Factor w(n).
4*n*(n + 2)
Find b, given that -9 + 2 + 1 - 45*b**3 - 35*b - 75*b**2 + 1 = 0.
-1, -1/3
Let c(a) be the first derivative of -2*a**6/3 - 12*a**5/5 - 3*a**4 - 4*a**3/3 + 9. Suppose c(v) = 0. What is v?
-1, 0
Let q(h) = 39*h**2 + 12*h - 105. Let n(x) = 3*x**2 + x - 8. Let f(d) = 27*n(d) - 2*q(d). Factor f(l).
3*(l - 1)*(l + 2)
Let p(q) be the first derivative of q**6/18 - q**5/5 + q**4/4 - q**3/9 - 6. Let p(n) = 0. What is n?
0, 1
Let w(y) be the third derivative of y**7/630 + y**6/360 + y**2. Factor w(m).
m**3*(m + 1)/3
Let r(m) be the third derivative of m**7/420 - m**6/180 - m**5/60 + m**4/4 - 4*m**2. Let a(h) be the second derivative of r(h). Solve a(u) = 0.
-1/3, 1
Let b(p) be the second derivative of 9*p**5/20 - 7*p**4/4 + 6*p**2 + 6*p. Factor b(v).
3*(v - 2)*(v - 1)*(3*v + 2)
Let q(h) be the second derivative of 1/12*h**3 - h - 1/24*h**4 + 1/2*h**2 + 0. Factor q(l).
-(l - 2)*(l + 1)/2
Let j(v) be the first derivative of 0*v**2 + 6/5*v**5 - 1/3*v**6 - 3/2*v**4 + 2/3*v**3 - 5 + 0*v. Let j(x) = 0. What is x?
0, 1
Let u = 493/15 + -161/5. Factor 2/3*a**3 + 2*a**2 + 2*a + u.
2*(a + 1)**3/3
Suppose i = -3*c + 18, -5*i = -0*c + 5*c - 40. Factor 0*z - 3/2*z**4 + 3/4*z**c + 0*z**2 + 3/4*z**3 + 0.
3*z**3*(z - 1)**2/4
Let s be 9/(-36) + 45/84. Let q(h) be the first derivative of 2/7*h**2 + 1 + 2/21*h**3 + s*h. Find y, given that q(y) = 0.
-1
Let p be ((-7728)/(-1929))/(-4) + 1. Let t = p - -6437/4501. Determine f so that -2/7 + 8/7*f**4 + 10/7*f - 6/7*f**2 - t*f**3 = 0.
-1, 1/4, 1
Let d = -2/7 - -11/14. Let -d - 1/4*c**2 - 3/4*c = 0. What is c?
-2, -1
Factor 2/11 - 4/11*p**2 + 0*p + 0*p**3 + 2/11*p**4.
2*(p - 1)**2*(p + 1)**2/11
Suppose -j = 2*d + 4*j + 16, 3*d + 14 = -5*j. Let 7/6*m + 1/2 + 5/6*m**d + 1/6*m**3 = 0. Calculate m.
-3, -1
Let p(l) = -7*l**3 - 7*l**2. Let x(y) = -35*y**3 - 36*y**2 - y. Let v(c) = -11*p(c) + 2*x(c). Factor v(k).
k*(k + 1)*(7*k - 2)
Let d(a) be the second derivative of -1/6*a**3 - a + 1/24*a**4 - 1/240*a**5 + 0 - 1/2*a**2. Let r(x) be the first derivative of d(x). Factor r(c).
-(c - 2)**2/4
Let n(t) = 3*t**2 - 4*t - 7. Let m be n(5). What is z in 28*z**2 - 10 - 3 - m*z + 2 - 5 = 0?
-2/7, 2
Factor 3/2 + 2*z + 1/2*z**2.
(z + 1)*(z + 3)/2
Let u(n) = -n**3 - 4*n**2 - 3*n. Let t(k) = 2*k**3 + 9*k**2 + 7*k. Let f(y) = -2*t(y) - 5*u(y). Factor f(z).
z*(z + 1)**2
Let i(k) be the second derivative of -1/15*k**6 - 7*k + 0*k**3 - 1/21*k**7 + 0*k**4 + 0 + 0*k**5 + 0*k**2. Factor i(p).
-2*p**4*(p + 1)
Find l such that 0 + 3/4*l**3 + 6*l - 9/2*l**2 = 0.
0, 2, 4
Let h(y) be the third derivative of -y**7/70 + 17*y**6/120 - y**5/2 + y**4/2 + 4*y**3/3 + 6*y**2. Factor h(w).
-(w - 2)**3*(3*w + 1)
Let j(z) be the third derivative of z**7/1155 - z**6/165 + z**5/66 - z**4/66 - 15*z**2. Solve j(n) = 0 for n.
0, 1, 2
Let x(f) be the third derivative of f**8/448 + f**7/70 + 3*f**6/160 - f**2. Find s, given that x(s) = 0.
-3, -1, 0
Factor 8*f**4 - 3*f**4 - 13*f**3 - 5*f + 10*f**3 - 12*f**3 + 15*f**2.
5*f*(f - 1)**3
Let p(q) = -q + 1. Let i = 0 - 4. Let h be p(i). Suppose -h*x + 2*x + x**2 - 4 + 6 = 0. Calculate x.
1, 2
Let d(o) be the third derivative of -o**7/840 + o**6/160 - o**4/24 + 2*o**2. Factor d(g).
-g*(g - 2)**2*(g + 1)/4
Find x, given that -4*x**2 + 0*x**2 + 6*x + 2*x**2 = 0.
0, 3
Determine l, given that 12/5*l - 6/5*l**2 + 1/5*l**3 - 8/5 = 0.
2
Let u = 2 + 3. Suppose 5*d**5 + 5*d**5 - 12*d**u = 0. What is d?
0
Solve -2/15*s**3 - 4*s**2 + 56/15*s**4 + 4/15 + 2/15*s = 0.
-1, -1/4, 2/7, 1
Let f(m) be the second derivative of -m**8/53760 - m**7/10080 + m**6/1920 + m**4/6 + 3*m. Let q(r) be the third derivative of f(r). Factor q(h).
-h*(h - 1)*(h + 3)/8
Let h = -70 - -72. Let m(d) be the third derivative of 3*d**h - 1/18*d**4 + 1/90*d**5 + 1/9*d**3 + 0 + 0*d. Factor m(i).
2*(i - 1)**2/3
Let x(a) = -a**4 + 7*a**3 + 4*a**2 + 2*a. Let j(k) = k**4 - 6*k**3 - 4*k**2 - k. Let b(i) = 6*j(i) + 5*x(i). Suppose b(n) = 0. Calculate n.
-2, 0, 1, 2
Let d be -3*(-2 - 14/(-6)). Let x = d + 4. What is t in t**x + 2 - t - t - 2*t**2 + t**3 = 0?
-1, 1
Let u = -140 + 702/5. Let p(h) be the first derivative of 0*h**3 - 2 + 0*h**2 + u*h**5 + 0*h**4 + 1/3*h**6 + 0*h. Factor p(i).
2*i**4*(i + 1)
Let p(u) = 9*u**4 - 35*u**3 + 69*u**2 - 45*u + 11. Let j(a) = a**4 + a**3 + a**2 - a + 1. Let s(z) = 3*j(z) - p(z). Determine g so that s(g) = 0.
1/3, 1, 4
Let l = -9 + 6. Let v be l - -1 - (-1 + -4). Determine t so that -4*t**4 + 5*t**3 + 2*t**4 - v*t**3 = 0.
0, 1
Factor -15 - 18 + 23*f + 6 - 3*f**2 - 5*f.
-3*(f - 3)**2
Find z such that -6 + 8*z**4 + 25*z**2 - 14 - 20*z + 25*z**3 - 5*z**5 - 13*z**4 = 0.
-2, -1, 1, 2
Let z(t) = t**4 - 2*t**3 + t**2 + t. Let y(s) = 6*s**4 - 15*s**3 + 9*s**2 + 3*s. Let b(k) = -y(k) + 3*z(k). Factor b(a).
-3*a**2*(a - 2)*(a - 1)
Let k(l) be the first derivative of 5*l**6/6 - 15*l**4/4 - 10*l**3/3 - 3. Solve k(p) = 0 for p.
-1, 0, 2
Let t(y) be the first derivative of 0*y**2 + 4 + 0*y**3 + 1/6*y**6 - 6/5*y**5 + 9/4*y**4 + 0*y. Factor t(s).
s**3*(s - 3)**2
Let u(v) be the first derivative of -v**7/70 + v**6/40 + v**5/20 - v**4/8 - 2*v**2 - 4. Let i(k) be the second derivative of u(k). Find a such that i(a) = 0.
-1, 0, 1
Let o = -235/4 + 59. Let x = 5/12 + o. Factor -1/3*l**5 + 1/3*l - x*l**2 + 0 + 0*l**3 + 2/3*l**4.
-l*(l - 1)**3*(l + 1)/3
Let f(z) be the third derivative of -z**8/560 - z**7/140 + z**5/20 + z**4/8 + z**3/3 - 5*z**2. Let p(a) be the first derivative of f(a). Factor p(b).
-3*(b - 1)*(b + 1)**3
Let v(i) be the third derivative of -i**5/270 + 5*i**4/108 - 2*i**3/9 - 23*i**2. Factor v(j).
-2*(j - 3)*(j - 2)/9
Let x(s) be the first derivative of -s**8/336 + s**7/420 + s**6/72 - s**5/60 + s**3 - 3. Let w(p) be the third derivative of x(p). Let w(d) = 0. Calculate d.
-1, 0, 2/5, 1
Suppose 2*k + 80 = -4*a, a + 0*a + 164 = -5*k. Let l = -63/2 - k. Let -1/2*r - 1/2*r**4 + 0 + 1/2*r**3 + l*r**2 = 0. What is r?
-1, 0, 1
Let m be -3 + 1/(2 - 1). Let z be (11/(-429))/(m/12). Suppose z + 4/13*o + 0*o**2 - 2/13*o**4 - 4/13*o**3 = 0. Calculate o.
-1, 1
Determine d, given that 2*d**3 + 0*d - 2/3*d**2 - 2*d**4 + 0 + 2/3*d**5 = 0.
0, 1
Let s(f) = f**3 + 4*f**2 + f - 4. Let k be s(-3). Suppose -2/7*h**5 + 8/7*h**k + 0 - 12/7*h**3 + 8/7*h**4 - 2/7*h = 0. What is h?
0, 1
Let u(q) = 29*q**3 + 22*q**2 - 7*q - 22. Let k(i) = 15*i**3 + 11*i**2 - 4*i - 12. Let d(l) = -11*k(l) + 6*u(l). Factor d(p).
p*(p + 1)*(9*p + 2)
Suppose -5*f + 0*f = -4*k - 25, -2*k = 0. Let i(g) be the second derivative of 1/7*g**3 - 1/14*g**4 + 0 - 2*g - 1/7*g**2 + 1/70*g**f. Find w such that i(w) = 0.
1
Let n(s) be the first derivative of s**6/225 + 2*s**5/75 + s**4/15 + 4*s**3/45 + s**2/15 - 2*s + 5. Let r(h) be the first derivative of n(h). Factor r(j).
2*(j + 1)**4/15
What is r in 7*r**5 - 686*r - 7*r**5 - 392*r**2 - 40*r**4 + 2*r**5 + 252*r**3 = 0?
-1, 0, 7
Let s(y) be the second derivative of -1/2*y**2 + 0 - 5/12*y**3 + 4*y + 1/20*y**6 - 1/24*y**4 + 1/8*y**5. Solve s(l) = 0 for l.
-1, -2/3, 1
Let u(n) = -4*n. Let c be u(1). Let d = c + 8. Let 8*m**4 - 9*m**4 - 30*m**3 - 14*m**2 - 17*m**d - 2*m = 0. What is m?
-1, -1/3, 0
Let n(h) be the second derivative of -5*h**5/4 - 5*h**4/4 + 25*h**3/6 + 15*h**2/2 - 4*h. Let n(v) = 0. Calculate v.
-1, -3/5, 1
Let r be 3*(-7)/((-63)/(-24)). Let b be -2*5*r/30. Factor 2/3 - b*l - 4/3*l**3 + 10/3*l**2.
-2*(l - 1)**2*(2*l - 1)/3
Let t be (-5)/(20/(-12)) - 1. Let o(w) be the second derivative of 0*w**3 + 0*w**t - 1/42*w**4 - w + 0. Determine d so that o(d) = 0.
0
Factor -278*g + 15*g**2 + 5*g**3 + 278*g.
5*g**2*(g + 3)
Let r(q) be the second derivative of q**6/120 + q**5/10 + q**4/2 + 5*q**3/6 + 5*q. Let g(d) be the second derivative of r(d). What is a in g(a) = 0?
-2
Let i = 13643329/95810 - -3/19162. Let m = i + -142. What is p in -m*p**3 + 2/5 - 2/5*p**2 + 2/5*p = 0?
-1, 1
Let s(d) be the third derivative of 0 + 0*d + d**2 - 1/2*d**4 - 3*d**3 - 1/30*d**5. Factor s(r).
-2*(r + 3)**2
Let h be (0/(6/(-2)))/(-2). Let j(v) be the second derivative of 0*v**4 - v - 1/20*v**5 + 1/45*v**6 + 0 + 1/18*v**3 + h*v**2. Factor j(m).
m*(m - 1)**2*(2*m + 1)/3
Let y(o) = -o - 3. Let q be y(-5). Let v(d) be the first derivative of -1/16*d**4 + 0*d + 1/12*d**3 + 0*d**2 - q. Solve v(j) = 0.
0, 1
Let z(q) = q**3 - 7*q**2 - 2*q + 6. Let j be z(7). 