 - 10. Let h(n) = -32*n**5 + 60*n**4 - 12*n**3 - 13*n**2 - 3. Let c(s) = 10*h(s) - 3*y(s). Factor c(w).
-5*w**2*(w - 1)**2*(7*w + 2)
Suppose 0*s - 3 = 3*p + 3*s, 0 = -3*p - s - 1. What is a in 2/5*a**2 + 18/5*a**4 + p*a - 12/5*a**3 + 0 = 0?
0, 1/3
Let r(y) = y - 9. Let c be r(10). Suppose -t + 5*m = 3*t - 3, 0 = t - 3*m + c. Factor 1/4 + 1/4*o**5 - 3/4*o**4 - 3/4*o + 1/2*o**3 + 1/2*o**t.
(o - 1)**4*(o + 1)/4
Factor 4/5*h**2 - 2/5*h**3 - 4/5 + 2/5*h.
-2*(h - 2)*(h - 1)*(h + 1)/5
Let l(i) = i**2 + 1 - 4*i + 1 - 1. Let j be l(4). Find w such that -j - 2*w**2 + 5*w**2 - 2*w**2 = 0.
-1, 1
Let g(d) be the first derivative of -d**7/2100 + d**6/75 - 4*d**5/25 + 16*d**4/15 + 8*d**3/3 - 8. Let o(i) be the third derivative of g(i). Factor o(x).
-2*(x - 4)**3/5
Factor -1/3*k**5 + 0 + 0*k**4 + 4/3*k**3 + 0*k**2 + 0*k.
-k**3*(k - 2)*(k + 2)/3
Solve 4/3*d**4 - 4/3*d**2 + 0*d + 0 + 0*d**3 = 0 for d.
-1, 0, 1
Let k = -89 + 449/5. Factor -k*n - 4/5 + 1/5*n**4 + 4/5*n**3 + 3/5*n**2.
(n - 1)*(n + 1)*(n + 2)**2/5
Factor -2*v**2 - 4*v + 4*v**2 + 4*v**3 - 5*v**2 + 4 - v**2.
4*(v - 1)**2*(v + 1)
Let b(o) be the first derivative of -o**4/28 - 8*o**3/7 - 96*o**2/7 - 512*o/7 + 18. Factor b(w).
-(w + 8)**3/7
Let i be (10/(-25))/(12/(-42)). Factor q**3 + 0*q + 2/5*q**2 - i*q**4 + 0.
-q**2*(q - 1)*(7*q + 2)/5
Let i(f) be the third derivative of 2/35*f**7 + 0*f + 0*f**3 + 3/20*f**6 + 0 - 3*f**2 + 0*f**4 + 1/168*f**8 + 0*f**5. Factor i(z).
2*z**3*(z + 3)**2
Factor -30*a**2 + 19*a**2 - 34*a**2 + 0*a**3 - 225*a - 375 - 3*a**3.
-3*(a + 5)**3
Let r(p) be the first derivative of -4*p**6/3 - 4*p**5 - 3*p**4 + 4*p**3/3 + 2*p**2 + 8. Factor r(l).
-4*l*(l + 1)**3*(2*l - 1)
Suppose 3*f - 5 = j + 5, 0 = 3*j - 6. Let m(h) be the third derivative of 1/240*h**5 + 0 + 0*h + 0*h**f + h**2 + 0*h**3. Factor m(c).
c**2/4
Let u(o) = -o**3 + 8*o**2 - 8*o + 9. Let z be u(7). Let k(c) = -c**2 - 7*c - 6. Let f be k(-4). Factor f*i**3 - z*i - 7*i**3 + 2*i.
-i**3
Determine y, given that 5 - 21 - 25*y - 2 - 2 - 5*y**2 = 0.
-4, -1
Let t(d) be the first derivative of -7*d**3/24 + 19*d**2/16 + 3*d/4 - 32. Factor t(k).
-(k - 3)*(7*k + 2)/8
Find a, given that -1/6*a**2 - 5/3*a - 3/2 = 0.
-9, -1
Let q(c) be the second derivative of -1/10*c**3 - 1/5*c**2 - 1/60*c**4 + 0 + 4*c. Factor q(v).
-(v + 1)*(v + 2)/5
Suppose 2*l = -2*l. Let p be 0*(1 + (-5)/4 - 0). Solve -4/7*c**2 + 2/7 + 2/7*c**4 + l*c**3 + p*c = 0.
-1, 1
Suppose 0 = -5*v + 4*v. Let s(y) be the third derivative of v - 1/72*y**4 - 3*y**2 + 1/360*y**6 + 0*y**5 + 0*y**3 + 0*y. Determine p, given that s(p) = 0.
-1, 0, 1
Let p(s) be the first derivative of s**3/3 + 3*s**2/2 - 2*s - 2. Let x be p(-4). Determine t so that 0*t + 8/5 - 6/5*t**x + 2/5*t**3 = 0.
-1, 2
Let r(d) be the first derivative of 16*d**5/5 - 3*d**4 - 20*d**3/3 + 6*d**2 + 4*d + 19. Factor r(a).
4*(a - 1)**2*(a + 1)*(4*a + 1)
Let m = 2 - 2. Let w(l) be the second derivative of 0*l**6 + 1/63*l**7 - 3*l - 1/15*l**5 + 0 + 1/9*l**3 + 0*l**2 + m*l**4. Factor w(h).
2*h*(h - 1)**2*(h + 1)**2/3
Let w be (3 - 3)/(-3 - -1). Let x(m) be the first derivative of w*m**2 + 2 - 2/5*m**5 + m**4 - 2/3*m**3 + 0*m. Factor x(i).
-2*i**2*(i - 1)**2
Suppose -2*b - s + 7 = 0, -4*b + 5*s - 23 = -8*b. Factor 0*t + 2/9*t**b - 2/9.
2*(t - 1)*(t + 1)/9
Suppose 16 = 3*d - 11. Factor q + 3 + 3 + 0 - d*q + 2*q**2.
2*(q - 3)*(q - 1)
Let g be 3/(4 + 1 + -4). Factor 6*q**g + 33/2*q - 3 - 39/2*q**2.
3*(q - 2)*(q - 1)*(4*q - 1)/2
Let q(p) be the second derivative of -p**5/10 - 3*p**4/8 - p**3/6 + 23*p. Factor q(r).
-r*(r + 2)*(4*r + 1)/2
Factor -27/4 + 27/4*k + 1/4*k**3 - 9/4*k**2.
(k - 3)**3/4
Let n be (-6 + 6)*(-2 + 3). Let f(p) be the first derivative of -8/55*p**5 + 2 + 3/11*p**4 + 1/33*p**6 - 8/33*p**3 + n*p + 1/11*p**2. What is d in f(d) = 0?
0, 1
Let f(j) be the second derivative of -j**5/70 + 2*j**4/21 - 4*j**3/21 + j. Determine n, given that f(n) = 0.
0, 2
Let l(w) be the second derivative of 7/12*w**4 + 9/2*w**2 - 1/20*w**5 + 0 - 5/2*w**3 - 4*w. Factor l(z).
-(z - 3)**2*(z - 1)
Let r = -4 + 1. Let d = r + 6. Determine c so that -d*c**3 - 3*c**2 + c**2 + c**3 = 0.
-1, 0
Let -8/5*h**2 - 2/5 - 4/3*h - 4/5*h**3 - 2/15*h**4 = 0. Calculate h.
-3, -1
Let f(i) = -4*i - i**2 + 2*i**2 + 0*i**2 - 5 - 4*i**2. Let h(j) = 2*j**2 + 2*j + 3. Let a(r) = 6*f(r) + 10*h(r). Factor a(b).
2*b*(b - 2)
Let m(r) be the first derivative of -1 + 0*r**2 - 2/21*r**3 + 2/7*r. Factor m(z).
-2*(z - 1)*(z + 1)/7
Let b(g) be the first derivative of g**7/630 + g**6/180 + g**5/180 - 3*g**2/2 - 2. Let r(v) be the second derivative of b(v). Factor r(q).
q**2*(q + 1)**2/3
Let y(i) = 2*i - 1. Let a be y(2). Let 4*z**3 + 12*z**4 - 10*z**4 - 4*z**a = 0. Calculate z.
0
Let w = 6 - 4. Factor 1 - 6*d**3 + 5*d**3 + 3*d + w*d**3 + 3*d**2.
(d + 1)**3
Let j(v) be the first derivative of v**7/42 - v**6/30 - v**5/10 + v - 2. Let n(s) be the first derivative of j(s). Find d such that n(d) = 0.
-1, 0, 2
Suppose 4*i = f + 1, 0 = -3*i - 5*f + 3*f - 2. Let r(g) be the second derivative of i*g**2 + 14/45*g**5 + 2/27*g**3 + 0 + 3*g - 5/18*g**4. Factor r(d).
2*d*(4*d - 1)*(7*d - 2)/9
Let w(u) be the second derivative of 0 + 1/15*u**3 - 1/50*u**5 - 1/30*u**4 + 1/5*u**2 - 9*u. Factor w(z).
-2*(z - 1)*(z + 1)**2/5
Determine l, given that -2/5*l**3 - 4/5 - 18/5*l**2 + 18/5*l + 6/5*l**4 = 0.
-2, 1/3, 1
Let w(x) be the second derivative of x**5/300 + x**4/60 - 3*x**2/2 - 5*x. Let z(d) be the first derivative of w(d). Solve z(o) = 0.
-2, 0
Let h(m) be the second derivative of m**4/12 - 5*m**3/6 - 3*m**2 - 3*m. Let s be h(7). Factor -7*b - 4*b - b**3 + 4 + b - b**3 + s*b**2.
-2*(b - 2)*(b - 1)**2
Let l = 8 - 8. Suppose -4*b - 1 + 9 = l. Factor -12/5*h**3 - 2/5*h**5 - 8/5*h**b - 2/5*h + 0 - 8/5*h**4.
-2*h*(h + 1)**4/5
Suppose -12 = -2*n - 4*n. Let s(q) be the first derivative of 0*q + 0*q**n + 0*q**4 - 2/5*q**5 + 2/3*q**3 - 2. Factor s(i).
-2*i**2*(i - 1)*(i + 1)
Let u be -3 + 6 - 11*(-4)/(-16). Let q = 12/5 + -43/20. Factor 3/4*l + q + 3/4*l**2 + u*l**3.
(l + 1)**3/4
Suppose -4*c - m - 46 = -9*c, -22 = -c - 3*m. Suppose q - 3*q + c = -3*w, 15 = 4*w + 3*q. Find f such that 8/11 + w*f - 6/11*f**2 - 2/11*f**3 = 0.
-2, 1
Let a(k) be the second derivative of 9/80*k**5 + 0*k**2 + 0 + 1/30*k**6 + 0*k**3 + 1/24*k**4 - 2*k. Solve a(q) = 0 for q.
-2, -1/4, 0
Let k(o) be the first derivative of -o**6/2 - 12*o**5/5 - 15*o**4/4 - 2*o**3 + 25. Suppose k(r) = 0. Calculate r.
-2, -1, 0
Let r(y) be the third derivative of y**7/50 + y**6/40 - 37*y**5/100 + 31*y**4/40 - 3*y**3/5 - 6*y**2. Suppose r(v) = 0. Calculate v.
-3, 2/7, 1
Let c = 1 - 2. Let x be (-8 + 4)/(-3 - c). Factor -2 + 9 + 4*q - 3 + q**x.
(q + 2)**2
Let r = -8 + 13. Let x(d) = 4*d**2 + 4*d - 5. Let o(u) = 5*u**2 + 5*u - 6. Let t(j) = r*o(j) - 6*x(j). Factor t(h).
h*(h + 1)
Determine p, given that -3/4*p**3 + 3/2*p**2 - 3/4*p + 0 = 0.
0, 1
Let z be -5*(-2 - (-32)/20). Suppose -4*i**2 + i**z - i**2 - 4*i = 0. Calculate i.
-1, 0
Let a(d) be the second derivative of 1/90*d**6 + 0 + 5/18*d**3 - 1/60*d**5 + 3*d - 1/12*d**4 - 1/3*d**2. Factor a(g).
(g - 1)**3*(g + 2)/3
Let o(l) be the first derivative of l**4/4 + 2*l**3/3 - 3*l**2/2 - 6. Find d such that o(d) = 0.
-3, 0, 1
Suppose 6*s - s + 90 = 0. Let y(g) = g**4 - g - 1. Let j(d) = d**5 - d**4 + 36*d**3 - 54*d**2 + 18*d - 9. Let w(a) = s*y(a) + 2*j(a). Factor w(x).
2*x*(x - 3)**3*(x - 1)
Suppose 4 = 2*h - 4. Factor 3*p - p**2 - 8*p + h*p**2 - p.
3*p*(p - 2)
Let s be (2/(-720))/((-1)/2). Let g(u) be the third derivative of 0*u + 0*u**3 + u**2 - 1/45*u**5 + 1/36*u**4 + 0 + s*u**6. Suppose g(f) = 0. What is f?
0, 1
Suppose v = 2*n - 17, 5*n + 1 = 3*n - 5*v. Factor n*k**5 + 2*k**4 + 5*k + k**5 - 44*k**2 + 11*k + 56*k**3 - 2 - 36*k**4.
2*(k - 1)**4*(4*k - 1)
Suppose 1 = -4*z - 3, 0 = -m - 4*z. Let p(h) be the third derivative of 2*h**2 - 1/48*h**m + 1/480*h**6 + 0*h + 1/240*h**5 + 0 + 0*h**3. Factor p(l).
l*(l - 1)*(l + 2)/4
Let v = 73/4 + -18. Let z = 169/708 - -2/177. Determine j so that -1/4*j + 1/4 - v*j**5 - 1/2*j**2 + z*j**4 + 1/2*j**3 = 0.
-1, 1
Let r(s) be the second derivative of 0*s**3 + 0 + 0*s**2 + 3*s + 2/63*s**7 + 0*s**4 + 1/30*s**5 + 1/15*s**6. Suppose r(j) = 0. Calculate j.
-1, -1/2, 0
Let i be 4 - (-6 + 2) - 5. Factor 0 - y**i + 1/3*y**4 + 2/3*y**2 + 0*y.
y**2*(y - 2)*(y -