r).
-(r - 1)*(r + 1)**2/5
Let s(v) be the first derivative of 9*v**4/4 + 13*v**3 - 21*v - 3. Let j(h) = -h**3 - 4*h**2 + 2. Let o(n) = -21*j(n) - 2*s(n). Factor o(f).
3*f**2*(f + 2)
Suppose -60*f + 59*f + 6 = -3*q, -5*q = 10. Factor f + 4/9*i - 4/9*i**2.
-4*i*(i - 1)/9
Let o(w) = w**5 - w**4 + w**3 - w**2 + w. Let g(q) = 4*q**4 + 12*q**3 - 20*q**2 + 8. Let p(t) = g(t) - 4*o(t). Solve p(u) = 0.
-1, 1, 2
Let q(m) = 5*m**3 + 5*m**2 + 28*m + 12. Let x(g) = 6*g**3 + 4*g**2 + 30*g + 12. Let a(f) = 5*q(f) - 4*x(f). Factor a(n).
(n + 1)*(n + 2)*(n + 6)
Let a(o) be the third derivative of 2*o**7/105 - o**6/5 - o**5/5 + 8*o**4/3 + 8*o**3 + 119*o**2. Find z such that a(z) = 0.
-1, 2, 6
Let c(h) = -h**3 + 7*h**2 + 6*h + 11. Let j be c(8). Let l be 4/j*(-3 + -2). Let -24/5*k**3 - 3*k**l - 3/5*k**5 + 0 + 0*k - 12/5*k**2 = 0. What is k?
-2, -1, 0
Factor -2/15*s**3 - 34*s + 22/5*s**2 - 578/15.
-2*(s - 17)**2*(s + 1)/15
Let m(j) be the first derivative of 0*j**3 - 1/15*j**5 + 15 + 0*j**2 - 1/12*j**4 + 0*j. Suppose m(h) = 0. Calculate h.
-1, 0
Factor 229/6*a**2 + 2166 + 2204*a + 1/6*a**3.
(a + 1)*(a + 114)**2/6
Let j(n) = n**2 - n + 1. Let p(h) be the first derivative of -5*h**3/3 - h**2/2 - h + 2. Let r(m) = 14*j(m) + 2*p(m). Find i such that r(i) = 0.
1, 3
Suppose 2*w = 1 + 5. Let q be (4/w)/((-1)/(-3)). Find m, given that 113*m**2 + q - 44*m - 76*m**2 + 84*m**2 = 0.
2/11
Let h(c) = 40*c**2 + 34*c - 6. Let d(y) = 2*y + 4*y - 2 - 4*y + 13*y**2 + 9*y. Let k(a) = -16*d(a) + 5*h(a). Determine l, given that k(l) = 0.
-1, 1/4
Suppose -2*y + 8 = -6. Let m(d) = d - 2. Let z be m(y). Factor 5*f**3 - 3*f**2 - 9*f**3 - z*f**3 + 12*f**5.
3*f**2*(f - 1)*(2*f + 1)**2
Suppose 111 = 51*w - 42. Let z(q) be the third derivative of 0*q**3 - 1/105*q**7 - w*q**2 + 0*q**4 + 0 + 0*q**5 + 0*q + 1/30*q**6. Factor z(y).
-2*y**3*(y - 2)
Let 7*g**4 + 8*g**4 + 14 - 4*g**2 - 10 + 55*g**3 + g**2 + 60*g - 99*g**3 = 0. Calculate g.
-1, -1/15, 2
Factor 36 + 3/4*d**3 - 21/2*d**2 - 105/4*d.
3*(d - 16)*(d - 1)*(d + 3)/4
Let j(w) be the second derivative of -w**6/135 + 4*w**5/45 - 19*w**4/54 + 4*w**3/9 + 23*w. Factor j(o).
-2*o*(o - 4)*(o - 3)*(o - 1)/9
Let f(t) be the second derivative of t**5/5 - 5*t**4/3 + 14*t**3/3 - 6*t**2 + 408*t. Factor f(q).
4*(q - 3)*(q - 1)**2
Let v = -2822/423 + 324/47. Let d be (-2)/((-2 + 1)*9). Factor d*p**2 - 4/9 - v*p.
2*(p - 2)*(p + 1)/9
Factor 1/2*p**4 + 2*p**3 + 1/2 + 3*p**2 + 2*p.
(p + 1)**4/2
Suppose -32*u = -21*u - 55. Let d = 0 - -3. Solve -6*y**5 - 5*y**d - 6*y**4 + 13*y**u + 13*y**5 - 9*y**4 = 0 for y.
-1/4, 0, 1
Let w(c) = c**5 - c**4 - 4*c**3. Let b(r) = -8*r**5 - 32*r**4 - 23*r**3 + 115*r**2 + 40*r - 80. Let j(s) = b(s) + 3*w(s). Find i, given that j(i) = 0.
-4, -1, 1
Let w(x) = x + 3. Let f be w(-1). Determine n, given that -13*n - 50*n**2 - 5*n - 24 + 47*n**f = 0.
-4, -2
Factor 50/9*x - 2/9*x**3 - 26/9 - 22/9*x**2.
-2*(x - 1)**2*(x + 13)/9
Let p(z) = 12*z**2 + z - 1. Let l(a) = -31*a**2 - 13*a - 492. Let r(u) = l(u) + 3*p(u). Factor r(q).
5*(q - 11)*(q + 9)
Suppose 0 = -5*n - 5*o + 2*o + 3, o = 3*n + 1. Let p(s) be the first derivative of 7 + n*s - 2*s**2 + 4/3*s**3. Factor p(y).
4*y*(y - 1)
Let j be (6 + -6)/(-4 - (5 - 10)). Solve -1/3*u**5 + j - 2/3*u**2 + 1/3*u + 2/3*u**4 + 0*u**3 = 0 for u.
-1, 0, 1
Let o be 6 + (10/(-2))/5. Let w = 11 - o. Find b, given that -2*b + w*b - 8*b + 2*b**2 + 2 = 0.
1
Let b = -3443/427 - -518/61. Find y such that 33/7*y + b*y**2 - 36/7 = 0.
-12, 1
Let v(k) be the first derivative of 0*k**3 + 1/15*k**5 + 1/36*k**6 + 1/24*k**4 - 4 + 0*k**2 + 0*k. Determine h, given that v(h) = 0.
-1, 0
Solve 56/5*w + 4/5*w**4 - 76/5*w**2 + 16/5*w**3 + 0 = 0.
-7, 0, 1, 2
Let l(q) be the second derivative of -q**4/66 - 17*q**3/33 + 18*q**2/11 + 20*q. Factor l(p).
-2*(p - 1)*(p + 18)/11
Let m(d) be the second derivative of -13*d - 2*d**2 - 19/9*d**3 + 0 - 13/18*d**4. Find z, given that m(z) = 0.
-1, -6/13
Find w such that 1/3*w**2 + 3 - 10/3*w = 0.
1, 9
Let o = 14 - 12. Factor -15*b**2 + 0*b**2 - 4*b**4 + 3*b**3 + 13*b**3 + 3*b**o.
-4*b**2*(b - 3)*(b - 1)
Let 1/9*a**2 + 529/9 - 46/9*a = 0. Calculate a.
23
Let d(t) = 7*t**3 + 7*t**2 + 21*t - 5. Let b(s) = 4*s**3 + 3*s**2 + 11*s - 3. Let a(g) = 5*b(g) - 3*d(g). Suppose a(v) = 0. What is v?
-4, -2, 0
Suppose k - 11 = -4*o, -22*o + 24*o - 1 = k. Let m(h) be the second derivative of 0 + 1/4*h**o - 7*h + 0*h**3 - 1/24*h**4. Factor m(y).
-(y - 1)*(y + 1)/2
Let l = -473 - -473. Let z(q) be the second derivative of 4/5*q**3 - 1/70*q**7 - 9/50*q**5 - 1/5*q**4 + l*q**2 + 2*q + 0 + 1/10*q**6. Factor z(r).
-3*r*(r - 2)**3*(r + 1)/5
Suppose -1053 = -362*q + 221 - 188. Find s, given that 16/5*s + 2*s**2 + 8/5 + 2/5*s**q = 0.
-2, -1
Suppose 22 = 7*g - 6. Let u be (-16)/(-36)*6/g. Factor -2*x**2 + u*x + 2*x**3 - 2/3*x**4 + 0.
-2*x*(x - 1)**3/3
Let t(h) be the third derivative of h**10/50400 + h**9/4032 + h**8/960 + h**7/560 + h**5/12 + 34*h**2. Let s(m) be the third derivative of t(m). Solve s(d) = 0.
-3, -1, 0
Suppose -4*m = 3*z + 10, 0*m + 4*m + 18 = z. Let i(f) be the second derivative of -3*f**3 + 2*f**2 - 3*f + 0 - 1/2*f**5 + z*f**4. Factor i(u).
-2*(u - 1)**2*(5*u - 2)
Let j(a) be the third derivative of a**8/131040 - a**7/8190 + a**6/1560 - 3*a**5/20 - 5*a**2 - 3. Let h(b) be the third derivative of j(b). Solve h(v) = 0.
1, 3
Factor -28*r + 4*r**3 - r**2 - 4*r + 22 - 3*r**2 + 26.
4*(r - 2)**2*(r + 3)
Let h = 13022/7 + -1860. Factor 4/7*j + h + 2/7*j**2.
2*(j + 1)**2/7
Let q(s) be the third derivative of -3*s**5/20 - 47*s**4/4 - 31*s**3/2 - 556*s**2. Factor q(z).
-3*(z + 31)*(3*z + 1)
Let h(g) be the first derivative of g**6/3060 - g**5/1020 - g**4/102 + 8*g**3/3 + 12. Let n(q) be the third derivative of h(q). Factor n(j).
2*(j - 2)*(j + 1)/17
Let s(d) = 3*d**3 - 13*d**2 - 8*d. Let u be 115/20 + 2/8. Let h(p) = 52 - u*p**2 - 52 + p**3 - 4*p. Let l(y) = 5*h(y) - 2*s(y). Find n such that l(n) = 0.
-2, 0
Let c(x) = -x**3 + x**2 + 4*x - 3*x - 1 - 4*x + 2*x. Let h(a) = -2*a**5 + 4*a**3 - 10*a. Let r(f) = -4*c(f) + h(f). Factor r(n).
-2*(n - 1)**3*(n + 1)*(n + 2)
Let a(v) = v**4 - v**3 - 1. Let k = 14 - 6. Let n = k - 9. Let i(w) = -6*w**4 + 6*w**3 + 5. Let p(j) = n*i(j) - 5*a(j). Determine h so that p(h) = 0.
0, 1
Find t such that 5*t**4 + 30*t**2 - 7*t**3 + 37*t**3 + 55*t + 45*t + 15*t**3 + 90*t**2 = 0.
-5, -2, 0
Suppose 62/7*w**3 + 32/7*w**5 - 160/7*w**4 - 16/7 + 38*w**2 - 4/7*w = 0. Calculate w.
-1, -1/4, 1/4, 2, 4
Let j(u) be the second derivative of -u**4/3 + 64*u**3/3 - 512*u**2 + 62*u + 1. Let j(m) = 0. What is m?
16
Let f(u) be the second derivative of 1/9*u**4 - 4/9*u**3 + 0 + u + 0*u**2. What is t in f(t) = 0?
0, 2
Factor 1/4*c + 7/4*c**3 + 0 + 2*c**2.
c*(c + 1)*(7*c + 1)/4
Let u be 9/3*-12*12/(-108). What is k in -8*k**2 + 2*k**u - 16/3*k + 0 + 4/3*k**3 = 0?
-2, -2/3, 0, 2
Let b be (((-6)/(-2))/12)/((-4)/(-352)). Factor -b*i**2 - 47/2*i - 7/2*i**3 - 5.
-(i + 1)*(i + 5)*(7*i + 2)/2
Let q(u) be the second derivative of u**4/72 + 4*u**3/9 + 16*u**2/3 + 19*u - 2. Factor q(z).
(z + 8)**2/6
Determine p so that 1/5*p**2 + 4/5*p + 4/5 = 0.
-2
Factor -5*y**4 - 268*y + 12*y**2 + 22*y**3 + 2*y**5 + 17*y**4 + 134*y + 134*y.
2*y**2*(y + 1)*(y + 2)*(y + 3)
Let y(a) = -a**5 - a**4 + 65*a**3 - 95*a**2 + 39*a. Let l(d) = 32*d**3 - 48*d**2 + 20*d. Let b(k) = 7*l(k) - 4*y(k). Solve b(q) = 0.
-4, 0, 1
Let b(s) be the third derivative of -s**7/735 + s**6/60 - s**5/42 - s**4/12 + 2*s**3/7 + 104*s**2. Suppose b(v) = 0. What is v?
-1, 1, 6
Let z(k) be the first derivative of 2*k**3/3 + 101*k**2 - 204*k + 385. Suppose z(i) = 0. Calculate i.
-102, 1
Suppose 85*f - 78 = 72*f. Let u(n) be the first derivative of 1/6*n**6 + 0*n**3 + 0*n - 1/2*n**4 - f + 1/2*n**2 + 0*n**5. Determine k, given that u(k) = 0.
-1, 0, 1
Let g(o) = 8*o**2 - o - 5. Let u be (-58)/(-8) + (-6)/(-8). Let d(k) = -k + u + 3*k + 0*k - 7*k**2 - 4. Let y(w) = 5*d(w) + 4*g(w). Let y(f) = 0. What is f?
0, 2
Suppose -3*y + 4 = -y. Let -7 + 24*v + 12*v**2 + 0*v**y + 9*v**2 - 15*v**3 - 5 = 0. What is v?
-1, 2/5, 2
Let k(l) = l**3 - 4*l**2 - 4*l - 3. Let f be k(5). Solve 1 + 8*j**3 - f + 1 + 12*j**2 - 8*j = 0.
-2, 0, 1/2
Find o, given that 5*o**2 - o**2 + 35*o - 4*o**2 - 5*o**2 + 774 - 834 = 0.
3, 4
Let k = -68 + 68. Suppose -4*t - 21*g = -16*g - 7, k = -5*