*3.
-2*(n + 2)**2*(n + 3)/5
Let k = -7 - -9. Solve 5*q**3 - 4*q**k - 5*q**2 - 2*q**3 + 6*q = 0 for q.
0, 1, 2
Let h be (1*9)/(78/104). Let y be (h/8 + -3)*-2. Factor 1/5*m**y + 0*m**2 + 0 + 1/5*m**4 + 0*m.
m**3*(m + 1)/5
Let v(j) be the third derivative of -j**6/8 - 11*j**5/20 - 7*j**4/8 - j**3/2 - 6*j**2. Factor v(w).
-3*(w + 1)**2*(5*w + 1)
Let g(m) be the third derivative of -m**5/270 - m**4/108 + 2*m**3/27 - 2*m**2. Find h such that g(h) = 0.
-2, 1
Let c(l) be the first derivative of l**6/45 + 6*l**5/25 + 4*l**4/5 + 32*l**3/45 + 32. Factor c(i).
2*i**2*(i + 1)*(i + 4)**2/15
Let j(x) be the third derivative of x**9/1512 - x**8/420 + x**6/90 - x**5/60 - x**3/6 - 4*x**2. Let t(u) be the first derivative of j(u). Factor t(m).
2*m*(m - 1)**3*(m + 1)
Let x be 82/(-55) - (-6)/4. Let s(a) be the second derivative of -a + 1/66*a**4 + x*a**5 - 1/33*a**3 + 0 - 1/11*a**2. Solve s(t) = 0.
-1, 1
Let y(z) be the second derivative of -z**7/210 - z**6/60 - z**5/60 - z**2 - z. Let g(i) be the first derivative of y(i). Factor g(n).
-n**2*(n + 1)**2
Let t = 171/2 + -85. Solve z + t*z**3 - 3/2*z**2 + 0 = 0 for z.
0, 1, 2
Let d = -21 + 12. Let u be (d/5)/((-6)/10). Let 1/4*p**u - p**2 + p + 0 = 0. Calculate p.
0, 2
Let 6*m + m**2 + 3*m**4 + 156*m**3 - 165*m**3 + 3*m**5 - 4*m**2 = 0. What is m?
-2, -1, 0, 1
Let y(i) be the second derivative of -i**5/10 - i**4/2 - 40*i. Factor y(h).
-2*h**2*(h + 3)
Suppose 17 + 18 = 5*k - 5*q, -5*k - 4*q - 1 = 0. Let f(v) be the first derivative of -2*v**2 + 2/3*v**k - 1 + 0*v. Let f(b) = 0. What is b?
0, 2
Let m(n) = 3*n**2 + 19*n + 19. Let y(j) = -j**2 - 6*j - 6. Let t = 4 - 2. Suppose -t*x - 4 = 10. Let s(p) = x*y(p) - 2*m(p). Suppose s(q) = 0. Calculate q.
-2
Let g(h) = -35*h**3 - 24*h**2 + 9*h - 1. Let f(z) = -z**2 + z + 1. Let j(t) = f(t) + g(t). Suppose j(m) = 0. What is m?
-1, 0, 2/7
Let d(t) = t**2 + 6*t - 1. Let s be d(-7). Factor y**5 + s*y**4 + 0*y**5 + y**5 - 4*y**4.
2*y**4*(y + 1)
Suppose 46*x = 41*x. Let u(k) be the second derivative of 0 + 2*k - 1/90*k**5 - 1/54*k**4 + 1/135*k**6 + x*k**3 + 1/189*k**7 + 0*k**2. Factor u(o).
2*o**2*(o - 1)*(o + 1)**2/9
Let o = 1/262 + 196/131. Factor o + 3/2*z**3 - 3/2*z - 3/2*z**2.
3*(z - 1)**2*(z + 1)/2
Let s be 12/5 - (-4)/(-10). Suppose 7*q = 5*g + 2*q, -5*g - s*q + 14 = 0. Factor -2*o**3 - o + o - 4*o**g - 2*o.
-2*o*(o + 1)**2
Let h be (-2)/1 + 3 + 3. Find g such that -4/7*g**3 + 0*g**2 + 2/7 + 4/7*g - 2/7*g**h = 0.
-1, 1
Let c = -3 + 6. Suppose c*n = 4 + 2. Factor q + q**n + 5 - 5.
q*(q + 1)
Let a(q) be the second derivative of q**4/4 - q**3/2 + q. Factor a(i).
3*i*(i - 1)
Determine n so that 0 + 7/4*n**2 + 1/2*n = 0.
-2/7, 0
Let x be ((-7)/70)/(2 - 4). Let o(w) be the first derivative of 1/4*w**2 - 1/8*w**4 + 0*w**3 + x*w**5 - 2 - 1/4*w. Determine m so that o(m) = 0.
-1, 1
Let l be (42/49)/((-4)/(-14)). Factor j**2 + 4*j**2 - 2*j**2 - 3*j**l.
-3*j**2*(j - 1)
Let u(i) = 0*i**2 - 11 + 6*i + 7*i + i**2 - 3*i**2. Let g(m) = -m**2 + 6*m - 5. Let l(o) = 9*g(o) - 4*u(o). Solve l(v) = 0.
1
Let k = 9 - 6. Find i such that -2 + 1 + 2*i**k - 3*i**2 + 3*i + 0 - i**3 = 0.
1
Let n(d) = 8*d**2 - 24*d + 5. Let a(g) = -44*g**2 + 132*g - 28. Let u(r) = -5*a(r) - 28*n(r). Determine j so that u(j) = 0.
0, 3
Let w(j) be the second derivative of -j**7/2520 + j**6/720 + 3*j**4/4 - 7*j. Let l(d) be the third derivative of w(d). Factor l(f).
-f*(f - 1)
Suppose 0*i + i - 2 = 0. Factor -1 + 4*r + 0*r + 2*r**2 - 2*r**3 - i*r + r**5 - r - r**4.
(r - 1)**3*(r + 1)**2
Let o(t) be the first derivative of -4 + 0*t**3 + 0*t - 4/5*t**5 - 3/2*t**4 + t**2. Factor o(s).
-2*s*(s + 1)**2*(2*s - 1)
Let n(y) be the first derivative of -1 + 2/5*y**5 - 4/3*y**3 + 0*y**2 + 2*y + 0*y**4. Suppose n(l) = 0. What is l?
-1, 1
Let t be 13/14 + 8/14. Suppose 3*x**3 - 3*x + 0*x**2 - t*x**4 + 3/2 = 0. What is x?
-1, 1
Factor 14/9*b + 2/3*b**2 + 4/9.
2*(b + 2)*(3*b + 1)/9
Factor -1/6*f + 1/3*f**3 + 0*f**2 + 0*f**4 + 0 - 1/6*f**5.
-f*(f - 1)**2*(f + 1)**2/6
What is w in -11 - 8 + 1 + 15*w**5 - 48*w**2 + 54*w**3 + 66*w**4 - 69*w = 0?
-3, -1, -2/5, 1
Let w(d) = d + 7. Let i be w(-2). Factor 0*o**3 + 0*o + 1/2*o**i + 0*o**2 + 0 + 1/2*o**4.
o**4*(o + 1)/2
Factor -8/3 - 8/3*l - 2/3*l**2.
-2*(l + 2)**2/3
Let x(k) be the first derivative of -k**5/40 - k**4/8 - k**3/4 - k**2/4 - 2*k + 2. Let z(g) be the first derivative of x(g). What is p in z(p) = 0?
-1
Let r(k) be the third derivative of -k**8/196 + k**7/735 + k**6/84 - k**5/105 + 3*k**2. Find m such that r(m) = 0.
-1, 0, 1/2, 2/3
Let j(z) = 11*z**4 - 6*z**3 - 35*z**2 + 36*z - 6. Let p(n) = -45*n**4 + 25*n**3 + 140*n**2 - 145*n + 25. Let b(y) = -25*j(y) - 6*p(y). Factor b(q).
-5*q*(q - 2)*(q - 1)*(q + 3)
Let p = 40 + -38. Factor 0*h - 1/2*h**p + 0.
-h**2/2
Let b(k) = -3 + 0 - 11*k - 4*k**2 - 2 + 9. Let u(l) = -2*l**2 - 6*l + 2. Let x(s) = -6*b(s) + 11*u(s). Determine j, given that x(j) = 0.
-1, 1
Let t(b) = b**2 + 9*b + 12. Let g be ((-8)/(-10))/2*-20. Let f be t(g). Factor -i - 5/4*i**3 - 4*i**2 + 25/4*i**f + 0.
i*(i - 1)*(5*i + 2)**2/4
Let b(d) be the second derivative of d**7/210 + d**6/150 - d**5/100 - d**4/60 - 3*d. Factor b(a).
a**2*(a - 1)*(a + 1)**2/5
Let s be (3*6/(-63))/((-3)/7). Factor s*n**4 - 6 + 4*n**3 - 4*n + 16/3*n**2.
2*(n - 1)*(n + 1)*(n + 3)**2/3
Let q = 5/12 - 11/84. Factor q - 2/7*m**2 + 2/7*m - 2/7*m**3.
-2*(m - 1)*(m + 1)**2/7
Let p(l) = -2*l - 6. Suppose -3*s - 24 = -s - 4*q, -2*s - 20 = -3*q. Let x be p(s). Factor 5*t**2 - x*t - 3*t**2 + t**3 + 0*t + 3*t.
t*(t + 1)**2
Determine g so that 0 + 16/3*g**2 + 2/3*g**3 + 32/3*g = 0.
-4, 0
Let b(w) be the second derivative of -w**2/2 + 6*w. Let l(c) = -c**3 + c + 2. Let u(g) = 6*b(g) + 3*l(g). Factor u(f).
-3*f*(f - 1)*(f + 1)
Let i(r) be the second derivative of -1/14*r**7 + 0*r**2 + 0*r**4 - 1/5*r**6 - 3/20*r**5 + 0*r**3 - 5*r + 0. Determine a, given that i(a) = 0.
-1, 0
Let y be (0 + 8)*(-1)/2. Let g = 6 + y. Factor -2*q**3 - 2*q**2 + g*q**2 + 2*q**5.
2*q**3*(q - 1)*(q + 1)
Let x(a) be the first derivative of a**5/25 - a**4/10 + a**3/15 - 8. Suppose x(g) = 0. What is g?
0, 1
Let p(o) be the first derivative of 5*o**4/2 - 8*o**3 + 4*o**2 - 10. Factor p(u).
2*u*(u - 2)*(5*u - 2)
Let p(y) be the second derivative of y**5/60 + y**4/12 - 2*y**3/9 - 26*y. Factor p(r).
r*(r - 1)*(r + 4)/3
Let t be 2 + (0 - (-1 - -2)) + 1. Solve 1/4*k + 0 + 1/4*k**t = 0.
-1, 0
Let p be (-12)/(-208)*-1*-16. Factor -18/13 - 2/13*f**2 + p*f.
-2*(f - 3)**2/13
Let n(z) be the first derivative of z**6/60 + z**5/25 + z**4/40 - 2. Solve n(h) = 0.
-1, 0
Let o = 49 + -47. Factor -2/9*q**o - 2/9*q + 0.
-2*q*(q + 1)/9
Let c(x) be the first derivative of x**3/27 - 11*x**2/9 + 121*x/9 + 54. Determine j, given that c(j) = 0.
11
Let w be ((-12)/10)/(4/20). Let a = -4 - w. Factor 1/2*r**a - 3/2*r**3 + 0 + r.
-r*(r - 1)*(3*r + 2)/2
Let i = 66 + -989/15. Let z(w) be the third derivative of 3*w**2 + 0*w**6 + 1/12*w**4 + 2/105*w**7 - 1/168*w**8 - i*w**5 + 0*w + 0*w**3 + 0. Factor z(r).
-2*r*(r - 1)**3*(r + 1)
Let c(g) be the second derivative of g**9/45360 - g**8/20160 - 5*g**4/12 - g. Let l(z) be the third derivative of c(z). Factor l(b).
b**3*(b - 1)/3
Let x be (-2)/4 - 152/(-16). Find y, given that 9*y + 3 - x*y - 3*y**2 = 0.
-1, 1
Let r = 2/379 + 369/1895. Factor 0*x + 1/5*x**5 + 0 + 3/5*x**3 - 3/5*x**4 - r*x**2.
x**2*(x - 1)**3/5
Suppose -4*l + 3 = -3*v, 0*l - 2*l = 3*v - 15. Let h(r) = r**3 - 4*r**2 + 6*r - 5. Let u be h(3). Factor 2/3 + 1/3*w**u + 3*w**2 + 5/3*w**l + 7/3*w.
(w + 1)**3*(w + 2)/3
Let y(s) = -3*s - 9. Let p be y(-4). Suppose 3*x + 0*c = 3*c + p, x - 5*c - 5 = 0. Factor -b**2 + 1/2*b**5 + 0*b**3 + b**4 - 1/2*b + x.
b*(b - 1)*(b + 1)**3/2
Determine r, given that 0 + 1/4*r**3 + 1/2*r**2 - 3/4*r = 0.
-3, 0, 1
Let g(z) be the second derivative of z**4/15 - 4*z**3/15 - 6*z**2/5 - 2*z. Factor g(u).
4*(u - 3)*(u + 1)/5
Let t(r) = -r**3 - r**2 - r. Let s(m) = -4*m**4 - 6*m**3 - 4*m**2 + 4*m + 1. Let a(q) = -s(q) - 5*t(q). Factor a(u).
(u + 1)**3*(4*u - 1)
Factor -2/11*z**3 - 2/11*z**4 + 2/11*z**2 + 2/11*z**5 + 0*z + 0.
2*z**2*(z - 1)**2*(z + 1)/11
Let w be (-4)/(-6)*(-2 - -5). Let q(f) be the first derivative of 1/4*f**4 + 0*f + 1/3*f**3 + 0*f**2 - w. Factor q(r).
r**2*(r + 1)
Suppose o - 4 = y, 0*o + 6 = o - 2*y. Let f(l) be the third derivati