e of 2/3*q**3 - q**2 - 2 - n*q**5 + 0*q + 1/2*q**4. Factor s(l).
-2*l*(l - 1)**2*(l + 1)
Let k(q) = -q**2 + 2*q. Let h be k(2). Suppose p + 0 - 3 = h. Let 4 - 4*v**3 + 5*v**p - 4*v**2 + 5*v**3 - 6*v + 0*v**3 = 0. What is v?
-1, 2/3, 1
Let z be (-5)/(20/16*-1). Suppose 2/3*c**z - 2/3*c**3 + 0*c + 0 + 0*c**2 = 0. Calculate c.
0, 1
Factor 0*f + 2/17*f**3 + 2/17*f**2 + 0.
2*f**2*(f + 1)/17
Suppose -5 = -5*j - 0. Let v be (-4*6/(-16))/j. Suppose 0*i - i**2 - 1/2*i**4 + 0 - v*i**3 = 0. Calculate i.
-2, -1, 0
Let o(u) be the third derivative of -u**8/672 + u**7/70 - 13*u**6/240 + u**5/10 - u**4/12 - 7*u**2. Factor o(i).
-i*(i - 2)**2*(i - 1)**2/2
Let o(m) = 2*m**3 + 2*m**2 + 8*m. Let y(j) = -2*j**3 - j**2 - 7*j. Let k(n) = 5*o(n) + 6*y(n). Factor k(s).
-2*s*(s - 1)**2
Factor 1/3*i**3 - 2*i**4 + 0 - 3/2*i**5 + 2/3*i**2 - 1/6*i.
-i*(i + 1)**2*(3*i - 1)**2/6
Solve 25*a**4 - a**5 + 0*a**2 - a + 2*a**3 - 2 + 4*a**2 - 27*a**4 = 0 for a.
-2, -1, 1
Let 8/3*x**2 + 6 - 8*x = 0. What is x?
3/2
Let g(o) be the second derivative of 0*o**2 + 1/24*o**4 - 7*o + 0*o**3 + 0 - 1/40*o**5. Solve g(a) = 0 for a.
0, 1
Suppose 12 = 5*g - 3*i + 5*i, -i = -4*g + 20. Let m be 9/(-15) - (g + -7). Let -11/5*p**3 - 1/5 + 3/5*p + 1/5*p**2 + m*p**4 - 4/5*p**5 = 0. Calculate p.
-1/2, 1/2, 1
Let n(t) be the first derivative of 21*t**6/2 - 249*t**5/5 + 117*t**4/2 + 12*t**3 - 12*t**2 - 55. Find c such that n(c) = 0.
-1/3, 0, 2/7, 2
Factor 2 + 4/3*t**3 - 14/3*t**2 + 4/3*t.
2*(t - 3)*(t - 1)*(2*t + 1)/3
Let f be ((-131)/7)/(96/(-7)). Let s = -1/32 + f. Factor 1/3*n**2 - s*n + 4/3.
(n - 2)**2/3
Let t = 116 + -810/7. Let z be 1*(6 + -2) + -2. Factor -t*y**3 + 2/7*y + 2/7 - 2/7*y**z.
-2*(y - 1)*(y + 1)**2/7
Let x(q) be the first derivative of 3/4*q**4 + 5 - 2*q**3 + 3/2*q**2 + 0*q. Let x(j) = 0. What is j?
0, 1
Let a(l) be the first derivative of 3*l**5/35 + 3*l**4/14 - l**3/7 - 3*l**2/7 + 5. Solve a(f) = 0.
-2, -1, 0, 1
Let h(u) be the third derivative of u**7/42 + u**6/8 + u**5/4 + 5*u**4/24 + 2*u**2. Factor h(n).
5*n*(n + 1)**3
Let q be 9/10*60/45. Solve -3/5*v**2 - 3/5 + q*v = 0 for v.
1
Suppose 2 - 6 = -k. Suppose k*y + 2*r - 16 = -0*r, -3*r + 2 = -5*y. Find g such that -3*g + 0*g**y + g + g**2 = 0.
0, 2
Suppose -18*m = -15*m. Let p(v) be the second derivative of 3*v + 0*v**2 + m*v**4 - 3/20*v**5 + 0 + 1/15*v**6 + 1/6*v**3. Factor p(g).
g*(g - 1)**2*(2*g + 1)
Let g(y) = y**2 + 1. Let q(c) = 5*c**2 + 50*c - 115. Let b(m) = 10*g(m) - q(m). Find k, given that b(k) = 0.
5
Let d(l) be the second derivative of -2*l + 1/21*l**3 + 0 + 1/42*l**4 + 0*l**2. Factor d(p).
2*p*(p + 1)/7
Determine g, given that 9 - 14*g**2 + 5 - 10 + 6*g**3 + 4 = 0.
-2/3, 1, 2
Let k(i) = i**2 - 5*i - 50. Let a be k(-5). Solve 2/5*c**2 - 2/5*c + a = 0 for c.
0, 1
Let y(h) be the second derivative of -h**7/189 - h**6/135 + h**5/45 + h**4/27 - h**3/27 - h**2/9 - 15*h. Solve y(u) = 0.
-1, 1
Let s be (-6)/8*16/(-6). Let m(l) be the first derivative of s + l**2 - 2/3*l**3 + 0*l. Solve m(w) = 0 for w.
0, 1
Factor 3*b - 66*b**2 + 11*b + 2 + 50*b**2.
-2*(b - 1)*(8*b + 1)
Let s(y) be the second derivative of -y**6/150 - y**5/50 - y**4/60 + 12*y. Factor s(a).
-a**2*(a + 1)**2/5
Solve -3/5*q**3 - 3/5*q**4 - 1/5*q**2 - 1/5*q**5 + 0*q + 0 = 0.
-1, 0
Let u(m) = -m**2 - 5*m - 1. Let h(y) = -y**2 - 6*y - 1. Let a(o) = -3*h(o) + 4*u(o). Determine s, given that a(s) = 0.
-1
Let a(h) = 84*h**3 - 276*h**2 + 232*h - 48. Let t(c) = 56*c**3 - 184*c**2 + 155*c - 32. Let n(s) = -5*a(s) + 8*t(s). Factor n(w).
4*(w - 2)*(w - 1)*(7*w - 2)
Let n(d) be the third derivative of 0*d**3 + 0 + 0*d + 1/840*d**7 + 1/240*d**6 + 1/240*d**5 + 0*d**4 + 6*d**2. Solve n(k) = 0 for k.
-1, 0
Let l(i) = -i - 1. Let b be l(-5). Let r(w) be the third derivative of 1/48*w**b - 1/80*w**6 + 0 + 0*w**3 - 1/60*w**5 + 0*w - w**2. Factor r(n).
-n*(n + 1)*(3*n - 1)/2
Suppose -1 = 3*u - h - 4, 3*h + 9 = -3*u. Let d(f) be the second derivative of 2*f - 1/12*f**3 + 1/48*f**4 + 1/8*f**2 + u. Factor d(x).
(x - 1)**2/4
Let t(z) = -z**2 - 9*z - 5. Let l be t(-8). Determine w, given that -3*w + w**2 - 10*w**3 - 4*w**2 + w**4 + 25*w**l - 10*w**4 = 0.
-1/3, 0, 1
Let d(l) = -3*l**2 - 15*l - 27. Let y(m) be the third derivative of m**5/10 + 31*m**4/24 + 9*m**3 - 6*m**2. Let r(h) = 5*d(h) + 3*y(h). Factor r(o).
3*(o + 3)**2
Suppose 4/7 - 2*s + 2/7*s**5 + 16/7*s**2 - 4/7*s**4 - 4/7*s**3 = 0. What is s?
-2, 1
Let l(u) = -8*u**3 - 2*u**3 + 2*u**4 + 8*u**2 + 0*u**2 - 6*u. Let y(d) = 2*d**4 - 11*d**3 + 7*d**2 - 7*d. Let h(f) = -3*l(f) + 2*y(f). Let h(o) = 0. What is o?
0, 1, 2
Let h(l) be the second derivative of l**6/105 - l**5/14 + 3*l**4/14 - l**3/3 + 2*l**2/7 - 32*l. Factor h(r).
2*(r - 2)*(r - 1)**3/7
Let j = -22 - -22. Let p(d) be the second derivative of 1/2*d**4 + d**3 + 1/10*d**5 + j + d**2 - d. Determine i so that p(i) = 0.
-1
Let d be 1302/(-9) + 6/9. Let s = d + 1298/9. Find h such that 2/3*h**3 + s*h - 8/9*h**5 + 0 + 10/9*h**2 - 10/9*h**4 = 0.
-1, -1/4, 0, 1
Let u(j) be the third derivative of 9*j**7/70 - 3*j**6/2 - 173*j**5/20 - 35*j**4/2 - 18*j**3 + 9*j**2. Factor u(c).
3*(c - 9)*(c + 1)*(3*c + 2)**2
Let x(c) be the third derivative of -25*c**8/1848 + 16*c**7/231 - 47*c**6/330 + 8*c**5/55 - 3*c**4/44 - 10*c**2. Solve x(a) = 0.
0, 3/5, 1
Factor -3/2 - 17/4*q - 5/4*q**2.
-(q + 3)*(5*q + 2)/4
Let s(q) = -14*q**5 + 46*q**4 - 54*q**3 + 24*q**2 - 4*q. Let i(g) = 28*g**5 - 92*g**4 + 108*g**3 - 47*g**2 + 8*g. Let h(t) = -2*i(t) - 5*s(t). Factor h(x).
2*x*(x - 1)**3*(7*x - 2)
Let o(x) be the second derivative of x**6/60 - x**5/30 - x**4/12 + x**3/3 - 2*x**2 - 3*x. Let k(r) be the first derivative of o(r). Find f, given that k(f) = 0.
-1, 1
Let c be -3 - (-2)/4*10. Let b(k) = k. Let q(i) = -i**2 + 3*i. Let d(a) = c*b(a) - q(a). Factor d(u).
u*(u - 1)
Let z be 5/(-35)*(-14)/96. Let o(s) be the third derivative of 0 + z*s**4 + 1/240*s**6 - s**2 + 0*s**3 - 1/60*s**5 + 0*s. Factor o(d).
d*(d - 1)**2/2
Let k(v) = 35*v**4 + 25*v**3 - 96*v**2 + 25*v. Let g(l) = 12*l**4 + 8*l**3 - 32*l**2 + 8*l. Let m(b) = -11*g(b) + 4*k(b). Factor m(j).
4*j*(j - 1)*(j + 3)*(2*j - 1)
Let r = 141 + -138. What is y in -y**r + 1/2*y**2 - 3/4*y**4 + y + 1/4 = 0?
-1, -1/3, 1
Let q(n) be the second derivative of -n**4/12 - n**3/6 + n**2 + 21*n. Factor q(w).
-(w - 1)*(w + 2)
Suppose -2*q**2 + 2 - 8*q**3 + 16/3*q + 8/3*q**4 = 0. What is q?
-1/2, 1, 3
Let v(i) = -4*i**3 + 4*i + 4. Let t(m) = -m**4 - m**3 - m - 1. Let u(k) = -4*t(k) - v(k). Factor u(j).
4*j**3*(j + 2)
Suppose -s + 7 = 2*t, 5*t + 4*s - 13 = 3*s. Factor -t*q - q**4 - 6*q**2 - q - 3 - q + 2 - 4*q**3.
-(q + 1)**4
Let n(b) be the second derivative of b**4/3 + 8*b**3/3 - 18*b. Let n(f) = 0. What is f?
-4, 0
Suppose 1/3*x**3 + 2/3*x**5 + 0*x - x**4 + 0*x**2 + 0 = 0. What is x?
0, 1/2, 1
Let v(y) be the third derivative of y**7/70 + y**6/40 - 3*y**5/20 - 5*y**4/8 - y**3 - 4*y**2. Solve v(t) = 0 for t.
-1, 2
Suppose x + 4*z = 4*x + 10, 24 = 2*x + 5*z. Let g be 3 - x - 1 - -4. Let -2/7*q**g - 2/7*q**5 + 0*q + 2/7*q**3 + 0 + 2/7*q**2 = 0. Calculate q.
-1, 0, 1
Let m(h) be the first derivative of 4*h**5/5 - 21*h**4 + 196*h**3 - 686*h**2 + 32. Suppose m(q) = 0. Calculate q.
0, 7
Determine a, given that 13*a**2 + 4*a**2 + 1 - 18*a**2 = 0.
-1, 1
Let y(f) be the first derivative of -f**6/6 - 3*f**5/5 - f**4/2 + 2*f**3/3 + 3*f**2/2 + f + 2. Determine o so that y(o) = 0.
-1, 1
Let n = -23 + 20. Let g be 26/(-56) + n/(-4). Determine f so that 2/7 + 4/7*f + g*f**2 = 0.
-1
Let f be 2/(-6) - 536/(-24). Let d be (-1)/(f/(-4) + 3). Find p, given that 0*p + d*p**3 - 2/5*p**2 + 0 = 0.
0, 1
Let o be 4/6*((0 - -8) + -7). Solve 0 + o*h**2 + 2/3*h = 0 for h.
-1, 0
Let i(w) = -w**2 - 8*w - 7. Let m be i(-7). Let r be m/(-2 - -6) - -2. Find k, given that -16/5*k - 8/5 + r*k**2 = 0.
-2/5, 2
Let y(k) be the second derivative of 1/24*k**5 + 0 - k - 7/48*k**4 + 1/6*k**3 - 1/2*k**2. Let n(s) be the first derivative of y(s). Factor n(h).
(h - 1)*(5*h - 2)/2
Let k be (4/12)/(6/12). Factor 1/3*g**2 - k - 1/3*g.
(g - 2)*(g + 1)/3
Let t(f) be the first derivative of 5 + 1/2*f - 1/12*f**3 - 1/8*f**2. Suppose t(p) = 0. What is p?
-2, 1
Let m(b) be the second derivative of 2*b**2 + 2*b - 1/10*b**5 + b**3 + 0*b**4 + 0. Factor m(q).
-2*(q - 2)*(q + 1)**2
Let v(s) be the first derivative of 5*s*