2/7 + 4*n/7 + 2. Let w(j) = 0. What is j?
-1, 1
Let t be 6*((-3)/(-2) + -1). Factor 2*j**2 + 3*j**4 + t*j**2 - 8*j**2.
3*j**2*(j - 1)*(j + 1)
Let w be ((-9)/(-36))/(2/16). Let o(t) be the third derivative of 0 - 1/28*t**4 - 2/21*t**3 - 1/210*t**5 + 0*t + w*t**2. Find z such that o(z) = 0.
-2, -1
Let 21 - 20 - 6*r + 4*r + r**2 = 0. What is r?
1
Let f(t) be the first derivative of t**6/3 - 6*t**5/5 + t**4/2 + 2*t**3 - 2*t**2 + 30. Suppose f(j) = 0. What is j?
-1, 0, 1, 2
Suppose 2 = -0*g + g. Factor -3*b**3 - b + b - 37*b**4 + 38*b**4 + g*b**2.
b**2*(b - 2)*(b - 1)
Let m(i) = i - 1. Let s(u) = 16*u**2 + 46*u - 2. Let p(x) = -x**3 + 13*x**2 + x - 3. Let t be p(13). Let q(d) = t*m(d) - s(d). Let q(c) = 0. What is c?
-2, -1/4
Suppose c - 28 = -6*c. Factor 15/4*j**2 + 0 - 3/4*j + 9/4*j**c - 21/4*j**3.
3*j*(j - 1)**2*(3*j - 1)/4
Let h(g) = 5*g + 27. Let f be h(-5). Let t(q) be the second derivative of 1/2*q**2 - f*q + 0*q**3 + 0 + 0*q**5 - 1/6*q**4 + 1/30*q**6. Solve t(y) = 0.
-1, 1
Factor 2/7 - 17/7*c + 44/7*c**3 + 25/7*c**2.
(c + 1)*(4*c - 1)*(11*c - 2)/7
Let k(s) be the third derivative of s**8/16 - 121*s**7/70 + 83*s**6/5 - 234*s**5/5 - 162*s**4 + 216*s**3 + 15*s**2 - s. Factor k(m).
3*(m - 6)**3*(m + 1)*(7*m - 2)
Factor -41 + 51*k - 54*k**2 + 9*k**3 + 23 + 9*k**2 + 3*k**4.
3*(k - 1)**3*(k + 6)
Let q(x) be the first derivative of 1/40*x**6 + 7/240*x**5 + 0*x + 1/96*x**4 + 0*x**3 - 1 + x**2. Let g(c) be the second derivative of q(c). Factor g(i).
i*(3*i + 1)*(4*i + 1)/4
Let o(y) be the second derivative of 0*y**3 - 16/15*y**5 - 7/9*y**7 - 2/9*y**4 - 3*y + 0 + 0*y**2 - 77/45*y**6. Factor o(z).
-2*z**2*(z + 1)*(7*z + 2)**2/3
Let s be 3/3 + 1 + 2. Let h be 1 + -2*3/(-6). Determine a, given that -4 + 4*a**3 - 2*a**2 + 4 - h*a**s = 0.
0, 1
Let y = 315/2 + -157. Factor 1/2*w**2 + 0*w + 0 - y*w**3 - 1/2*w**4 + 1/2*w**5.
w**2*(w - 1)**2*(w + 1)/2
Let k(h) be the first derivative of 0*h**5 - 3/11*h**2 + 2/11*h**4 + 4/11*h - 4/33*h**3 - 1/33*h**6 - 10. Solve k(g) = 0.
-2, -1, 1
Let u = -34 - -37. Let v = -1 - -5/3. Factor v - u*f**3 + 20/3*f**2 - 13/3*f.
-(f - 1)**2*(9*f - 2)/3
Let m(l) be the second derivative of -l**7/112 - l**6/80 + 3*l**5/80 + l**4/16 - l**3/16 - 3*l**2/16 - 5*l. Solve m(d) = 0 for d.
-1, 1
Let a be (-2)/6 + 56/(-12). Let u(i) = i**4 - 4*i**3 - 6*i**2 + 1. Let n(z) = -z**4 + 5*z**3 + 7*z**2 - 1. Let y(s) = a*u(s) - 4*n(s). Factor y(l).
-(l - 1)**2*(l + 1)**2
Let d = -92 - -96. Factor 0*l + 2/7*l**d - 4/7*l**3 + 0 + 2/7*l**2.
2*l**2*(l - 1)**2/7
Let x(n) = -4*n**3 - 4*n**2 + n + 7. Let c(f) = -20*f**3 - 20*f**2 + 4*f + 36. Let v(u) = 3*c(u) - 16*x(u). Solve v(g) = 0.
-1, 1
Let d(n) be the second derivative of 1/40*n**5 + 1/120*n**6 + 0*n**4 + 0 + 7*n - 1/12*n**3 - 1/8*n**2. Factor d(q).
(q - 1)*(q + 1)**3/4
Factor -8/5 + 2/5*j**3 - 2*j**2 + 16/5*j.
2*(j - 2)**2*(j - 1)/5
Let t be 2 - ((0 - -1) + (-4)/(-8)). Suppose 4*y - 13 + 5 = 0. What is m in 0 + t*m**3 + 0*m + m**y = 0?
-2, 0
Let b be (0/2)/(-2) - -2. Factor 2*p - b*p**2 - 1 + 5 - 4*p.
-2*(p - 1)*(p + 2)
Let c = -2 - -8/3. Factor 0 + c*i - 2/3*i**2.
-2*i*(i - 1)/3
Let b(f) = -f**3 + 2*f**2 + f + 1. Let q be b(-2). Let d be (-8)/q*(-24)/16. Factor 0 - 2/5*g**2 - d*g.
-2*g*(g + 2)/5
Let f be (0 + -1)/(-205 + -5). Let q(x) be the second derivative of f*x**7 + 0*x**6 - x + 0 + 0*x**2 + 1/30*x**3 - 1/50*x**5 + 0*x**4. Factor q(o).
o*(o - 1)**2*(o + 1)**2/5
Suppose -4/7*a**3 + 0 - 20/7*a**2 + 0*a = 0. What is a?
-5, 0
Let r = 428/15 - 57/2. Let u(f) be the second derivative of 1/15*f**3 - 2*f + 0*f**2 + r*f**4 + 0. Factor u(i).
2*i*(i + 1)/5
Let j = -11 - -5. Let b = j + 8. Suppose 4*y**3 - 4*y**2 - 4 + b + 4*y**3 - 7*y - 4*y**3 = 0. What is y?
-1/2, 2
Let b(a) be the first derivative of a**6/360 + a**5/90 - 5*a**2/2 + 6. Let s(m) be the second derivative of b(m). What is g in s(g) = 0?
-2, 0
Let u(h) be the third derivative of -h**7/150 + h**6/120 + h**5/150 + 4*h**2. Factor u(b).
-b**2*(b - 1)*(7*b + 2)/5
What is o in -16*o**3 + 3*o**5 + 20*o**3 + 6*o + 0*o**5 + 23*o**3 - 21*o**2 - 15*o**4 = 0?
0, 1, 2
Let s(r) = r + 10. Let o be s(-7). Let j be (2/(-6))/((-3)/6) - 0. Factor -j*x**2 - 4/9*x + 0 - 2/9*x**o.
-2*x*(x + 1)*(x + 2)/9
Let c(m) = m**3 + 2*m**2 - 1. Let x be c(1). Factor 9 - 27*y**x + 12*y + 9 + 29*y**2.
2*(y + 3)**2
Let u(k) = k**3 + 8*k**2 + 6. Let t be u(-8). Let r(m) be the second derivative of 0*m**2 + m - 1/10*m**5 + 0 - 1/15*m**t + 1/3*m**3 + 1/6*m**4. Factor r(s).
-2*s*(s - 1)*(s + 1)**2
Let j(u) = -u**3 + 7*u**2 - u - 8. Let h be j(7). Let k = h - -17. What is a in -5*a**k - 8/3*a - 1/3 = 0?
-1/3, -1/5
Let h(y) be the second derivative of -y**4/28 + y**3 - 21*y**2/2 - 29*y. Factor h(n).
-3*(n - 7)**2/7
Let q = -13 - -9. Let g(u) = -10*u - 5. Let x be g(q). Factor p**4 - 37*p**3 - 20*p + 4 + x*p**2 - 4*p**4 + 4*p**2 + 20*p**4 - 3*p**5.
-(p - 2)*(p - 1)**3*(3*p - 2)
Let v be ((-24)/(-64))/((-15)/(-4)). Let j(y) be the second derivative of 0 - y**3 - 2*y + 0*y**2 + v*y**6 - 3/4*y**4 + 0*y**5. Factor j(h).
3*h*(h - 2)*(h + 1)**2
Factor 4/19 - 2/19*n - 2/19*n**2.
-2*(n - 1)*(n + 2)/19
Let i(n) = 10*n**3 - 45*n**2 - 10*n + 5. Let q(f) = -11*f**3 + 44*f**2 + 11*f - 4. Let p(h) = -4*i(h) - 5*q(h). Determine u so that p(u) = 0.
-1/3, 0, 3
Let a(x) be the second derivative of 1/42*x**4 + 0*x**2 + 0 - 4*x - 1/7*x**3. Factor a(g).
2*g*(g - 3)/7
Let -12/13 + 2/13*u**2 + 2/13*u = 0. Calculate u.
-3, 2
Let i(g) be the second derivative of 8*g**6/5 - 17*g**5/5 - g**4/3 + 10*g**3/3 + 2*g**2 + 16*g. Find a such that i(a) = 0.
-1/3, -1/4, 1
Let a(w) be the third derivative of 0 + 1/15*w**5 - 1/6*w**4 - 4/3*w**3 + 0*w + 5*w**2. Let a(x) = 0. What is x?
-1, 2
Let g = -674 - -674. Factor 0*q + g + 4/3*q**3 + 2/3*q**4 + 2/3*q**2.
2*q**2*(q + 1)**2/3
Let l(g) be the third derivative of g**5/12 - 65*g**4/12 + 845*g**3/6 - 50*g**2. Suppose l(w) = 0. Calculate w.
13
Factor 34/5*m**2 + 0 + 36/5*m**3 + 0*m + 2/5*m**4.
2*m**2*(m + 1)*(m + 17)/5
Let z be (3/2)/(-3 - -6). Let i be (11/44)/(2/4). Find y such that -i - z*y**2 + y = 0.
1
Let g = -211 - -213. Determine j, given that 4/3*j + 2/3*j**g + 2/3 = 0.
-1
Let q(h) be the third derivative of h**6/270 - h**5/30 + h**4/9 + 2*h**3/3 + 10*h**2. Let j(w) be the first derivative of q(w). Factor j(g).
4*(g - 2)*(g - 1)/3
Let d(i) be the second derivative of 1/2*i**4 - 7*i + 0 - 3/20*i**5 + 1/2*i**3 - 3*i**2. Factor d(g).
-3*(g - 2)*(g - 1)*(g + 1)
Factor 18*u**2 - 7*u**2 - 10*u**2 + 0*u + 3 + 4*u.
(u + 1)*(u + 3)
Let n(f) be the third derivative of 1/24*f**4 + 1/3*f**3 + 0 + f**2 + 1/70*f**7 - 1/12*f**5 + 0*f - 1/120*f**6. Factor n(j).
(j - 1)**2*(j + 1)*(3*j + 2)
Suppose 0 - 4/3*d - 10/3*d**2 = 0. What is d?
-2/5, 0
Factor 6/7*h + 10/7*h**3 + 0 - 2*h**2 - 2/7*h**4.
-2*h*(h - 3)*(h - 1)**2/7
Let i(y) = 5*y**5 - 10*y**4 - 10*y**3 + 15*y**2 + 5*y. Let x(l) = l**4 - l**2 - 1. Let z(k) = i(k) + 5*x(k). Let z(h) = 0. Calculate h.
-1, 1
Suppose i + 3*h - 13 = 7*h, 3*h = -2*i - 7. Let f = i - -4. Determine o so that -17*o**5 + 64*o**f + 40*o**4 + 3*o**5 + 8*o**3 = 0.
-2/5, 0
Let a be 25/9 + 12/54. Let m(o) be the second derivative of 0*o**2 + 1/6*o**4 + 0 + 1/10*o**5 + 0*o**a + o. Factor m(j).
2*j**2*(j + 1)
Let a = 512 + -5622/11. Let a*w**3 - 8/11*w + 16/11 - 12/11*w**2 - 2/11*w**4 = 0. What is w?
-1, 2
Suppose -b - 50 = 4*b. Let a = -6 - b. Solve 8*d**4 + 2*d**a - 2 - 7*d**4 + 11*d**3 + d + 11*d**2 = 0 for d.
-2, -1, 1/3
Let h be ((-8)/(-140))/(432/14). Let c(x) be the third derivative of 3*x**2 + 0*x - h*x**6 + 1/108*x**4 + 1/27*x**3 + 0 - 1/270*x**5. Solve c(b) = 0 for b.
-1, 1
Let p(a) be the second derivative of -a**6/900 + a**4/60 - a**3/6 - 4*a. Let q(k) be the second derivative of p(k). Let q(i) = 0. What is i?
-1, 1
Suppose 0 + 3*g**2 - 5*g**2 - 4*g + 0 - 2 = 0. What is g?
-1
Let x = -3504 + 63053/18. Let o = 14/9 + x. Factor 0 + 0*h - o*h**2.
-h**2/2
Let o(p) be the second derivative of p**5/14 + 3*p**4/14 + p**3/7 - p**2/7 - 10*p. Factor o(x).
2*(x + 1)**2*(5*x - 1)/7
Let b(p) = p**2 + 6*p. Let s be b(-6). Factor s*x - 5*x**2 + 7*x**3 + x + 0*x - 3*x.
x*(x - 1)*(7*x + 2)
Suppose 5*u + 2 = -5*s + 27, -25 = 5*u - 5*s. Factor 0 + u*i - 2/5*i**2 - 1/5*i**4 - 3/5*i**3.
-i**2*(i + 1)*(i + 2)/5
Factor 8*f**2 + 119*f**3 + 0*f + 113*f**3 + 4*f - 228*f**