 c(l) = b*s(l) - w(l). Determine k, given that c(k) = 0.
-1, 1
Let m(a) = -4*a**5 - 16*a**4 - 7*a**3 + 5*a. Let r(p) = 10*p**5 + 40*p**4 + 18*p**3 - 12*p. Let s(k) = 12*m(k) + 5*r(k). Factor s(c).
2*c**3*(c + 1)*(c + 3)
Factor -2*y**4 + 3*y**2 + 9*y**3 - 6*y**3 - y**4 - 3*y.
-3*y*(y - 1)**2*(y + 1)
Suppose 0 = 17*q - 19*q + 6. Factor 2/7 + 2/7*l - 2/7*l**q - 2/7*l**2.
-2*(l - 1)*(l + 1)**2/7
Let r(u) be the first derivative of -4*u**5/5 + 4*u**4 - 4*u**3 - 8*u**2 + 16*u + 12. Find h such that r(h) = 0.
-1, 1, 2
Let m(n) be the third derivative of 7*n**2 + 1/280*n**6 - 3/490*n**7 + 0*n**4 + 0*n**3 + 0 - 1/196*n**8 + 0*n**5 + 0*n. Factor m(d).
-3*d**3*(d + 1)*(4*d - 1)/7
Let f(q) be the first derivative of -3*q**5/5 + 3*q**4/2 - 3*q**2 + 3*q - 3. Factor f(n).
-3*(n - 1)**3*(n + 1)
Let z(j) be the first derivative of j**8/6720 + j**7/1120 + j**6/480 + j**5/480 - j**3 - 2. Let w(b) be the third derivative of z(b). Solve w(h) = 0.
-1, 0
Suppose 2*b = 10, -b = -q + 4*q - 5. Let s(p) be the second derivative of -1/30*p**5 + q*p**2 + 0 + 1/9*p**3 + p + 0*p**4. Factor s(z).
-2*z*(z - 1)*(z + 1)/3
Let -2/21*x**2 + 0 + 2/21*x = 0. Calculate x.
0, 1
Let d(u) be the third derivative of -u**5/50 + 4*u**3/5 - 2*u**2 - 3*u. Factor d(s).
-6*(s - 2)*(s + 2)/5
Let p(h) = h + 4. Let z be p(-4). Let j(x) be the second derivative of -x + z + x**2 - 2/3*x**3 + 1/6*x**4. Factor j(o).
2*(o - 1)**2
Let 5/6*i**2 + 605/6 - 55/3*i = 0. What is i?
11
Factor 3/8*s**2 + 15/8*s + 0.
3*s*(s + 5)/8
Suppose -5 - 4 = -3*k. Let l(x) be the third derivative of x**2 - 1/240*x**5 + 0*x + 0 + 1/480*x**6 + 1/24*x**k - 1/96*x**4. Find s such that l(s) = 0.
-1, 1
Let l be (1 - 2)*(2 + -2). Let y be (l/1)/(30/15). Factor y + 1/3*p - 1/3*p**2.
-p*(p - 1)/3
Let n = 49/212 - -1/53. Factor 0 + n*a**2 - 1/4*a**4 + 1/4*a**3 - 1/4*a**5 + 0*a.
-a**2*(a - 1)*(a + 1)**2/4
Suppose 0 = c - 29 + 25. Determine n, given that 4/3*n**2 - 2/3 - 2/3*n**c + 0*n + 0*n**3 = 0.
-1, 1
Let m(s) be the second derivative of -s**4/42 + s**3/7 + 4*s. Factor m(q).
-2*q*(q - 3)/7
Suppose -4*j + 3*v = -5 + 4, 0 = 3*j - 2*v. Let l(d) = d**3 + 3*d**2 + d + 1. Let a be l(j). Factor 2/11*x**a + 0 + 0*x**2 - 2/11*x.
2*x*(x - 1)*(x + 1)/11
Let g be ((-18)/(-48))/(6/4). Find o such that g + 5*o**5 - 19/4*o**3 - 1/4*o + 4*o**4 - 17/4*o**2 = 0.
-1, -1/2, 1/5, 1
Let a(o) be the second derivative of -o**7/11340 - o**6/3240 + o**4/4 + 6*o. Let m(z) be the third derivative of a(z). Factor m(q).
-2*q*(q + 1)/9
Suppose 12 = -88*i + 92*i. Factor 0 - 3/5*z**i - 1/5*z**2 + 2/5*z.
-z*(z + 1)*(3*z - 2)/5
Let f = 828/5 - 165. Factor -12/5*b - 12/5*b**4 + 3/5*b**5 + 6*b**2 - 24/5 + f*b**3.
3*(b - 2)**3*(b + 1)**2/5
Let u(i) be the third derivative of 0 + 0*i - 1/360*i**5 - 1/144*i**6 + 1/144*i**4 + 0*i**3 - 1/420*i**7 - 4*i**2. Solve u(n) = 0.
-1, 0, 1/3
Let j(v) = 2*v**4 - 28*v**3 - 64*v**2 - 68*v - 26. Let s(r) = r**4 - 9*r**3 - 21*r**2 - 23*r - 9. Let q(d) = 3*j(d) - 8*s(d). Suppose q(b) = 0. Calculate b.
-3, -1
Let o(h) be the first derivative of -3*h**5/5 - 9*h**4/4 - h**3 + 9*h**2/2 + 6*h - 3. Find p, given that o(p) = 0.
-2, -1, 1
Let w(b) = b**3 + 3*b**2 + 2*b + 2. Let q(i) = 8*i**3 + 24*i**2 + 16*i + 17. Let a(c) = -6*q(c) + 51*w(c). Solve a(n) = 0.
-2, -1, 0
Let -32/5 + 16/5*t - 2/5*t**2 = 0. What is t?
4
Let r(v) be the second derivative of v**4/22 + v**3/11 - 6*v**2/11 + 8*v. Solve r(s) = 0.
-2, 1
Determine m so that 6/7*m**3 + 0*m - 4/7*m**2 - 2/7*m**4 + 0 = 0.
0, 1, 2
Suppose 0 = 3*w + 2*j + 4, -w + 2*j = -7 + 3. Let s be (13/65)/(1/2). Determine y, given that w - s*y**2 + 0*y = 0.
0
Let u = -1/280 - -81/280. Suppose 4/7*r**3 - u*r**4 + 0 + 0*r + 2/7*r**2 - 4/7*r**5 = 0. Calculate r.
-1, -1/2, 0, 1
Let i(g) be the first derivative of -g**6/2 + 12*g**5/5 - 3*g**4 - 2*g**3 + 15*g**2/2 - 6*g + 4. Factor i(v).
-3*(v - 2)*(v - 1)**3*(v + 1)
Suppose -s = -3*f + 2, 4*f - 7*s = -3*s + 8. Suppose f = 3*c - 18 - 0. Factor -c*o + 3*o + 2*o**2 + o**2.
3*o*(o - 1)
Suppose -3*u + 10 = 4. Let -1/5*w**3 - 3/5*w + 1/5 + 3/5*w**u = 0. Calculate w.
1
Let d(n) = -n**3 + 4*n**2 - 2. Let w be d(4). Let o(s) = s**2 + 5*s - 4. Let f(u) = -15*u**2 - 81*u + 63. Let t(z) = w*f(z) - 33*o(z). Factor t(x).
-3*(x - 1)*(x + 2)
Let z be 8/(-2) + -2 + 5. Let f be 0/(z - -2 - 0). Solve 0*w - 2/7*w**2 + f - 2/7*w**3 = 0 for w.
-1, 0
Let c = 633 - 633. Factor 0*o + c + 6/7*o**2 - 3/7*o**3.
-3*o**2*(o - 2)/7
Let k(o) be the second derivative of 2*o - 1/5*o**2 + 1/5*o**3 + 0*o**6 + 1/30*o**4 - 7/50*o**5 + 4/105*o**7 + 0. Solve k(m) = 0.
-1, 1/2, 1
Let o(u) be the first derivative of 3 - 2/5*u**5 + 2/7*u**2 - 22/21*u**3 + 0*u + 8/7*u**4. Let o(l) = 0. Calculate l.
0, 2/7, 1
Let k be ((-26)/39)/(1/(-6)). Let z be (k/(-3))/(26/(-39)). Factor 0*t**z + 1/4*t - 1/4*t**3 + 0.
-t*(t - 1)*(t + 1)/4
Let d(t) = -t + 1. Let i(u) = 2*u**3 + 4*u**2 - 7*u + 1. Let r(j) = -5*d(j) + i(j). Factor r(p).
2*(p - 1)*(p + 1)*(p + 2)
Let u = -3 + 4. Let r be u/(((-3)/(-6))/1). Factor -2*w**r + 0*w**2 + 2*w**3 + w**3.
w**2*(3*w - 2)
Let m(k) be the first derivative of 4*k**5/5 + 8*k**4 + 52*k**3/3 + 12*k**2 + 21. Determine n so that m(n) = 0.
-6, -1, 0
Suppose a - 5*j = -2*a + 58, -a + 24 = -4*j. Let t = -47/3 + a. Factor 0*l - 1/3*l**2 - t*l**3 + 0.
-l**2*(l + 1)/3
Let u = -15 + 15. Let 0*o**4 - 2/7*o**3 + 0*o + 2/7*o**5 + u*o**2 + 0 = 0. What is o?
-1, 0, 1
Let w(c) be the first derivative of -c**4/14 + 4*c**2/7 + 6. Factor w(v).
-2*v*(v - 2)*(v + 2)/7
Let s(y) = 35*y**4 - 10*y**3 - 30*y**2 + 30*y. Let n(a) = a**4 - a**2 + a. Let w(x) = 30*n(x) - s(x). Suppose w(k) = 0. What is k?
0, 2
Factor 10*g**2 + 21*g - 25*g**3 + 20*g**3 - 6*g.
-5*g*(g - 3)*(g + 1)
Let y(p) be the first derivative of 2*p**5/5 - p**4/4 - p**3 + p**2/2 + p + 8. Factor y(m).
(m - 1)**2*(m + 1)*(2*m + 1)
Let l = 34 + -4. Let x = l - 27. Solve -1/3 - 1/3*u**x - u**2 - u = 0 for u.
-1
Let v(n) be the third derivative of n**6/5 + 23*n**5/30 - 5*n**4/12 + n**2. Let y(i) = -8*i**3 - 15*i**2 + 3*i. Let l(h) = -5*v(h) - 16*y(h). Factor l(s).
2*s*(s + 1)*(4*s + 1)
Let l(d) be the first derivative of -7/33*d**6 + 1/11*d**2 - 52/55*d**5 - 17/11*d**4 - 32/33*d**3 + 4 + 4/11*d. Factor l(o).
-2*(o + 1)**4*(7*o - 2)/11
Factor 0 - 3/5*a**2 + 1/5*a**4 + 2/5*a**3 + 0*a.
a**2*(a - 1)*(a + 3)/5
Let j(p) be the second derivative of 0 + 4*p - 3*p**2 + 1/2*p**3 + 1/4*p**4. Factor j(w).
3*(w - 1)*(w + 2)
Suppose -p - 5 = -2*p - z, -5 = -2*p + 3*z. Let h(r) be the second derivative of 1/21*r**3 - 1/42*r**p + 0 + 0*r**2 - r. What is c in h(c) = 0?
0, 1
Let w = 19 - 15. Let d(p) = 1. Let g(c) = -3*c**4 - 18*c**3 - 39*c**2 - 36*c - 8. Let y(k) = w*d(k) - g(k). Factor y(t).
3*(t + 1)**2*(t + 2)**2
Factor -1/3*s**4 + 32/3*s - 16/3 + 8/3*s**3 - 8*s**2.
-(s - 2)**4/3
Let j be ((-2)/2 + 2)*7. Let l(u) be the second derivative of 1/5*u**5 + 0 - 1/8*u**6 + 1/42*u**j + u - 1/12*u**3 - 1/16*u**4 + 0*u**2. Let l(c) = 0. What is c?
-1/4, 0, 1, 2
Let f(s) = -17*s**4 - 38*s**3 - 35*s**2 - 8*s + 2. Let a(v) = 52*v**4 + 113*v**3 + 105*v**2 + 23*v - 7. Let i(w) = 2*a(w) + 7*f(w). Find l, given that i(l) = 0.
-1, -2/3, 0
Determine o, given that 0 + 0*o**3 + 2/3*o**5 + 4/3*o**4 - 4/3*o**2 - 2/3*o = 0.
-1, 0, 1
Suppose -3*b + 2*c = -2 - 3, 6 = 3*c. Suppose a + b + 0 = g, -2*g = 3*a - 16. Factor -1/3*u**2 + 0*u + 1/3*u**4 + 1/3*u**g + 0 - 1/3*u**3.
u**2*(u - 1)*(u + 1)**2/3
Suppose 2*k + 20*p + 16 = 25*p, 0 = 2*k - p. Factor -5/4*d**4 + 0 + 1/2*d**3 - 1/2*d + 5/4*d**k.
-d*(d - 1)*(d + 1)*(5*d - 2)/4
Let h(c) be the third derivative of c**8/672 + c**7/210 - c**6/240 - c**5/60 - 8*c**2. Determine k, given that h(k) = 0.
-2, -1, 0, 1
Let a(y) = -y**3 + 5*y**2 + 15*y - 6. Let c be a(7). Let n(i) be the first derivative of -c + 4*i - 1/2*i**4 - 5*i**2 + 8/3*i**3. Let n(g) = 0. What is g?
1, 2
Let f(m) be the second derivative of -4*m**7/147 - 3*m**6/35 - m**5/35 + 4*m**4/21 + 2*m**3/7 + m**2/7 - 2*m + 10. Solve f(n) = 0.
-1, -1/4, 1
Factor 8*j**3 + 4*j**2 + 4*j**3 - 16*j**3 + 2*j**5 - 4*j**4 + 2*j**5.
4*j**2*(j - 1)**2*(j + 1)
Let p(r) = r**4 + r**2 - r - 1. Let y(u) = u**4 + 20*u**3 - 19*u**2 + 4*u - 6. Let x(a) = -6*p(a) + y(a). Factor x(o).
-5*o*(o - 2)*(o - 1)**2
Let l = 22 - 6. Let f be l + -10 + 1 + -5. Factor 0 - n**4 + 3/2*n**3 - n**f + 1/4*n**5 + 1/4*n.
n*(