-7. Factor 7*x - 5*x**n + z*x**2 + x**2 - 3*x**3 - 4*x**3 - x**2 + 2.
-(x - 1)*(x + 1)**2*(5*x + 2)
Let s(i) be the second derivative of -9/4*i**2 + 7/4*i**3 + 0 + 4*i + 3/40*i**5 - 5/8*i**4. Factor s(q).
3*(q - 3)*(q - 1)**2/2
Let k = 863/15 - 172/3. Let -k*s**3 + 1/5*s - 2/5*s**2 + 2/5 = 0. What is s?
-2, -1, 1
Let l(j) be the third derivative of 1/84*j**4 + 0*j**3 + 0 + 0*j - 2*j**2 + 1/210*j**5. Find a, given that l(a) = 0.
-1, 0
Let v(h) = h**2 - h + 1. Let w(t) = 12*t**2 - 16*t + 20. Let n(d) = -16*v(d) + w(d). Factor n(m).
-4*(m - 1)*(m + 1)
Let j(z) = z**3 + z**2 - 3*z - 1. Let y be j(-2). Let o = -1 + y. Find x, given that -3*x**3 + x**3 + o*x**3 + 2*x = 0.
-1, 0, 1
Let o(z) be the third derivative of -z**5/120 + z**4/16 + z**3/3 + 13*z**2. Let o(w) = 0. Calculate w.
-1, 4
Let s(r) be the second derivative of -3*r + 0 + 1/30*r**5 + 1/3*r**2 + 1/6*r**4 + 1/3*r**3. Find f such that s(f) = 0.
-1
Let u(a) = -4*a**2. Let c(k) = -k**3 - k. Let t(f) = 2*c(f) - u(f). Determine y, given that t(y) = 0.
0, 1
Let k be (3/2)/(36/96). Find d, given that -2/15*d**k + 2/15*d**2 - 2/15*d + 2/15*d**3 + 0 = 0.
-1, 0, 1
Let v(t) = 8*t**3 + 48*t**2 + 89*t. Let k = -26 + 77. Let u(d) = -d**3 - 6*d**2 - 11*d. Let m(l) = k*u(l) + 6*v(l). Factor m(a).
-3*a*(a + 3)**2
Let m(x) be the second derivative of 1/11*x**3 + 0 + 2/11*x**2 + 1/66*x**4 + 8*x. Factor m(b).
2*(b + 1)*(b + 2)/11
Let z be (9 - 7)/(2 + 10)*2. Factor 1/3 - 1/3*a**2 - 1/3*a + z*a**3.
(a - 1)**2*(a + 1)/3
Solve -2*b**5 - b**4 - 8*b**4 + 23*b**5 + 3*b**4 = 0.
0, 2/7
Suppose 2*x - 8 - 6 = 0. Let l = x - 7. Factor l + 2/5*p + 2/5*p**3 + 4/5*p**2.
2*p*(p + 1)**2/5
Let s(q) be the third derivative of q**6/360 + q**5/90 - q**4/72 - q**3/9 + 7*q**2. Factor s(u).
(u - 1)*(u + 1)*(u + 2)/3
Let 3/2*g**2 + 6 - 6*g = 0. Calculate g.
2
Let d = -46 - -48. Find m such that 1/4*m**4 + 1/2*m - 1/2*m**3 - 1/4 + 0*m**d = 0.
-1, 1
Let a be (448/(-48))/((-2)/12). Let z = a + -164/3. Factor 2/3 + 4/3*t**3 - z*t + 0*t**2 - 2/3*t**4.
-2*(t - 1)**3*(t + 1)/3
Let c(d) be the first derivative of d**7/315 + d**6/72 + d**5/45 + d**4/72 + 4*d**2 - 3. Let x(q) be the second derivative of c(q). Factor x(b).
b*(b + 1)**2*(2*b + 1)/3
Let d = -7/2 + 23/6. Let n(l) be the first derivative of -d*l**3 + 2 - 1/2*l**2 + 2*l. Determine q so that n(q) = 0.
-2, 1
Let c(a) be the first derivative of -3*a**5/10 + a**4/4 + a**3/2 + 10*a + 7. Let q(h) be the first derivative of c(h). Solve q(o) = 0 for o.
-1/2, 0, 1
Let m(y) be the third derivative of -1/100*y**6 + 0*y**4 + 0 + 1/840*y**8 + 1/75*y**5 + 0*y + 0*y**3 + 3*y**2 + 0*y**7. Factor m(o).
2*o**2*(o - 1)**2*(o + 2)/5
Let q(x) be the second derivative of x**6/360 - x**5/40 + x**3 + 3*x. Let c(f) be the second derivative of q(f). Factor c(n).
n*(n - 3)
Let y be (-12)/(-66) - 60/(-33). Factor 4/5*t**3 - 6/5*t + 2/5 + 2/5*t**5 + 4/5*t**y - 6/5*t**4.
2*(t - 1)**4*(t + 1)/5
Suppose 2 - 12 = -a. Let t = a + -3. Factor -o**2 - 4*o**5 + t*o**5 - 3*o**3 - 2*o**2 + 3*o**4.
3*o**2*(o - 1)*(o + 1)**2
Let a(r) be the third derivative of -r**6/120 - r**5/30 - r**4/24 + 23*r**2. Factor a(m).
-m*(m + 1)**2
Suppose 2*j + 4*h - 18 = 6, j + 3*h - 17 = 0. Let 50/9*r**j + 2/9 - 20/9*r = 0. Calculate r.
1/5
Let z = -95 - -99. Let u(f) be the first derivative of f**5 - 2*f**3 - 1/2*f**4 - 1/2*f**2 + f + 1/2*f**6 + z. Suppose u(b) = 0. Calculate b.
-1, 1/3, 1
Suppose -3*w**3 - 6 + 43*w**2 - 11*w**2 - 11*w**2 + 3*w - 15*w**2 = 0. What is w?
-1, 1, 2
Suppose 8 = -5*t - 2, 4*v + 5*t - 14 = 0. Factor u - 2 - v + 0*u + 4*u**2 + 3*u.
4*(u - 1)*(u + 2)
Let s(z) be the second derivative of -z**7/42 - z**6/15 + z**4/6 + z**3/6 - 8*z. Factor s(c).
-c*(c - 1)*(c + 1)**3
Let a be 6/(-8)*12*10/(-585). Suppose 2/13*m**3 - 2/13*m**2 - 2/13*m + a = 0. Calculate m.
-1, 1
Suppose 6*k - 5 = 7. Factor m**k + 1/2*m**3 + 1/2*m + 0.
m*(m + 1)**2/2
Suppose 4*h - 2*v - 1 = 3, 3*h = 2*v + 1. Find i such that 6*i + 6*i**2 + 5*i**h + 4*i**3 - 7*i**3 + 2 = 0.
-1
Let s = -12 - -7. Let h = 7 + s. Factor 0*x**2 + h*x + 0*x**3 - 2*x**2 + 2*x**3 - 4*x**3 + 2.
-2*(x - 1)*(x + 1)**2
Suppose 10 = 5*o - 0. Let w be (-1)/o + -1 + 3. Factor 3/2 + 3/2*n - 3/2*n**2 - w*n**3.
-3*(n - 1)*(n + 1)**2/2
Let h(i) be the second derivative of 0*i**2 - i + 0*i**4 + 1/3*i**3 - 1/10*i**5 + 0. Factor h(t).
-2*t*(t - 1)*(t + 1)
Let u(z) = z**2 - 8*z - 7. Suppose 0 = 3*t - 18 - 9. Let b be u(t). Factor -a**4 + 2*a**2 - 3 + a**3 + a**3 + b - a - a**5.
-(a - 1)**2*(a + 1)**3
Let y(m) be the first derivative of m**5/100 - m**4/60 - m**3/30 + m**2/10 - 2*m + 1. Let u(n) be the first derivative of y(n). Factor u(v).
(v - 1)**2*(v + 1)/5
Let b = 36 - 33. Let h(c) be the second derivative of 0 - 1/30*c**5 + 0*c**2 - 1/18*c**4 + 1/45*c**6 + b*c + 1/9*c**3. Solve h(o) = 0.
-1, 0, 1
Suppose 0 = 5*v - 9 - 1. Suppose -32*c = -36*c + 16. Solve -2/7*n**c + 0*n - 2/7*n**v + 0 - 4/7*n**3 = 0.
-1, 0
Let h(o) = -2*o - 18. Let q be h(-9). Let c(v) be the second derivative of -1/60*v**5 + 0*v**3 + 0 + v - 1/90*v**6 + 0*v**4 + q*v**2. Factor c(a).
-a**3*(a + 1)/3
Suppose -4*m + 2*m = 2*w - 2, -2*m = -5*w + 5. Find l such that 1/5*l**2 + 1/5*l + m = 0.
-1, 0
Suppose -2 - 46/3*y**4 + 46/3*y + 2*y**5 - 356/9*y**2 + 356/9*y**3 = 0. What is y?
1/3, 1, 3
Let f(w) be the first derivative of w**5/210 + w**4/84 - 2*w**3/21 - 5*w**2/2 + 3. Let a(t) be the second derivative of f(t). Factor a(i).
2*(i - 1)*(i + 2)/7
Let r = 8 - 6. Suppose -1 = r*u - 5. Factor 2*b**2 - 6*b - 2*b**3 + 4*b**u + 0*b**2 + 2.
-2*(b - 1)**3
Let k(y) = -y**4 + y**2 + y - 1. Let z(f) = 1 + 9*f**3 - 3 - 4*f + 6 - 3*f**4 - 6*f**2. Let c(j) = -4*k(j) - z(j). Suppose c(n) = 0. Calculate n.
0, 2/7, 1
Let -2/3*q**4 - 2*q**3 - 2/3*q**2 + 4/3 + 2*q = 0. Calculate q.
-2, -1, 1
Suppose 2 = 2*x - 4. Determine o so that -7*o**2 - 2 - 6*o**x + 4*o**3 + 10 + o**2 = 0.
-2, 1
Let l(k) be the third derivative of k**7/1680 - k**6/720 - k**5/240 + k**4/48 - 5*k**3/6 + 3*k**2. Let x(w) be the first derivative of l(w). Factor x(c).
(c - 1)**2*(c + 1)/2
Let g(d) be the first derivative of -256*d**5/5 - 240*d**4 - 208*d**3 - 74*d**2 - 12*d - 8. Factor g(y).
-4*(y + 3)*(4*y + 1)**3
Let l(m) = 2*m**3 - 3*m**2 - 2*m + 1. Let q be l(-2). Let s = -45/2 - q. Let 4 + s*k**3 + 3*k**2 + 6*k = 0. Calculate k.
-2
Let q(j) = -6*j**3 + 6*j**2 - 9*j. Let w(d) = -5*d**3 + 7*d**2 - 9*d + 1. Let r(c) = 2*q(c) - 3*w(c). Factor r(s).
3*(s - 1)**3
Let i(p) be the second derivative of -p**5/80 - p**4/48 + p**3/24 + p**2/8 + 7*p. Suppose i(q) = 0. What is q?
-1, 1
Let k(u) be the second derivative of u**5/160 + u**4/96 - u**3/48 - u**2/16 + 15*u. Factor k(y).
(y - 1)*(y + 1)**2/8
Find f such that 54/11*f**3 - 2/11 - 72/11*f**4 + 26/11*f**2 - 6/11*f = 0.
-1/3, -1/4, 1/3, 1
Let q(k) = k**2 + 2*k + 5. Let g be q(-5). Let l be (1/(-6))/(g/(-30)). Factor -l*z + 0 - 1/2*z**2.
-z*(2*z + 1)/4
Let y be ((-20)/6 + 0)/((-6)/9). Let j(n) be the second derivative of 0 - 2*n + 0*n**2 + 1/24*n**4 - 1/60*n**6 + 0*n**3 + 0*n**y. Let j(b) = 0. What is b?
-1, 0, 1
Let r(n) be the second derivative of -n**7/3780 + n**6/1080 - n**4/4 - n. Let g(i) be the third derivative of r(i). Determine k, given that g(k) = 0.
0, 1
Let t be (2/(-3))/(42/81). Let k = 101/35 + t. Factor 8/5*g + k + 2/5*g**2.
2*(g + 2)**2/5
Suppose 5*c = 15, 4*c - 2*c - 21 = -5*r. Suppose h - r*h + 4 = 0. Factor 6/5*n**h + 4/5 + 2*n.
2*(n + 1)*(3*n + 2)/5
Suppose -q = -5*k - 5 - 17, -2*k + 2 = 5*q. Suppose 4 = 5*p - c - q, -p - c = -6. Factor 3/4*y - 1/2*y**p + 1/2.
-(y - 2)*(2*y + 1)/4
Determine t, given that -35*t**3 - 21*t - 9 + 8*t**3 + 14*t**3 + 10*t**3 - 15*t**2 = 0.
-3, -1
Let c = -3 + -1. Let y = c - -6. Factor y*z**3 + 5*z**4 - z**5 - z**4 + 3*z**5.
2*z**3*(z + 1)**2
Let z be (5/(-50))/(15/(-20))*5. Let 2/3*u**3 - 2/3*u + 2/3*u**4 + 0 - z*u**2 = 0. Calculate u.
-1, 0, 1
Suppose -4*s + 19 = -1. Let h = s + -3. Factor 0 + b**h - 3 + 5 + 3*b.
(b + 1)*(b + 2)
Factor 4*a - 16*a - 345*a**2 + 363*a**2 + 2.
2*(3*a - 1)**2
Let u(b) = b**3 + 11*b**2 + 10*b + 4. Let z be u(-10). Factor 24*a**2 + 0*a**4 - 48 - a**4 - 2*a**z.
-3*(a - 2)**2*(a + 2)**2
Let b(m) = m**3 + 5*m**2 + 3*m - 4. Let p be b(-4). Factor 0 + 0*i + 1/2*i**3 + p*i**2.
i**3/2
Let -1/3 - 1/3*n**2 + 2/3*n = 0. Calculate n.
1
Let m = 155 + -773/5. Factor