(a).
4*(a + 1)**2*(a + 5)/5
What is o in -3*o**2 - 3*o**2 - 4 + 16 + 0*o**2 - 21*o = 0?
-4, 1/2
Suppose 0 = -h + 4*h + 4*h. Let f(i) be the first derivative of 2/45*i**5 - 2/27*i**3 + 0*i + 4 + 0*i**4 + h*i**2. Factor f(x).
2*x**2*(x - 1)*(x + 1)/9
Let s = 41/2 - 20. Let z(k) be the first derivative of -s*k**2 - 2/3*k - 1 - 1/9*k**3. Determine r, given that z(r) = 0.
-2, -1
Let b(q) be the second derivative of q**4/4 + 9*q**3/2 - 32*q. Find j, given that b(j) = 0.
-9, 0
Let o(z) be the second derivative of -z**7/2940 - z**6/420 + z**4/21 - z**3/6 + z. Let d(p) be the second derivative of o(p). Determine y, given that d(y) = 0.
-2, 1
Let l(v) = v + 1. Let g(i) = -5*i**2 - 7*i - 2. Let o(t) = g(t) + 2*l(t). Factor o(r).
-5*r*(r + 1)
Let s(a) = -a**2 + 6*a - 3. Let f be s(5). Let b(w) be the first derivative of 0*w**f + 0*w - 1/6*w**3 - 2 + 1/8*w**4. Solve b(l) = 0.
0, 1
Let l(c) be the third derivative of c**7/3780 + c**6/810 + c**5/540 - c**3/2 - c**2. Let b(y) be the first derivative of l(y). Solve b(r) = 0.
-1, 0
Let d(i) = -i**2 + 1 + 0*i + 5*i + 3*i**4 + 2*i**3 - 5 - 5*i**4. Let y(v) = v**4 - v**3 - 2*v + 2. Let p(r) = -6*d(r) - 14*y(r). Suppose p(n) = 0. What is n?
-1, 1, 2
Let n(b) = b**4 + b**3 - b**2 + b + 1. Let v(o) = -7*o**4 + 13*o**3 - 17*o**2 + 5*o - 3. Let m(j) = 3*n(j) + v(j). Determine l, given that m(l) = 0.
0, 1, 2
Let l(w) be the third derivative of w**6/140 - w**5/140 + 14*w**2. Factor l(n).
3*n**2*(2*n - 1)/7
Factor -4/13 - 10/13*o - 4/13*o**2.
-2*(o + 2)*(2*o + 1)/13
Let k be (-16)/6*(-3)/2. Let h = k - 2. Factor -4*d + 2*d - 2*d**2 - 2*d**h + 6*d**2.
2*d*(d - 1)
Let o(u) be the third derivative of 5*u**2 + 0*u**4 + 0*u**3 + 1/15*u**6 + 0*u + 1/42*u**7 + 0 + 1/15*u**5 + 1/336*u**8. Find y, given that o(y) = 0.
-2, -1, 0
Let g(q) be the first derivative of -q**3 - 21*q**2/2 + 24*q - 16. Factor g(l).
-3*(l - 1)*(l + 8)
Let d = 1169 - 15185/13. Let u = d - 58/91. Let -2/7*o**2 + 4/7*o - u = 0. Calculate o.
1
Let r be (-414)/2 + (-6)/6. Let s = r - -1874/9. Determine u so that -4/9 - s*u**2 - 2/3*u = 0.
-2, -1
Let u(j) be the third derivative of 0*j + 0 - 1/6*j**4 - 1/3*j**3 - 1/30*j**5 + 3*j**2. Find z such that u(z) = 0.
-1
Let u = -127 - -128. Let j(q) be the first derivative of 2*q - u - 2*q**2 + 2/3*q**3. Factor j(m).
2*(m - 1)**2
Let h(o) be the second derivative of -25*o**7/21 + 71*o**6/36 - o**5/12 - 55*o**4/72 + 5*o**3/18 - 3*o. Let h(a) = 0. Calculate a.
-2/5, 0, 1/4, 1/3, 1
Let k(s) be the second derivative of -s**7/15 + s**6/5 - s**5/10 - s**4/6 - s**2/2 - 3*s. Let m(c) be the first derivative of k(c). Let m(z) = 0. What is z?
-2/7, 0, 1
Let o(a) = -a + 12. Let w be o(12). Let l(u) be the second derivative of 1/100*u**5 + 0 + w*u**4 - 1/30*u**3 + 0*u**2 + 3*u. Find r such that l(r) = 0.
-1, 0, 1
Let w(q) be the third derivative of 1/60*q**5 + 1/360*q**6 + 0*q - 2*q**2 + 1/24*q**4 + 1/18*q**3 + 0. Let w(n) = 0. Calculate n.
-1
Determine f so that 8*f + 3*f**2 - 7*f + 6 + 8*f = 0.
-2, -1
Let x(a) be the third derivative of 7*a**7/6 - 7*a**6/6 - 15*a**5/4 + 35*a**4/6 - 10*a**3/3 - 2*a**2. Factor x(k).
5*(k - 1)*(k + 1)*(7*k - 2)**2
Let s(d) be the third derivative of 0*d + 0 + 0*d**3 + 0*d**4 + 0*d**6 + 3*d**2 + 0*d**5 - 1/672*d**8 + 1/420*d**7. Suppose s(f) = 0. Calculate f.
0, 1
Let h(u) be the second derivative of -u**5/5 + 4*u**4/3 - 10*u**3/3 + 4*u**2 - 6*u. Suppose h(g) = 0. What is g?
1, 2
Factor -15*a**4 - 367*a + 50*a**3 - 15*a**2 + 377*a - 30*a**2.
-5*a*(a - 2)*(a - 1)*(3*a - 1)
Let k be -6*((-14)/(-4) + -3). Let d = 6 + k. Determine p so that -9/2*p**4 - 18*p**2 + 15*p**d + 9*p - 3/2 = 0.
1/3, 1
Let i = -4652/13 + 358. Solve -i*v**3 + 16/13 - 4/13*v**2 + 8/13*v = 0.
-2, 2
Suppose 0 = t + 2*a - 22, 2*t = 7*t - 4*a - 40. Suppose -4*q + t = -q. Determine z so that -2/5*z**q + 0 + 2/5*z**3 + 0*z + 0*z**2 = 0.
0, 1
Suppose 0*i - 6/5*i**2 - 2/5*i**3 + 0 = 0. What is i?
-3, 0
Let a(y) be the third derivative of -y**6/60 - y**5/30 + y**4/3 + 4*y**3/3 + 13*y**2. Factor a(o).
-2*(o - 2)*(o + 1)*(o + 2)
Suppose -f - 8 = 3*f. Let p be (1/(-6))/(f/16). Let 0 - 4/3*m**4 + 2/3*m**5 + p*m**2 + 0*m**3 - 2/3*m = 0. What is m?
-1, 0, 1
Let k(h) be the second derivative of 0*h**5 + 0*h**3 - 1/7*h**2 + 0 + 1/21*h**4 - 4*h - 1/105*h**6. Suppose k(t) = 0. Calculate t.
-1, 1
Let 3*l**3 + 1345*l - 1345*l - 18*l**2 = 0. Calculate l.
0, 6
Let m = -283/6 - -48. Let q(y) be the first derivative of -7/8*y**4 + 0*y + 1/2*y**2 + m*y**3 + 4. Determine f so that q(f) = 0.
-2/7, 0, 1
Let v(k) be the third derivative of 0*k**3 + 0*k - 1/6*k**4 + 2/105*k**7 + 1/30*k**6 - 1/15*k**5 + k**2 + 0. Find g, given that v(g) = 0.
-1, 0, 1
Let c(u) be the third derivative of u**8/840 - u**7/175 + 2*u**5/75 - 26*u**2. What is x in c(x) = 0?
-1, 0, 2
Let a(p) be the third derivative of 0 + 0*p**4 + 1/6*p**3 + 0*p - 4*p**2 - 1/60*p**5. Factor a(d).
-(d - 1)*(d + 1)
Suppose -6*x**4 + 6*x**2 + 12*x**5 - 19*x**5 + 10*x**5 - 3*x**3 = 0. What is x?
-1, 0, 1, 2
Suppose 16 = -4*r - 0*r. Let o be (r + 1)/(-16 + 11). Factor -12/5 + 12/5*c - o*c**2.
-3*(c - 2)**2/5
Let u(l) = -l - 5. Let x be u(-7). Suppose 2*r + 2*f = -x, -2*r + 13 = -0*r - 3*f. Solve -j + j - 2*j**r = 0 for j.
0
Solve -10/11*t + 2/11*t**2 + 0 = 0.
0, 5
Suppose 2*z + 2*z = -3*u - 20, 4*z + 20 = -u. Factor 2*i - 2*i**2 - 4*i**3 + 2*i**5 + u*i**5 - 2*i**4 + 0 + 6*i**2 - 2.
2*(i - 1)**3*(i + 1)**2
Let g = -6 - -4. Let x be 2/2 - (g - 0). Suppose 2*i**3 + i**5 - 2*i**x - i**3 = 0. Calculate i.
-1, 0, 1
Let x(n) be the first derivative of n**5/50 + n**4/5 + 3*n**3/5 + 3*n + 5. Let u(k) be the first derivative of x(k). Factor u(a).
2*a*(a + 3)**2/5
Let f be (12/10)/(12/(-30)). Let c be (-2)/(-6) + f/(-9). Suppose 2/3*m**2 - 2/3 + 2/3*m - c*m**3 = 0. What is m?
-1, 1
Factor -o**2 + 8*o - 4*o**3 - o + o**4 - 6*o + 3*o**3.
o*(o - 1)**2*(o + 1)
Let o(f) = -f**2 + 13*f - 5. Let c(q) = q**2 - 19*q + 7. Let m be 2/((-4)/(-7))*-2. Let k(a) = m*o(a) - 5*c(a). Factor k(u).
2*u*(u + 2)
Let l = -24 - -35. Find b, given that -l*b**2 - 6*b**4 - 5*b**2 - 9*b + 0 - 4 - 14*b**3 + 2 - b**5 = 0.
-2, -1
Suppose 0 = 2*j - f - 3*f - 30, 5*f + 5 = -4*j. Suppose 0*y + 4*y**j - 11*y**3 - 5*y**4 + 7*y**2 + 5*y**5 - 2*y**4 + 2*y = 0. Calculate y.
-1, -2/9, 0, 1
Let m = 9 + -3. Factor 2*g + 4*g + 3*g - m + 15*g**2.
3*(g + 1)*(5*g - 2)
Let f(d) be the second derivative of d**8/5040 - d**6/1080 + 2*d**3/3 - 4*d. Let x(c) be the second derivative of f(c). Factor x(y).
y**2*(y - 1)*(y + 1)/3
Let q(r) be the second derivative of 3*r**5/80 + r**4/4 + r**3/2 - 15*r. Factor q(m).
3*m*(m + 2)**2/4
Suppose -4*l = -2*j - l + 5, -5*j = 3*l - 23. Let f be (2 + -3)/((-6)/j). Factor -2/3*w**3 + 0 - f*w - 4/3*w**2.
-2*w*(w + 1)**2/3
Let j(c) = c**2 - 1. Let g(x) = -3*x**2 + 2. Let m(t) = -2*g(t) - 4*j(t). Let m(b) = 0. Calculate b.
0
Let s be 1/2*(1 + -1). Suppose -3*m + s*r = -5*r - 6, -2*r + 4 = 2*m. Let -t + 2*t + 3*t**2 + 4*t**2 - 3*t**m = 0. What is t?
-1/4, 0
Determine d, given that 12/5 + 2/5*d**3 - 9/5*d**2 - 4*d = 0.
-2, 1/2, 6
Let x(h) be the second derivative of -h**5/30 + 5*h**4/18 - 7*h**3/9 + h**2 - 5*h. Determine d, given that x(d) = 0.
1, 3
Suppose 102 = 5*u + u. Suppose -2*k - 4*t + 2 = -12, -t + u = 5*k. Find v such that -v - 1/4*v**k + 0 - v**2 = 0.
-2, 0
Let v(g) be the first derivative of -3*g**4/4 - 8*g**3 - 24*g**2 + 62. Determine s, given that v(s) = 0.
-4, 0
Suppose 0 = 7*n - 3*n + 56. Let f = n - -18. Factor 0*g**2 + 0 + 0*g**3 + 2/9*g**f + 0*g.
2*g**4/9
Let 0*i + 0 - 2/3*i**4 - 10/3*i**2 - 4*i**3 = 0. What is i?
-5, -1, 0
Let h(d) be the first derivative of d**5/90 - d**4/108 - 3*d**2/2 - 1. Let y(z) be the second derivative of h(z). Determine j, given that y(j) = 0.
0, 1/3
Let l = -17 + 95. Let n be 64/l - 6/39. Factor -7/3*q**2 + n*q + 0.
-q*(7*q - 2)/3
Suppose 0 = -4*s + s + 5*y + 34, 3*s + y = 22. Determine x, given that -x**3 + 0*x - s*x**4 - 8*x**2 - 11*x**3 - 2*x - 2*x**5 = 0.
-1, 0
Let w = 218/165 + -4/33. Factor -w*c - 2/5 - 2/5*c**3 - 6/5*c**2.
-2*(c + 1)**3/5
Let s be -3 + 57/21 - (-11)/14. Factor -s*t**3 + 0 + t - 1/2*t**2.
-t*(t - 1)*(t + 2)/2
Let r(d) = 3*d**2 - d. Let q be r(1). Suppose 2*o + 3*o - 2*x - 23 = 0, q*o - 9 = x. Suppose 4*k**o - k**3 - 2*k**3 - 5*k**4 + 4*k**3 = 0. What is k?
0, 1/4, 1
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