ivative of 0*t**2 + 0 + 1/168*t**7 + 4*t + 1/120*t**6 - 1/80*t**5 - 1/48*t**4 + 0*t**3. Determine s, given that g(s) = 0.
-1, 0, 1
Suppose 2*g = -7*g + 3*g. Let f(w) be the second derivative of 0 - w**2 + 1/20*w**5 - 2*w + g*w**4 - 1/2*w**3. Factor f(y).
(y - 2)*(y + 1)**2
Let v = -133/12 + 47/4. Suppose 0*n = 2*n. Solve 1/3*o + v*o**2 + n - o**3 = 0 for o.
-1/3, 0, 1
Let r = 227/819 + 1/117. Factor 0 - r*n - 2/7*n**3 + 4/7*n**2.
-2*n*(n - 1)**2/7
Let 5*b**2 + 4*b**3 - b**2 + 0*b**3 - 2*b**3 = 0. What is b?
-2, 0
Let r(a) = a**2 - 9*a + 2. Let z be r(10). Let s be 1/(0 + 3/z). Factor -p**2 - p**3 - 2*p**2 + 3*p**2 + p**s.
p**3*(p - 1)
Suppose 13 = 2*j - 4*s - 3, 4*j = 3*s + 12. Factor 1/2*t - 1/2*t**4 + 1/2*t**2 + j - 1/2*t**3.
-t*(t - 1)*(t + 1)**2/2
Let n(m) be the third derivative of -m**7/945 - m**6/540 + m**5/45 + m**4/27 - 8*m**3/27 + 3*m**2. Solve n(q) = 0 for q.
-2, 1, 2
Let c(f) = -f**2 - 12*f - 15. Let d be c(-10). Let p(a) be the first derivative of 0*a**4 + 0*a**2 - 1 - 2/25*a**d + 0*a + 0*a**3. Solve p(w) = 0.
0
Let b = -6 - -5. Let k be (b/(-3))/(3 - 2). Suppose 0 - k*f**4 + 0*f + 1/3*f**3 + 0*f**2 = 0. What is f?
0, 1
Let u(y) be the first derivative of -y**4/2 - 2*y**3 - 3*y**2 - 2*y + 7. Factor u(p).
-2*(p + 1)**3
Find j, given that 21*j**2 - 4*j**2 - 20*j**5 - 5*j**2 + 13*j**2 + 5*j + 15*j**3 - 25*j**4 = 0.
-1, -1/4, 0, 1
Let t(u) be the first derivative of u**8/560 + u**7/280 - u**6/120 - u**5/40 + u**3 - 2. Let a(m) be the third derivative of t(m). Factor a(d).
3*d*(d - 1)*(d + 1)**2
Let z(v) = 20*v**3 + 24*v**2 - 12*v + 16. Let t(p) = -p**3 - p**2 - p. Let o(u) = -16*t(u) - z(u). Factor o(n).
-4*(n - 1)**2*(n + 4)
Let x(n) be the first derivative of n**4/12 - 4*n**3/9 - n**2/6 + 4*n/3 - 7. Determine y so that x(y) = 0.
-1, 1, 4
Let n(y) be the second derivative of y**4/4 + 3*y**3/2 + 3*y**2 + 10*y. Factor n(m).
3*(m + 1)*(m + 2)
Let h(b) = 2*b**2 + 7*b. Let p be h(-5). Suppose 5*i = -p, -4*n + 18 = -3*i - 79. Let -28*d + n*d**2 + 3 - 5*d**3 + 3 + 1 + 1 = 0. What is d?
2/5, 2
Suppose -63*f + 6 = -61*f. Let w(d) be the second derivative of 1/12*d**4 - 2*d - 1/2*d**f + 0 + d**2. Factor w(j).
(j - 2)*(j - 1)
Let u(i) be the second derivative of -i**4/6 + i**2 + i. Determine n so that u(n) = 0.
-1, 1
Let u be (-341)/(-62) + (0 - 5). Solve -1/2*c + 0 - u*c**2 = 0 for c.
-1, 0
Factor -6*l + 0 + 12 - 4*l + 3 - 5*l**2.
-5*(l - 1)*(l + 3)
Let t(d) = -d**3 + 9*d**2 - 12*d + 6. Let j be t(8). Let v = j - -29. Factor -n**v + 1/2 + n + 0*n**2 - 1/2*n**4.
-(n - 1)*(n + 1)**3/2
Factor 0 - 4/9*v**4 - 4/9*v**3 + 8/9*v**2 + 0*v.
-4*v**2*(v - 1)*(v + 2)/9
What is n in 1 - 5*n**2 - 7*n**2 + 11*n**2 = 0?
-1, 1
Let i(w) be the first derivative of w**6/30 - w**4/12 + w + 1. Let k(s) be the first derivative of i(s). Factor k(j).
j**2*(j - 1)*(j + 1)
Determine h, given that -2/3 + 1/3*h**3 - 1/3*h + 2/3*h**2 = 0.
-2, -1, 1
Let v(t) be the first derivative of t**4/4 + t**3/6 - 5*t**2/4 + t + 14. Factor v(q).
(q - 1)*(q + 2)*(2*q - 1)/2
Suppose -2/13*o - 12/13*o**2 + 6/13 + 6/13*o**4 - 2/13*o**5 + 4/13*o**3 = 0. Calculate o.
-1, 1, 3
Factor 2*y**3 - 9*y**3 - y**4 - y**2 + 5*y**3 + 0*y**4.
-y**2*(y + 1)**2
Let s(v) be the second derivative of -v**7/168 + v**5/40 - v**3/24 + 5*v. Factor s(p).
-p*(p - 1)**2*(p + 1)**2/4
Let i(r) be the first derivative of r**4/6 - 2*r**3/3 + r**2 - 2*r/3 - 26. Factor i(z).
2*(z - 1)**3/3
Let j be -1*(-1)/(-4)*(1 + -13). Factor -2/3*c**5 - 2/3*c**4 + 4/3*c**j + 4/3*c**2 - 2/3*c - 2/3.
-2*(c - 1)**2*(c + 1)**3/3
Determine o so that -9*o + 0 - 2*o**2 + 2 + 19*o**3 + 6*o - 16*o**3 = 0.
-1, 2/3, 1
Let x(z) = -z**4 + z**3 + z. Let u be (-2 + -3)*(-12)/(-20). Let l(f) = 6*f**4 - 9*f**3 - 9*f**2 + 9*f + 12. Let d(o) = u*x(o) - l(o). Factor d(c).
-3*(c - 2)**2*(c + 1)**2
Let x(z) be the second derivative of -1/24*z**4 + 4*z + 0 - z**2 + 1/3*z**3. Let x(s) = 0. What is s?
2
Suppose 6*a = 5*a + 3. Let y(u) be the third derivative of 1/24*u**4 - 1/120*u**6 - 2*u**2 + 0*u + 1/6*u**a + 0 - 1/60*u**5. Factor y(s).
-(s - 1)*(s + 1)**2
Let q be ((-10)/8)/(2/24). Let x be 3/12 + q/(-4). Factor -4*p**4 - p**x + 7*p**4.
2*p**4
Let h = -6 + 9. Let s be 3/4*8/h. Determine k so that 2/5 - 4/5*k + 2/5*k**s = 0.
1
Let n = 4 + 0. Let c(m) = -m - 1. Let r(l) = 6*l + l + 2*l**2 - l + 4. Let k(y) = n*c(y) + r(y). Suppose k(t) = 0. What is t?
-1, 0
Let y(d) be the second derivative of -d**7/2520 - d**6/180 - d**5/30 - d**4/9 + d**3/2 + 6*d. Let c(m) be the second derivative of y(m). Factor c(t).
-(t + 2)**3/3
Let z(r) be the third derivative of r**7/420 + 7*r**6/240 + r**5/8 + 3*r**4/16 - 8*r**2. Factor z(y).
y*(y + 1)*(y + 3)**2/2
Suppose -6/7*j + 4/7 + 2/7*j**2 = 0. What is j?
1, 2
Let f = -2/471 - -1898/3297. Determine p, given that 0 - f*p**4 + 0*p**3 + 4/7*p**2 + 0*p = 0.
-1, 0, 1
Factor -2/3*b**3 + 0*b + 1/3*b**4 + 0 + 1/3*b**2.
b**2*(b - 1)**2/3
Let o(b) be the first derivative of -1/2*b**2 + 1/12*b**3 + 1/24*b**4 - b - 2. Let t(z) be the first derivative of o(z). Factor t(v).
(v - 1)*(v + 2)/2
Let d = 8 + -2. Let b(u) = 0*u**2 - d*u**2 + u**4 + u + 0*u**2 - u**3. Let c(x) = x**2. Let m(j) = b(j) + 5*c(j). Factor m(z).
z*(z - 1)**2*(z + 1)
Let n(c) be the first derivative of c**4/6 + 2*c**3/3 - 3*c - 3. Let i(s) be the first derivative of n(s). Suppose i(f) = 0. What is f?
-2, 0
Let f(o) be the third derivative of -o**8/112 - 3*o**7/70 - o**6/20 + 6*o**2. Factor f(t).
-3*t**3*(t + 1)*(t + 2)
Let g(a) = -a**2 - 10*a - 10. Let j be g(-7). Let f = j + -11. Factor -4/9*x - 2/3*x**2 + f.
-2*x*(3*x + 2)/9
Let g(v) be the second derivative of v**7/2520 - v**6/360 + v**5/120 + v**4/4 + v. Let h(t) be the third derivative of g(t). Suppose h(x) = 0. Calculate x.
1
Let a(b) = 3*b**3. Let t be a(1). Factor -162*v**2 - 39*v - 135 - 285*v - 36*v**t - 3*v**4 - 108.
-3*(v + 3)**4
Let z = 8 + 7. Suppose -z*i + 20*i - 10 = 0. Factor 1/2 - 1/2*v**3 - 3/2*v + 3/2*v**i.
-(v - 1)**3/2
Let r(h) be the third derivative of -h**7/42 + h**5/4 + 5*h**4/12 + 35*h**2. Let r(y) = 0. What is y?
-1, 0, 2
Let n be 2*(5 - 1 - 2). Suppose 0*p - n = -k + p, 2*k - p = 7. Factor 6*q**2 + k*q**3 - 5*q + 2 - q - 5*q**3.
-2*(q - 1)**3
Let r(v) be the third derivative of 0*v**3 + 0*v**4 - v**2 + 1/280*v**7 + 1/40*v**6 + 0*v + 3/80*v**5 + 0. Factor r(a).
3*a**2*(a + 1)*(a + 3)/4
Let g be (4/10)/(7/(-315)). Let k(a) = -a**2 + 3*a + 7. Let s(w) = 1. Let q(u) = 2. Let o(z) = q(z) - 3*s(z). Let n(v) = g*o(v) - 2*k(v). Factor n(p).
2*(p - 2)*(p - 1)
Let d = 61/6 - 29/3. Find w, given that -3/2*w**2 - d - 3/2*w - 1/2*w**3 = 0.
-1
Let c(i) = i**3 + 4*i**2 + i + 4. Let f be c(-4). Let y = -31 - -219/7. Factor y*p**2 + 0 - 8/7*p**3 + f*p.
-2*p**2*(4*p - 1)/7
Let d(i) = -9*i**3 + 6*i**2. Let n(g) = g**4 + 10*g**3 - 7*g**2. Let k(m) = -4*d(m) - 3*n(m). Factor k(b).
-3*b**2*(b - 1)**2
Let a(n) be the third derivative of -n**7/840 - n**6/180 - n**5/120 - 2*n**3/3 + n**2. Let k(q) be the first derivative of a(q). Factor k(i).
-i*(i + 1)**2
Let c(w) be the first derivative of -w**5 + 25*w**4/4 - 10*w**3 - 10*w**2 + 40*w - 12. Factor c(f).
-5*(f - 2)**3*(f + 1)
Let u(i) be the third derivative of 0*i**3 + 0 + 0*i + 3*i**2 - 1/120*i**6 + 0*i**4 - 1/70*i**7 + 1/30*i**5. Solve u(s) = 0 for s.
-1, 0, 2/3
What is i in -3/10*i**2 + 0*i**3 + 1/10*i**4 - 1/5*i + 0 = 0?
-1, 0, 2
Let t(u) be the first derivative of u**4/12 - u**3/8 - u - 2. Let x(i) be the first derivative of t(i). Factor x(z).
z*(4*z - 3)/4
Let q = 13 + -9. Let d be 1/q + 3/4. Let i(f) = -f**3 + f. Let v(c) = -c**3 - c**2 + c + 1. Let t(b) = d*v(b) - 4*i(b). Factor t(y).
(y - 1)*(y + 1)*(3*y - 1)
Let j(i) be the second derivative of 0*i**2 + 0*i**3 - 1/6*i**4 + 0 + i. Solve j(p) = 0.
0
Let z(s) be the second derivative of s**7/105 - 4*s**6/75 + 2*s**5/25 + s**4/15 - s**3/3 + 2*s**2/5 + 56*s. Suppose z(g) = 0. Calculate g.
-1, 1, 2
Let y(u) be the second derivative of u**7/42 - u**5/10 + u**3/6 + 7*u. Factor y(d).
d*(d - 1)**2*(d + 1)**2
Let k(w) be the third derivative of -w**6/320 + 3*w**5/160 - w**4/32 + 5*w**2. Factor k(q).
-3*q*(q - 2)*(q - 1)/8
Let q(d) be the second derivative of d**4/9 + 4*d**3/3 + 10*d**2/3 - 57*d. Let q(y) = 0. What is y?
-5, -1
Let j be (3/(-45))/((-9)/15). Let l(s) be the first derivative of 1/3*s - 1/6*s**2 - 