 b**6/2700 + 2*b**5/225 + 4*b**4/45 + b**3/3 + 2*b**2. Let w(g) be the first derivative of f(g). Suppose w(l) = 0. What is l?
-4
Let l(t) be the first derivative of -5*t**3/3 - 10*t**2 - 5. Factor l(v).
-5*v*(v + 4)
Let i(z) be the first derivative of -4 - 18*z**2 - 8 - 8*z**3 - z**4 + 4 + 0. Find r, given that i(r) = 0.
-3, 0
Let t be ((-10)/25)/((-9)/15). Factor t*y**2 + 2/9 - 2/9*y**3 - 2/3*y.
-2*(y - 1)**3/9
Suppose -n + 6 = 2*n. Suppose 2*q**5 - 2*q**3 + 25*q**2 - 2*q**4 - 23*q**n + 0*q**3 = 0. What is q?
-1, 0, 1
Let b(v) be the first derivative of 0*v**4 + 1/15*v**5 + 0*v + 0*v**2 - 1/9*v**3 + 1. Factor b(q).
q**2*(q - 1)*(q + 1)/3
Let q(z) = z**4 + 25*z**3 - 29*z**2 + 15*z. Let k(i) = i**4 + 50*i**3 - 59*i**2 + 30*i. Let c(u) = 6*k(u) - 11*q(u). Determine d so that c(d) = 0.
0, 1, 3
Factor -4/9*i - 2/9*i**2 - 2/9.
-2*(i + 1)**2/9
Let z be ((-14)/8)/(4/(-16)). Let k = z + -5. Factor 0*h - 1/2*h**k + 0.
-h**2/2
Let f(k) = 17*k**3 + 10*k**2 - 60*k + 7. Let y(b) = 9*b**3 + 5*b**2 - 30*b + 4. Let x(t) = 4*f(t) - 7*y(t). Let x(s) = 0. Calculate s.
-3, 0, 2
Let i(k) be the second derivative of k**7/11340 - k**6/1620 + k**5/540 + k**4/3 - k. Let x(d) be the third derivative of i(d). Factor x(z).
2*(z - 1)**2/9
Let o(g) be the third derivative of -g**7/105 + g**6/30 + g**5/30 - g**4/6 - 13*g**2. Suppose o(x) = 0. Calculate x.
-1, 0, 1, 2
What is g in -48*g**3 + 2*g**2 + 15*g**4 - 3*g + 6*g**4 + 15*g**4 + 19*g**2 = 0?
0, 1/3, 1/2
Let t(q) be the third derivative of q**2 + 1/24*q**4 + 1/9*q**3 + 1/180*q**5 + 0*q + 0. Solve t(m) = 0.
-2, -1
Let r(c) = -3*c - 1. Let o(d) = 2*d + 1. Let i(z) = 4*o(z) + 3*r(z). Let v(p) = 3*p**3 - 5*p**2 + 5*p - 3. Let k(f) = 4*i(f) + v(f). Factor k(q).
(q - 1)**2*(3*q + 1)
Let l(f) = 9*f**4 + 20*f**3 + 21*f**2 + 15*f + 5. Let s(i) = 8*i**4 + 20*i**3 + 22*i**2 + 14*i + 4. Let v(z) = -2*l(z) + 3*s(z). Solve v(x) = 0 for x.
-1, -1/3
Let x(f) be the third derivative of 3*f**5/35 - f**4/8 + f**3/14 + 24*f**2. Factor x(p).
3*(3*p - 1)*(4*p - 1)/7
Let 10*w**3 - 9*w**4 + 11*w**4 - 10*w - 18*w**2 - 16*w**3 = 0. What is w?
-1, 0, 5
Suppose 0 = 4*x + 3*l, 2*x + 2*x = -4*l. Let m(q) be the first derivative of 0*q**3 - 1/8*q**2 + x*q - 2 + 1/16*q**4. Suppose m(a) = 0. What is a?
-1, 0, 1
Let m be -5*4/(-2) - -2. Suppose -4*w - m = -32. Find p, given that -1/4*p**w - 5/2*p**2 - 5/4*p**4 - 1/4 - 5/4*p - 5/2*p**3 = 0.
-1
Solve 51*t - 18*t**2 + 3*t**3 - 17 - 7 - 15*t = 0 for t.
2
Suppose -4*g - 25 = -3*o, -2*o - 8*g - 10 = -4*g. Determine r so that -3/7*r**2 + 3/7*r**o - 1/7*r**4 + 1/7*r + 0 = 0.
0, 1
Let j(t) be the second derivative of t**6/50 + 3*t**5/25 + 3*t**4/10 + 2*t**3/5 + 3*t**2/10 - 3*t. Determine w, given that j(w) = 0.
-1
Let v(r) be the second derivative of r**4/30 - 4*r**2/5 - 8*r. Suppose v(l) = 0. What is l?
-2, 2
Let v be (-20)/(-42)*(58/10 - 4). Let j(z) be the first derivative of -2/7*z**3 + 0*z - 2/7*z**2 - 2/5*z**5 - 2 + v*z**4. Let j(a) = 0. Calculate a.
-2/7, 0, 1
Let d(w) = -w**2 - 3*w + 2. Let o be d(-3). Suppose -o*t = -f + 6, -4*f = f + t - 8. Factor 0 - f*p**2 + 4/7*p.
-2*p*(7*p - 2)/7
Let r(a) be the third derivative of -a**5/270 + 5*a**4/54 - 25*a**3/27 + 30*a**2. Factor r(m).
-2*(m - 5)**2/9
Let k(r) be the third derivative of -r**5/60 - 5*r**4/12 - 25*r**3/6 - 50*r**2. Factor k(z).
-(z + 5)**2
Let r(j) = 11*j**2 - 86*j + 331. Let b(n) = 5*n**2 - 42*n + 165. Let u(d) = 7*b(d) - 3*r(d). Find i, given that u(i) = 0.
9
Let q(r) = r + 2. Let x be q(0). Let v(f) = -f**2 - f - 1. Let p(u) = 2*u + 10 - 7 + 4*u**2 + 0*u. Let n(s) = x*p(s) + 6*v(s). Solve n(i) = 0 for i.
0, 1
Suppose -5*v = -n + 4, -6*n - 9 = -n + 4*v. Let l = 1 - n. Let -1/3*z - 2/3*z**l + 2/3*z**3 - 1/3*z**5 + 1/3 + 1/3*z**4 = 0. Calculate z.
-1, 1
Let p(f) be the second derivative of 5*f**4/12 + 35*f**3/3 - 75*f**2/2 - 5*f - 1. Factor p(g).
5*(g - 1)*(g + 15)
Suppose 4*i + 6*d + 17 = d, -i - 4*d - 18 = 0. Suppose -a + i*a + 9 = 2*m, 5 = -a. Factor p**4 + 0*p**4 + m*p**3 + p**4.
2*p**3*(p + 1)
Suppose 0 = -6*n + 12*n - 24. Factor 0*b**2 - b**3 - 1/3*b**n + 4/3*b + 0.
-b*(b - 1)*(b + 2)**2/3
Let r = -323/2 + 166. Let c(j) be the first derivative of r*j**2 - 2*j - 7/3*j**3 - 4. What is q in c(q) = 0?
2/7, 1
Let a(o) be the first derivative of o**5/30 - o**3/3 + o**2/2 - 1. Let g(y) be the second derivative of a(y). Factor g(k).
2*(k - 1)*(k + 1)
Let i be (-1)/(2/4) + 2. Let b = 8 - 6. Find q, given that i*q - 2/3*q**3 + 0 - 2/3*q**b = 0.
-1, 0
Factor 2/21*o**3 + 2/7*o**2 - 8/7 - 8/21*o.
2*(o - 2)*(o + 2)*(o + 3)/21
Let a(m) be the second derivative of -m**6/240 + m**5/160 + m**4/32 - 5*m**3/48 + m**2/8 - 8*m. Factor a(n).
-(n - 1)**3*(n + 2)/8
Solve 1/2*o + 1/2*o**2 + 0 = 0 for o.
-1, 0
Let m = 60 - 56. Let f(p) be the third derivative of -1/150*p**5 + 0*p**3 + 0*p + 0 + 1/60*p**m - p**2. Factor f(z).
-2*z*(z - 1)/5
Suppose -j + 0*j + 0*j = 0. Let h(z) be the first derivative of -1 - 7/25*z**5 + j*z + 1/10*z**4 + 0*z**3 + 0*z**2. Determine u so that h(u) = 0.
0, 2/7
Let f(l) be the first derivative of l**6/420 - l**5/105 - 3*l**2 + 4. Let y(t) be the second derivative of f(t). Determine v so that y(v) = 0.
0, 2
Let i(c) be the first derivative of -4/9*c**3 - 1/9*c**6 + 0*c**4 + 1/3*c**2 + 1 + 4/15*c**5 + 0*c. Factor i(r).
-2*r*(r - 1)**3*(r + 1)/3
Let z(v) be the first derivative of -v**6/300 + v**5/75 - v**4/60 - 2*v**2 - 1. Let o(w) be the second derivative of z(w). Factor o(q).
-2*q*(q - 1)**2/5
Suppose 0 = -3*b + 4*a + 21, 4*b - 3*a - 3 = -6*a. Let m(y) be the first derivative of 1/4*y**b + 2 + 1/2*y - 7/8*y**2. Factor m(f).
(f - 2)*(3*f - 1)/4
Let u(h) = h - 4. Let c be u(4). Factor 0*v**3 + c*v - 1/4 - 1/4*v**4 + 1/2*v**2.
-(v - 1)**2*(v + 1)**2/4
Let c = 0 + 3. Suppose 3 = -c*t + 9. Solve 2*b**2 - b**2 - 3*b**2 + t*b = 0 for b.
0, 1
Let r(p) be the second derivative of p**4/3 + 2*p**3/3 - 7*p. Factor r(z).
4*z*(z + 1)
Let m = 48 - 46. Let l(d) be the first derivative of -1/6*d**2 - 2/9*d**3 + 1/3*d + m. Factor l(a).
-(a + 1)*(2*a - 1)/3
Factor 4*d**3 + 3*d**5 + 12*d**4 + 10*d**5 - 9*d**5 + 4*d**2 + 8*d**3.
4*d**2*(d + 1)**3
Suppose 3*a + 3*i = 3, 3*a + 0*i = 3*i - 3. Determine w, given that 0*w + a + 2/5*w**2 = 0.
0
Suppose -6*q = -2*q - 8. Let h(o) be the first derivative of -4/9*o**3 + 2 - 1/3*o**4 + 1/3*o**q + 2/15*o**5 + 2/3*o + 1/9*o**6. Determine a so that h(a) = 0.
-1, 1
Let w = 595 + -593. Factor -6/7*b**3 + 0*b + 0 - 3/7*b**4 - 3/7*b**w.
-3*b**2*(b + 1)**2/7
Let w(f) be the third derivative of -f**6/180 + f**5/18 - 2*f**4/9 + 4*f**3/9 - 11*f**2. Let w(o) = 0. What is o?
1, 2
Let h(x) be the first derivative of -x**6/16 + 9*x**5/40 - 3*x**4/16 - x**3/4 + 9*x**2/16 - 3*x/8 + 20. Solve h(s) = 0.
-1, 1
Suppose 2*i = 4*j + 12, 5*i - 2*i = 2*j + 6. Suppose i = 4*s - 11 - 1. Let -s*w**2 + 1 - 2*w - 2*w**2 + 6*w**2 = 0. What is w?
1
Suppose -31 = 12*t - 55. Let -8/11*p**t - 10/11*p - 4/11 - 2/11*p**3 = 0. What is p?
-2, -1
Let v(d) be the third derivative of -d**8/672 + 11*d**7/420 - d**6/10 - 3*d**5/10 + 2*d**2. Factor v(n).
-n**2*(n - 6)**2*(n + 1)/2
Solve -21/5*k**3 + 0 - 3/5*k**5 + 0*k - 3*k**4 - 9/5*k**2 = 0.
-3, -1, 0
Let y = 78 - 75. Factor -2*x**y + 8*x**4 + 0 - 14/3*x**5 - 4/3*x**2 + 0*x.
-2*x**2*(x - 1)**2*(7*x + 2)/3
Let v(o) be the first derivative of o**6/360 + o**5/40 - 4*o**3/3 + 3. Let x(i) be the third derivative of v(i). Factor x(n).
n*(n + 3)
Let i be -1 - (38/(-8))/(27/12). Factor 8/9*n**3 + 2/9*n**4 + i*n**2 + 4/9*n + 0.
2*n*(n + 1)**2*(n + 2)/9
Let f be (2/(-4))/((-2)/12). Suppose f*a - 2*a = 0. Let a*h + 2*h + 2*h**2 - 4*h = 0. Calculate h.
0, 1
Let x(k) be the first derivative of 6 - 10*k**2 - k**4 + 16/3*k**3 + 8*k. Let x(v) = 0. What is v?
1, 2
Let b(h) be the first derivative of h**6/27 + h**5/15 - h**4/18 + 43. Factor b(y).
y**3*(y + 2)*(2*y - 1)/9
Let d(o) be the second derivative of o**7/21 + o**6/15 - o**5/10 - o**4/6 + 10*o. Factor d(c).
2*c**2*(c - 1)*(c + 1)**2
Let w(z) = 6*z**3 - 3*z. Let k(o) = -o**3 - o**2 - o. Suppose b = -2*b + 9. Let h(q) = b*k(q) + w(q). Factor h(c).
3*c*(c - 2)*(c + 1)
Factor 5 - 6*g**2 + 5 + g**2 - 15*g + 10.
-5*(g - 1)*(g + 4)
Let y(c) = 4*c**3 + 16*c**2 + 8*c - 1. Let h(j) be the first derivative of -j**4/4 - j**2/2 - j - 1. Let k(w) = 6*h(w) - 2*y(w). Suppose k(n) = 0.