 of i**6/60 + i**5/40 - i**4/6 - i**3/3 + 7*i. Factor f(k).
k*(k - 2)*(k + 1)*(k + 2)/2
Solve r**3 - 5*r**3 + r**2 + 2*r + 4*r**4 + 2 - 2*r**4 - 5*r**2 + 2*r**5 = 0 for r.
-1, 1
Let t = 15 - 11. Let j be ((-4)/18)/(9 - 492/54). Solve -5/2*d**3 + 1/2*d**j + 1/2*d + 3/2*d**t + 0 = 0 for d.
-1/3, 0, 1
Let r(x) be the third derivative of -x**5/180 - x**4/12 - x**3/2 + x**2. Solve r(m) = 0.
-3
Let t(n) = n**2 + n - 1. Let u(v) = v**3 - 5*v**2 + 4*v - 1. Let x(s) = 3*t(s) + 3*u(s). Let x(d) = 0. What is d?
1, 2
Let o(n) = -20*n - 180. Let a be o(-9). Determine z, given that 0*z + a - 1/3*z**3 - 1/3*z**2 = 0.
-1, 0
Suppose 0 = -3*j + 2*j + 8. Let f be 8 + -8 + j/10. Factor -f + 0*a**2 - 6/5*a + 2/5*a**3.
2*(a - 2)*(a + 1)**2/5
Factor 4/5*j**5 + 0*j**2 + 0 + 0*j + 4/5*j**4 + 0*j**3.
4*j**4*(j + 1)/5
Let d(t) be the second derivative of 1/5*t**2 + 0 - 1/60*t**4 - 1/30*t**3 + 6*t. Suppose d(r) = 0. What is r?
-2, 1
Let o(k) be the second derivative of 0*k**2 + 1/147*k**7 + 0 + 1/35*k**6 + 2*k + 3/70*k**5 + 0*k**3 + 1/42*k**4. Factor o(a).
2*a**2*(a + 1)**3/7
Let h(g) = -g. Let y be h(-4). Determine j so that -7/5*j**3 + 2/5*j + j**5 - 3/5*j**2 + 0 + 3/5*j**y = 0.
-1, 0, 2/5, 1
Let s(x) be the second derivative of 1/18*x**4 + 1/90*x**5 + 1/2*x**2 + x + 0 + 0*x**3. Let n(y) be the first derivative of s(y). Factor n(a).
2*a*(a + 2)/3
Suppose -137 = 5*y - 57. Let l = -14 - y. Factor -4/5 + 6/5*w - 2/5*w**l.
-2*(w - 2)*(w - 1)/5
Let j(b) be the first derivative of 2 - 1/4*b**3 + 0*b - 1/4*b**2 + 0*b**4 + 1/20*b**5. Let j(t) = 0. Calculate t.
-1, 0, 2
Let b = -4745/2 - -24349/10. Let f = -62 + b. Factor f*d + 4/5 - 2/5*d**2.
-2*(d - 2)*(d + 1)/5
Let v(h) be the third derivative of -1/24*h**4 + 0 - 1/60*h**5 + 0*h + 7*h**2 + 1/6*h**3 + 1/120*h**6. Find r such that v(r) = 0.
-1, 1
Let w = -17 - -24. Let m = 11 - w. Factor 7*h + 26*h**2 + m*h**3 + 13*h - 5*h**3 - 8 + 8*h**3.
(h + 2)**2*(7*h - 2)
Find g, given that -12/5*g - 8/5 - 4/5*g**2 = 0.
-2, -1
Let c(f) be the third derivative of -1/6*f**3 - 2*f**2 + 0*f + 0 - 1/120*f**5 - 1/16*f**4. Let c(n) = 0. What is n?
-2, -1
Let m(t) = -t**2 + t. Let z(x) = x**2 + 1. Let g(j) = 5*m(j) + 6*z(j). Find b, given that g(b) = 0.
-3, -2
Factor 1/2*f**2 + 0 - 1/2*f**4 - 1/2*f**3 + 1/2*f.
-f*(f - 1)*(f + 1)**2/2
Suppose 5*v - 9*v = -12. What is q in 6*q + 2*q**2 + q**v + 2*q**4 - 7*q**3 + 0*q**2 - 4 = 0?
-1, 1, 2
Let q(r) be the third derivative of -6*r**2 - 4/15*r**3 + 1/50*r**5 + 0 + 0*r**4 - 1/300*r**6 + 0*r. What is f in q(f) = 0?
-1, 2
Let k be 19/(-7) - (-12)/(-42). Let a = -14/5 - k. Determine n so that 0*n**2 - a*n**3 + 1/5*n + 0 = 0.
-1, 0, 1
Let g(v) = 6*v**5 + 2*v**4 - 2*v**2 + 8*v + 7. Let z(i) = -i**5 - i - 1. Let c(h) = 3*g(h) + 21*z(h). Find j, given that c(j) = 0.
-1, 0, 1
Factor -52*p - 5*p**5 + 5*p**3 + 52*p.
-5*p**3*(p - 1)*(p + 1)
Find m such that 0*m**2 - 6*m**2 + 6 + 2 + 4*m**2 = 0.
-2, 2
Suppose -4*f = -4*p, -78*p = -5*f - 79*p. Suppose x - 5*u - 20 = 0, x + 2*x = -2*u - 8. Suppose x*i - 1/4*i**2 + f = 0. What is i?
0
Let w = 3 + 0. Let f be 24/(-56) - 13/(-14). Factor -3/2*j**2 + 3/2*j**4 + f*j**5 - j + 0 + 1/2*j**w.
j*(j - 1)*(j + 1)**2*(j + 2)/2
Solve 0*u**4 - u**4 - u**5 + 3*u**4 - u**3 = 0 for u.
0, 1
Determine y, given that 4*y**2 + 2*y**4 - 3*y**2 + 4*y**5 - 4*y**3 + y**4 - 4*y**4 = 0.
-1, 0, 1/4, 1
Let x be (-2)/16 - 4/(-32). Factor 0*w + x - 3/7*w**2.
-3*w**2/7
Let h(x) be the first derivative of 1/2*x**2 + 1/9*x**3 + 2/3*x + 1. Factor h(g).
(g + 1)*(g + 2)/3
Let f = 8 + -8. Let h be (f/1)/((-6)/(-3)). Factor 0*o**2 + 0*o + 1/5*o**3 + h.
o**3/5
Let k(m) be the first derivative of 1/60*m**5 - 3 - 1/6*m**3 - 2*m**2 + 0*m**4 + 0*m. Let o(f) be the second derivative of k(f). Factor o(g).
(g - 1)*(g + 1)
Let s = 1499/1757 - -1/251. Let u(c) = c**3 + 31*c**2 - 66*c + 2. Let n be u(-33). Solve 6/7*a**n + 2/7 - 2/7*a**3 - s*a = 0.
1
Let z(i) = -i**3 + 4*i**2 + 6*i - 5. Let y be z(5). Let s = y + 2. Determine r, given that 16*r**3 - 2 - 14*r**3 - 2*r + 4 - 2*r**s = 0.
-1, 1
Let 0 + 6/7*r**2 - 3/7*r + 12/7*r**3 - 9/7*r**5 - 6/7*r**4 = 0. Calculate r.
-1, 0, 1/3, 1
Let y(c) be the third derivative of -c**6/180 - c**5/20 - c**4/6 + 4*c**3/3 - 4*c**2. Let k(r) be the first derivative of y(r). Factor k(t).
-2*(t + 1)*(t + 2)
Let t(l) = 5*l**3 - 5*l**2 - 54*l - 36. Let j(y) = 10*y**3 - 10*y**2 - 109*y - 71. Let f(n) = 4*j(n) - 9*t(n). Solve f(o) = 0 for o.
-2, -1, 4
Let o(i) be the third derivative of i**8/672 - i**7/210 - i**6/80 + i**5/30 + i**4/12 - 17*i**2. Factor o(b).
b*(b - 2)**2*(b + 1)**2/2
Let j be (-10)/(-3) - 0/4. Let n(w) be the first derivative of 2 + 3*w**2 - 4*w + j*w**3. Factor n(i).
2*(i + 1)*(5*i - 2)
What is j in -15/8 - 9/8*j**2 + 3/8*j**3 - 27/8*j = 0?
-1, 5
Suppose 2*v - 7 = -3*l + 1, -2*v = -l - 24. What is i in 3*i + 6*i**3 + v*i**2 - 8 - 6*i - 5*i = 0?
-2, -2/3, 1
Let h(y) be the third derivative of -4*y**5/135 + 5*y**4/54 - 2*y**3/27 - 11*y**2. Suppose h(v) = 0. What is v?
1/4, 1
Suppose v + 5*i = 15, -v - 3*i = 4*v - 31. Let q = 8 + -6. Factor 0 + 8 + 13*k + q*k**2 - v*k.
2*(k + 2)**2
Suppose h = -0*h + 4. Determine u so that 6 + 4*u**3 - 4*u**2 + 0*u**2 - h*u + 2 - 4 = 0.
-1, 1
Let f(x) be the third derivative of 2*x**2 - 1/180*x**5 + 0*x**3 - 1/72*x**4 + 0*x + 0. Find m, given that f(m) = 0.
-1, 0
Let a(i) = -i**2 - 3*i + 3. Let t(h) = -3*h**2 - 9*h + 8. Let o(v) = 8*a(v) - 3*t(v). Factor o(f).
f*(f + 3)
Let z(r) = -r**2 - 7*r - 5. Let m be z(-5). Suppose 0 = 2*c + f - 6, 18 = 3*c - m*f + 2*f. Factor -6*k**2 + 4*k**4 + 0*k**2 - 4*k**4 - 2*k**c + 2*k + 6*k**3.
-2*k*(k - 1)**3
Let f(u) be the third derivative of u**6/30 + u**5/5 + u**4/3 + 4*u**2. Let f(h) = 0. Calculate h.
-2, -1, 0
Factor 0 + 2/3*i**2 + 0*i + 2*i**4 - 2*i**3 - 2/3*i**5.
-2*i**2*(i - 1)**3/3
Let h(l) be the first derivative of 0*l**3 + 0*l - l**2 + 4 + 1/2*l**4. Factor h(m).
2*m*(m - 1)*(m + 1)
Let t = 167/3 + -1163/21. Factor t*n**2 + 0*n - 2/7.
2*(n - 1)*(n + 1)/7
Let z(i) be the second derivative of -1/35*i**7 + 0*i**4 + 0 - 1/5*i**5 + 1/3*i**3 - 2/5*i**2 - 2*i + 2/15*i**6. Factor z(j).
-2*(j - 1)**4*(3*j + 2)/5
Suppose 1/4*l - 1/4*l**3 - 1/2 + 1/2*l**2 = 0. What is l?
-1, 1, 2
Factor -7/6*h - 1/3*h**2 + 1/6*h**3 - 2/3.
(h - 4)*(h + 1)**2/6
Solve 8*y**2 + 8*y**3 + 10*y**2 + 16*y**3 + 3*y + 3*y**3 = 0 for y.
-1/3, 0
Let k(c) = -c**3 + 3*c**2 + 1. Let q be k(2). Suppose -4*p - 9 = z - p, -5*z + q*p + 35 = 0. What is l in 4/5 + 6/5*l**2 + 14/5*l**z - 14/5*l - 2*l**4 = 0?
-1, 2/5, 1
Let f(i) be the third derivative of -8*i**7/7 - 9*i**6/5 - 21*i**5/20 - i**4/4 + 4*i**2. Determine t so that f(t) = 0.
-2/5, -1/4, 0
Suppose -4 = -y - 0*y. Solve 20/3*n**2 - 20/3*n**3 + 10/3*n**y + 2/3 - 10/3*n - 2/3*n**5 = 0.
1
Let j be 6 - (5 - (-18)/30). Suppose 0 + 2/5*h**3 + 0*h + j*h**2 = 0. What is h?
-1, 0
Let 1037*i**2 - 3*i**3 + i - 1022*i**2 - 10*i - 27 = 0. What is i?
-1, 3
Solve 1/6*u**4 - 1/2*u**2 - 1/6*u + 1/3 + 1/6*u**3 = 0 for u.
-2, -1, 1
Let m(g) = -g + 8. Let l be m(9). Let d be ((2/2)/(-4))/l. Find y, given that 0 - d*y**3 + 1/2*y**2 - 1/4*y = 0.
0, 1
Factor -3/4*q + 0*q**2 + 0 + 3/4*q**3.
3*q*(q - 1)*(q + 1)/4
Suppose 15 = -3*a + 24. Let x(u) be the third derivative of 0*u - 3*u**2 + 0*u**4 + 0*u**a - 1/30*u**5 + 0. Solve x(z) = 0.
0
Let n be (-1*(-4)/10)/8. Let o(h) be the first derivative of 0*h**2 + 0*h + 3 - 1/16*h**4 + 0*h**3 + n*h**5. Factor o(q).
q**3*(q - 1)/4
Let x(y) be the second derivative of -y**4/12 - 11*y**3/6 - 3*y**2 - y. Let z be x(-10). Let 2/9*a**5 - 2/9*a**z + 0*a**2 + 0*a**3 + 0*a + 0 = 0. What is a?
0, 1
Let b(r) = -r**3 + 9*r**2 - 7*r - 5. Let o be b(8). Suppose y**2 - y**2 + 4 - 3*y**2 + 0*y**3 + y**o = 0. What is y?
-1, 2
Let h = -10 - -11. Find o such that 9*o**2 - 7*o**2 + 0*o**2 - h - o**4 = 0.
-1, 1
Suppose 0 = -59*y + 57*y + 10. Let w(i) be the first derivative of 0*i**3 - 2/15*i**y - 4 - 1/6*i**4 + 0*i + 0*i**2. Factor w(p).
-2*p**3*(p + 1)/3
Let n be -1 + -2*(-2 + 177/120). Let i(q) be the second derivative of n*q**5 + 3*q + 0*q**3 + 0 + 0*q**2 + 1/12*q**4. Factor i(s).
s**2*(s + 1)
Let y(c) be the third derivative of -c**5/20 - c**4/3 - 8*c**3/9 + c**2. Suppose y(h) = 0. What is h?
-4/3
Let l(m) = -7*m - 124. Let o be l(-18). Factor 1 + 1/4*f**o + f.
(f + 2)**2/4
Let r(z) = 4