 + 119*m**3.
(m + 1)*(m + 2)*(7*m - 2)**2
Let q(u) be the third derivative of 0*u**3 + 0*u + 0*u**4 + 0 + 1/105*u**7 - 1/112*u**8 + 0*u**6 + 6*u**2 + 0*u**5. Factor q(d).
-d**4*(3*d - 2)
Let l(i) = -4*i**2 + 5*i - 1. Let m(g) = -6*g**2 - 2 + 4*g + 0*g + 1 + 3*g**2. Let c(k) = 4*l(k) - 6*m(k). Let c(u) = 0. What is u?
1
Let k(v) be the second derivative of -v**7/42 + 2*v**6/15 - 3*v**5/10 + v**4/3 - v**3/6 - v. Determine w so that k(w) = 0.
0, 1
Let a(v) be the second derivative of 3*v**5/160 - 3*v**4/32 + 3*v**3/16 - 3*v**2/16 - 5*v. Find m such that a(m) = 0.
1
Let w(a) be the third derivative of 1/210*a**6 + 0*a + 0*a**4 + 0 + 1/588*a**8 + 0*a**3 - 8*a**2 + 0*a**5 - 4/735*a**7. Suppose w(m) = 0. What is m?
0, 1
Let i(h) be the second derivative of 2*h**7/21 - 2*h**6/5 + 3*h**5/5 - h**4/3 - 3*h + 17. Factor i(x).
4*x**2*(x - 1)**3
Factor u**2 + 51*u**3 + 4*u**4 - 1 - 55*u**3 + 1.
u**2*(2*u - 1)**2
Let w(r) be the third derivative of 2*r**7/105 - r**6/30 - r**5/15 + r**4/6 - 3*r**2. Find t such that w(t) = 0.
-1, 0, 1
Factor -2*l**2 - l**3 + l + 1/2*l**4 + 3/2.
(l - 3)*(l - 1)*(l + 1)**2/2
What is h in h - 9/4*h**3 - 7/4*h**4 + 3*h**2 + 0 = 0?
-2, -2/7, 0, 1
Let m(y) be the first derivative of 2 + 0*y + 0*y**3 + 1/2*y**4 + 0*y**2 + 2/5*y**5. Factor m(b).
2*b**3*(b + 1)
Let d(x) be the third derivative of 0*x - 1/45*x**5 + 0*x**3 - 1/180*x**6 + 3*x**2 - 1/36*x**4 + 0. Factor d(r).
-2*r*(r + 1)**2/3
Factor 0*t**2 - 15*t - 48 + 5*t**2 + 19 + 39.
5*(t - 2)*(t - 1)
Let c be (12/6 - 3) + 6. Let y(j) be the second derivative of -4/3*j**3 - 2*j - 1/2*j**4 + 0 + 1/5*j**c + 4*j**2 + 1/15*j**6. Solve y(q) = 0.
-2, 1
Let z(t) be the second derivative of -t**7/70 + 3*t**5/100 + 10*t. Find r, given that z(r) = 0.
-1, 0, 1
Factor 3*n**3 + 3*n + 3 - 3*n**2 + n**3 - 6*n**3 - n**3.
-3*(n - 1)*(n + 1)**2
Let a be (-20)/90 + 2/9. Factor -3*q**3 + q + a*q**3 + 0*q**3 + 2*q.
-3*q*(q - 1)*(q + 1)
Let g(m) = -4*m + 2. Let x be g(0). Factor 1/2*f**x + 1/2 - f.
(f - 1)**2/2
Let b = 96 - 94. Factor -4/3*k**3 + 2/3*k**4 + 2/3*k**b + 0 + 0*k.
2*k**2*(k - 1)**2/3
What is t in -2*t**5 + 5*t**2 - t**3 + 10*t**4 - 5*t**3 - 20*t**2 - 3*t**2 = 0?
-1, 0, 3
Let q(g) = -g**2 - g. Let u(a) = 1 + 5*a + 0*a + 8*a**2 - 4. Let f(m) = -5*q(m) - u(m). Suppose f(t) = 0. Calculate t.
-1, 1
Let o(d) be the third derivative of 1/1008*d**8 + 1/90*d**5 + 0*d + 0*d**3 + 3*d**2 - 1/120*d**6 + 0 + 0*d**4 + 0*d**7. Factor o(y).
y**2*(y - 1)**2*(y + 2)/3
Let i(m) be the third derivative of -1/240*m**6 + 0*m**3 + 0*m**5 + 0*m + 2*m**2 + 0*m**4 + 0 + 1/420*m**7. Solve i(w) = 0 for w.
0, 1
Let i be 3/2 - (-3)/6. Suppose -i*z + s + 0*s = -8, -22 = -5*z + 3*s. Let 2*y**z - y - 3*y**2 + 0*y = 0. Calculate y.
-1, 0
Let f = 23 - 18. Let w = f - 9/2. Factor w*d**4 + 0*d + 0 + 0*d**2 + 1/2*d**3.
d**3*(d + 1)/2
Factor 3/7*f**2 - 3/7*f + 0.
3*f*(f - 1)/7
Let l = 1270/957 + 2/319. Determine s, given that 2*s + l + 2/3*s**2 = 0.
-2, -1
Let i(f) be the first derivative of -8/3*f**3 + 0*f - 1 + f**2 + 3/2*f**4. Factor i(m).
2*m*(m - 1)*(3*m - 1)
Let j(o) = -o**2 - 7*o - 5. Let k be j(-6). Let d be ((-30)/12)/(k/(-2)). Factor 3*n**d - n**3 - 12*n**4 - 3*n**2 + 3*n**4 + 10*n**3.
3*n**2*(n - 1)**3
Let l(d) be the first derivative of d**3/6 + d**2/4 + 1. Determine w so that l(w) = 0.
-1, 0
Let j(a) be the second derivative of -a**6/30 + a**5/15 + a**4/18 - 2*a**3/9 + a**2/6 + 4*a. Let j(t) = 0. What is t?
-1, 1/3, 1
Let a(m) be the first derivative of -1/3*m**3 + 3 + m**2 - m. Factor a(i).
-(i - 1)**2
Let a(i) be the second derivative of 9*i**4/8 + i**3/2 - 4*i. Factor a(k).
3*k*(9*k + 2)/2
Suppose 5*f + j = -36, -3*f - 2*j = f + 24. Let w = f - -8. Factor -5/3*y**2 + w - 2/3*y.
-y*(5*y + 2)/3
Let z(a) = -a**2 - a + 1. Let n(j) = 98 - 11*j**2 - 80 - 18*j - 10*j**2. Suppose 0 = -2*q + 14 + 22. Let k(f) = q*z(f) - n(f). Factor k(l).
3*l**2
Let n = 15 - 6. Let v = n - 6. Factor v*p**3 - 6*p + 0*p**3 + 2*p + p.
3*p*(p - 1)*(p + 1)
Let z(y) be the second derivative of -y**4/15 + 8*y**2/5 - 23*y. Factor z(m).
-4*(m - 2)*(m + 2)/5
Suppose 5*r = 2*r. Let a(d) be the third derivative of 0*d**3 + 0*d**5 + 0*d**4 - 1/672*d**8 + 1/420*d**7 + 0*d + r*d**6 + 0 + d**2. Factor a(q).
-q**4*(q - 1)/2
Factor 1/4*a**5 - a**4 + 0*a + 5/4*a**3 - 1/2*a**2 + 0.
a**2*(a - 2)*(a - 1)**2/4
Suppose 5*u**2 + u**2 + 2*u**2 + 20*u**4 - 28*u**3 = 0. Calculate u.
0, 2/5, 1
Let 44/7*m + 16/7*m**2 + 24/7 - 4/7*m**3 = 0. What is m?
-1, 6
Factor -3 - 9*r**2 + 3*r + 12*r**3 - 15*r - 3*r**4 + 15.
-3*(r - 2)**2*(r - 1)*(r + 1)
Let i(a) be the first derivative of -a**7/3360 + a**5/160 - a**4/48 - 7*a**3/3 - 4. Let b(x) be the third derivative of i(x). What is r in b(r) = 0?
-2, 1
Let o(p) be the third derivative of -p**9/30240 - p**8/3360 - p**7/1008 - p**6/720 - p**4/8 + 3*p**2. Let r(b) be the second derivative of o(b). Factor r(v).
-v*(v + 1)**2*(v + 2)/2
Let l(r) be the first derivative of 0*r - 1/2*r**2 + 7/4*r**4 + 6 + 2/3*r**3 + 4/5*r**5. Solve l(h) = 0 for h.
-1, 0, 1/4
Suppose 2*y + 4*l = -6, -5*l - 5 = -2*y + 5*y. Factor 8/3*b**4 + 0*b + 8/9*b**3 + 0 + 0*b**2 + 2*b**y.
2*b**3*(3*b + 2)**2/9
Let a(o) be the third derivative of o**8/26880 + o**7/5040 + o**4/6 + 2*o**2. Let d(b) be the second derivative of a(b). Determine t so that d(t) = 0.
-2, 0
Factor 8/15*m**3 - 2/15 + 8/15*m - 2/15*m**4 - 4/5*m**2.
-2*(m - 1)**4/15
Factor -13*k**3 + 168*k - 11*k**3 - 142*k**4 + 44*k**2 + 144*k**4 + 98.
2*(k - 7)**2*(k + 1)**2
Let z(k) be the third derivative of -k**6/1800 + k**5/200 - k**3/6 + k**2. Let g(u) be the first derivative of z(u). Solve g(b) = 0.
0, 3
Let f(l) be the second derivative of 2/15*l**3 + 3*l + 0*l**2 + 1/30*l**4 - 1/75*l**6 - 1/25*l**5 + 0. Factor f(a).
-2*a*(a - 1)*(a + 1)*(a + 2)/5
Let p be 2 + 10*(-8)/(-80). Solve 2/9*n**2 - 4/9*n**p + 4/9*n - 2/9*n**4 + 0 = 0.
-2, -1, 0, 1
Let h(o) be the first derivative of -o**3 + 9*o**2 - 27*o - 30. Factor h(c).
-3*(c - 3)**2
Let u be 1/2 - (-15)/10. Suppose 4*s + 22 = 4*b + u, 0 = 4*s. Factor -x**b - x**4 + x**3 + 9 - 9 + x**2.
-x**2*(x - 1)*(x + 1)**2
Let n(w) be the second derivative of w**5/40 + w**4/24 - w**3/12 - w**2/4 + 13*w. Factor n(u).
(u - 1)*(u + 1)**2/2
Suppose s - 11 = -4*z, 6*s = 4*s + 6. Factor -4/3 - 8/3*x**z + 10/3*x + 2/3*x**3.
2*(x - 2)*(x - 1)**2/3
Let k be (-92)/(-112) - ((-51)/21 - -3). Factor 4 + k*a**2 - 2*a.
(a - 4)**2/4
What is k in 54/7*k - 36/7*k**2 - 1/7*k**4 + 10/7*k**3 - 27/7 = 0?
1, 3
Let x(b) = 24*b + 2. Let m be x(3). Let u = m - 44. Factor -u*j**2 - 2 - 3*j**4 + 2*j**4 + 14*j + 0*j**4 + 26*j**3 - 7*j**4.
-2*(j - 1)**3*(4*j - 1)
Let b = -898 + 8084/9. Factor -2/3*y + b*y**2 - 4/9 + 2/9*y**4 + 2/3*y**3.
2*(y - 1)*(y + 1)**2*(y + 2)/9
Factor 4/7*k + 6/7*k**2 + 1/7*k**4 - 5/7*k**3 - 8/7.
(k - 2)**3*(k + 1)/7
Let w(o) = 5*o**3 + o**2 + 2*o + 4. Let y(b) = 4*b**3 - 10*b**3 - 2*b - 5 + 4*b**2 - 5*b**2 - b. Let r(f) = -5*w(f) - 4*y(f). Let r(h) = 0. Calculate h.
-2, 0, 1
Let w = 2425/7 + -338. Let k = -57/7 + w. Factor 0 - k*m**4 - 6/7*m**3 - 2/7*m - 6/7*m**2.
-2*m*(m + 1)**3/7
Let g(p) = -4*p**5 + 8*p**3 + 4*p**2 - 4. Let i(o) = 8*o**4 - 10*o**4 + 3*o**4 - o**2 + o. Let r(j) = -g(j) + 4*i(j). What is h in r(h) = 0?
-1, 1
Let y(v) be the first derivative of 2/5*v**5 + 0*v + 1/2*v**6 - 2 - v**4 - 2/3*v**3 + 1/2*v**2. Solve y(k) = 0 for k.
-1, 0, 1/3, 1
Suppose -15*r + 5 = -70. Find q, given that 1/2*q**r + 2*q**4 + 3*q**3 + 2*q**2 + 0 + 1/2*q = 0.
-1, 0
Let b(q) = -q + 10. Let m be b(7). Let h(l) be the second derivative of 0 + 0*l**6 - 1/20*l**5 - l + 0*l**2 + 0*l**m + 1/42*l**7 + 0*l**4. Factor h(c).
c**3*(c - 1)*(c + 1)
Let l(s) = -9*s**3 - 2*s**2 + 8*s. Let i(z) = z**3 - z. Let o(d) = -d**2 - 2*d + 3. Let b be o(0). Let a(r) = b*l(r) + 24*i(r). Let a(p) = 0. Calculate p.
-2, 0
Let f(w) = -w**2 - 11*w + 5. Let d be f(-11). Let q(b) be the third derivative of 1/30*b**d + 0*b**3 + 0*b + 0 + 0*b**4 - 2*b**2. Let q(z) = 0. Calculate z.
0
Let p(c) be the second derivative of c**6/12 + 5*c**5/8 + 5*c**4/3 + 5*c**3/3 - 13*c. Find t, given that p(t) = 0.
-2, -1, 0
Suppose 4*a + w = 4*w - 4, 3*w = 3*a + 6. Suppose 0 = -z - a*g + 6, g + 4 + 0 = 3*z. Factor -z*q**3 - q**3 + 2*q**4 + 0 - q**3 + 4*q - 2.
2*(q - 1)**3*(q + 1)
Factor 6*a - 25 + 15 + 13 + 3*a**2.
3*(a + 1)**2
Let h