 4. Let r(y) = -3*a(y) - 4*v(y). Factor r(f).
-5*f**2*(f + 3)
Suppose 0 = -z + 2 + 6. Suppose -2*k + 6*k = z. Suppose -4*y + 2*y + k*y**2 - 2*y**3 + 0*y**3 + 2*y**2 = 0. What is y?
0, 1
Let w(h) = 5*h**3 + 108*h**2 - 105*h. Let m(c) = -30*c**3 - 650*c**2 + 630*c. Let q(f) = -4*m(f) - 25*w(f). Solve q(i) = 0 for i.
-21, 0, 1
Let s(h) be the second derivative of h**4/66 - 2*h**3/33 + 505*h. Let s(k) = 0. Calculate k.
0, 2
Let j = 14 - -40. Factor 52*t**4 - 3*t**2 - j*t**4 + 3*t**2.
-2*t**4
Let w be (3 - -1)*(-18)/(-8). Let t(v) = 3*v**3 - 11*v + 6. Let n(z) = 12*z**3 - 45*z + 24. Let i(u) = w*t(u) - 2*n(u). Factor i(h).
3*(h - 1)**2*(h + 2)
Let h(u) be the third derivative of u**6/180 + u**5/5 + 3*u**4 - u**3/3 + 14*u**2. Let d(f) be the first derivative of h(f). Suppose d(t) = 0. Calculate t.
-6
Factor -1 + 3*o**3 + 24*o - 35*o + 8*o + o**2.
(o - 1)*(o + 1)*(3*o + 1)
Let c(d) be the third derivative of d**7/504 + d**6/16 - 41*d**4/24 - 2*d**2 - 5. Let q(o) be the second derivative of c(o). Factor q(i).
5*i*(i + 9)
Let l be (8 - 10)/(0 + -1). Find z such that 0 + 3 + z + l + 9*z + 5*z**2 = 0.
-1
Let d(r) = 2*r**2 - r + 1. Let y(f) = -11*f**2 + 3*f - 2. Let g(i) = 20*d(i) + 4*y(i). Factor g(h).
-4*(h - 1)*(h + 3)
Let u = 138/41 - -2031/164. Factor -57/4*k - 9/2 - 27/4*k**3 - u*k**2 - 3/4*k**4.
-3*(k + 1)**3*(k + 6)/4
Let y(r) be the first derivative of 0*r + 8/3*r**3 + 2/3*r**6 + 16/5*r**5 + 2 + 0*r**2 + 5*r**4. Factor y(l).
4*l**2*(l + 1)**2*(l + 2)
Let y(r) be the first derivative of 3*r**5/40 - 9*r**4/16 + 3*r**3/2 - 3*r**2/2 + 9. Solve y(l) = 0 for l.
0, 2
Let g(n) be the first derivative of n**8/420 + n**7/168 - 7*n**6/360 - n**5/60 + 23*n**3/3 - 26. Let q(h) be the third derivative of g(h). Factor q(p).
p*(p - 1)*(p + 2)*(4*p + 1)
Let v(b) = b**3 - 9*b**2 + 28*b - 60. Let q be v(6). Let k(r) be the first derivative of q*r - r**3 + 4 + 3/2*r**2. Factor k(g).
-3*g*(g - 1)
Let z be (0 - -20)*162/4050*(-5)/(-6). Factor z*b**3 + 2*b**4 + 0*b - 8/3*b**5 + 0*b**2 + 0.
-2*b**3*(b - 1)*(4*b + 1)/3
Let v(f) = -135*f + 45. Let a(s) = -s**2 - 5*s - 1. Let i(o) = 6*a(o) - v(o). Factor i(d).
-3*(d - 17)*(2*d - 1)
Let 0 - 30/13*m - 18/13*m**3 + 46/13*m**2 + 2/13*m**4 = 0. What is m?
0, 1, 3, 5
Let a(j) be the third derivative of 0 - 6*j**2 - 1/210*j**7 + 1/180*j**6 - 1/24*j**4 + 0*j + 1/18*j**3 + 1/1008*j**8 + 1/90*j**5. Determine c so that a(c) = 0.
-1, 1
Let i(f) be the second derivative of f**6/360 - f**5/45 + f**4/18 - 9*f**2/2 - 2*f. Let l(g) be the first derivative of i(g). Factor l(w).
w*(w - 2)**2/3
Find v such that 1/2*v**3 + 0 - 3*v + 1/2*v**2 = 0.
-3, 0, 2
Let g(n) = -n**3 - 4*n**2 + 2*n. Let m be g(0). Factor 3/5*f**5 + m*f - 3/5*f**3 - 3/5*f**2 + 0 + 3/5*f**4.
3*f**2*(f - 1)*(f + 1)**2/5
Let i = 26 + -36. Let d(o) = 3*o + 32. Let s be d(i). What is g in -1/5*g**s + 2/5 + 1/5*g = 0?
-1, 2
Let y(q) = q - 5. Let p be y(7). Let b(n) = 34*n + 6. Let d be b(4). Suppose 32*i**4 - 100*i**3 - d*i + 9 + 152*i**p + 30*i - 5*i**5 + i**5 + 23 = 0. What is i?
1, 2
Suppose -p - 3*m - 6 = 0, -4*p + m + 25 = 10. Find v, given that v**4 - 8*v + 24*v**5 - 7*v**3 - p*v**4 - 48*v**2 - 59*v**3 = 0.
-1, -2/3, -1/4, 0, 2
Let j = 7234 + -7232. Factor 8/13*w - 6/13 - 2/13*w**j.
-2*(w - 3)*(w - 1)/13
Let 48/7*j + 4/7*j**2 + 144/7 = 0. What is j?
-6
Let q be 7/(-49) - 22/(-56). Let o(i) be the first derivative of 0*i - 3 - 1/3*i**3 + 0*i**2 - q*i**4. Suppose o(k) = 0. What is k?
-1, 0
Let a be -1*11*4/(-2). Suppose 2*o + 6*l - l + 11 = 0, a = 5*o - 4*l. Suppose -2*q**2 - 2 + o*q + 3 + 3*q**2 = 0. Calculate q.
-1
Suppose 3*r + 3*r = -42. Let d be 12/(-21)*(r - 0). Factor d*h**2 + 1 + 7 - 12*h + 0*h**2.
4*(h - 2)*(h - 1)
Suppose 61/2*a**2 + 0 + a = 0. Calculate a.
-2/61, 0
Let x(u) = u**3 - 5*u**2 - 2*u + 10. Let k be x(5). Suppose -4*y + 4*i = k, 3*i + 2*i - 10 = 0. Determine z, given that y*z + 2/3 - 8/3*z**2 = 0.
-1/4, 1
Factor 5*t**3 + 216*t - 181*t + 8*t**2 + 75 - 43*t**2.
5*(t - 5)*(t - 3)*(t + 1)
Factor -3/2*x**2 - 3/2 + 3*x.
-3*(x - 1)**2/2
Let n(q) be the first derivative of -3*q**5/10 - 33*q**4/8 - 12*q**3 + 27*q**2 + 4. Factor n(m).
-3*m*(m - 1)*(m + 6)**2/2
Let s(u) = -u**3 + 9*u**2 + 20*u - 17. Let h be s(8). Let c = 1037/5 - h. Factor -1/5*p + 3/5*p**2 - c.
(p - 1)*(3*p + 2)/5
Let u be (-4)/(-14) - (-8616)/28. Let q = -5850/19 + u. Factor -8/19*v + q*v**2 + 6/19.
2*(v - 3)*(v - 1)/19
Let f(b) = b**2 - b + 1. Let s be ((-10)/(-4) - 2)*4. Let r(o) = 4*o**2 - 3*o + 4. Let t(x) = s*r(x) - 10*f(x). Factor t(n).
-2*(n - 1)**2
Factor -65/2*t**3 - 295/2*t + 5/2*t**4 + 235/2*t**2 + 60.
5*(t - 8)*(t - 3)*(t - 1)**2/2
Let d(x) be the second derivative of x**4/6 + 5*x**3/3 - 14*x**2 + 2*x - 2. Find z such that d(z) = 0.
-7, 2
Let u(w) = 6*w - 14. Let x be u(3). Factor 41*v**3 - 38*v**3 - v**2 - 3*v**x - 3*v**5 + 4*v**5.
v**2*(v - 1)**3
Find r such that -110*r + 2570*r + 10 - 75645*r**2 + 0 - 30 = 0.
2/123
Let g(m) be the second derivative of m**7/42 - m**6/2 + 3*m**5 + 23*m**2/2 + 17*m. Let h(d) be the first derivative of g(d). Factor h(k).
5*k**2*(k - 6)**2
Factor 9*h**2 + 27/4*h + 3/2 + 15/4*h**3.
3*(h + 1)**2*(5*h + 2)/4
Let f(s) be the first derivative of s**6/3 - 92*s**5/5 + 673*s**4/2 - 5216*s**3/3 - 7424*s**2 - 8192*s - 205. Factor f(d).
2*(d - 16)**3*(d + 1)**2
Let x be (2/(-6))/((-980)/840). Let r(t) be the first derivative of 2/7*t**4 + 2/35*t**5 + 4/7*t**3 + 11 + x*t + 4/7*t**2. Find u, given that r(u) = 0.
-1
Let p = -3 + 13. Suppose p*y - 5*y - 20 = 0. Factor -4*f - 6*f**3 - 15*f**2 - 4 + y - 8*f - 3.
-3*(f + 1)**2*(2*f + 1)
Factor -264*v**2 - 259*v**2 + 511*v**2 + 9*v - 5*v**3.
-v*(v + 3)*(5*v - 3)
Let r be 2/(-18) - 28/(-9). Let n(q) be the second derivative of 0*q**2 + r*q + 0 + 1/45*q**3 + 0*q**4 - 1/150*q**5. Solve n(c) = 0 for c.
-1, 0, 1
Let s(k) = 25*k - 2595. Let x be s(104). What is n in 5/4*n**x + 3/2 - 2*n**4 - 6*n**3 + 19/4*n + 1/2*n**2 = 0?
-1, -2/5, 1, 3
Factor 16/5*m - 24/5 - 2/5*m**2.
-2*(m - 6)*(m - 2)/5
Suppose v = 2*h - 15, h + 4*v + v - 2 = 0. Let x = -5 + h. Factor 0*l + 0*l**x - 1/2*l**3 + 0 - 1/2*l**4.
-l**3*(l + 1)/2
Let k(d) be the second derivative of -d**5/120 + 25*d**4/72 - 47*d**3/36 + 23*d**2/12 - 18*d. Suppose k(a) = 0. What is a?
1, 23
Let t = 214/195 - 35/39. Determine f so that -2/5*f**2 - 3/5*f - t = 0.
-1, -1/2
Let p(n) = -9*n**3 - 9*n**2 - 17*n. Let i(s) = -7*s**3 - 8*s**2 - 15*s + 2. Let f(d) = 5*i(d) - 4*p(d). Factor f(k).
(k - 5)*(k - 1)*(k + 2)
Let p(q) be the first derivative of 20 + 0*q - 4/9*q**3 + 1/18*q**6 + 1/2*q**4 - 4/15*q**5 + 1/6*q**2. Solve p(r) = 0.
0, 1
Let h = 6/1837 + 3656/5511. Factor 2*m**2 - 2/3*m - 2 + h*m**3.
2*(m - 1)*(m + 1)*(m + 3)/3
Suppose -k - 1/2*k**5 - 1/2*k**4 + 1/2*k**2 + 3/2*k**3 + 0 = 0. What is k?
-2, -1, 0, 1
Let 2/7*i**5 + 0*i**4 + 0*i**2 + 2/7*i - 4/7*i**3 + 0 = 0. Calculate i.
-1, 0, 1
Let b(a) = -a**2 + 10*a. Let x be b(10). Suppose x = k - 2*k + 2. Factor -2*f**3 + 4*f + 4*f**k - 2*f**4 - 2*f**2 - 2*f + 0*f.
-2*f*(f - 1)*(f + 1)**2
Let i(n) be the second derivative of n**7/1400 - 3*n**5/200 + n**4/20 + n**3/2 + 11*n. Let a(p) be the second derivative of i(p). Let a(u) = 0. What is u?
-2, 1
Factor -108*y + 45*y**2 - 44*y**2 - 145 + 3061.
(y - 54)**2
Let n be (-191)/300 + ((-120)/(-18) - 6). Let w(j) be the second derivative of 1/30*j**3 + n*j**5 - j + 0 - 1/150*j**6 + 0*j**2 - 1/20*j**4. Factor w(f).
-f*(f - 1)**3/5
Factor 619*m - 108*m**3 - 59*m - 103*m**3 + 206*m**3 + 270*m**2.
-5*m*(m - 56)*(m + 2)
Find f such that 1/2*f + 1/4*f**4 + 5/4*f**2 + 0 + f**3 = 0.
-2, -1, 0
Let z = -699/5 + 140. Let k = 168/305 + 3/61. Factor 1/5*d**5 + k*d**4 + 0 - 3/5*d**2 + z*d**3 - 2/5*d.
d*(d - 1)*(d + 1)**2*(d + 2)/5
Let j be (9/(-78))/(213/(-568)). Find v such that 6/13 - 2/13*v**2 - j*v = 0.
-3, 1
Let r = 71 + 31. Suppose -3*k = -r + 30. Suppose -p + 2*p**3 - p**5 - k + 24 = 0. What is p?
-1, 0, 1
Factor 3/5*z**2 + 42/5*z + 72/5.
3*(z + 2)*(z + 12)/5
Let m be (0 + 3)/(108/8). Let f(r) be the first derivative of 0*r + r**2 + m*r**3 + 3. Factor f(h).
2*h*(h + 3)/3
Let d(a) = -4*a**2 + 29*a + 69. Let t(p) = 5*p**2 - 3*p. Let i(l) = 5*d(l) + 5*t(l). Factor i(x).
5*(x + 3)*(x + 23)
Let w(q) be the second derivative of q**5/4 - 35*q**4/12 + 55*q**3/6 - 25*q**2/2 - 10*q. Let w(n) = 0. What is