1. Factor u(w).
-(w - 1)*(w + 3)/2
Let c = -2 - -11. What is k in -5*k - 2 + 1 - 4*k - 3*k**3 - 2 - c*k**2 = 0?
-1
Let p(b) be the third derivative of -2*b**7/945 + 2*b**6/135 - b**5/27 + b**4/27 + 5*b**2. Let p(r) = 0. What is r?
0, 1, 2
Let t(a) be the first derivative of 28*a**5/5 - 19*a**4 + 32*a**3/3 + 8*a**2 + 3. Let t(p) = 0. What is p?
-2/7, 0, 1, 2
Let u = 36/7 + -857/168. Let n(d) be the second derivative of 1/48*d**4 - u*d**6 + 1/80*d**5 + 4*d + 1/56*d**7 + 0 + 0*d**2 + 0*d**3. Factor n(x).
x**2*(x - 1)**2*(3*x + 1)/4
Let t be (-5 - 760/(-112)) + 2/(-7). Factor -15/2*l**4 - 6*l**2 - t*l**5 + 0 + 0*l - 12*l**3.
-3*l**2*(l + 1)*(l + 2)**2/2
Let p be 6*(-65)/10 - 2. Let u = 207/5 + p. Solve u*a**2 + 0 - a**3 + 3/5*a**4 + 0*a = 0 for a.
0, 2/3, 1
Let r = -96 - -98. Solve 0*j + 2/7*j**r + 0 = 0 for j.
0
Factor 0*n + 1/3*n**2 + 1/3*n**3 + 0.
n**2*(n + 1)/3
Let z(t) be the second derivative of 0*t**2 + 0*t**3 + 1/48*t**4 - 1/80*t**5 + 0 - t. Find q, given that z(q) = 0.
0, 1
Let s(v) = -60*v**3 - 156*v**2 - 68*v - 8. Let w(i) = 59*i**3 + 155*i**2 + 68*i + 8. Let d(p) = -5*s(p) - 4*w(p). Find h such that d(h) = 0.
-2, -1/4
Suppose -2*s + 3 - 1 = 0. Let n(k) be the first derivative of 0*k - 1/6*k**4 - 1/9*k**3 + 0*k**2 - s. Factor n(q).
-q**2*(2*q + 1)/3
Let m(g) be the second derivative of -1/5*g**5 - g**4 + 0 + 0*g**2 - 4/3*g**3 - 4*g. Let m(p) = 0. Calculate p.
-2, -1, 0
What is i in -2/7*i + 2/7*i**2 - 12/7 = 0?
-2, 3
Let j be (-6 + -39)/9*(-6)/70. Solve 6/7*n**2 - 3/7*n**4 + 3/7*n**5 + j*n - 6/7*n**3 - 3/7 = 0 for n.
-1, 1
Factor -2*o**5 + 2*o**4 - 2*o**3 - 4*o**4 + 2*o**2 + 4*o**5.
2*o**2*(o - 1)**2*(o + 1)
Let v(j) = j**2 + 6*j + 7. Let y be v(-5). Suppose g + l = 4, -y*l + l = -2*g + 8. Factor 0*w**5 + 2*w**5 - w**4 + 3*w**g.
2*w**4*(w + 1)
Let f be ((-16)/4 - -4)*-1. Let m(p) be the first derivative of f*p - 4/7*p**2 - 13/14*p**4 + 2 - 8/7*p**3 - 1/21*p**6 - 12/35*p**5. Let m(b) = 0. What is b?
-2, -1, 0
Suppose -5*x = -13 - 7. Suppose 0 = -q - q + x. Factor 6/13*t**q - 6/13*t - 2/13*t**3 + 2/13.
-2*(t - 1)**3/13
Let s(t) be the first derivative of -4*t**2 + 10/3*t**3 - t**4 - 2 + 2*t. Suppose s(z) = 0. Calculate z.
1/2, 1
Let g(l) be the second derivative of -l**7/1260 - l**6/360 + l**5/30 - l**4/6 + 3*l. Let y(a) be the third derivative of g(a). Let y(c) = 0. What is c?
-2, 1
Let w(b) = -b + 5. Let k be w(3). Find j, given that -1 - 10*j - 2*j**k + 3 - 23*j**3 + 33*j**3 = 0.
-1, 1/5, 1
Let g(p) be the third derivative of p**6/80 - p**5/10 + p**4/16 + 3*p**3/2 + 11*p**2. Factor g(j).
3*(j - 3)*(j - 2)*(j + 1)/2
Let d(q) be the third derivative of q**8/56 - q**7/21 - 7*q**6/60 + 3*q**5/10 + q**4/3 - 4*q**3/3 - 4*q**2. Find a such that d(a) = 0.
-1, 2/3, 1, 2
Solve 2/13*z**3 - 2/13*z**5 + 0 - 2/13*z**2 + 0*z + 2/13*z**4 = 0.
-1, 0, 1
Let c(v) be the third derivative of v**8/112 + v**7/21 + 37*v**6/360 + v**5/9 + v**4/18 - 10*v**2. Factor c(b).
b*(b + 1)**2*(3*b + 2)**2/3
Factor 0 + 15/2*q**3 + 3*q + 21/2*q**2.
3*q*(q + 1)*(5*q + 2)/2
Suppose -3*j - 5*n = -2, -4*n + 12 = 4*j + j. Let k(f) be the second derivative of 0*f**2 + 1/15*f**6 + 3*f + 0*f**3 + 0*f**5 + 0 - 1/6*f**j. Factor k(i).
2*i**2*(i - 1)*(i + 1)
Factor 54/7 + 3/7*b**2 + 27/7*b.
3*(b + 3)*(b + 6)/7
Suppose -3*r = -q + 1 - 3, 5*q = 20. Factor 4*x**r + 7*x**2 + 10*x - 3 - 13*x**2 - 5.
-2*(x - 4)*(x - 1)
Let w(l) be the first derivative of -l**6/33 + 4*l**5/55 - 4*l**3/33 + l**2/11 + 6. Determine g so that w(g) = 0.
-1, 0, 1
Let t(w) be the first derivative of -1/6*w**3 + 0*w**2 + 2 + 5/16*w**4 + 0*w. Factor t(c).
c**2*(5*c - 2)/4
Let j(f) be the second derivative of 5/6*f**4 + 0 - 2/3*f**3 + 1/15*f**6 - 2/5*f**5 + f + 0*f**2. Determine i so that j(i) = 0.
0, 1, 2
Let h be (-23 + 5)*3/(-9). Find m such that -9 - m**2 + 1 - 2 + 1 - h*m = 0.
-3
Let l(v) be the third derivative of -5*v**8/112 - 3*v**7/70 + 7*v**6/40 + 3*v**5/20 - v**4/4 - 9*v**2. Determine j, given that l(j) = 0.
-1, 0, 2/5, 1
Let n(a) be the first derivative of -3*a**5/5 + 3*a**4/4 + a**3 - 3*a**2/2 - 7. Factor n(t).
-3*t*(t - 1)**2*(t + 1)
Let k(j) = j**3 - 3*j**2 - 4. Let m(i) = 3*i**2 + 3. Let y(s) = 3*k(s) + 4*m(s). Suppose y(f) = 0. What is f?
-1, 0
Let a(b) be the third derivative of 7/360*b**6 + 0*b + 0 + 1/60*b**5 + 0*b**4 - 2*b**2 - 1/3*b**3. Let n(g) be the first derivative of a(g). Factor n(u).
u*(7*u + 2)
Let k(t) be the first derivative of 2*t - 2 - 1/6*t**3 + 1/4*t**2 + 1/24*t**4. Let x(d) be the first derivative of k(d). Let x(o) = 0. What is o?
1
Let n(v) be the first derivative of -v**7/2940 - v**6/1260 + v**5/420 + v**4/84 + 4*v**3/3 - 4. Let p(h) be the third derivative of n(h). Factor p(y).
-2*(y - 1)*(y + 1)**2/7
Let v be 19 + -3 - (-6 + 4). Let w = v + -52/3. Determine y so that -2/3*y - w*y**5 - 4/3 + 8/3*y**2 - 4/3*y**4 + 4/3*y**3 = 0.
-2, -1, 1
Let t be (1 - -2)*(-7)/(525/(-10)). Factor -t + 1/5*s**2 - 1/5*s.
(s - 2)*(s + 1)/5
Suppose 5*c - 9 = 2*c. Factor 7 - 2*m**c - 7 - 2*m**2.
-2*m**2*(m + 1)
Suppose 0 = 2*t - 5*s + 10, 5*t + 8 = 8*t + 4*s. Suppose t = h - 4 - 1. Solve 20/3*g**2 + 20/3*g**3 + 10/3*g**4 + 2/3 + 10/3*g + 2/3*g**h = 0.
-1
Let o(c) be the second derivative of c**6/55 + 4*c**5/55 + 7*c**4/66 + 2*c**3/33 + 38*c. Factor o(d).
2*d*(d + 1)**2*(3*d + 2)/11
Let u(m) = -4*m**2 - 3*m. Let d = -4 + 7. Suppose -d*w + 0*w = -18. Let i(q) = -15*q**2 - 11*q. Let g(b) = w*i(b) - 22*u(b). What is t in g(t) = 0?
0
Find z, given that -40/7*z - 8/7 - 50/7*z**2 = 0.
-2/5
Let w be (-104)/16*6/(-74). Let p = -1/37 + w. Solve 0 + r - p*r**2 = 0 for r.
0, 2
Factor 0*q + 6/11*q**4 + 0 - 18/11*q**3 + 12/11*q**2.
6*q**2*(q - 2)*(q - 1)/11
Let t = -248 - -250. Suppose 8/3 - 250/3*m**4 - 44/3*m + 10*m**t + 175/3*m**3 = 0. Calculate m.
-1/2, 2/5
Let d(c) = -c - 6. Let v be d(-8). Suppose 5*u - 6 = v*u. What is q in -16*q**3 + 2*q - 5*q**4 - 4*q**2 + 9*q**u + 14*q**4 = 0?
-2/9, 0, 1
Let j = -27 - -30. Let l(y) be the third derivative of 0*y + 1/9*y**j + 0 + 1/90*y**5 + y**2 - 1/18*y**4. Factor l(m).
2*(m - 1)**2/3
Let u be 6/(-10)*(-3 - 7). Let d be (-13)/(-5) - u/(-10). What is a in -d*a - 8/5 - 6/5*a**2 = 0?
-2, -2/3
Factor -20/3*z - 5/3*z**2 + 25/3.
-5*(z - 1)*(z + 5)/3
Suppose -f = 12 - 14. Factor -1/5*r**3 - 4/5*r**f - 2/5 - r.
-(r + 1)**2*(r + 2)/5
Let a(g) = -60*g**4 + 120*g**3 - 35*g**2 - 85*g + 25. Let u(n) = -5*n**4 + 10*n**3 - 3*n**2 - 7*n + 2. Let c(x) = 3*a(x) - 35*u(x). Factor c(o).
-5*(o - 1)**3*(o + 1)
Let k(i) be the second derivative of i**7/252 + 19*i**6/180 + 53*i**5/60 + 35*i**4/36 - 539*i**3/36 + 343*i**2/12 - 36*i. Factor k(t).
(t - 1)**2*(t + 7)**3/6
Let q(j) = -j**3 + j**2 - 2. Let o be q(2). Let b be (4/o)/((-2)/12). Factor 2*n - 2*n**5 - 2*n - 2*n**3 - b*n**4.
-2*n**3*(n + 1)**2
Let -4*c**3 - c - 3*c + 8*c**3 = 0. Calculate c.
-1, 0, 1
Factor 0*i - i + i**3 + 5*i**3 - 5*i**3.
i*(i - 1)*(i + 1)
What is b in 0 - 18/11*b**4 + 2/11*b - 14/11*b**2 + 30/11*b**3 = 0?
0, 1/3, 1
Suppose -2*m = -5*m - 0*m. Factor m*z**2 - 1/5*z**3 + 3/5*z - 2/5.
-(z - 1)**2*(z + 2)/5
Let x(q) = q**3 - q**2 + q + 1. Let g(i) = -i**3 - 11*i**2 + 2*i + 2. Let a(j) = -g(j) + 2*x(j). Factor a(p).
3*p**2*(p + 3)
Let l(a) be the first derivative of 3*a**5/5 + 21*a**4/4 + 18*a**3 + 30*a**2 + 24*a - 3. Factor l(c).
3*(c + 1)*(c + 2)**3
Let d(a) be the second derivative of -a**4/48 + a**3/24 + 18*a. What is s in d(s) = 0?
0, 1
Let k = 26/15 + -2/5. Factor k*i**3 + 0*i - 2/3*i**4 - 2/3*i**2 + 0.
-2*i**2*(i - 1)**2/3
Let y be 3*(-1 - -1 - -3). Let w = y - 5. Factor 1/3*b**w + 0*b + 1/3*b**2 + 0 + 2/3*b**3.
b**2*(b + 1)**2/3
Let u = 582 + -2908/5. Factor -2/5*x**3 + u*x - 2/5*x**2 + 2/5.
-2*(x - 1)*(x + 1)**2/5
Solve -17 - 23 - w + 48*w + 4*w**2 - 11*w = 0.
-10, 1
Let -4*a**2 + 0*a**4 + 0*a**4 - 4*a**5 + 8*a**2 - 4*a**4 + 4*a**3 = 0. Calculate a.
-1, 0, 1
Let c(k) be the first derivative of k**9/7560 - k**8/2100 + k**6/450 - k**5/300 - k**3/3 + 3. Let t(n) be the third derivative of c(n). Factor t(v).
2*v*(v - 1)**3*(v + 1)/5
Let r be (-2)/(-3) + (-18)/27. Suppose 2*l - 2*v + 0 = 12, 5*l - v - 22 = r. Factor -3*x**2 + 15*x**l + 0*x**2 - 12*x**4.
3*x**2*(x - 1)*(x + 1)
Let t(a) = -13*a**3 - 4*a**2 + 4*a + 5. Let f(x) = -7*x**3 - 2*x**2 + 2*x + 3. Let r(o) = 10*f(o) - 6*t(o). Factor r(h).
4*h*(h + 1)*(2*h - 1