. Suppose 0 = -l - 4*h - 9, -3*l = l - g*h - 24. Suppose -12*u**l - 6*u**2 - 15/2*u**4 + 0 - 3/2*u**5 + 0*u = 0. What is u?
-2, -1, 0
Let u(b) be the first derivative of 5*b**3/3 - 15*b**2 - 35*b - 20. Factor u(j).
5*(j - 7)*(j + 1)
Let u(c) be the first derivative of c**3/9 - c/3 + 7. Find a, given that u(a) = 0.
-1, 1
Let r(z) = -z**3 - 8*z**2 - 2*z - 11. Let d = 4 - 12. Let w be r(d). Factor -p - 2 + 4*p - p**2 - w*p - p.
-(p + 1)*(p + 2)
Let d be 45/(-60)*16/(-6). Factor -3*p - 2*p**3 + d*p**2 + 0*p + 7*p.
-2*p*(p - 2)*(p + 1)
Let b(v) be the first derivative of -v**6/180 - v**5/36 - v**4/18 + 2*v**3/3 + 5. Let a(m) be the third derivative of b(m). Suppose a(h) = 0. Calculate h.
-1, -2/3
Let d be (-2)/(-11) - 155/(-55). Let a(v) be the first derivative of 2 + 0*v + 1/9*v**d - 1/6*v**2. Find h such that a(h) = 0.
0, 1
Let v = 2/173 + 1378/519. Suppose 5*s = -15, 7 = -2*h + 4*h - s. Determine w, given that h*w**2 + v + 4*w + 1/3*w**3 = 0.
-2
Suppose 0 = 2*j - 5*j. Let h(k) be the first derivative of 0*k - 1 + j*k**2 - 1/15*k**5 + 0*k**4 + 1/9*k**3. Factor h(w).
-w**2*(w - 1)*(w + 1)/3
Let n(m) = -2*m - 6. Let z be n(-4). Factor 5*b**z + 4*b + 2*b**3 + 2*b**3 - 3*b**2 + 6*b**2.
4*b*(b + 1)**2
Suppose -2*z = -3*z + 4. Determine j so that -11*j**4 + 4*j + 2*j**2 + 3*j**3 - 7*j**3 + 8*j**z + 1 = 0.
-1, -1/3, 1
Let s be (-1)/8 + 49/360. Let j(v) be the third derivative of 0*v - 4*v**2 + 0 - s*v**5 - 1/9*v**3 - 1/18*v**4. Factor j(a).
-2*(a + 1)**2/3
Let h(j) = j**3 + j**2 + 12. Let a be h(0). Let f be (5/10)/(3/a). Determine z so that -1/3*z**f + 0 + 1/3*z = 0.
0, 1
Suppose -4*o - 18 = -2*m, -4*o - 15 = -5*m - 0*o. Let t = m - -3. Find h, given that 3*h - 15*h**2 + 7*h**t - 2 - 13*h = 0.
-1, -1/4
Suppose -5*g + 9*g - 16 = 0. Suppose 0 = 5*x - 4*r - 23, 15 = 3*x - 0*x - 3*r. Let 3/2*h**5 + 0*h**2 + h**g + 0 - 1/2*h**x + 0*h = 0. Calculate h.
-1, 0, 1/3
Let m(t) = 5*t**3 + 9*t**2 + 3*t + 3. Let b(s) = -9*s**3 - 17*s**2 - 7*s - 6. Let c(h) = 4*b(h) + 7*m(h). Solve c(f) = 0 for f.
-3, -1
Find w such that -23*w**2 - 24 - 291*w**2 - 6*w**5 - 11*w**5 + 247*w**3 - 12*w**4 - 28*w**5 + 148*w = 0.
-3, 2/5, 2/3, 1
Let x be (-14)/21*1*-6. Let r be x/(-14) - (-39)/63. Factor -1/3*j**2 - r*j + 0.
-j*(j + 1)/3
Let d(x) be the third derivative of -1/96*x**4 + 0*x**3 + 0 - 1/480*x**6 - 2*x**2 + 1/120*x**5 + 0*x. Factor d(y).
-y*(y - 1)**2/4
Let r(t) be the third derivative of -t**5/40 + 5*t**4/16 - 3*t**3/2 - 24*t**2. Factor r(p).
-3*(p - 3)*(p - 2)/2
Let z = 162/5 - 32. Let v = -1952/5 - -392. Factor 2*n - v*n**2 - z.
-2*(n - 1)*(4*n - 1)/5
Let q(n) = 12*n**3 - 12*n**2 + 32*n. Let s(r) = -r**3 + r**2 - 3*r. Let g(l) = -3*q(l) - 32*s(l). Solve g(a) = 0 for a.
0, 1
Let p = 21/10 + -2. Let w(d) be the first derivative of 3 + 0*d**2 - p*d**4 + 0*d + 2/15*d**3. Factor w(u).
-2*u**2*(u - 1)/5
Factor 6*r**2 + 18/5*r**4 + 0 + 9/5*r + 3/5*r**5 + 36/5*r**3.
3*r*(r + 1)**3*(r + 3)/5
Let u be 2 - (-8)/(-1 - 0). Let a(k) = 7*k**3 - 15*k**2 - 11*k + 11. Let l(c) = 2*c**3 - 4*c**2 - 3*c + 3. Let t(h) = u*a(h) + 22*l(h). Factor t(f).
2*f**2*(f + 1)
Let b(w) = w**5 + 7*w**3 - 3*w**2 - 5*w + 3. Let h(k) = 4*k**5 + 34*k**3 - 14*k**2 - 24*k + 14. Let r(g) = 14*b(g) - 3*h(g). Let r(t) = 0. Calculate t.
-1, 0, 1
Let l(f) be the third derivative of f**5/90 - f**4/9 + f**3/3 + 5*f**2. Determine o, given that l(o) = 0.
1, 3
Let c = 61274093/35430080 - 2012/15817. Let w = c + -1/448. Determine