+ 5. Let y = 82 - 86. Let r(i) = 15*i**4 - 85*i**3 + 55*i**2 + 140*i - 70. Let t(o) = y*r(o) - 55*u(o). Factor t(a).
-5*(a - 1)**3*(a + 1)
Let m be (-1*10)/(-2) + (-23 - 29 - -47). Factor -2/17*w**4 + m*w + 0 + 0*w**3 + 0*w**2 - 2/17*w**5.
-2*w**4*(w + 1)/17
Let u(h) be the third derivative of -28*h**2 - 2*h**3 + 1/20*h**5 + 0*h + 0 + 0*h**4. Factor u(p).
3*(p - 2)*(p + 2)
Factor 12 - 3*h**2 + h**2 - 6 + 2.
-2*(h - 2)*(h + 2)
Let n(i) = -4*i**4 + 54*i**3 + 210*i**2 + 218*i + 72. Let h(b) = -b**3 + b**2 + b. Let m(s) = -6*h(s) + n(s). Let m(f) = 0. What is f?
-1, 18
Factor -5*i**2 + 5*i - 13*i**4 + 8*i**4 - i**2 + 6*i**2 - 5*i**3 + 5*i**2.
-5*i*(i - 1)*(i + 1)**2
Let g(v) be the first derivative of v**3 + 9*v**2/2 + 263. Suppose g(h) = 0. What is h?
-3, 0
Let g = 349/2106 - -1/1053. Factor -g*c**3 + 5/6*c**2 + 1/2 - 7/6*c.
-(c - 3)*(c - 1)**2/6
Suppose 0 = -0*h + 2*h. Suppose h = 4*c + 4*s - 16, 3*s = c - s + 16. Let -z**3 + c*z**5 + 0*z**5 + 4*z**5 - 3*z**3 = 0. What is z?
-1, 0, 1
Let g(l) be the second derivative of -l**7/105 + l**6/5 - 63*l**5/50 + 49*l**4/30 + 3*l + 3. Factor g(a).
-2*a**2*(a - 7)**2*(a - 1)/5
Suppose 0 = 20*p - 18*p - 2. Let w be (p + (-5)/(-5))/6. Determine x, given that w*x**2 + 1/3 + 2/3*x = 0.
-1
Suppose 7*u - 12 = 4*u. Factor 3*q**4 - 17*q**4 - 9*q**3 + 17*q**3 - 6*q**u.
-4*q**3*(5*q - 2)
Let t be (195/(-702))/((-10)/(-8))*-6. Let t*u**2 + 2/3*u - 4/3*u**4 + 0*u**3 - 2/3*u**5 + 0 = 0. What is u?
-1, 0, 1
Let b(w) be the second derivative of w**7/84 + w**6/60 - w**5/8 - w**4/24 + 2*w**3/3 - w**2 - 221*w. Factor b(l).
(l - 1)**3*(l + 2)**2/2
Factor -37*x**2 - 209*x + 204 - 3*x**3 + 85*x**2 - 22*x + 90.
-3*(x - 7)**2*(x - 2)
Let w(d) be the third derivative of -d**8/2240 + d**7/105 - d**6/15 - 13*d**4/24 + 6*d**2. Let f(y) be the second derivative of w(y). Find c such that f(c) = 0.
0, 4
Let l be (-6 + -2 - -9)*3*(-1)/(-6). Factor 5/2*o**3 + l*o**4 - 9/2*o + 3/2*o**2 + 0.
o*(o - 1)*(o + 3)**2/2
Factor 0*a - 1/2*a**2 + 1/2.
-(a - 1)*(a + 1)/2
Let v(d) = -5*d + 17. Let q be v(3). Let w(z) be the first derivative of -1/4*z**3 + 0*z**q + 3*z + 6. Determine p so that w(p) = 0.
-2, 2
Suppose 2*x = -37 + 13. Let d = x + 15. Find f such that d*f**4 + 3*f**3 - 5*f - 2*f - 3*f**2 + 4*f = 0.
-1, 0, 1
Factor -125*q**4 - 1329*q - 1100*q**3 - 289 - 223*q - 208*q - 3487*q**2 - 31 + 667*q**2.
-5*(q + 4)**2*(5*q + 2)**2
Let s = 42022/5 - 8404. Factor 2/5*j**3 + 0*j + 2/5*j**2 + 0 - 2/5*j**4 - s*j**5.
-2*j**2*(j - 1)*(j + 1)**2/5
Let a(q) be the second derivative of 1/7*q**3 - 3/140*q**5 + 0*q**2 + 0 + 7*q + 1/28*q**4. Factor a(z).
-3*z*(z - 2)*(z + 1)/7
Let i be 1864/1165*((-5)/(-4) + -1). Suppose 0 - i*f**5 - 4/5*f**2 + 0*f - 2*f**3 - 8/5*f**4 = 0. What is f?
-2, -1, 0
Let b = 104/1485 + -1/297. Let w(f) be the third derivative of f**2 + 0*f**3 + 0 - 1/2*f**4 - b*f**5 + 0*f. Factor w(m).
-4*m*(m + 3)
Let m(f) = -f**3 + 11*f**2 - 9*f - 6. Let t be m(10). Let g be t/(-12)*((-16)/5 + 2). Factor 2/5*l**3 - g*l**2 + 0 + 0*l.
2*l**2*(l - 1)/5
Let 42*k - 4*k**2 + 26*k**2 + 0*k**4 + 6*k**3 + 14*k**2 - 2*k**4 + 14*k**2 = 0. What is k?
-3, -1, 0, 7
Let n = 161 - 161. Let k(x) be the third derivative of n - x**3 + 0*x + x**2 + 1/40*x**5 + 0*x**4. Factor k(j).
3*(j - 2)*(j + 2)/2
Let z(q) = 8*q - 5*q - 4*q**4 + q**4 - 7*q**3 - 2*q**2 + q**2. Let b(u) = 3*u**4 + 6*u**3 - 3*u. Let j(r) = 4*b(r) + 3*z(r). Let j(p) = 0. What is p?
-1, 0, 1
Let a = 35 + -31. Suppose 0 = -3*v + 2 + 7. Let 3*i**4 + 3*i**4 - 3*i**3 + 0*i**4 - v*i**a = 0. What is i?
0, 1
Suppose 3*t - 15 = -0*t. What is b in -8*b - 14*b**5 + 106*b**4 - 2*b - 6*b**t - 21*b**4 - 120*b**3 + 65*b**2 = 0?
0, 1/4, 1, 2
Let a be (-14)/1 + (-2 - -5). Let w = a + 14. Suppose 0*l**3 - 2*l**4 - 4*l - 2*l**w + 2*l**2 + 7*l - l = 0. What is l?
-1, 0, 1
Let i(r) be the third derivative of -r**5/120 - 11*r**4/12 + 13*r**2 + 2. Factor i(y).
-y*(y + 44)/2
Let d be 1704/(-3834) - 22/(-36). Factor 0*w + d*w**4 + 1/6*w**2 + 1/3*w**3 + 0.
w**2*(w + 1)**2/6
Let t be (0/(-4 + 5))/(-5 - -8). Let -2/3*f**3 + t*f**2 + 0 + 0*f = 0. Calculate f.
0
Let z(h) = -6*h - 3. Let o be z(-3). Let u = o - 11. Find s such that -u*s**2 - 3 + 18*s**3 - 21*s**3 - 5*s**2 - 9*s = 0.
-1
Let a(o) be the first derivative of 10/21*o**3 - 16/7*o - 4 + 18/7*o**2. Factor a(p).
2*(p + 4)*(5*p - 2)/7
Let t be (-9)/(-2)*-1*(-2)/3. Let l(y) be the first derivative of t + 1/15*y**5 - 1/18*y**6 - 1/9*y**3 - 4/3*y + 5/12*y**4 - 4/3*y**2. Solve l(d) = 0.
-1, 2
Factor 23*c**4 + 12*c**5 - 3*c**5 - 26*c**4 + 4*c**2 - 10*c**5.
-c**2*(c - 1)*(c + 2)**2
Let m(a) be the second derivative of a**4/42 + 16*a**3/21 + 15*a**2/7 + 85*a. Factor m(t).
2*(t + 1)*(t + 15)/7
Solve -106/17 + 108/17*b - 2/17*b**2 = 0.
1, 53
Let p(a) be the third derivative of a**5/30 - 2*a**4/3 + 16*a**3/3 + 71*a**2 - 4*a. Factor p(i).
2*(i - 4)**2
Let x be (3050/500 - 3*2)/(5/25). Factor -x*d**2 - 3/2 - 2*d.
-(d + 1)*(d + 3)/2
Let a(i) be the second derivative of -10*i + 1/21*i**4 + 4/21*i**3 + 0 + 2/7*i**2. Factor a(j).
4*(j + 1)**2/7
Let s = 1335 - 1335. Let n(x) be the third derivative of -1/130*x**5 + 3*x**2 + 0*x**3 + 0 - 1/780*x**6 - 1/78*x**4 + s*x. Factor n(i).
-2*i*(i + 1)*(i + 2)/13
Let o be (0 + -1)*-2 + 33/6. Let b(r) = -r**3 + 11*r**2 + 12*r + 2. Let d be b(12). Factor 8*j**d + o*j**3 - 1/2*j - 1.
(j + 1)*(3*j - 1)*(5*j + 2)/2
Let t = 2510 + -2506. Solve 4*k - t*k**2 - 4/3 + 4/3*k**3 = 0.
1
Suppose -4 = -4*j - 19*o + 17*o, 3*j - 2 = -o. Solve -2*d**4 - 1/2*d**5 - 5/2*d**3 - d**2 + j*d + 0 = 0.
-2, -1, 0
Let a(z) be the third derivative of z**8/16800 - z**7/2100 + z**5/75 - 11*z**4/12 + 31*z**2. Let h(p) be the second derivative of a(p). Factor h(n).
2*(n - 2)**2*(n + 1)/5
Let f be (-12)/(-2)*3/9. Suppose -4*r - 21*r**2 + 12*r**f - r**2 = 0. What is r?
-2/5, 0
Determine i so that -2/5*i**4 - 46/5*i**2 + 16/5*i**3 - 24/5 + 56/5*i = 0.
1, 2, 3
Let n(r) be the third derivative of 0 - 1/5*r**5 + 17/120*r**6 + 1/70*r**7 + 0*r + 0*r**3 - 1/6*r**4 - 1/84*r**8 - 37*r**2. What is o in n(o) = 0?
-2, -1/4, 0, 1, 2
Let x(i) = i**2 - 613*i - 6228. Let h be x(-10). Determine s, given that 0*s - 5/4*s**3 - 40 + 15/2*s**h = 0.
-2, 4
Let h(u) be the third derivative of -2/15*u**5 + 0 + 0*u + 3*u**2 - 1/15*u**6 + 1/6*u**4 + 2/3*u**3 + 1/84*u**8 + 2/105*u**7. Determine a, given that h(a) = 0.
-1, 1
Let r = -561 + 561. Factor -15/4*a**2 + r + 0*a - 5/4*a**3.
-5*a**2*(a + 3)/4
Find c such that 70/3*c + 17/3*c**2 + 8/3 = 0.
-4, -2/17
Let s(f) be the third derivative of f**7/15 - 23*f**6/60 - 11*f**5/15 + 2*f**4/3 - 108*f**2 - 2*f. Factor s(o).
2*o*(o - 4)*(o + 1)*(7*o - 2)
Let o(t) = 2*t - 3*t - 3*t + 2*t. Let g(f) = -f**2 - 3*f + 1. Suppose -3 = -27*s + 28*s. Let q(h) = s*o(h) + 2*g(h). Factor q(r).
-2*(r - 1)*(r + 1)
Let z(r) be the first derivative of -2*r**6/3 - 23*r**5/5 - 21*r**4/2 - 20*r**3/3 + 4*r**2 - 283. Factor z(y).
-y*(y + 2)**3*(4*y - 1)
Let z(k) be the second derivative of -k**5/20 + 5*k**4/6 - 17*k**3/6 + 4*k**2 + 59*k. Factor z(r).
-(r - 8)*(r - 1)**2
Let s(z) = z - 1. Let u(r) = 3. Let d(x) = 2*s(x) + u(x). Let o be d(2). What is v in -8*v**3 - 7*v**3 - 5*v**3 + 5*v**3 + o*v**4 = 0?
0, 3
Suppose -25 = -5*f + 5*j, 4*j - 7*j = -f + 9. Let g(r) be the second derivative of -3/7*r**2 + 4/21*r**f + 0 - 1/42*r**4 + 3*r. Factor g(c).
-2*(c - 3)*(c - 1)/7
Let d(f) be the second derivative of -f**4/6 + 9*f**3 - 92*f**2 + 275*f. Factor d(o).
-2*(o - 23)*(o - 4)
Let k(n) be the second derivative of -11/42*n**4 - 13/42*n**3 - 1/14*n**2 + 25*n + 0. Find y such that k(y) = 0.
-1/2, -1/11
Determine x so that -26/9*x**2 + 0*x - 2/9*x**3 + 0 = 0.
-13, 0
Let j(g) = g + 1. Suppose 2*a + 4 = 4*a. Let q(n) = -4*n + 4*n**a - n**2 - 8*n - 3. Let b(r) = 6*j(r) + q(r). Factor b(h).
3*(h - 1)**2
Let s = -55 - -161. Factor 5*g**4 - 96*g**3 + g + s*g**3 - 11*g - 5*g**2.
5*g*(g - 1)*(g + 1)*(g + 2)
Let b = 3 + 8. Let w = b - -5. Solve -21*p**3 + 9*p**2 - 5*p**4 + 3*p + 3*p - p**5 + w*p**5 - 4*p**4 = 0 for p.
-1, -2/5, 0, 1
Let o be ((-5)/6)/(57 + 25245/(-440)). Factor o*k + 0 + 4/9*k**2.
4*k*(k + 5)/9
Let u be 80/(-12)*(-28 + 1). Let t = 182 - u. Determine b, given that 8/7*b**4 - 8/7*b**t + 0 + 4/7*b + 0*b**3 - 4/7*b**5 = 0.
-1, 0, 1
Let t(d) be the first derivative of d**7/112 + 11*d**6/160 + 7*d*