(i). Factor o(m).
(m + 1)**2*(m + 2)
Factor -75*g + 7*g**4 - 2*g**3 + 75*g.
g**3*(7*g - 2)
Let x be (38 - 6)*3/6. Suppose x = j + 4*j - 4*s, -2 = -j + 2*s. Find h, given that 10*h**5 + 0*h - 40/7*h**3 + 0 + 8/7*h**2 + 22/7*h**j = 0.
-1, 0, 2/7, 2/5
Let p(o) be the third derivative of -1/480*o**6 + 1/840*o**7 + 0*o + 0*o**3 + 2*o**2 + 0*o**5 + 0 + 0*o**4. Factor p(a).
a**3*(a - 1)/4
Let x(i) be the second derivative of i**8/560 - i**6/120 + 2*i**3/3 + i. Let m(f) be the second derivative of x(f). Factor m(u).
3*u**2*(u - 1)*(u + 1)
Suppose -5*i = 2*k - 11, -k - 1 - 13 = -4*i. Factor 2*r**2 - r**2 - i*r**2.
-2*r**2
Let v(o) be the first derivative of o**2 + 6*o + 11. Let n be v(-3). Factor -3/2*u**3 + n + 3*u + 3/2*u**2.
-3*u*(u - 2)*(u + 1)/2
Let t = 4/73 + 718/219. Factor -4/3*f + 14/3*f**3 + 0 - t*f**2.
2*f*(f - 1)*(7*f + 2)/3
Suppose -d = -2*d + 4. Suppose d*w = -w. Factor -b - 1/2*b**4 - 2*b**3 - 5/2*b**2 + w.
-b*(b + 1)**2*(b + 2)/2
Let x(f) = 0*f**2 - 2*f**2 + 10 + f**2 - 6*f. Let s be x(-7). Factor -h**s + 2*h**4 + 3*h**3 + 0*h**2 - 2*h**2 - 2*h**5.
-2*h**2*(h - 1)**2*(h + 1)
Let p(y) be the second derivative of 3*y**5/20 - 3*y**4/2 + 9*y**3/2 - 3*y. Suppose p(n) = 0. Calculate n.
0, 3
Let x be -1 + (-2 - -3) + 10. Suppose -x = -r - r. Let -5*b**3 + r*b - 3*b + 3*b**3 = 0. Calculate b.
-1, 0, 1
Factor 6/7*v**2 + 8/7*v + 2/7.
2*(v + 1)*(3*v + 1)/7
Factor -2 + u**2 - 2*u**2 + 5*u**2 - 2*u**2.
2*(u - 1)*(u + 1)
Let r(c) = 2*c - 3. Let g be r(3). Suppose 4*a + 0*x - 11 = -g*x, -5*x = -a - 3. Suppose 4 - s**2 - s**2 + 0*s**2 - a*s = 0. Calculate s.
-2, 1
Suppose 2*f - 58 = -16. Suppose 0 = q + 3*q + 3*a - f, 3*q - 3*a = 0. Determine m so that 0*m + 2*m**4 + 2*m**q + 0*m = 0.
-1, 0
Let 0 + 0*c - 2/5*c**3 - 4/5*c**2 = 0. What is c?
-2, 0
Let s(o) be the third derivative of o**2 - 3/2*o**4 - 2/3*o**3 + 0*o + 0 - 27/20*o**5. Solve s(h) = 0.
-2/9
Let q(w) be the first derivative of w**5/15 + w**4/4 + w**3/3 + w**2/6 + 8. Factor q(z).
z*(z + 1)**3/3
Suppose -2/3*z + 1/3 + 1/3*z**2 = 0. What is z?
1
Factor 4/3*b + 0 + 1/3*b**3 + 4/3*b**2.
b*(b + 2)**2/3
Let b be -1 - 4*(1 - 2). Let d be (6/9)/(1/b). Let 1 + 3/2*g + 6*g**4 - 7*g**2 - 7/2*g**5 + d*g**3 = 0. Calculate g.
-1, -2/7, 1
Let r be ((-60)/(-8) + -2)*-4. Let u be (-2 - 0)/(r - -18). Solve 0 + u*z**2 - 1/2*z = 0 for z.
0, 1
Suppose -9*m + 24 = -m. Factor -12/7*u**2 - 8/7*u - 8/7*u**m - 2/7*u**4 - 2/7.
-2*(u + 1)**4/7
Suppose -8*c = -7*c - 4. Let v be (-3 - 6/10) + c. Let 4/5*f + v*f**2 + 0 = 0. Calculate f.
-2, 0
Determine w so that 2/3*w**5 + 2/3*w**2 - 4*w + 0 - 38/9*w**4 + 62/9*w**3 = 0.
-2/3, 0, 1, 3
Factor 5/2*m - 1/2*m**4 - 5/2*m**3 + 2 - 3/2*m**2.
-(m - 1)*(m + 1)**2*(m + 4)/2
Determine g so that 2/9*g**3 + 2/3*g**2 - 8/9 + 0*g = 0.
-2, 1
Suppose -11 = -5*d - l, 0*d - 3*l + 11 = 4*d. Let h be d*13/8 - 2. Determine x, given that 3/4*x**5 + 0*x**2 - 1/2 - h*x + 5/2*x**4 + 5/2*x**3 = 0.
-1, 2/3
Let x(u) = -u**2 - 25*u + 31. Let w be x(-26). Factor -12/5*m**2 + 0 + 0*m - 63/5*m**4 + 27/5*m**w + 48/5*m**3.
3*m**2*(m - 1)*(3*m - 2)**2/5
Let s = -8 - -10. Let -5*h**2 + 5*h**s - 2*h**4 - 2*h**5 = 0. What is h?
-1, 0
Let l(d) be the first derivative of 1/90*d**5 + 0*d + 3 + 2/9*d**3 - 3/2*d**2 - 1/12*d**4. Let n(m) be the second derivative of l(m). Let n(r) = 0. What is r?
1, 2
Let m = 57 - 40. Factor 31*s**2 + 2*s**2 + 3*s + m*s**3 + 12*s**4 + 22*s**3 + 3*s.
3*s*(s + 1)*(s + 2)*(4*s + 1)
Let n(c) be the first derivative of -1/2*c**2 + 2/3*c**6 + 2 - c**5 + 0*c - 3/4*c**4 + 5/3*c**3. Factor n(a).
a*(a - 1)**2*(a + 1)*(4*a - 1)
Let 4/13 - 6/13*r + 2/13*r**2 = 0. Calculate r.
1, 2
Suppose -3*v + 96 = -v - 2*k, 2*v - k = 95. Factor 2*n**2 + 4*n**4 + v*n - 2*n**4 + 4*n**3 - 47*n.
2*n**2*(n + 1)**2
Factor w**2 + 14*w - 9*w + w**2 - 9*w.
2*w*(w - 2)
Let x(f) be the third derivative of f**6/480 - f**5/16 + 25*f**4/32 - 125*f**3/24 - 13*f**2. Suppose x(n) = 0. Calculate n.
5
What is s in 0*s**2 + 1/4*s**5 + 1/2*s**4 + 0*s**3 + 0*s + 0 = 0?
-2, 0
Suppose -5*o + 4 = -1, -6 = -2*w - 2*o. Suppose -12*g + 1 - 8 + g**2 - 11 - 3*g**w = 0. Calculate g.
-3
Let j(w) be the third derivative of -w**5/12 + 5*w**4/12 - 33*w**2. Determine p so that j(p) = 0.
0, 2
Let b(l) be the first derivative of -4*l**3/3 + 4*l**2 - 4*l + 1. Factor b(i).
-4*(i - 1)**2
Let n(h) = 17*h**5 + 17*h**4 - 12*h**3 - h**2 + 6*h + 6. Let d(k) = 6*k**5 + 6*k**4 - 4*k**3 + 2*k + 2. Let p(t) = 11*d(t) - 4*n(t). Factor p(u).
-2*(u - 1)**2*(u + 1)**3
Let h(t) = 2*t - 23. Let k be h(12). Let l(p) be the first derivative of 0*p**2 + 2/3*p**3 + 0*p**4 - p + k - 1/5*p**5. Factor l(n).
-(n - 1)**2*(n + 1)**2
Let y(o) be the second derivative of 0*o**3 - 3*o + 0*o**2 - 1/14*o**7 + 0*o**4 - 1/10*o**6 + 0 + 0*o**5. Factor y(s).
-3*s**4*(s + 1)
Let c(j) = -j + 16. Let i be c(12). What is v in -i*v**4 - 4*v**5 - 25*v + 25*v = 0?
-1, 0
Let i = -77 - -49. Let n be ((-4)/10)/(i/35). Factor -1 + 1/2*x + 3/2*x**2 - n*x**3 - 1/2*x**4.
-(x - 1)**2*(x + 1)*(x + 2)/2
Let v(j) be the second derivative of 0*j**2 - j + 0*j**3 - 1/6*j**4 - 2/15*j**6 + 0 + 3/10*j**5. Find k such that v(k) = 0.
0, 1/2, 1
Solve w**2 + 0 + 7/6*w - 1/6*w**3 = 0 for w.
-1, 0, 7
Let w(z) = 9*z**2 + 8*z + 8. Suppose -4*t = -2*t - 14. Let d(r) = 5*r**2 + 4*r + 4. Let c(j) = t*d(j) - 4*w(j). Determine q, given that c(q) = 0.
-2
Suppose 0*y - 4*y - 12 = 0. Let o = y - -6. What is f in -5*f + o*f - 2*f**2 + 4*f = 0?
0, 1
Suppose -2*k - 4 = 0, n + 2 = -0*n - 2*k. Factor 1 + 5*m**2 - 2*m**3 + n*m**4 + 2*m - 3*m**4 - 5*m**2.
-(m - 1)*(m + 1)**3
Let -1/8*r - 1/8*r**2 + 1/8 + 1/8*r**3 = 0. What is r?
-1, 1
Let f = 35 - 32. Let m(p) be the second derivative of p**f - p + 0*p**4 + 0 - 1/10*p**5 + 2*p**2. Let m(t) = 0. Calculate t.
-1, 2
What is a in 23 - 10 - 3*a**2 - 16 - 6*a = 0?
-1
Let r = 46 - 43. Let k(p) be the first derivative of r + 0*p**2 + 0*p - 2/9*p**3. Determine s, given that k(s) = 0.
0
Factor 2/9*t**5 - 2/3 - 14/9*t + 10/9*t**4 - 4/9*t**2 + 4/3*t**3.
2*(t - 1)*(t + 1)**3*(t + 3)/9
Determine l, given that -l**3 - 2*l**2 - 4*l**2 + 0*l**3 + 3*l + 4*l**3 = 0.
0, 1
Suppose -4*r**2 - 9*r**2 - 2*r**2 + 18*r**3 - 5 - 13*r**3 + 15*r = 0. Calculate r.
1
Let i(x) = x**3 - 3*x**2 + x - 1. Let b be i(3). Solve 2*t**2 - 4*t + 0*t**b + 2*t**2 = 0 for t.
0, 1
Determine s, given that -2/5*s**2 - 2/5 - 4/5*s = 0.
-1
Let p(j) be the first derivative of -7*j**6/1440 - 3*j**5/160 - j**4/48 - j**3/3 + 4. Let k(v) be the third derivative of p(v). What is q in k(q) = 0?
-1, -2/7
Suppose 5/2*d**2 + 5/4*d**4 + 1/4 - 5/4*d - 5/2*d**3 - 1/4*d**5 = 0. Calculate d.
1
Let t(g) be the third derivative of g**5/12 + g**4/24 - 13*g**3/6 + g**2. Let l(a) = a**2 - 3. Let x(b) = 18*l(b) - 4*t(b). Factor x(y).
-2*(y + 1)**2
Find x, given that -2/3*x - 4 + 2/3*x**2 = 0.
-2, 3
Let j(u) = -u + 7. Let s be j(5). Let v(b) be the first derivative of -2*b - 2/5*b**5 + 2 - 4*b**3 + 4*b**2 + s*b**4. Factor v(i).
-2*(i - 1)**4
Suppose -4*c = -9*c. Let w be (-36)/(-60)*10/24. Determine s, given that -w*s**4 + c*s + 0 + 1/4*s**2 + 0*s**3 = 0.
-1, 0, 1
Suppose 3*v = -2 + 11. Suppose z - 6*z + 4*a + 4 = 0, 3*a = 5*z - v. Suppose 5/2*h**2 - 7/2*h**3 + z + h = 0. Calculate h.
-2/7, 0, 1
Let f = -1442/5 + 289. Determine n, given that -3*n**2 + 0 + 3/5*n**5 - 9/5*n**3 - 6/5*n + f*n**4 = 0.
-1, 0, 2
Let r be ((-6)/(-20))/(60/80). Factor -1/5*w**2 + 0 - r*w.
-w*(w + 2)/5
Let j(c) = c + 2. Let b be j(0). Let -4*d**2 - 2*d + 2*d**2 + b*d + 4*d + 6 = 0. What is d?
-1, 3
Let h = -11 + -3. Let j = -10 - h. Find w such that -4 + j - 2*w**2 = 0.
0
Let v = -4/35 - -51/140. Let f be 588/140 - 1/5. Suppose 0*i**3 + 0 - v*i**f + 1/4*i**2 + 0*i = 0. What is i?
-1, 0, 1
Suppose 5*d - 25 - 5 = -4*h, -5*h - d = -27. Let v - 3 - 3 + v**2 + h - v**3 = 0. Calculate v.
-1, 1
Suppose -2*r - 15 = 3*r. Let s = -1 - r. Let 2/3*t**s + 1/3*t - 2/3 - 1/3*t**3 = 0. What is t?
-1, 1, 2
Let u(s) be the first derivative of -s**5/20 + s**4/8 + 5*s**2/2 + 5. Let w(c) be the second derivative of u(c). Factor w(k).
-3*k*(k - 1)
Let c = -28 + 50. Let i(v) = v. Let q be i(4). Factor 0 - c*r**2 - 11*r**2 + 40*r**3 - 16*r**q + 0 - 1 + 10*r.
-(r - 1)**2*(4*r - 1)**2
Suppose 17 = 10*s - 3. Suppose -g + 7/2*g**2 - s*g**3 - 1/2 = 0. Calculate g.
-1/4, 1
What is k in k**5 - 7*k**5 + k