y(w) = -3*a(w) - 5*g(w). Suppose y(r) = 0. What is r?
-1/3, 0
Let o(q) = -q**4 - q**3 - 1. Let n(w) = -6*w**4 - 5*w**3 + w**2 - 7. Let b(p) = 4*n(p) - 28*o(p). Factor b(m).
4*m**2*(m + 1)**2
Solve -11*b + 11*b - 4 + b**3 + 3*b**2 = 0.
-2, 1
Solve 80/11*m**3 + 6*m**2 + 32/11*m**4 + 20/11*m + 2/11 = 0.
-1, -1/4
Let n(l) be the third derivative of -1/12*l**3 + 1/120*l**5 - l**2 + 0 + 0*l**4 + 0*l. Factor n(x).
(x - 1)*(x + 1)/2
Suppose -4*t - 10 = 2. Let g(k) = -5*k**2 + k - 6. Let o(b) = 4*b**2 + 5. Let v be -1*(-1)/((-4)/16). Let z(i) = t*g(i) + v*o(i). Factor z(f).
-(f + 1)*(f + 2)
Let d be -3 + 10 + -2 - -2. Let i = d + -5. Factor 1/2 + 3/4*n + 1/4*n**i.
(n + 1)*(n + 2)/4
Find c, given that 1/9*c**2 + 2/9 - 1/3*c = 0.
1, 2
Let h(z) be the third derivative of -z**8/3360 - z**7/420 - z**6/180 + 5*z**4/24 + z**2. Let r(n) be the second derivative of h(n). Factor r(b).
-2*b*(b + 1)*(b + 2)
Let u be (-3)/(27/(-51)) - (5 - 0). Find d such that -u + 0*d + 2/3*d**2 = 0.
-1, 1
Let p(d) be the first derivative of 4*d**5/5 - 12*d**4 + 140*d**3/3 + 24*d**2 - 144*d + 47. Solve p(z) = 0.
-1, 1, 6
Suppose 5 + 1 = w. Suppose 20*p + 3 - 16*p - w - p**2 = 0. Calculate p.
1, 3
Let g(j) be the first derivative of 1/20*j**4 + 0*j**3 + 0*j + 4 + 0*j**2. Determine n so that g(n) = 0.
0
Suppose 3*o + 6 = 6*o. Solve 3/4*d**3 + 0*d + 1/4*d**5 - 3/4*d**4 + 0 - 1/4*d**o = 0 for d.
0, 1
Let w(p) be the third derivative of -p**6/40 + 3*p**5/10 - 5*p**4/8 - 13*p**2. Factor w(j).
-3*j*(j - 5)*(j - 1)
What is q in -q**3 + 7/3*q**2 + 1/3 - 5/3*q = 0?
1/3, 1
Let v(s) be the first derivative of 3*s**4/2 - 4*s**3 + 4*s**2 - 3*s + 2. Let k(b) be the first derivative of v(b). Factor k(h).
2*(3*h - 2)**2
Let b(m) = -m**2 + m - 1. Let y(f) = -2*f**2 - f - 2. Let k(d) = 2*b(d) - 2*y(d). Factor k(n).
2*(n + 1)**2
Suppose 0 = 2*i - 22 + 2. Let v be (4/15)/(4/i). Factor 2/3 + 0*y**2 - v*y**4 + 4/3*y**3 - 4/3*y.
-2*(y - 1)**3*(y + 1)/3
Let x(n) be the first derivative of -7*n**6/30 - 16*n**5/15 - 11*n**4/6 - 4*n**3/3 + n**2/2 - 3. Let y(r) be the second derivative of x(r). Factor y(z).
-4*(z + 1)**2*(7*z + 2)
Let x(p) be the third derivative of p**5/15 + p**4 + 6*p**3 - 4*p**2. Solve x(l) = 0 for l.
-3
Find q such that 0 + 2/5*q**4 - 2/5*q**2 + 2/5*q**3 - 2/5*q = 0.
-1, 0, 1
Factor -2/5*t**4 - 2/5 + 4/5*t**2 + 0*t + 0*t**3.
-2*(t - 1)**2*(t + 1)**2/5
Let k = 9 + -9. Let o(y) be the third derivative of 0 - 1/60*y**5 + 1/6*y**3 + 0*y + y**2 + k*y**4. Factor o(t).
-(t - 1)*(t + 1)
Let v(u) = -u - 6. Let q be v(-8). Suppose q = 6*f - f - 4*o, -4*o = -2*f - 4. Determine n so that 2/3 + 2/3*n - 2*n**f + 4/3*n**4 - 2/3*n**3 = 0.
-1, -1/2, 1
Let j be (-24)/30 - 2/10. Let v = 1 + j. Factor 0*y**2 + v*y + 0 - 1/3*y**3 - y**4.
-y**3*(3*y + 1)/3
Suppose 0 = -f - 4*x + 20, -x + 4 + 1 = -f. Let h be (-138)/(-135) - 4/18. Factor -2*u**3 + 0*u + f + h*u**2.
-2*u**2*(5*u - 2)/5
Let u(p) = 3*p**4 - p**3 - 3*p**2 + p. Let b(z) = -5*z**4 + 2*z**3 + 5*z**2 - 2*z. Let d(w) = 4*b(w) + 7*u(w). Factor d(q).
q*(q - 1)*(q + 1)**2
Suppose 3*q + n - 293 = 0, n + 3*n + 200 = 2*q. Let a be 1*4*7/q. Let -a*d + 2/7*d**2 + 0 = 0. Calculate d.
0, 1
Suppose 3*r = -3 + 12. Let -7*x**2 - r*x**3 + 0*x - 2*x + 4*x**2 + 8*x**3 = 0. Calculate x.
-2/5, 0, 1
Let j(z) be the second derivative of -z**7/462 + z**6/110 + z**5/110 - z**4/22 - z**3/66 + 3*z**2/22 - 20*z. Determine x, given that j(x) = 0.
-1, 1, 3
Let n = 266/15 - 52/3. Suppose -4/5*b - 6/5*b**2 + 0 - n*b**3 = 0. Calculate b.
-2, -1, 0
Factor -5*g**3 + 4 + 10*g**2 - 13 + 9.
-5*g**2*(g - 2)
Let r(p) = 6*p**5 - 2*p**4 + 8*p**3 - 6*p - 2. Let i(x) = -5*x**5 + 3*x**4 - 7*x**3 - x**2 + 6*x + 1. Let k(w) = -4*i(w) - 3*r(w). Factor k(j).
2*(j - 1)**4*(j + 1)
Factor 0 + 8/7*f + 4/7*f**2.
4*f*(f + 2)/7
Factor 1 - 1 + 2*h**2 - h - h.
2*h*(h - 1)
Let i be (-15)/25*3 + 2. Factor 2/5*q - 1/5 - i*q**2.
-(q - 1)**2/5
Let s = 21 - 41. Let q be ((-2)/8)/(s/48). Factor 12/5*b**3 - 18/5*b**2 - q - 3/5*b**4 + 12/5*b.
-3*(b - 1)**4/5
Factor 0 - 2*l + 8/9*l**2.
2*l*(4*l - 9)/9
Suppose 0 = 4*i - 3*i - 3. Determine h, given that -h**2 + 2 + h - i + 3 = 0.
-1, 2
Let d be (0 - 1)/(2/(-40)). Factor -3*q - q**2 + d - 20.
-q*(q + 3)
Let s = 204 - 202. Factor 2/3*k**2 - 8/3*k + s.
2*(k - 3)*(k - 1)/3
Let k(g) be the third derivative of -g**8/112 - 3*g**7/70 - g**6/40 + 3*g**5/20 + g**4/4 + 15*g**2. Solve k(s) = 0.
-2, -1, 0, 1
Let f(p) be the third derivative of p**10/196560 - p**8/43680 - p**4/12 - 2*p**2. Let g(t) be the second derivative of f(t). Factor g(v).
2*v**3*(v - 1)*(v + 1)/13
Let d be (5/50)/(235/225 + -1). Determine s so that -3/4*s**3 + 3/4 + d*s**2 - 9/4*s = 0.
1
Let k(y) be the third derivative of y**5/20 - 3*y**4/8 - 5*y**3 - 32*y**2 - y. Factor k(q).
3*(q - 5)*(q + 2)
Let y(c) = 13*c**3 + 16*c**2 + 3*c - 5. Let r(a) = 7*a**3 + 8*a**2 + a - 3. Let w(v) = 5*r(v) - 3*y(v). Factor w(i).
-4*i*(i + 1)**2
Let b(l) be the first derivative of 2*l**5/25 - 9*l**4/20 + l**3 - 11*l**2/10 + 3*l/5 + 12. Find i such that b(i) = 0.
1, 3/2
Let a = -317/39 + 8. Let y = a - -6/13. Factor 0 + 1/6*u**4 + y*u**3 + 1/6*u**2 + 0*u.
u**2*(u + 1)**2/6
Let u(v) be the third derivative of -1/12*v**4 + 0 - 3*v**2 - 1/60*v**5 + 0*v - 1/6*v**3. Solve u(r) = 0.
-1
Let d = 36 - 36. Let t(w) be the first derivative of 3 - 1/6*w**3 + d*w + 1/8*w**4 + 0*w**2. Let t(q) = 0. Calculate q.
0, 1
Suppose -4*a = -5*q - 21 + 5, 3*a - 12 = -5*q. Let z(l) be the second derivative of q*l**2 + 0*l**3 - 1/90*l**6 + 1/18*l**4 - 1/60*l**5 + 0 - l. Factor z(b).
-b**2*(b - 1)*(b + 2)/3
Factor -z**3 - 23 - 3*z**2 + 4*z + 26 + z**3 - 4*z**3.
-(z - 1)*(z + 1)*(4*z + 3)
Let d = 674 - 2021/3. What is j in -d*j**3 + 0*j + 0 + 1/3*j**2 = 0?
0, 1
Let o(p) be the first derivative of -p**6/24 + p**5/30 + 3*p**2/2 - 1. Let n(x) be the second derivative of o(x). Determine g, given that n(g) = 0.
0, 2/5
Let a(p) = p**3 + 9*p**2 - p + 1. Let f be a(-9). Suppose -x - 8*r + 3*r = 20, -3*x - f = 5*r. Find d, given that x + 2*d + 4*d**2 - 5 + 2*d**3 = 0.
-1, 0
Let d be (-1)/(-1) - (-41)/4. Let j = 23/2 - d. Determine u so that 0*u + 0 + 0*u**2 + j*u**3 + 1/4*u**4 = 0.
-1, 0
Suppose -8*w + 20 = -4*w. Let b(l) be the first derivative of 3/4*l**4 - 1 + 0*l - l**2 - 1/6*l**6 + 1/5*l**w - 1/3*l**3. Factor b(x).
-x*(x - 2)*(x - 1)*(x + 1)**2
Suppose -2*z + 15 = 3*z. Suppose 0 = z*d - 11 + 2. Factor g**3 - 5*g**2 + 6*g**2 - d*g**3 + g**4.
g**2*(g - 1)**2
Let z be (-2)/(-3) - (-170)/(-3). Let n = z + 618/11. Factor -n*w - 8/11*w**2 + 0.
-2*w*(4*w + 1)/11
Let h(u) = 100*u**2 - 85*u + 11. Suppose -5 = -3*y - 11. Let c(m) = -50*m**2 + 42*m - 6. Let b(f) = y*h(f) - 5*c(f). Let b(n) = 0. What is n?
2/5
Let g(r) be the second derivative of 3*r**7/56 + r**6/8 - 7*r**5/40 - r**4/4 + r**3/3 - 6*r. Let g(d) = 0. What is d?
-2, -1, 0, 2/3
Suppose 2*b = -4*i + 2, 3*i - 7*i = -2*b + 18. Determine u so that u**3 - 5*u**4 + 0*u**3 - u**2 - u**b + 6*u**4 = 0.
-1, 0, 1
Suppose -3/8*y + 0 - 27/2*y**3 - 9/2*y**2 = 0. Calculate y.
-1/6, 0
Factor -48*l**3 - 5 - 16*l**4 - 2*l**5 - 64*l**2 - 32*l - 6 + 11.
-2*l*(l + 2)**4
Let w(j) be the third derivative of 0*j - 7/180*j**5 + 0*j**3 + 1/36*j**4 + 0 - 4*j**2. Find k, given that w(k) = 0.
0, 2/7
Let f(n) = 2*n**3 + 4*n**2 - 4. Let w(q) = q**4 - q**2 + q. Let h(p) = f(p) - 2*w(p). Factor h(k).
-2*(k - 2)*(k - 1)*(k + 1)**2
Suppose -4/7*v + 0 - 10/7*v**2 + 48/7*v**3 + 18*v**4 = 0. Calculate v.
-1/3, 0, 2/7
Let n be 27/9 - (-2 - -5). Factor 1/3*x**3 - 1/6*x**4 + 0 + n*x - 1/6*x**2.
-x**2*(x - 1)**2/6
Let n be (4/(-7))/(-3 - -1). Factor 0 - 4/7*q**2 - n*q - 2/7*q**3.
-2*q*(q + 1)**2/7
Let g(k) be the second derivative of -1/30*k**5 - 1/9*k**3 - 1/9*k**4 + 0 + 0*k**2 - 2*k. Factor g(p).
-2*p*(p + 1)**2/3
Find n, given that 2/11*n**3 - 2/11*n**2 + 0 - 4/11*n = 0.
-1, 0, 2
Suppose -4*j + n + 12 = -2*n, -5*n + 12 = 4*j. Factor -1/4*f**2 + 0*f + 0*f**j + 1/4*f**4 + 0.
f**2*(f - 1)*(f + 1)/4
Let v(o) = 5*o**2 - 1. Let f(g) = -6*g**2 + 1. Suppose 2*w = -p + 12, 2*p - 3*p + 4*w - 12 = 0. Let q(i) = p*f(i) + 5*v(i). Factor q(a).
(a - 1)*(a + 1)
Let y(q) be the second derivative of -q**7/70 + 3*q**6/50 - 3*q**5/50 - q**4/10 + 3*q**3/10 - 3*q**2/10 - 16*q. Let y(m) = 0. What is m?
-1, 1
Let h(r) be the third derivative of r**6/900 - r**5/75 + r*