*k**6 - 2*k**2 + 0*k**3 + 0 + 1/6*k**4 - 1/84*k**8 - 2/15*k**5 + 4/105*k**7 + 0*k. Factor y(q).
-4*q*(q - 1)**3*(q + 1)
Suppose 10*k - 20 - 30 = 0. Let h(g) be the third derivative of 3/2*g**3 + 6*g**2 + 0*g + 0 - 1/4*g**4 + 1/60*g**k. Factor h(v).
(v - 3)**2
Let k(p) be the second derivative of -1/30*p**3 - 28*p + 1/5*p**2 + 1/100*p**5 - 1/30*p**4 + 0. Solve k(o) = 0.
-1, 1, 2
Factor -2*f**2 + 5/3*f + 0 + 1/3*f**3.
f*(f - 5)*(f - 1)/3
Let m(b) be the second derivative of -3*b**5/20 - b**4/2 + 3*b**3/2 + b + 46. Suppose m(s) = 0. What is s?
-3, 0, 1
Let s(z) be the second derivative of -1/5*z**2 + 0 + 7/30*z**3 - 12*z - 1/12*z**4. Factor s(k).
-(k - 1)*(5*k - 2)/5
Let g(y) = -9*y**4 + 18*y**3 + 21*y**2 - 105*y + 108. Let w(k) = 2*k**4 - 2*k**3 - 2*k**2 - k. Let a(u) = g(u) + 3*w(u). Factor a(b).
-3*(b - 3)*(b - 2)**2*(b + 3)
Let o(n) be the second derivative of 0*n**2 + 1/9*n**4 - 12*n + 1/30*n**5 + 1/9*n**3 + 0. Factor o(j).
2*j*(j + 1)**2/3
Let z(v) be the first derivative of -4*v**5/5 + 15*v**4 - 104*v**3 + 320*v**2 - 384*v - 490. Suppose z(h) = 0. What is h?
1, 4, 6
Let f(x) be the second derivative of -1/8*x**4 + 1/9*x**3 - 9*x + 7/2*x**2 + 0 + 1/45*x**5. Let j(z) be the first derivative of f(z). Factor j(c).
(c - 2)*(4*c - 1)/3
Let j be -3*5 + (-270)/(-12). Let -5/2*x**2 - j*x - 5 = 0. What is x?
-2, -1
Suppose -250 = -7*m - 3*m. Suppose 2*w - 5*n = -0*w - m, w = -n + 5. Find o such that -8/7*o - 6/7*o**3 - 16/7*o**2 + w = 0.
-2, -2/3, 0
Suppose 2*r - 4*v + 1 = 3, -3*v = 4*r + 51. Let c(g) = g**2 + 8*g - 7. Let h be c(r). Factor -1/4*n**h + 0 + 1/2*n.
-n*(n - 2)/4
Let q(y) = -7*y**5 - 5*y**4 + 30*y**3 + 2*y**2 + 4*y. Let z(b) = 50*b**5 + 35*b**4 - 210*b**3 - 15*b**2 - 30*b. Let d(j) = -15*q(j) - 2*z(j). Factor d(l).
5*l**3*(l - 2)*(l + 3)
Let c(f) = f**3 + 9*f**2 + 92*f + 1262. Let z be c(-11). Factor -4/5*r**2 - z - 44/5*r.
-4*(r + 1)*(r + 10)/5
Let l = 62 - 18. Solve -36*s**3 - 13*s**5 + 37*s**5 + 16 + 28*s**2 - 24*s**5 + 48*s - l*s**4 - 12*s**5 = 0.
-2, -1, -2/3, 1
Let n(w) be the third derivative of 0 - 1/300*w**5 + 1/20*w**4 - 3/10*w**3 + 0*w - 9*w**2. Factor n(t).
-(t - 3)**2/5
Suppose 11*r = -104*r. Suppose r*q + 0 - 2/3*q**2 + 2/3*q**3 = 0. Calculate q.
0, 1
Let q(w) be the second derivative of -w**7/300 - w**6/450 + 7*w**5/75 + 2*w**4/15 + 23*w**3/6 - 19*w. Let f(l) be the second derivative of q(l). Factor f(a).
-2*(a - 2)*(a + 2)*(7*a + 2)/5
Let w(v) be the first derivative of -v**7/504 + v**6/72 - v**5/24 + 5*v**4/72 + 23*v**3/3 - 32. Let u(r) be the third derivative of w(r). Factor u(q).
-5*(q - 1)**3/3
Let k = 8 + -1. Suppose -5*v = -5*s + 5, 3*v - s = k*v - 11. Solve -2*z**3 - v + 4*z + 2*z - 1 - 1 = 0.
-2, 1
Let y(j) be the second derivative of j**3 + 9*j + 0*j**2 + 0 + 27/40*j**5 + 7/40*j**6 + 1/56*j**7 + 5/4*j**4. Factor y(k).
3*k*(k + 1)*(k + 2)**3/4
Let h = -61 + 37. Let p be ((-10)/(-4))/((-12)/h). Determine l so that 2/9*l**p + 28/9*l**3 - 4/9 - 4/3*l**4 - 32/9*l**2 + 2*l = 0.
1, 2
Let d = 108/155 - 3/31. Factor -9/5*p**3 - d*p**2 + 0 + 0*p - 9/5*p**4 - 3/5*p**5.
-3*p**2*(p + 1)**3/5
Let z(u) be the second derivative of 2*u**7/21 - 2*u**6/15 - 2*u**5/5 + 2*u**4/3 + 2*u**3/3 - 2*u**2 + 252*u. Factor z(w).
4*(w - 1)**3*(w + 1)**2
Let l(j) = -j. Let h = 15 + -19. Let p be l(h). Factor -4*n**3 + 3*n**2 - 5*n**2 + 32*n**4 + 4*n - 30*n**p.
2*n*(n - 2)*(n - 1)*(n + 1)
Let h(x) be the third derivative of x**7/945 - x**6/135 - x**5/15 - 5*x**4/27 - 7*x**3/27 - 12*x**2. Factor h(a).
2*(a - 7)*(a + 1)**3/9
Let s(l) = -3*l**3 + 3*l - 3. Suppose 0 = -2*o - 4*x - 10, 4*x + 20 = 4*o + 2*x. Let i(n) = 1. Let m(w) = o*i(w) + s(w). Factor m(q).
-3*q*(q - 1)*(q + 1)
Let l(i) be the second derivative of i**5/100 + 9*i**4/10 + 26*i**3 + 676*i**2/5 + 7*i + 12. Find y such that l(y) = 0.
-26, -2
Let f(g) be the first derivative of -924 + g**3 + 47*g**2 - 14*g**2 + 907 + 363*g. Factor f(b).
3*(b + 11)**2
Solve -56/9*t**2 + 4 + 4/3*t - 8/9*t**3 + 20/9*t**4 - 4/9*t**5 = 0.
-1, 1, 3
Let i(x) be the third derivative of x**5/150 - 9*x**4/20 - 147*x**2. Suppose i(y) = 0. What is y?
0, 27
Let u(o) be the first derivative of o**8/7560 - 7*o**6/1620 + o**5/90 - o**3 + 17. Let k(x) be the third derivative of u(x). Factor k(h).
2*h*(h - 2)*(h - 1)*(h + 3)/9
Let b(l) = -5*l**2 + 5*l. Let w(c) = -c**2 + c + 2. Let i(a) = -b(a) + 6*w(a). Let t be i(4). Factor 2/5*y**3 + t*y**2 + 0 - 2/5*y.
2*y*(y - 1)*(y + 1)/5
Let f(s) be the first derivative of 49*s**5/40 + 1701*s**4/16 + 58069*s**3/24 - 8505*s**2/4 + 1225*s/2 - 62. Find h, given that f(h) = 0.
-35, 2/7
Let x(a) = a**2 + a - 1. Suppose 2*b - 6 = 6. Let y(w) = -9*w**2 + 24*w - 69. Let o(f) = b*x(f) + y(f). What is j in o(j) = 0?
5
Let b(a) be the second derivative of -49*a**5/4 - 70*a**4 - 275*a**3/2 - 125*a**2 + a - 60. Factor b(i).
-5*(i + 2)*(7*i + 5)**2
Factor -242*a**2 - 1366*a + 797*a - 6636 - 1411*a + 2586.
-2*(11*a + 45)**2
Let o(n) be the first derivative of -1/3*n**3 - 25*n + 6 + 5*n**2. Factor o(t).
-(t - 5)**2
Find l such that -55*l**2 + 114 + 9*l + 146*l + 98 - 62 + 60*l**2 = 0.
-30, -1
Let c = 53 - 158/3. Let i(x) be the first derivative of 2/15*x**5 + 0*x + c*x**4 + 0*x**3 + 0*x**2 - 2 - 1/9*x**6. Factor i(m).
-2*m**3*(m - 2)*(m + 1)/3
Find j such that 34/13*j + 0 + 38/13*j**3 + 2/13*j**4 + 70/13*j**2 = 0.
-17, -1, 0
Let b be ((-4)/(-10))/(-8 + ((-468)/(-65) - -4)). Solve b*a**5 + 1/4*a - 1/8*a**2 + 1/8*a**4 + 0 - 3/8*a**3 = 0 for a.
-2, -1, 0, 1
Let p(o) = 3*o**2 - o. Let t be p(-1). Let u(g) = 9*g**2 + 1. Let b be u(1). Find j, given that -2*j**4 - 2*j**t + b*j**4 - 3*j**4 = 0.
0
Let x(o) be the first derivative of o**3 + 9*o**2/2 - 17*o + 30. Let r(t) = 1. Let b(m) = -5*r(m) - x(m). Factor b(g).
-3*(g - 1)*(g + 4)
Suppose 0 = -2*k - 110 + 116. Factor 0*u**4 - 4*u**2 + 7*u - 2*u**3 - 2*u**2 + k*u + 2*u**4 - 4.
2*(u - 1)**3*(u + 2)
Let c = 20 + -29. Let z = c + 18. Factor -20*j**3 + 45*j**2 - 27*j - 8*j**3 - 5*j**3 + 6 + z*j**4.
3*(j - 1)**3*(3*j - 2)
Let p(x) be the third derivative of x**8/2520 + x**7/315 + x**6/135 + 8*x**3/3 + 13*x**2. Let k(m) be the first derivative of p(m). Factor k(r).
2*r**2*(r + 2)**2/3
Let j(i) = -6*i - 1. Let l be j(-1). Let b(s) be the first derivative of 6/7*s - 3/7*s**3 - 6 + 3/14*s**2 - 3/28*s**4 + 3/35*s**l. Determine x so that b(x) = 0.
-1, 1, 2
Let j = -895 - -899. Suppose 0*c + 8/3*c**2 - 16/3*c**3 - 2/3*c**5 + 0 + 10/3*c**j = 0. What is c?
0, 1, 2
Let n(a) = 3*a + 2. Let g(f) = -f**3 - f**2 + 7*f + 6. Let q(r) = 5*g(r) - 5*n(r). Factor q(j).
-5*(j - 2)*(j + 1)*(j + 2)
Factor -1/2*z**2 - 200 - 20*z.
-(z + 20)**2/2
Let b(w) = -w**3 - w**2 + w. Let y = -8 - -9. Let k(f) = -10*f**3 - 10*f**2 + 10*f + 2. Let m(s) = y*k(s) - 8*b(s). Suppose m(q) = 0. Calculate q.
-1, 1
What is j in -2/9*j**2 + 176/9*j - 3872/9 = 0?
44
Let x(p) = p**2 + 56*p - 1920. Let n be x(24). Determine t so that n + 16/3*t**2 + 2/3*t = 0.
-1/8, 0
Let c = -79 + 163. Let o be (-80)/c*-1 + 2/(-3). Let -2/7*w**3 + 0*w + 2/7*w**5 + 2/7*w**2 - o*w**4 + 0 = 0. What is w?
-1, 0, 1
Let j = 10 - 6. Suppose 3*q - 5*q = -j. Determine w so that 2/9*w - 2/9*w**3 + 2/9*w**q - 2/9 = 0.
-1, 1
Let k = 108 - 110. Let q be (-22)/(-6) - k - 4. Find d, given that -11/3*d**3 + 16/3*d + 17/3*d**4 - 4/3 - 13/3*d**2 - q*d**5 = 0.
-1, 2/5, 1, 2
Let s(z) = 3*z - 11. Let c be s(5). Factor -4*g + g + c*g**2 + 3*g.
4*g**2
Let a(j) be the second derivative of -1/4*j**4 - j**3 + 0 - 18*j + 0*j**2. Factor a(n).
-3*n*(n + 2)
Let b = 2 + 22. Let l be ((-6)/(-4))/(9/b). Factor -2*w - 4*w**3 - 3*w**2 - 11*w**4 - 2*w**2 + 10*w**l.
-w*(w + 1)**2*(w + 2)
Let w be -212*6/160 + 8. Let x(o) be the third derivative of -w*o**5 + 3*o**2 + 0*o**3 - 1/8*o**4 + 0*o + 0. Factor x(v).
-3*v*(v + 1)
Suppose -5*q + 19 = 9. Suppose -3 = q*r - 9. Factor 0*y**2 + 0*y + 2/9*y**r + 2/9*y**4 + 0.
2*y**3*(y + 1)/9
Factor 147*c - 1/2*c**2 - 21609/2.
-(c - 147)**2/2
Let v be (-16 - -4)*(-24)/9. Find m, given that 10*m**4 - 16*m**2 + 17*m**5 + 7*m**5 - 30*m**5 + v*m**3 - 8*m**2 = 0.
-2, 0, 2/3, 3
Find q, given that 4/5*q + 4*q**3 - 81/5*q**2 + 0 = 0.
0, 1/20, 4
Let g(l) = 2*l**2 + 6*l - 14. Let t be 7 + -2 - 0/(-9). Let u(m) = -3*m**2 - 11*m + 29. Let i(d) = t*g(d) + 2*u(d). Let i(x) = 0. Calculate x.
-3, 1
Let n(o) be the first derivative of 