7/51710015. Let i = j - -1/155. Factor -8/7*y**4 + 2/7*y**5 + 2/7*y + 0 + i*y**3 - 8/7*y**2.
2*y*(y - 1)**4/7
Suppose 4*c - 2 = 5*c, 4*c = -4*w + 8. Let d = 1 - -3. Find q, given that -4*q - 4*q**w + d*q**2 + 3*q + 4*q**3 - q**3 - 2*q**3 = 0.
-1, 0, 1/4, 1
Let n(y) be the second derivative of y**8/11200 + y**7/2100 + y**6/1200 - y**4/12 + 2*y. Let x(d) be the third derivative of n(d). Factor x(h).
3*h*(h + 1)**2/5
Find p such that 0*p - 1/3*p**2 - 2/3*p**5 + 0*p**3 + 0 + p**4 = 0.
-1/2, 0, 1
Let y be (2/8)/(3 + (-10)/4). Let y*q**4 - 1/2*q**3 + 0*q + 0 + 0*q**2 = 0. Calculate q.
0, 1
Let w(a) = a**2 + 2*a + 4. Let v(d) = -3*d**2 - 5*d - 11. Let l(i) = 4*v(i) + 11*w(i). Factor l(j).
-j*(j - 2)
Let t(l) = -4*l**4 + 24*l**3 + 16*l + 16. Let c(g) = -g**4 + 5*g**3 + 3*g + 3. Let x(r) = 16*c(r) - 3*t(r). Solve x(a) = 0 for a.
0, 2
Let u(q) = 2*q**3 - q**2 - 3*q**4 + 3 + q**2 + 2*q**2 + 0*q**4. Let n(i) = -7*i**4 + 4*i**3 + 5*i**2 + i + 7. Let l(m) = 2*n(m) - 5*u(m). Factor l(r).
(r - 1)**3*(r + 1)
Let b(u) be the third derivative of -u**9/15120 + u**8/2520 - u**7/1260 + 2*u**5/15 + 2*u**2. Let p(k) be the third derivative of b(k). Factor p(o).
-4*o*(o - 1)**2
Let g(s) be the third derivative of s**6/420 + s**5/42 - s**4/84 - 5*s**3/21 + 42*s**2. Factor g(d).
2*(d - 1)*(d + 1)*(d + 5)/7
Let x(n) = n**5 + n**4 - 1. Let y(l) = 2 + 2*l**4 - 4*l**5 + 0*l**2 + 2*l - l**5 + l**5 - 4*l**2. Let j(t) = 2*x(t) + y(t). Factor j(g).
-2*g*(g - 1)**3*(g + 1)
Let a(x) be the first derivative of x**6/21 - x**4/14 + 2. Factor a(n).
2*n**3*(n - 1)*(n + 1)/7
Let n = 17/14 - 6/5. Let i(o) be the second derivative of 0 - 1/42*o**4 + 1/7*o**2 + 2*o + 1/21*o**3 - n*o**5. What is p in i(p) = 0?
-1, 1
Let z(m) = -m**2 - 60*m + 64. Let l be z(-61). Let 1/2*o**5 - o + 5/2*o**2 - 3/2*o**l - 1/2*o**4 + 0 = 0. What is o?
-2, 0, 1
Let a be 2/4 - (-6)/4. Let h(f) be the second derivative of 0*f**a + 2*f + 1/54*f**4 + 0 - 1/27*f**3. Let h(v) = 0. Calculate v.
0, 1
Let j(x) be the second derivative of x**6/15 + 3*x**5/10 - 5*x**4/6 - x**3 + 4*x**2 + 5*x - 2. Find d such that j(d) = 0.
-4, -1, 1
Suppose -2/3*j**2 - 2/3*j + 4/3 = 0. What is j?
-2, 1
Let -2*x**3 - 9*x**2 - 3*x**2 + 131*x - 129*x + 12 = 0. What is x?
-6, -1, 1
Suppose 3*b + 3*p - 3 = 0, b - 2*p - 2*p - 26 = 0. Factor 2*n**5 + b*n**3 + 3*n**4 - 2*n**4 + 5*n**4 + 0*n**5 + 2*n**2.
2*n**2*(n + 1)**3
Let l be (80/25 + -3)*(-5)/(-2). Let o(w) be the first derivative of 0*w - 1/6*w**3 + l*w**2 - 4. What is j in o(j) = 0?
0, 2
Let m(v) be the second derivative of -25*v**5/24 + 25*v**4/2 - 60*v**3 + 144*v**2 - 20*v. Factor m(z).
-(5*z - 12)**3/6
Suppose 0 = -4*t + 16 - 4. Let l = -54 - -56. Factor 3/4*d**4 + 0*d**t + 0*d + 3/4 - 3/2*d**l.
3*(d - 1)**2*(d + 1)**2/4
Let m(z) be the second derivative of -z**5/140 - z**4/42 - z**3/42 - 20*z. Factor m(q).
-q*(q + 1)**2/7
Let d(f) be the third derivative of f**8/1008 + f**7/126 + f**6/60 - f**5/45 - f**4/9 - 5*f**2. Let d(a) = 0. What is a?
-2, 0, 1
Let m = 13 - 7. Let q be ((-56)/m)/4 - -3. Factor q*n**4 + 2/3*n**5 + 2/3 - 4/3*n**3 + 2/3*n - 4/3*n**2.
2*(n - 1)**2*(n + 1)**3/3
Let s(c) = -35*c**2 + 25*c - 30. Let b(f) = f**2 + 1. Let w(d) = -30*b(d) - s(d). What is o in w(o) = 0?
0, 5
Let t(i) be the first derivative of -3*i**6/2 + 51*i**5/5 - 93*i**4/4 + 23*i**3 - 9*i**2 + 13. Determine r, given that t(r) = 0.
0, 2/3, 1, 3
Determine l, given that -26*l - l**4 + 5*l**4 - 20*l + 30*l + 24*l**2 + 4 - 16*l**3 = 0.
1
Let c(a) = 5*a**3 + 2*a**2 + 6*a. Let j(l) = 14*l**3 + 6*l**2 + 17*l. Let q(y) = 17*c(y) - 6*j(y). Factor q(f).
f**2*(f - 2)
Find h such that 0*h**5 - 22*h - 55*h**3 - 2*h + 4 + 5*h**4 - 5*h**5 + 22*h**4 + 53*h**2 = 0.
2/5, 1, 2
Let d(b) = b + 1. Let f be d(2). Factor 14*r**4 + 18*r - 14*r**3 - 1 - 10*r**2 - 4*r**3 - f.
2*(r - 1)**2*(r + 1)*(7*r - 2)
Let p = -1825 + 51115/28. Let g = p - 1/28. Factor 1/2*s**5 + 0*s**3 + s**2 - g*s + 0 - s**4.
s*(s - 1)**3*(s + 1)/2
Let a(l) = 4*l**3 + 10*l**2 - 4*l - 8. Let u(k) = -20*k**3 - 51*k**2 + 20*k + 40. Let i(p) = 11*a(p) + 2*u(p). Factor i(y).
4*(y - 1)*(y + 1)*(y + 2)
Let n(o) = -20*o**3 - 40*o**2 + 100*o + 136. Let u(a) = 4*a**3 + 8*a**2 - 20*a - 27. Let l(m) = -3*n(m) - 16*u(m). Determine y, given that l(y) = 0.
-3, -1, 2
Solve -2/5*q**2 + 4/5*q - 2/5 = 0 for q.
1
Let a be 1/(-4) - 63/(-12). Let f(w) be the third derivative of 1/140*w**6 - 1/210*w**a + 0*w + 4/735*w**7 + 0 + 0*w**4 + 0*w**3 + 2*w**2. Solve f(r) = 0.
-1, 0, 1/4
Let a(l) = -35*l**3 + 120*l**2. Let y(t) = -3*t**3 + 10*t**2. Let w(q) = -2*a(q) + 25*y(q). Find m, given that w(m) = 0.
0, 2
Let l(a) be the first derivative of -1/4*a**4 + 0*a**2 + 5 + 0*a - a**3. Factor l(c).
-c**2*(c + 3)
Let h(u) = -u - 1. Let f be h(3). Let r(b) = -2*b. Let l be r(f). Let 2*j**2 - l*j**4 + 9*j**3 - 4*j**2 + j**4 = 0. Calculate j.
0, 2/7, 1
Let d(o) be the first derivative of -o**5/20 + 13. Suppose d(k) = 0. What is k?
0
Find g such that 15*g**2 + 21*g**2 + 12*g + 27*g**4 + 3*g**5 - 9*g**4 + 13*g**3 + 26*g**3 = 0.
-2, -1, 0
Let x(w) be the third derivative of w**5/420 + w**4/84 - w**2. What is s in x(s) = 0?
-2, 0
Let n = 0 - -5. Suppose -n*k + 4 = -4*k. Solve -g**4 + g**5 + 2*g**k - 2*g**4 + g**2 - g**3 = 0.
-1, 0, 1
Let v be 21/28*(-4)/(-90). Let s(t) be the second derivative of -v*t**4 + 2*t + 1/15*t**3 + 0 + 0*t**2. Let s(y) = 0. Calculate y.
0, 1
Let h(l) = 3*l**5 - 6*l**4 - 2*l**3 - 5*l - 6. Let d(c) = -8*c**5 + 17*c**4 + 5*c**3 - c**2 + 14*c + 17. Let n(t) = -4*d(t) - 11*h(t). Solve n(y) = 0 for y.
-2, -1, 1
Let f(v) be the second derivative of v**7/420 + v**6/180 - v**5/60 - v**4/12 - 2*v**3/3 - 2*v. Let p(u) be the second derivative of f(u). Factor p(q).
2*(q - 1)*(q + 1)**2
Factor -2/17 - 8/17*r + 2/17*r**2 + 8/17*r**3.
2*(r - 1)*(r + 1)*(4*r + 1)/17
Let n = 23 - 16. Let z(l) be the second derivative of 0*l**2 + 1/3*l**6 + 2/3*l**3 + 0 + 1/10*l**5 - 1/7*l**n - 5/6*l**4 + l. Find y such that z(y) = 0.
-1, 0, 2/3, 1
Suppose -30*d + 9*d + 14*d**4 + 24*d**3 + 17*d + 6*d**2 = 0. Calculate d.
-1, 0, 2/7
Let k(n) be the second derivative of 3*n**5/40 - n**4/16 - 5*n**3/8 - 3*n**2/4 + 8*n. Suppose k(l) = 0. What is l?
-1, -1/2, 2
Suppose -7*n = n - 0*n. Let v(y) be the third derivative of 0 + y**2 + n*y**3 + 0*y**5 + 1/60*y**4 - 1/300*y**6 + 0*y. What is u in v(u) = 0?
-1, 0, 1
Let g(f) be the second derivative of f**4/18 - 2*f**3/9 - f**2 - 8*f. Factor g(i).
2*(i - 3)*(i + 1)/3
Let d(t) be the first derivative of -t**6/27 - 2*t**5/9 - 4*t**4/9 - 8*t**3/27 + 8. Suppose d(y) = 0. What is y?
-2, -1, 0
Let x(o) be the second derivative of 2*o - o**2 - 2/3*o**3 - 1/6*o**4 + 0. Let x(a) = 0. What is a?
-1
Let h(z) be the first derivative of 2*z**5/5 + z**4/2 - 8*z**3/3 - 4*z**2 + 1. Factor h(f).
2*f*(f - 2)*(f + 1)*(f + 2)
Factor -5*k**3 + 24*k**2 + k - 30*k + 2*k**3 - 19*k.
-3*k*(k - 4)**2
Factor -20*f**3 - 6*f**2 + 9*f**2 + 12*f**4 + 4*f + f**2.
4*f*(f - 1)**2*(3*f + 1)
Suppose 0 - 2 = -h + 3*z, -5*h - 5*z = 10. Let g = h + 4. Factor -m**g + 3*m - 3*m + m**2.
-m**2*(m - 1)
Let b(y) be the third derivative of y**7/630 + y**6/360 - y**5/45 - y**4/18 - 34*y**2. Find w such that b(w) = 0.
-2, -1, 0, 2
Let y(b) be the second derivative of -b**6/75 + b**4/30 + 11*b. Find s such that y(s) = 0.
-1, 0, 1
Suppose k + 3*k = 0. Let h(y) be the third derivative of k*y + 1/24*y**4 + 0 + 1/60*y**5 - 1/3*y**3 + 2*y**2. Let h(t) = 0. What is t?
-2, 1
Let j = -24 - -29. Let r(h) be the second derivative of 1/6*h**4 - 3*h - 1/10*h**j + 1/3*h**3 - h**2 + 0. Determine m so that r(m) = 0.
-1, 1
Let g(f) be the third derivative of f**6/540 + f**5/60 + 5*f**3/6 - 4*f**2. Let j(b) be the first derivative of g(b). What is y in j(y) = 0?
-3, 0
Let f(i) be the third derivative of -i**5/270 + i**4/108 - 10*i**2. Find p such that f(p) = 0.
0, 1
Let i(l) be the second derivative of -13*l**7/14 + 37*l**6/10 - 99*l**5/20 + 7*l**4/4 + l**3 + l + 49. Determine p, given that i(p) = 0.
-2/13, 0, 1
Factor 0 + 0*t + 1/5*t**2 - 1/5*t**4 + 0*t**3.
-t**2*(t - 1)*(t + 1)/5
Find r such that 8/11*r**2 - 2/11*r**3 - 2/11*r**4 + 8/11*r + 0 = 0.
-2, -1, 0, 2
Let l(m) be the third derivative of m**5/15 + m**4/2 - 8*m**3/3 - m**2 - 18. Factor l(h).
4*(h - 1)*(h + 4)
Let w(g) = g**2 + 8*g + 7. Let x be w(-6). Let t = x - -9. Factor