 1)**3/2
Let j(q) = -5*q**5 + q**4 + q**3 + 3. Let y(i) = 9*i**5 - 3*i**4 - i**3 - 5. Suppose 4*n = 9*n - 15. Let w(m) = n*y(m) + 5*j(m). Factor w(v).
2*v**3*(v - 1)**2
Determine s so that -2/7*s - 23/7*s**2 + 64/7*s**5 - 80/7*s**4 + 0 - 12*s**3 = 0.
-1/4, 0, 2
Let l(s) = -5*s**3 + 12*s**2 - s - 2. Let h(b) = -14*b**3 + 36*b**2 - 2*b - 6. Let i(v) = 2*h(v) - 7*l(v). Suppose i(k) = 0. What is k?
-2/7, 1
Let h be (-8)/36 + 24/27. What is w in 0*w - 2/3*w**4 + 0 + 4/3*w**3 - h*w**2 = 0?
0, 1
Determine y so that -1/7 + 3/7*y**2 + 0*y - 2/7*y**3 = 0.
-1/2, 1
Let d(a) = a**5 - a**4 + a**3 - a**2 + a + 1. Let l(t) = 2*t**5 - 6*t**4 + 10*t**3 - 6*t**2 + 6*t + 6. Let h(o) = -6*d(o) + l(o). Factor h(y).
-4*y**3*(y - 1)*(y + 1)
Let n be (150/(-525))/(-1*10/14). Suppose 0 + n*y**2 + 0*y = 0. Calculate y.
0
Let d(q) be the first derivative of q**8/1680 - q**6/180 + q**4/24 - q**3 + 1. Let m(t) be the third derivative of d(t). Determine p so that m(p) = 0.
-1, 1
Let z(w) be the second derivative of -1/12*w**4 + 2/3*w**3 + 0 + w - 2*w**2. Solve z(g) = 0 for g.
2
Factor 8/3*r**2 - 8/3*r - 2/3*r**3 + 0.
-2*r*(r - 2)**2/3
Let n(c) be the second derivative of -2*c**7/3 + 2*c**6/3 + 23*c**5/5 - 29*c**4/3 + 8*c**3/3 + 8*c**2 - 2*c + 6. What is t in n(t) = 0?
-2, -2/7, 1
Let z be 4 + (-2 - (-5 + 7)). Determine x so that z + 1/4*x**2 - x = 0.
0, 4
Let a be 520/924 + (-4)/22. Let c(y) be the first derivative of -1/7*y**2 - a*y**3 + 0*y + 2. Factor c(s).
-2*s*(4*s + 1)/7
Find y, given that y - y**3 + 1/3*y**4 + 1/3*y**2 - 2/3 = 0.
-1, 1, 2
Let o(c) = 2*c**3 - 6*c - 2. Let b(w) = -2*w**3 + 5*w + 3. Let f(m) = 2*b(m) + 3*o(m). Determine x so that f(x) = 0.
-2, 0, 2
Let k(o) be the third derivative of 0 - 1/36*o**4 - 1/270*o**5 + 0*o**3 + o**2 + 0*o. Factor k(t).
-2*t*(t + 3)/9
Let n(w) be the first derivative of -w**6/180 - w**5/60 + w**4/6 + w**3 - 1. Let o(d) be the third derivative of n(d). Factor o(c).
-2*(c - 1)*(c + 2)
Let n(s) be the third derivative of -s**7/3360 + s**6/360 - s**5/160 - s**3/2 + 5*s**2. Let w(d) be the first derivative of n(d). Factor w(j).
-j*(j - 3)*(j - 1)/4
Let x = 24 - 47/2. Let s = 70 + -68. Let n - x*n**s - 1/2 = 0. Calculate n.
1
Factor 3/2*h**2 + 3*h + 0.
3*h*(h + 2)/2
Suppose -1 - 7 = c + 2*n, 5*n = -3*c - 25. Let u = -6 - c. Factor 0*s**2 + 3*s**2 - s + 2*s - u*s**2.
-s*(s - 1)
Suppose 4 = -t + 6. Let o(k) be the first derivative of 0*k**3 + 3/25*k**5 - 3/5*k + 3/10*k**4 - 3/5*k**t + 3. Let o(g) = 0. Calculate g.
-1, 1
Factor -1/6*d**4 + 0 + 1/6*d**3 + 1/2*d + 5/6*d**2.
-d*(d - 3)*(d + 1)**2/6
Let n(c) be the first derivative of -3*c**4/4 + 2*c**3 - 3*c**2/2 + 29. Factor n(s).
-3*s*(s - 1)**2
Determine m so that -4/5 - 81/5*m**2 + 36/5*m = 0.
2/9
Suppose 2736*s - 2742*s = -12. Factor 1/4*z + 1/2 - 1/4*z**s.
-(z - 2)*(z + 1)/4
Let j(c) = c - 1. Let u(s) = 2*s**2 - 6*s + 4. Let y(o) = -12*j(o) - 2*u(o). Factor y(z).
-4*(z - 1)*(z + 1)
Let n(g) be the first derivative of -g**6/9 + 5*g**4/3 + 40*g**3/9 + 5*g**2 + 8*g/3 - 41. Factor n(b).
-2*(b - 4)*(b + 1)**4/3
Let o(g) = g**3 - 16*g**2 + 34*g - 27. Let s(w) = -w**2 + w. Let m(p) = -4*o(p) + 28*s(p). Factor m(n).
-4*(n - 3)**3
Let f(j) = 2*j**4 + 10*j**2. Let c(b) = -4*b**4 + b**3 - 21*b**2. Let t(z) = 6*c(z) + 13*f(z). Factor t(n).
2*n**2*(n + 1)*(n + 2)
Let h(x) = -x + 12. Let n be h(8). Let i(y) be the second derivative of 0*y**2 + 0 + 1/4*y**n + y + 0*y**3. Factor i(l).
3*l**2
Let 28*o**2 - 711 + 12*o**4 - 8*o - 32*o**3 + 711 = 0. Calculate o.
0, 2/3, 1
Let b be 6 + (-5)/((-5)/(-4)). Let x(n) be the second derivative of 1/12*n**4 + 0 + n + 1/60*n**5 + 1/6*n**3 + 1/6*n**b. Suppose x(j) = 0. Calculate j.
-1
Let h = 0 - -4. Suppose 3*l - 5 = 3*x + 8*l, 0 = h*x + l - 16. Factor 3*p**5 - 4*p**5 + 0*p**x - p**4.
-p**4*(p + 1)
Let g(q) be the third derivative of q**5/60 - q**4/24 + 4*q**2. Find v, given that g(v) = 0.
0, 1
Suppose 0 = -8*p + 7*p. Let u = -7 - -15/2. Find x, given that p*x - u + 1/2*x**2 = 0.
-1, 1
Factor -1/2*v + 1/4 + 1/4*v**2.
(v - 1)**2/4
Suppose -23 + 5 = 2*v. Let u be (-3)/v - 24/(-9). What is t in 48/7*t**4 + 2/7*t**2 + 32/7*t**5 + 0*t + 18/7*t**u + 0 = 0?
-1, -1/4, 0
Let l be (-2786)/(-280) - (4/(-5) - -1). Solve -57/4*b**3 - l*b**2 + 3 + 27/4*b**4 + 9*b + 21/4*b**5 = 0 for b.
-2, -1, -2/7, 1
Let u(a) be the third derivative of -a**5/180 + 5*a**4/72 + a**3/3 + 4*a**2 - 1. Determine f so that u(f) = 0.
-1, 6
Let m be ((-6)/3 - 2)/(2/(-1)). Factor 2/9 + 4/9*w + 2/9*w**m.
2*(w + 1)**2/9
Let p = -1/66 + 2/11. Let a(l) be the first derivative of -2 - 1/8*l**2 + 0*l - p*l**3 - 1/16*l**4. Factor a(w).
-w*(w + 1)**2/4
Let y(h) be the second derivative of -h**6/1620 - h**5/90 - h**4/12 + h**3 - 2*h. Let t(p) be the second derivative of y(p). Factor t(v).
-2*(v + 3)**2/9
Let d(q) be the third derivative of -q**8/2184 - q**7/1365 + q**6/780 + q**5/390 - 9*q**2. Factor d(a).
-2*a**2*(a - 1)*(a + 1)**2/13
Let n(r) be the second derivative of -3/10*r**5 - 1/15*r**6 + 0 - 2*r - 1/2*r**4 + 0*r**2 - 1/3*r**3. Find u, given that n(u) = 0.
-1, 0
Let y(r) be the first derivative of -2/3*r**3 + 0*r - 2/15*r**5 + 2/3*r**4 + 0*r**2 - 3. Factor y(h).
-2*h**2*(h - 3)*(h - 1)/3
Let s(b) be the third derivative of b**5/3 - 25*b**4/24 + 46*b**2. Find k, given that s(k) = 0.
0, 5/4
Factor -1/2*a + 1/4*a**2 + 0.
a*(a - 2)/4
What is r in 3/5*r - 3/5*r**4 + 3/5*r**2 + 0 - 3/5*r**3 = 0?
-1, 0, 1
Let r(d) = -d**3 + 3*d**2 - d + 3. Let v be r(3). Factor 0*u**2 + v*u + 0 - 2/11*u**3.
-2*u**3/11
Let d(r) be the first derivative of -154*r**6/9 + 92*r**5/5 + 89*r**4/3 - 292*r**3/9 - 8*r**2 + 16*r/3 - 7. Solve d(q) = 0 for q.
-1, -2/7, 2/11, 1
Let u(f) be the third derivative of f**7/3780 - 7*f**6/1620 + f**5/36 - f**4/12 + f**3/6 + 5*f**2. Let i(s) be the first derivative of u(s). Factor i(c).
2*(c - 3)**2*(c - 1)/9
Let f be (-3 + 2)*1 + 1. Let w(p) be the first derivative of -2/5*p**5 + 0*p**3 - 1/4*p**4 + 1 - 1/6*p**6 + 0*p + f*p**2. Factor w(z).
-z**3*(z + 1)**2
Let h(t) be the first derivative of -3 + 3*t + 1/4*t**4 - 1/2*t**3 + 0*t**2. Let a(j) be the first derivative of h(j). Determine u, given that a(u) = 0.
0, 1
Let n be 8/(-6)*(-6)/44. Let g be 4 - 336/88 - 4/22. Factor g + n*c**2 - 2/11*c.
2*c*(c - 1)/11
Let s(t) = 2*t**3 - 2*t**2 - 7*t - 3. Let w(n) = -n - 1. Let a(o) = s(o) - 3*w(o). Solve a(u) = 0.
-1, 0, 2
Let w(z) be the third derivative of 5*z**8/84 - 4*z**7/21 - 11*z**6/24 + 13*z**5/12 + 10*z**4/3 + 10*z**3/3 - 10*z**2. Let w(m) = 0. What is m?
-1, -1/2, 2
Let o = 1955 + -13718/7. Let j = o - -5. Suppose 0*b - j*b**2 + 4/7*b**3 - 2/7*b**4 + 0 = 0. Calculate b.
0, 1
Let u(h) be the first derivative of h**6/300 - h**4/60 + 2*h**2 - 1. Let q(w) be the second derivative of u(w). Determine b so that q(b) = 0.
-1, 0, 1
Let r = 0 - -2. Let d be r/(-2*(-3)/12). Factor -5*n**4 + 0*n**3 - d*n**3 - n**2 - 2*n**5 + 0*n**4.
-n**2*(n + 1)**2*(2*n + 1)
Let v(y) be the first derivative of y**6/15 + 2*y**5/25 - 3. Factor v(z).
2*z**4*(z + 1)/5
Let y(z) be the third derivative of 0 - 1/60*z**5 + 0*z**4 + 0*z + 1/3*z**3 + z**2 + 1/180*z**6. Let v(m) be the first derivative of y(m). Factor v(k).
2*k*(k - 1)
Suppose n + 3 = 4. Let m be 3 + (-2 - (n - 2)). Factor -7*t**2 - 18*t - 13*t**m - 4 + 3*t**5 + 8*t**3 + 7*t**5 + 24*t**4.
2*(t - 1)*(t + 1)**3*(5*t + 2)
Let b(z) = -45*z**5 + 55*z**4 - 75*z**3 + 15*z**2 + 25*z. Let j(r) = 11*r**5 - 14*r**4 + 19*r**3 - 4*r**2 - 6*r. Let c(s) = 6*b(s) + 25*j(s). Factor c(h).
5*h**2*(h - 2)*(h - 1)**2
Let w(d) be the second derivative of d**5/4 + 5*d**4/12 - 10*d**3/3 - 10*d**2 - 16*d. Find j such that w(j) = 0.
-2, -1, 2
Let v(h) be the first derivative of h**7/56 + h**6/120 - 3*h**5/80 - h**4/48 + 3*h + 3. Let o(c) be the first derivative of v(c). Solve o(l) = 0 for l.
-1, -1/3, 0, 1
Factor -6/7*n - 4/7*n**2 + 4/7*n**3 + 2/7*n**5 + 6/7*n**4 - 2/7.
2*(n - 1)*(n + 1)**4/7
Let z(b) be the second derivative of b**5/60 - b**4/27 - 2*b**3/27 - 10*b. Factor z(i).
i*(i - 2)*(3*i + 2)/9
Let z(w) be the second derivative of 0*w**2 + 0 - 3*w - 1/36*w**4 - 1/18*w**3. Factor z(j).
-j*(j + 1)/3
Let h(d) = 2*d - 1. Let o be h(3). Suppose -25 = -5*w + 5*t, -5*t + 4*t = w + o. Find m, given that -2/9*m**5 + 0*m**4 - 2/9*m + 0 + w*m**2 + 4/9*m**3 = 0.
-1, 0, 1
Let z be (2 - 3)*(-1 + -5)