+ 27. Let g(u) = 4*a(u) + 3*w(u). Factor g(t).
3*(t + 3)**2
Let k(n) be the first derivative of n**4/20 + n**3/5 - 2*n**2/5 - 5. Solve k(v) = 0 for v.
-4, 0, 1
Factor -3*h - h**2 - 2*h**2 - 5 + 2*h**2 + 3.
-(h + 1)*(h + 2)
Let n = -6 + 8. Solve -18*m**3 + 2*m + 4*m**4 + 18*m**4 + 0*m**n - 8*m**5 + 2*m**2 = 0 for m.
-1/4, 0, 1
Let c(h) = -2*h + 0 + 1 + 3*h. Let v be c(3). Solve -2/5 - 1/5*r - 8/5*r**v + r**5 + 2*r**2 - 4/5*r**3 = 0 for r.
-1, -2/5, 1
Let d(w) = -30*w + 180. Let b be d(6). Factor 0*r + 0 + b*r**4 + 2/5*r**5 - 2/5*r**3 + 0*r**2.
2*r**3*(r - 1)*(r + 1)/5
Let q = 2/399 - -620/133. Let m(k) = 2*k**3 - 16*k**2 - 3*k + 29. Let g be m(8). What is i in 0 - 4/3*i**2 + q*i**g + 0*i - 32/3*i**4 + 22/3*i**3 = 0?
0, 2/7, 1
Let h(n) be the first derivative of -9*n**4/4 + n**3 + 7*n**2/2 + n - 2. Let c(b) = -b. Let a(s) = 2*c(s) + h(s). Factor a(k).
-(k - 1)*(3*k + 1)**2
Suppose -2*n - 1 = -5. Suppose 2*x - 3*h = 7, 5 = n*x + x + h. Factor m - m - x*m - m**2 - 1.
-(m + 1)**2
Let -405*s**3 - s**4 + s**2 + 0*s**4 - 3*s + 408*s**3 = 0. Calculate s.
-1, 0, 1, 3
Let 20/7*g**3 + 16/7*g - 4/7*g**4 - 32/7*g**2 + 0 = 0. What is g?
0, 1, 2
Let c(v) be the third derivative of -v**5/10 - v**4/16 + 20*v**2. Factor c(r).
-3*r*(4*r + 1)/2
Let o(g) = -g - 2. Let m be o(-4). Suppose -d - m*d = -3*j + 3, -3*d - 9 = -5*j. Solve 3*u**2 + 0*u**2 + 2 - d*u**2 - 3*u = 0 for u.
1, 2
Factor 5*r - 5*r**2 + 4 + 1 - 7*r**3 + 2*r**3.
-5*(r - 1)*(r + 1)**2
Let k = 1 + 4. Let m(b) = -6*b**3 - 19*b**2 - 24*b - 5. Let j(w) = 9*w**3 + 28*w**2 + 36*w + 8. Let s(c) = k*j(c) + 8*m(c). What is y in s(y) = 0?
-2, 0
Let z be 296/220 + 2/10. Let o = z + -7/33. Let -o*q - 1/3 - 4/3*q**3 - 2*q**2 - 1/3*q**4 = 0. Calculate q.
-1
Solve 0 + 36/5*z**3 + 0*z**4 - 48/5*z - 16/5*z**2 - 4/5*z**5 = 0.
-3, -1, 0, 2
Suppose 2/5*c**3 + 16/5 - 4/5*c**2 - 8/5*c = 0. What is c?
-2, 2
Let s be 0 + (2 - 2) + 2. Factor 2*r**2 - r - r - s + 2*r.
2*(r - 1)*(r + 1)
Let c(a) be the second derivative of -a**5/4 - 5*a**4/4 + 10*a**3/3 + 15*a. Factor c(r).
-5*r*(r - 1)*(r + 4)
Suppose 7*j = 3*j + 12. What is h in -5*h**2 + j*h**2 + 2*h - h**2 = 0?
0, 2/3
Let i(q) be the first derivative of -q**8/168 + q**7/147 + q**6/210 + 3*q**2 - 4. Let a(b) be the second derivative of i(b). Factor a(u).
-2*u**3*(u - 1)*(7*u + 2)/7
Let q(t) = 14*t**3 + 24*t**2 + 24*t + 8. Let o(s) = -9*s**3 - 16*s**2 - 16*s - 5. Let g(m) = -8*o(m) - 5*q(m). Factor g(n).
2*n*(n + 2)**2
Let n(u) be the second derivative of -u**7/14 - u**6/10 + 9*u**5/20 + 5*u**4/4 + u**3 - u. Factor n(b).
-3*b*(b - 2)*(b + 1)**3
Let a(u) be the third derivative of -12*u**7/35 + 11*u**6/10 - 4*u**5/3 + 2*u**4/3 + 29*u**2. Solve a(k) = 0 for k.
0, 1/2, 2/3
Let s(q) = q + 1. Let c(x) = -2*x**4 - 20*x**3 - 66*x**2 - 82*x - 34. Let i(u) = -c(u) - 2*s(u). Solve i(g) = 0 for g.
-4, -1
Find f such that -2/3*f**2 - 4/9*f**3 + 2/9*f**4 + 8/9*f + 8/9 = 0.
-1, 2
Let p be 4*((-20)/16 + 2). Factor p*n**4 - 10 - n**3 - 6*n**2 + 10 + 4*n**3.
3*n**2*(n - 1)*(n + 2)
Let o = 1477/3 + -492. Factor -2/3*h**2 + o*h**3 - 1/3*h + 0 + 2/3*h**4.
h*(h - 1)*(h + 1)*(2*h + 1)/3
Solve -3*n + 16*n**2 - 3*n - 19*n**2 = 0.
-2, 0
Let z = -51 - -55. Find b such that -4/7*b + 0 - 2/7*b**5 + 2/7*b**z + 6/7*b**3 - 2/7*b**2 = 0.
-1, 0, 1, 2
Let x(r) be the second derivative of 0*r**2 + 0*r**3 + 0*r**4 - 2/45*r**6 + 0 + 1/63*r**7 + 1/30*r**5 + 10*r. Suppose x(l) = 0. What is l?
0, 1
Let s be (2738/(-30))/(3/(-9)). Let q = 275 - s. What is a in q*a + 4/5 + 2/5*a**2 = 0?
-2, -1
Let o(n) be the third derivative of n**6/36 + 2*n**5/15 - n**4/3 + 5*n**3/6 - 3*n**2. Let j(q) be the first derivative of o(q). Factor j(z).
2*(z + 2)*(5*z - 2)
Suppose -3*p = -5*p + 4*l - 14, 2*p - 3*l + 9 = 0. Let v(f) = f**2 - 3*f + 3. Let a be v(p). Find t such that -3/2*t**a + 0 - 2*t**2 - 1/2*t = 0.
-1, -1/3, 0
Let b(p) = -2*p**2 + 4*p + 2. Let s(g) = g**2 - 5*g - 3. Let l(u) = 3*b(u) + 4*s(u). Factor l(n).
-2*(n + 1)*(n + 3)
Solve -10*w**3 + 14*w + 6*w**3 + 12 + 16*w**2 - 28*w**3 - 10 = 0 for w.
-1/4, 1
Let h(b) be the third derivative of 0*b**3 + 1/105*b**5 + 1/84*b**4 + 1/420*b**6 + 0*b - 6*b**2 + 0. Factor h(s).
2*s*(s + 1)**2/7
Let u(b) be the third derivative of -3*b**8/112 - b**7/10 + b**5/5 + 14*b**2. Determine l so that u(l) = 0.
-2, -1, 0, 2/3
Let x = 5 + -3. Suppose x*t = 13 + 15. Solve -t*j**2 - 1 + 2 + 3 - 10*j = 0.
-1, 2/7
Factor 0*f**2 - 2 - 7/3*f + 1/3*f**3.
(f - 3)*(f + 1)*(f + 2)/3
Let p(q) be the first derivative of -49*q**6/33 + 14*q**5/5 + 17*q**4/22 - 146*q**3/33 + 32*q**2/11 - 8*q/11 + 20. Let p(l) = 0. Calculate l.
-1, 2/7, 1
Suppose 2*c + 8 + 8 = 0. Let v be ((-2)/(-5))/(c/(-20)). Let p(y) = -7*y**2 - 3*y. Let t(i) = i**2. Let o(m) = v*p(m) + 4*t(m). Factor o(h).
-3*h*(h + 1)
Let h(t) be the third derivative of 3/40*t**5 + 0 + 0*t - t**2 - 1/80*t**6 + 0*t**4 - t**3. Factor h(y).
-3*(y - 2)**2*(y + 1)/2
Suppose 5 = 4*l - 4*x - 3, -4 = -2*l + 5*x. Let -7*j + 2*j**l - 6*j + 11*j = 0. Calculate j.
0, 1
Factor 5*k**3 + 5*k + k + 9*k**2 + k**2 - k.
5*k*(k + 1)**2
Let v(f) be the second derivative of -f**8/3840 - f**7/1120 - f**6/1440 + f**4/4 - f. Let p(c) be the third derivative of v(c). Factor p(l).
-l*(l + 1)*(7*l + 2)/4
Suppose 0 = 8*j + 2 - 2. Let z(i) be the third derivative of 1/60*i**6 + 3*i**2 + 0 + 0*i**5 + 0*i + 0*i**4 - 1/105*i**7 + j*i**3. Factor z(x).
-2*x**3*(x - 1)
Let i(x) be the third derivative of -x**7/350 - x**6/100 - x**5/100 - 3*x**2. Factor i(n).
-3*n**2*(n + 1)**2/5
Suppose 5*d + w = -3*w + 40, 2*d - w = 3. Suppose -3*y + 10 = d*k, -3*k - 8*y = -3*y - 2. Solve -1/3*x**k - 1/3 + 2/3*x**2 + 0*x + 0*x**3 = 0 for x.
-1, 1
Let w be 126/45 - 3 - (-2)/10. Let n(g) be the first derivative of w*g**2 + 4/9*g**3 + 0*g + 1/9*g**6 + 5/6*g**4 + 8/15*g**5 + 4. Factor n(d).
2*d**2*(d + 1)**2*(d + 2)/3
Let o(z) = -2*z**2 - 4*z + 1. Let s(j) = 3*j**2 + 6*j - 1. Let r(l) = 8*o(l) + 5*s(l). Solve r(d) = 0 for d.
-3, 1
Let o(j) be the third derivative of 7/75*j**7 + 0 + 77/300*j**6 + 8*j**2 + 0*j - 8/15*j**3 - 11/25*j**5 - 13/15*j**4. What is z in o(z) = 0?
-2, -2/7, 1
Let n(m) be the second derivative of 2*m**5/5 + 17*m**3/6 - 6*m. Let c(j) = j**3 + 2*j. Let o(d) = -51*c(d) + 6*n(d). Find p such that o(p) = 0.
0
Let y be 5/((-20)/8)*-1. Let k(v) be the second derivative of 0 - 1/24*v**4 + 0*v**y - 1/60*v**6 + 0*v**3 + 1/20*v**5 + v. Factor k(h).
-h**2*(h - 1)**2/2
Suppose 2/5*a**2 + 16/5 + 18/5*a = 0. Calculate a.
-8, -1
Let c(d) be the third derivative of d**7/70 - d**6/10 + 3*d**5/20 + d**4/2 - 2*d**3 + 11*d**2 - 2*d. Factor c(n).
3*(n - 2)**2*(n - 1)*(n + 1)
Factor 1/5*j**3 - 2/5 + 0*j**2 - 3/5*j.
(j - 2)*(j + 1)**2/5
Let g(m) be the second derivative of m**6/15 + m**5/10 + m. Find s such that g(s) = 0.
-1, 0
Let w = -10 + 14. Factor 4*l**5 + 4*l**4 + 5*l**w - l**4.
4*l**4*(l + 2)
Let w = -96 - -296/3. Let 4*h**3 + w*h**4 + 8/3*h**2 + 0 + 2/3*h + 2/3*h**5 = 0. What is h?
-1, 0
Let z(s) = -30*s + 0 + 1 + 19*s + 10*s**2. Let m(h) be the first derivative of h**3/3 - h**2/2 + 1. Let b(v) = 22*m(v) - 2*z(v). Solve b(f) = 0 for f.
-1, 1
Let l(d) be the first derivative of -d**4/14 - 2*d**3/7 - 24. Factor l(r).
-2*r**2*(r + 3)/7
Suppose -3*l = 4*l - 3*l. Let w(i) be the first derivative of 1/15*i**6 - 2/15*i**3 + 3/10*i**4 - 3 + l*i**2 + 0*i - 6/25*i**5. What is d in w(d) = 0?
0, 1
Let u = 3 - -27. Let x be u/9*(-6)/(-5). Factor 3/2*o + 0*o**3 + 0 - 9/4*o**2 + 3/4*o**x.
3*o*(o - 1)**2*(o + 2)/4
Let o(l) be the first derivative of 5*l**3/3 - 25*l**2 + 125*l + 24. Factor o(d).
5*(d - 5)**2
Suppose 0 + 1/6*w**2 - 1/2*w = 0. Calculate w.
0, 3
Let o be -4 - 1044/(-24)*6/63. What is f in -o*f + 0 - 1/7*f**2 = 0?
-1, 0
Let s(d) = 15*d**5 - 21*d**4 + d**3 + 5*d**2 - 4*d + 4. Let c(u) = 15*u**5 - 20*u**4 + 5*u**2 - 5*u + 5. Let z(j) = -4*c(j) + 5*s(j). What is g in z(g) = 0?
-1/3, 0, 1
Determine m so that -1 - 1/2*m**4 + 3/2*m**2 - 7/6*m**3 + 7/6*m = 0.
-3, -1, 2/3, 1
Suppose 30 = o - 150. Solve -2*f**5 - 2*f - 180 + o + f**3 + 3*f**3 = 0.
-1, 0, 1
Find y, given that -2/5*y + 0*y**2 + 0 + 2/5*y**3 = 0.
-1, 0, 1
Let o(f) be the second derivative of -f**4/96 + f**3/12 - f**2/4 - 4*f. Factor o(d).
-(d - 2)**2/8
Solve 0*i + 0*i**3 + 2/7*i**2 - 1/7 - 1/7*i**4 = 0 for i.
-1, 1
Suppose 0 = b + 4*u + 4, 0 = -3*b -