e 4*b - m - 48 = 22, 52 = 3*b - m. Factor 28*n**2 - 38*n - 10*n - 18*n**2 + b + 22*n**2.
2*(4*n - 3)**2
Let g be 74/(-360) - 26/(-117). Let b(k) be the third derivative of 0*k**4 - 1/6*k**3 + g*k**5 - 3*k**2 + 0 + 0*k. What is t in b(t) = 0?
-1, 1
Let t(n) be the third derivative of n**6/1080 - n**5/360 + n**3/3 + n**2. Let j(q) be the first derivative of t(q). Determine o so that j(o) = 0.
0, 1
Suppose -2/7*z**5 - 4*z**2 + 22/7*z + 12/7*z**3 + 2/7*z**4 - 6/7 = 0. Calculate z.
-3, 1
Let q = 28 + -24. Factor 16*x**2 + 16*x**3 + 0*x + 8*x + 12*x**2 - q.
4*(x + 1)**2*(4*x - 1)
Suppose -3*l + r - 3 - 3 = 0, -5*l = -5*r + 10. Let j be (3/l)/((-6)/12). Factor h + 2*h**3 + h**2 - 2*h**j + h - h**3.
-h*(h - 2)*(h + 1)
Suppose -19*q = -8*q + 18*q. Determine z, given that -9/4*z - 3/4*z**2 + q = 0.
-3, 0
Find d such that -8/9*d**3 + 0 - 2*d**2 - 10/9*d = 0.
-5/4, -1, 0
Let s be (-4 - 29/(-2))*3/9. What is i in -2 - 25/2*i**2 - 8*i - 1/2*i**5 - 19/2*i**3 - s*i**4 = 0?
-2, -1
Suppose -w - 8 = -5*w. Suppose 3*x - 11 = -w*k, x = 3*x - 5*k - 1. Factor 0*d - 4/11*d**2 - 10/11*d**x + 0.
-2*d**2*(5*d + 2)/11
Let p(u) be the first derivative of u**5/70 - u**4/14 + 4*u**2/7 + 4*u - 2. Let n(o) be the first derivative of p(o). Factor n(a).
2*(a - 2)**2*(a + 1)/7
Let x(t) = t**2 + 23*t - 174. Let z be x(6). Find w, given that 0*w - 1/5*w**4 + z + 0*w**3 + 1/5*w**2 = 0.
-1, 0, 1
Let z(y) be the first derivative of 0*y + 3/4*y**4 + 2*y**3 + 3 + 3/2*y**2. Factor z(k).
3*k*(k + 1)**2
Suppose 5*n = -2*d - 6, 0*n + n - 5*d - 15 = 0. Determine g, given that 0 + n*g + 2/9*g**2 + 2/9*g**3 = 0.
-1, 0
Let f(h) = -5*h**4 - 7*h**3 + h**2 - h + 4. Let y(u) = u**4 + u**3 - u**2 - 1. Let w(n) = -3*f(n) - 12*y(n). Factor w(o).
3*o*(o + 1)**3
Let j = 13 + -6. Suppose -j*q + 3*q + 64 = 0. Factor -5*r**4 + r + 19*r**3 - 3*r**2 + 4*r**4 - q*r**3.
-r*(r - 1)**3
Let b(k) be the second derivative of k**6/10 - 3*k**5/5 + k**4 + 4*k. Factor b(p).
3*p**2*(p - 2)**2
Factor -1/8*k**2 + 3/8 + 1/4*k.
-(k - 3)*(k + 1)/8
Let q(s) = -4*s**3 + 11*s**2 + 5*s - 6. Let c(y) = y**2 + y - 1. Let v(w) = -6*c(w) + q(w). Find x such that v(x) = 0.
0, 1/4, 1
Suppose -5*n - 4*a = -7*a - 27, -3 = 3*n + 3*a. What is q in 0*q**n + 1/3*q + 2/3*q**4 - 1/3*q**5 + 0 - 2/3*q**2 = 0?
-1, 0, 1
Let b(x) be the first derivative of 1/2*x - 1/8*x**4 + 1/2*x**3 - 3/4*x**2 + 3. Factor b(m).
-(m - 1)**3/2
Let o(g) be the third derivative of 1/420*g**6 + 0*g**4 + 3*g**2 + 1/210*g**5 + 0*g**3 + 0*g + 0. Factor o(f).
2*f**2*(f + 1)/7
Find c, given that -4/7 + 2/7*c**2 - 2/7*c = 0.
-1, 2
Let v(c) be the third derivative of -c**8/896 - 3*c**7/280 - 13*c**6/320 - 3*c**5/40 - c**4/16 - c**2. Factor v(x).
-3*x*(x + 1)**2*(x + 2)**2/8
Let i(z) be the third derivative of -1/8*z**4 + 0 + 0*z + 0*z**7 - 1/112*z**8 + 0*z**5 - z**2 + 1/20*z**6 + 0*z**3. Factor i(r).
-3*r*(r - 1)**2*(r + 1)**2
Suppose -o + 3*x = -171, -4*x + x = 3*o - 501. Let r be (-15)/(-2)*32/o. Determine s so that -16/7*s + r*s**2 - 2/7*s**3 + 8/7 = 0.
1, 2
Let b be 24/(-124) + 0/(-1). Let i = 116/279 + b. Factor 2/9*a**3 - i*a + 2/9*a**2 - 2/9.
2*(a - 1)*(a + 1)**2/9
Factor 4*g**3 - 5*g**2 - 2*g**2 + 2*g**2 + g**2.
4*g**2*(g - 1)
Let d(q) = -3*q**2 + 0 + 5*q - 2*q - 5. Let f(h) = 4*h**2 - 4*h + 6. Let x(y) = -6*d(y) - 5*f(y). Let x(s) = 0. What is s?
0, 1
Suppose 2*d + 3*z + 1 = 2*z, 0 = -3*d - z. Let j(n) be the first derivative of -n**2 + 1/4*n**4 + 0*n + 1/3*n**3 + d. Determine y so that j(y) = 0.
-2, 0, 1
Factor -j**4 - 12*j**2 - 12*j**2 - 6*j**3 + 27*j**2 - 15*j**2 - 8*j.
-j*(j + 2)**3
Suppose 0*h - 20 = -4*h. Let j be (2/27)/(h/15). Factor -2/9*t**3 + 2/9 + 2/9*t - j*t**2.
-2*(t - 1)*(t + 1)**2/9
Let m(l) be the first derivative of l**5 + 5*l**4/4 - 5*l**3/3 - 5*l**2/2 - 7. Solve m(s) = 0.
-1, 0, 1
Let l(b) be the third derivative of b**6/240 + 11*b**5/120 + 35*b**4/48 + 25*b**3/12 + 2*b**2. Factor l(g).
(g + 1)*(g + 5)**2/2
Let o(m) be the third derivative of 1/27*m**3 + 0*m + 1/540*m**5 - 1/72*m**4 + 0 + 3*m**2. Factor o(a).
(a - 2)*(a - 1)/9
Factor -20/9*b**3 + 0 + 4*b + 4/3*b**2 + 4/9*b**4.
4*b*(b - 3)**2*(b + 1)/9
Let g = -2 + 6. Let b = g - 1. Factor -12 - 2*z**b - 2*z + 12 + 4*z**2.
-2*z*(z - 1)**2
Let o = 76 + -4559/60. Let c(g) be the third derivative of 1/210*g**7 + 0*g - 2*g**2 + 0*g**5 - 1/6*g**3 + o*g**6 + 0 - 1/12*g**4. Factor c(l).
(l - 1)*(l + 1)**3
Let d(t) be the second derivative of t**4/18 + 4*t**3/3 + 12*t**2 - 3*t. Let d(h) = 0. What is h?
-6
Let d(h) = 1. Let l(m) be the third derivative of m**5/60 - m**3 + 2*m**2. Let k(f) = 10*d(f) + 2*l(f). Factor k(u).
2*(u - 1)*(u + 1)
Let d(u) be the second derivative of 11*u**9/68040 + 13*u**8/30240 + u**7/5670 + u**4/6 + 2*u. Let a(t) be the third derivative of d(t). Factor a(y).
2*y**2*(y + 1)*(11*y + 2)/9
Let z(k) = k + 7. Let j be z(-6). Let f(i) = 4*i**2 + 12*i + 12. Let l(a) = -a**2. Let s(y) = j*f(y) + l(y). Find h such that s(h) = 0.
-2
Let t(b) be the second derivative of -b**6/180 - b**5/60 + b**4/6 - b**3/3 - b. Let f(c) be the second derivative of t(c). Factor f(h).
-2*(h - 1)*(h + 2)
Let d be -7*(-3 + -7) + -2. Suppose w + 4*w - d = 3*n, -2*w - 5*n = -21. Factor 9*m**2 + 6 + 3*m - 25*m**3 - 2 + w*m - 4*m**2.
-(m - 1)*(5*m + 2)**2
Determine u so that 2*u**5 - 3*u**5 + 3*u**4 - u**3 - 17*u + 19*u - 3*u**2 = 0.
-1, 0, 1, 2
Suppose -2*v - 37 + 11 = 0. Let u be v/(-35) - (-2)/10. Factor -6/7*b**2 + u*b + 0.
-2*b*(3*b - 2)/7
Let i(y) be the second derivative of 0 - 4/105*y**5 + 2*y + 1/12*y**4 - 1/21*y**3 - 4/105*y**6 + y**2. Let r(g) be the first derivative of i(g). Factor r(o).
-2*(o + 1)*(4*o - 1)**2/7
Let y(t) be the first derivative of -4*t**4 + 176*t**3/3 + 94*t**2 + 48*t - 52. Factor y(r).
-4*(r - 12)*(2*r + 1)**2
Determine g, given that -2*g + 0*g - 6*g**2 - g - g - 2*g**3 = 0.
-2, -1, 0
Let m be 63/14*(-2)/(-3). Suppose -2 = m*u + 2*z - 0, 22 = 5*u - 3*z. Determine v so that 3*v - 4*v**2 - 3*v**2 - 1 + 5*v**u = 0.
1/2, 1
Let q(b) be the third derivative of -1/50*b**5 + 1/60*b**4 + 0*b**3 + 0*b + 4/525*b**7 + b**2 + 0 + 0*b**6. Factor q(x).
2*x*(x + 1)*(2*x - 1)**2/5
Let i(f) be the third derivative of 0*f**5 - 1/105*f**7 + 0*f**3 + 0*f**4 + 0 + 0*f + 4*f**2 - 1/60*f**6. Let i(s) = 0. What is s?
-1, 0
Find w such that -14/5*w**2 + 0 - 6/5*w - 8/5*w**3 = 0.
-1, -3/4, 0
Suppose b = -3*f - 9 + 6, 5*b - 5 = -5*f. Factor 4/5*g**2 + 0 - 4/5*g**b + 1/5*g**4 + 0*g.
g**2*(g - 2)**2/5
Find t, given that -16*t**2 + 2*t**5 - 2*t**5 + 8*t**3 - 4*t - 4*t**5 + 8*t**4 + 8 = 0.
-1, 1, 2
Let c = -1 + 3. Factor c*w**2 - w**4 + w**4 + 2*w**3 - 2*w - 2*w**4.
-2*w*(w - 1)**2*(w + 1)
Factor 0 + 3/2*u**3 + 0*u**2 - 6*u.
3*u*(u - 2)*(u + 2)/2
Let h(q) be the third derivative of -q**6/600 + q**5/300 + q**3/3 - 3*q**2. Let a(l) be the first derivative of h(l). Solve a(x) = 0 for x.
0, 2/3
Let d(f) be the third derivative of f**10/60480 + f**9/15120 - f**7/2520 - f**6/1440 - f**4/12 - 3*f**2. Let a(x) be the second derivative of d(x). Factor a(j).
j*(j - 1)*(j + 1)**3/2
Let v(i) be the second derivative of i**6/10 - 3*i**5/5 + i**4 + 32*i. Factor v(w).
3*w**2*(w - 2)**2
Find c, given that -1/3*c**4 + 0*c - 1/9*c**5 + 0 - 1/3*c**3 - 1/9*c**2 = 0.
-1, 0
Find u, given that -4/11*u**2 + 2/11*u**3 + 0 + 2/11*u = 0.
0, 1
Let v(l) be the second derivative of l**5/15 - 25*l**4/36 + 7*l**3/3 - 3*l**2/2 + 10*l. Factor v(r).
(r - 3)**2*(4*r - 1)/3
Let i be (-1)/(-1*1/8). Factor 10*u + i - u**3 - 2*u**2 - 14 - u**3.
-2*(u - 1)**2*(u + 3)
Let f be ((-2)/(-12))/1 - 38/(-76). Let l(t) be the second derivative of f*t**3 + 0 - 1/5*t**5 + 0*t**4 - t**2 + 1/15*t**6 - 3*t. Factor l(a).
2*(a - 1)**3*(a + 1)
Let k(s) = -s**4 - 1. Let g(n) = 2*n**4 - 14*n**3 + 12*n**2 - 2. Let f(v) = g(v) - 2*k(v). Find a, given that f(a) = 0.
0, 3/2, 2
Let o be ((-1)/(-5))/((-2)/(-10)). Let c be o/15 - 2/(-6). Let -4/5*v + c + 2/5*v**2 = 0. Calculate v.
1
Suppose 0*o - 6 = -2*j - o, -5*o - 18 = -2*j. Factor 0*a**2 - 1/2*a**3 + 0*a + 0 - 5/4*a**j.
-a**3*(5*a + 2)/4
Suppose -2/11*w**2 - 32/11 - 16/11*w = 0. What is w?
-4
Suppose -20 + 2 = 3*r. Let n be r/(-21) + 352/140. Let 18/5*b**2 + 2*b**3 + n*b + 2/5*b**4 + 4/5 = 0. Calculate b.
-2, -1
Let b(n) be the second derivative of n**7/2835 + n**6/810 + n**5/540 + 7*n**4/12 - 7*n. Let w(x) be the third