5). Factor 0 + 6/5*p**2 - 2/5*p - t*p**x + 2/5*p**4.
2*p*(p - 1)**3/5
Let h be (-1 - (-27)/33) + 1040/2574. Factor 2/3 + 2/9*g**2 + h*g**3 - 10/9*g.
2*(g - 1)**2*(g + 3)/9
Factor 31/2*i + 7*i**2 + 8 - 1/2*i**3.
-(i - 16)*(i + 1)**2/2
Suppose 4*k = 3*n - 113, -40 = -n - 4*k + 3*k. Let d be (n/(-26))/((-1)/2). Factor -4*u**3 - 13*u**3 + 16*u**d.
-u**3
Let v be 3/(-9) + 7/3. Let q be 35 - 34 - 1*-2. Factor -3 - q*i - v*i**2 - i**2 + 9*i.
-3*(i - 1)**2
Let p(z) be the second derivative of -z**7/11340 - z**6/648 - z**5/90 - z**4/12 - 21*z. Let k(t) be the third derivative of p(t). Factor k(i).
-2*(i + 2)*(i + 3)/9
Factor 1/2*u**3 + u**2 - 7/2*u + 2.
(u - 1)**2*(u + 4)/2
Let h be -2*((-44)/(-8) + -5). Let l(a) = -18*a**3 + 2*a**2 + 2*a. Let f be l(h). Suppose 0*v**3 + 0*v - f*v**2 + 81/4*v**4 + 4 = 0. What is v?
-2/3, 2/3
Suppose 5*r = -2*y + 5, -y = -15*r + 13*r - 7. Let g(q) be the second derivative of 0 + 9/4*q**3 + q - 27/4*q**2 + 1/40*q**y - 3/8*q**4. Factor g(f).
(f - 3)**3/2
Let g(m) = 2*m**4 + 19*m**3 + 10*m**2 + 7*m - 7. Suppose 86*w - 84*w = -4. Let q(i) = i**3 + i - 1. Let b(v) = w*g(v) + 14*q(v). Find a, given that b(a) = 0.
-5, -1, 0
Let h(b) be the first derivative of -49*b**5/5 - 84*b**4 + 144*b**3 - 64*b**2 - 847. Determine p so that h(p) = 0.
-8, 0, 4/7
Suppose 62 = 3*x - 40. Let h = 137/4 - x. Suppose 9/4*w**3 + 0 + 1/2*w + h*w**5 - 7/4*w**2 - 5/4*w**4 = 0. What is w?
0, 1, 2
Factor 48*j - 3/2*j**2 + 0.
-3*j*(j - 32)/2
Let i = 7 + -4. Let a be (-4 - 2)*59/(-708). Let -3/4*y**i + 0*y + a*y**2 + 1/4*y**4 + 0 = 0. What is y?
0, 1, 2
Let l = -21 + 17. Let v(f) = 5*f**2 + 23*f + 14. Let c be v(l). Suppose 4/7*y**5 + 32/7*y - 4/7*y**4 + 4/7*y**c + 16/7 - 20/7*y**3 = 0. What is y?
-1, 2
Let g = 15 - 11. Let q(y) = 2*y - 3. Let n be q(2). Determine x, given that n + 4*x**2 - 3 + 8*x**4 - 2*x + g*x**3 - 10*x**4 - 2*x**5 = 0.
-1, 1
Suppose -69*p + 292 = 154. Factor -2/3*r - 1/3*r**p + 1.
-(r - 1)*(r + 3)/3
Let d be (-2652)/(-612) - ((-1)/((-1)/4))/1. Suppose d*t - 1/9*t**2 + 4/9 = 0. What is t?
-1, 4
Let h be (-10)/((-3 - -2) + -1). Let s(l) = 5*l**2 + 35*l - 5. Let x(m) = -7*m**2 - 52*m + 8. Let k(p) = h*x(p) + 8*s(p). Suppose k(q) = 0. Calculate q.
-4, 0
Let o(y) be the second derivative of y**5/20 - y**4/4 - 5*y**3/3 - y + 19. Factor o(c).
c*(c - 5)*(c + 2)
Suppose -359 + 163 = -2*p + b, -5*p = -3*b - 492. Find q, given that 16*q - 2/3*q**2 - p = 0.
12
Let w be 3 + (9/18)/((-2)/(-4)). Suppose -23*f + 20*f**3 - 172*f**5 - w*f**2 + 174*f**5 + 14*f**4 + f - 10 = 0. Calculate f.
-5, -1, 1
Let h = -6 - -8. Let c be 2 - 1 - (-4 + -1 + 3). Solve 8*g - 4 - g**c + 8*g**h - 7*g**3 + 4*g**4 - 8*g**2 = 0.
-1, 1
Let v(f) = f**3 - 14*f**2 - 14*f - 9. Let o be v(15). Factor 0*w - 6*w**2 - 3*w**5 - 5*w + 8*w + o*w**4.
-3*w*(w - 1)**3*(w + 1)
Suppose 35 - 147 = -2*h. Let a = h - 38. Factor -3*p**4 - 14*p + 5 - 10*p**3 - 1 + a*p**2 + 5*p**4.
2*(p - 2)*(p - 1)**3
Let t be (-4)/((-40)/(-6))*(-10 + -35)/9. Determine u so that u**2 - 1/3*u**t + 0 - 2/3*u = 0.
0, 1, 2
Let n be (3/42)/((-12)/(-8)). Let v(l) be the second derivative of 0*l**2 - 5*l + 1/105*l**6 + 0 + n*l**3 - 1/70*l**5 - 1/42*l**4. Factor v(t).
2*t*(t - 1)**2*(t + 1)/7
Factor 26/11*v**2 + 13/11*v - 6/11 + 7/11*v**3.
(v + 1)*(v + 3)*(7*v - 2)/11
Let b(a) = 26*a**2 - 1886*a - 656. Let n(l) = 9*l**2 - 629*l - 218. Let t(g) = -3*b(g) + 10*n(g). Solve t(p) = 0 for p.
-1/3, 53
Let j = 13 - 7. Suppose 0 = 7*w - j*w - 3. Suppose -7*g - 2*g**3 + 14*g**w + 10*g - 15*g**2 = 0. What is g?
0, 1/4, 1
Let s(f) be the first derivative of f**3/21 - f**2/7 - 3*f/7 + 124. Solve s(z) = 0.
-1, 3
Let k(c) be the second derivative of c**7/63 - 2*c**6/15 + 11*c**5/30 - c**4/9 - 4*c**3/3 + 8*c**2/3 + 2*c + 1. Let k(q) = 0. Calculate q.
-1, 1, 2
Let v = 7697/9 + -855. Determine m so that 0*m + 2/9*m**3 + v*m**2 + 0 - 2/9*m**4 - 2/9*m**5 = 0.
-1, 0, 1
Let m(k) be the third derivative of 0*k - 1/12*k**5 - 245/6*k**3 + 35/12*k**4 + 11*k**2 + 0. Determine l, given that m(l) = 0.
7
Suppose 0 = -2*i + 2*h - 6, -4*h + 28 = 4*i. Suppose 2*f - q = 2, -2*f + 6 = i*q - q. Factor 4/5 + 8/5*s**2 + f*s + 2/5*s**3.
2*(s + 1)**2*(s + 2)/5
Let d(o) be the first derivative of o**4 - 52*o**3 + 864*o**2 - 3888*o - 402. Factor d(a).
4*(a - 18)**2*(a - 3)
Let k be -2 - (-48)/21 - 12/42. Suppose 8 = -4*j, h + 3*j + j + 5 = k. Factor -3*i**h - 6*i + 1/2*i**4 + 13/2*i**2 + 2.
(i - 2)**2*(i - 1)**2/2
Suppose 0 = 20*p - 26*p - 24. Let h be ((-10)/p)/(11/22). Let -18/19*f**4 + 0*f**2 - 4/19*f**3 + 0 + 0*f - 14/19*f**h = 0. Calculate f.
-1, -2/7, 0
Let w = 52021 - 104039/2. Factor 0 + 12*t**3 + w*t**5 + 0*t - 6*t**2 - 15/2*t**4.
3*t**2*(t - 2)**2*(t - 1)/2
Let b be -2 + -2 + 10 + -2. Suppose 0 = -5*t - b*t. Find n, given that 32/3*n**5 + 0 - 10*n**3 + t*n - 4/3*n**2 - 16*n**4 = 0.
-1/4, 0, 2
Let p(u) be the second derivative of 7*u**4/54 + 2*u**3/27 + u + 32. Solve p(n) = 0 for n.
-2/7, 0
Find b, given that -9/4*b**2 + 105/2 - 627/4*b = 0.
-70, 1/3
Let n(z) be the second derivative of z**6/480 - z**5/20 + z**4/2 + z**3 - 16*z. Let m(i) be the second derivative of n(i). Let m(p) = 0. Calculate p.
4
Suppose -3*b = -4*g - 8, 5*b + 5*g = -1 + 26. Factor -b*l**3 + 0*l**2 + l**4 - 8*l**4 - 2*l**2 + 5*l**4.
-2*l**2*(l + 1)**2
What is j in -4/5*j**3 - 112*j - 88/5*j**2 - 160 = 0?
-10, -2
Suppose 0 = -5*n + 2*y, 10*y = 8*y + 10. Solve 3/2*l**5 + 0 + 0*l - 9/2*l**3 + 0*l**4 + 3*l**n = 0 for l.
-2, 0, 1
Let a(c) = -4*c**2 - 98*c - 12. Let w(f) = 24*f**2 + 490*f + 60. Let u(z) = 14*a(z) + 3*w(z). Factor u(m).
2*(m + 6)*(8*m + 1)
Factor 324*n - 96 - 133*n - 36*n**2 - 3*n**3 - 142*n - 157*n.
-3*(n + 2)**2*(n + 8)
Let y(x) be the third derivative of x**6/420 - x**4/84 + x**2 - 127*x. Factor y(u).
2*u*(u - 1)*(u + 1)/7
Let y(z) = -z**2 - 5*z + 4. Let k be y(-3). Let o be (-5)/(-1*2/4). Factor 48*r**2 + 4*r**4 - 24*r**3 - 32*r + o - k.
4*r*(r - 2)**3
Let o(n) be the second derivative of -2*n**6/15 + 2*n**4 + 16*n**3/3 + 6*n**2 + 105*n. Factor o(c).
-4*(c - 3)*(c + 1)**3
Suppose -3*w = 3*x + 15 - 3, -2*w = -2*x - 8. Solve -6/5*b**2 - 9/5*b**3 + 0 + w*b - 3/5*b**4 = 0.
-2, -1, 0
Let z(o) be the third derivative of o**7/280 + 7*o**6/160 + 7*o**5/40 + o**4/4 + 24*o**2 - 6*o. Factor z(f).
3*f*(f + 1)*(f + 2)*(f + 4)/4
Factor -239*r**2 - 3*r**4 + 113*r**2 - 114 - 121*r**2 - 345*r - 123*r**3 - 104*r**2.
-3*(r + 1)**3*(r + 38)
Let z = -7/99 - -47/198. Let d(j) be the first derivative of -z*j - 1/6*j**2 - 1/18*j**3 + 9. Find y such that d(y) = 0.
-1
Suppose -3*h - 2*b + 7*b = -36, -3*h - 4*b = 18. Suppose 48*c**3 - 9*c**4 + 0*c + 768/5 + 3/5*c**5 - 96*c**h = 0. Calculate c.
-1, 4
Let r = -67 + 70. Let -r*n + 10*n + 8*n + 3*n**2 = 0. Calculate n.
-5, 0
Let l(m) be the second derivative of 0*m**2 - 1/3*m**3 + 0 - 1/21*m**7 + 1/5*m**5 + 0*m**6 - 22*m + 0*m**4. Determine f, given that l(f) = 0.
-1, 0, 1
Find m such that 2/7*m**3 + 4/7 - 2/7*m**4 + 6/7*m**2 - 10/7*m = 0.
-2, 1
Suppose 0 = 2*t + 8, 2*t + 88 = 4*q - 2*q. Find d such that -72*d - 15*d**5 + 72*d - 5*d**4 + q*d**3 - 20*d**2 = 0.
-2, 0, 2/3, 1
Let y(r) be the second derivative of r**7/210 + r**6/75 - r**4/30 - r**3/30 + 551*r. Factor y(g).
g*(g - 1)*(g + 1)**3/5
Let v(p) be the third derivative of p**7/42 + 145*p**6/24 - 147*p**5/4 + 2215*p**4/24 - 370*p**3/3 + 123*p**2. Factor v(i).
5*(i - 1)**3*(i + 148)
Let i(k) = 4*k**2 + 16*k. Let r(q) = -q**2 - q. Let l(v) = i(v) + 8*r(v). Factor l(w).
-4*w*(w - 2)
Let q = 17 - 17. Let w = 173/3 + -862/15. Suppose w*y**2 + q - 1/5*y = 0. Calculate y.
0, 1
Let n(f) be the third derivative of -f**8/56 + 4*f**7/21 - 29*f**6/36 + 5*f**5/3 - 5*f**4/3 + 8*f**3/9 + 76*f**2. Factor n(s).
-2*(s - 2)**3*(3*s - 1)**2/3
Let k = -380 - -384. Let p(b) be the second derivative of 0 - 1/2*b**3 + 0*b**2 - 1/4*b**4 + k*b. What is h in p(h) = 0?
-1, 0
Let c(z) be the third derivative of -36*z**2 - 1/120*z**5 + 0 + 1/6*z**4 + 0*z - 4/3*z**3. What is f in c(f) = 0?
4
Let r(v) be the first derivative of -2*v**3/7 - 47*v**2/7 + 32*v/7 - 122. Let r(d) = 0. What is d?
-16, 1/3
Let o(t) = -t - 5. Let v be o(4). Let b(x) = 11*x**2 + 21*x + 9. Let g(n) = 5*n**2 + 10*n + 5. Let f(w) = v*g(w) + 4*b(w). Factor f(c).
-(c + 3)**2
Suppose 6*o + 10 = 8*o. Let r(d) be the second derivative of -1/30*d**3 - 1/150