v) + 3*k(v). Factor d(n).
n*(3*n + 2)
Let w(d) be the third derivative of -d**6/30 - d**5/30 + d**4/6 + d**3/3 + 6*d**2. Let w(n) = 0. What is n?
-1, -1/2, 1
Let a(s) = 4*s**2 + 80*s - 116. Let t(m) = m**2 + 16*m - 23. Let d(c) = 3*a(c) - 16*t(c). Factor d(l).
-4*(l - 1)*(l + 5)
Determine g so that 0*g**3 + 5*g**3 - g**3 + 4*g**2 = 0.
-1, 0
Suppose -79*o**2 - 12*o + 3 + 77*o**2 - 13 = 0. What is o?
-5, -1
Let l(q) be the third derivative of q**8/672 - q**7/140 + q**6/80 - q**5/120 + 5*q**2. Solve l(d) = 0 for d.
0, 1
Let g(t) = t**3 + 3*t**2 - 4*t + 2. Let f be g(-4). Determine r, given that 4*r + 9*r**2 + 5*r**f + 8*r**3 + 0 - 2 = 0.
-1, 1/4
Let g be 120/(-100)*(-10)/6. Let b be (-1)/(g*(-9)/6). Factor 0*y + 0 - b*y**5 - 1/3*y**2 - y**4 - y**3.
-y**2*(y + 1)**3/3
Factor 1 + n**2 - 2*n**3 + 5/2*n - 1/2*n**5 - 2*n**4.
-(n - 1)*(n + 1)**3*(n + 2)/2
Let s(o) be the second derivative of -2/7*o**2 + 8*o + 1/7*o**3 + 1/105*o**6 + 0 - 3/70*o**5 + 1/42*o**4. Factor s(t).
2*(t - 2)*(t - 1)**2*(t + 1)/7
Suppose -3*r - 2*r = -15. Let u(v) = -5*v**4 + 8*v**3 - v**2 - 2*v + 4. Let s(o) = -1. Let a(f) = r*u(f) + 12*s(f). Solve a(q) = 0 for q.
-2/5, 0, 1
Suppose -12 = i + 5*i. Let o(r) = -r**2 - 3*r + 8. Let f(s) = 3*s - 9. Let z(h) = i*f(h) - 3*o(h). Find d such that z(d) = 0.
-2, 1
Let p(q) be the third derivative of q**5/30 - q**4/6 + q**3/3 - 6*q**2. Factor p(k).
2*(k - 1)**2
Let b be (-28)/(-8)*(-8)/(-14). Factor -4*f**2 + 6*f**2 - 3*f**b - 6*f**3 - f**2.
-2*f**2*(3*f + 1)
Let a(q) be the second derivative of -q**7/70 + 4*q**6/75 - 3*q**5/50 + q**3/30 + 4*q. Factor a(t).
-t*(t - 1)**3*(3*t + 1)/5
Let q(m) be the second derivative of -m**7/35 + 7*m**6/75 - m**5/10 + m**4/30 - 4*m. Factor q(o).
-2*o**2*(o - 1)**2*(3*o - 1)/5
Let i(x) be the third derivative of -x**5/270 + x**4/108 + 6*x**2. Suppose i(f) = 0. Calculate f.
0, 1
Let a be (-8 + 10)*(-1)/(-9). Let t(g) be the third derivative of 0 + 1/18*g**4 + 0*g - g**2 - a*g**3 - 1/180*g**5. Factor t(i).
-(i - 2)**2/3
Suppose -2*q = -5*w - 19, -w + 1 = -q - 2*w. Factor -1 + 1/4*n**3 + q*n - 5/4*n**2.
(n - 2)**2*(n - 1)/4
Let y(p) be the second derivative of 0 - 1/6*p**3 + 2*p - 1/6*p**4 + 3/20*p**5 + 0*p**2. Factor y(f).
f*(f - 1)*(3*f + 1)
Suppose -3*y**2 + 1 + 1 - 4*y + 14*y - 5 = 0. What is y?
1/3, 3
Let y(h) be the second derivative of -h - 8/15*h**3 + 0 - 16/5*h**2 - 1/30*h**4. Factor y(z).
-2*(z + 4)**2/5
Let o(f) be the third derivative of -f**5/40 + f**4/4 - f**3 + 2*f**2 - 14*f. What is z in o(z) = 0?
2
Let b(t) be the first derivative of -1/2*t**6 - 3/5*t**5 + 12*t - 6 + 15/4*t**4 - 12*t**2 + t**3. What is u in b(u) = 0?
-2, 1
Let w(m) = 9*m - 9. Let s(j) = -14*j + 14. Let p(t) = 5*s(t) + 8*w(t). Let b(u) = -u**2 + u - 1. Let y(q) = 2*b(q) - p(q). Solve y(h) = 0 for h.
0
Factor 1/10*c**3 - 2/5*c + 0 - 3/10*c**2.
c*(c - 4)*(c + 1)/10
Factor 72*j**3 - 3*j**4 - 33*j**2 + 3774*j - 3888 - 615*j**2 - 1182*j.
-3*(j - 6)**4
Find d, given that 2*d**3 - 4*d**4 + 3*d**4 - d**5 - 3*d**5 - 1 + 3*d**5 - d + 2*d**2 = 0.
-1, 1
Let f = 41 + -72. Let i = f + 33. Find b such that -2/5*b**i + 2/5*b**4 + 4/5*b**3 + 0 - 4/5*b = 0.
-2, -1, 0, 1
Let y(z) be the second derivative of -z**4/132 + z**3/66 - 37*z. Factor y(x).
-x*(x - 1)/11
Let y(b) = b**2 - 12*b + 14. Let u be y(11). Determine p, given that -p**2 + 7*p**2 + u*p - 5*p**2 = 0.
-3, 0
Let y be (175/90 - 2)*-3. Factor -1/6*j**4 + y + 0*j**2 - 1/3*j + 1/3*j**3.
-(j - 1)**3*(j + 1)/6
Suppose -2/7*i - 2/7*i**4 + 6/7*i**2 - 4/7 + 2/7*i**3 = 0. What is i?
-1, 1, 2
Solve -9/8*b**2 + 0*b + 3/8*b**3 + 3/2 = 0 for b.
-1, 2
Solve 3/4*z - 3/2*z**2 + 27*z**5 + 0 + 9*z**4 - 33/4*z**3 = 0.
-1/2, 0, 1/3
Let c(v) be the second derivative of -v**8/26880 + v**7/10080 + v**6/2880 - v**5/480 + v**4/12 + 5*v. Let m(x) be the third derivative of c(x). Factor m(r).
-(r - 1)**2*(r + 1)/4
Suppose 2*r - r = 0. Let m be (-8)/16*r/2. Determine c, given that m + 2*c**2 - 1/2*c = 0.
0, 1/4
Let c(z) = z**3 - z. Let p(u) = -11*u**3 + 5*u**2 + 6*u. Let o(b) = 6*c(b) + p(b). Determine y so that o(y) = 0.
0, 1
Let l = -118 - -591/5. Factor 0 + 1/5*c**2 - 1/5*c**3 - l*c**4 + 0*c + 1/5*c**5.
c**2*(c - 1)**2*(c + 1)/5
Factor 1/4*p**4 + 0 - 3/4*p**2 + 0*p**3 - 1/2*p.
p*(p - 2)*(p + 1)**2/4
Let c be -4*(18/(-4))/3. Let d be 2/5*(-1 + c). Let v**d + 4*v**2 + 6*v + 4 - 3*v**2 = 0. What is v?
-2, -1
Let n(w) be the first derivative of 5*w**4/4 - 25*w**3/3 + 5*w**2 + 40*w + 54. Factor n(r).
5*(r - 4)*(r - 2)*(r + 1)
Solve 6/7*w**4 + 3/7*w**3 + 0*w**2 + 0*w + 3/7*w**5 + 0 = 0 for w.
-1, 0
Let o be 28/6 + (2 - 6). Let v(j) be the second derivative of -1/6*j**4 + 0 + 2*j - j**2 - o*j**3. Factor v(t).
-2*(t + 1)**2
Let a(j) be the first derivative of 0*j + 1 + 1/7*j**2 - 2/21*j**3. Solve a(y) = 0 for y.
0, 1
Let -3*w**4 + 2*w**4 - w**2 + 0*w**2 + 2*w**4 = 0. What is w?
-1, 0, 1
Factor -18/7*g**2 + 2*g**3 + 0 + 4/7*g.
2*g*(g - 1)*(7*g - 2)/7
Let z(p) be the second derivative of -p**7/6300 - p**4/12 - 3*p. Let j(r) be the third derivative of z(r). Factor j(u).
-2*u**2/5
Factor 17*i**2 + 2*i**2 + 6 + 3*i - 22*i**2.
-3*(i - 2)*(i + 1)
Let w(p) = 2*p**2 + 4*p + 2. Let c be w(-3). Suppose 4*z - c = 8. Factor 6/5*b**z + 0 + 6/5*b**3 + 2/5*b**5 + 0*b + 2/5*b**2.
2*b**2*(b + 1)**3/5
Let m(b) be the second derivative of -b**5/50 - b**4/12 + b**3/10 + 40*b. Find v such that m(v) = 0.
-3, 0, 1/2
Let z(s) = -s**3 + 4*s**2 + 3*s. Let p(r) = -2*r**3 + 4*r**2 + 4*r. Let v(i) = -3*p(i) + 4*z(i). Suppose v(j) = 0. Calculate j.
-2, 0
Factor -45 + 3*b - 2*b**2 + 44 + 3*b**4 - b**5 - 3*b**3 + b**3.
-(b - 1)**4*(b + 1)
Let r(j) be the third derivative of 2*j**7/105 - j**5/5 + j**4/3 - 3*j**2. Suppose r(x) = 0. What is x?
-2, 0, 1
Let g(s) be the first derivative of s**7/2100 - s**3 - 4. Let p(t) be the third derivative of g(t). Find v such that p(v) = 0.
0
Let i be 24/(-20) + 128/90. Determine q, given that 2/9*q**5 - i*q**3 - 2/9*q**4 + 0*q + 0 + 2/9*q**2 = 0.
-1, 0, 1
Factor -1/3*m**2 + 2 - 5/3*m.
-(m - 1)*(m + 6)/3
Let y(x) be the first derivative of -4/5*x - 1/5*x**2 + 3 + 1/10*x**4 + 4/15*x**3. Factor y(w).
2*(w - 1)*(w + 1)*(w + 2)/5
Suppose k + 3 - 6 = 0. Suppose 3*f + 4 = 4*p, k*f + p - 1 = f. Factor 2/5*x + f - 2/5*x**2.
-2*x*(x - 1)/5
Let s(v) be the third derivative of -v**5/60 + 7*v**4/24 + v**3/6 + v**2. Let g be s(7). Factor -9/2*i**3 - g - 5/2*i**2 + 9/2*i + 7/2*i**4.
(i - 1)**2*(i + 1)*(7*i - 2)/2
Let x = 4 - 1. Let d(f) be the first derivative of -2 - 4/3*f**x - 2*f - 3*f**2. Factor d(l).
-2*(l + 1)*(2*l + 1)
Let u(w) = -3*w**2 - w + 2. Let r(m) = -8*m**2 - 2*m + 6. Let l = 20 + -38. Let t = -13 - l. Let v(h) = t*r(h) - 14*u(h). Let v(o) = 0. Calculate o.
-1
Suppose -13 = -5*w + 2. Let u(z) = -z**2 - 2 + 68*z - 72*z + 0*z**3 + z**3. Let p(r) = 3*r**3 - 2*r**2 - 11*r - 6. Let b(x) = w*p(x) - 8*u(x). Factor b(a).
(a - 1)*(a + 1)*(a + 2)
Let b(m) = m**3 - 2*m**2 - m - 6. Let s(i) = i**2 + 1. Let y(k) = 3*b(k) + 12*s(k). Solve y(t) = 0 for t.
-2, -1, 1
Let o be (-6)/4 + (-44)/(-8). Let g(y) be the second derivative of 0 - 1/8*y**2 + 1/12*y**3 + 2*y - 1/48*y**o. Factor g(f).
-(f - 1)**2/4
Suppose p - 44 = -4*x, -4*p - p - 55 = -5*x. Let d be x/12 - (-2)/(-8). Factor 4/3*z**3 + 0*z**4 + 0 - 2/3*z + 0*z**2 - d*z**5.
-2*z*(z - 1)**2*(z + 1)**2/3
Let y be -4 + (-4)/(-12)*0. Let c be (1 - -2) + (y - -4). Factor 2/3*k**c - 4/3*k**2 + 0 + 2/3*k.
2*k*(k - 1)**2/3
Let d = -365 + 368. Let 2/5*z**d + 0*z - 2/5*z**2 + 0 = 0. Calculate z.
0, 1
Let a(w) be the first derivative of w**5/20 + w**4/4 + w**3/2 + w**2/2 + 3*w + 1. Let k(l) be the first derivative of a(l). Find d such that k(d) = 0.
-1
Factor -2/3*z**4 - 8/3*z**3 - 4/3*z - 10/3*z**2 + 0.
-2*z*(z + 1)**2*(z + 2)/3
Factor -1/3 - 2/3*o**3 + 2/3*o**2 + 1/3*o**5 + 1/3*o - 1/3*o**4.
(o - 1)**3*(o + 1)**2/3
Suppose -y + 3 = -0*y. Suppose 2 = 3*w - w + 2*z, -y = 3*z. Factor j**3 + 4*j**2 - 7*j**3 - 4*j**w - 4*j**4 - 2*j**2.
-2*j**2*(j + 1)*(2*j + 1)
Let g(q) = -q**3 + q**2 + 1. Let a = 8 - 7. Let b(m) = m**4 - 4*m**3 + 10*m**2 - 8*m - 2. Let d(w) = a*b(w) + 2*g(w). Determine r, given that d(r) = 0.
0, 2
Let g be (-1)/5 + (-303)/60. Let c = -5 - g. Factor c*p - 1/2 + 1/4*p**2.
(p - 1)*(p + 2)/4
Suppose -x + 5*v = -8, x + v = 3*x - 7. Factor -2/3*t - 2*t**2 - 4/3*t**x + 0.
-2*t*