2. Let a(m) = -m**2 + 6*m + 2. Suppose 3*f + 40 = -2*f. Let j = f - -13. Let y(h) = j*c(h) + 6*a(h). Suppose y(x) = 0. What is x?
-1, 2
Let 4/13*v**5 - 2/13*v**3 - 2/13*v**4 + 0 + 0*v**2 + 0*v = 0. Calculate v.
-1/2, 0, 1
Let c(w) be the third derivative of w**8/168 + w**7/105 - w**6/20 - w**5/30 + w**4/6 + w**2 + 4. Factor c(i).
2*i*(i - 1)**2*(i + 1)*(i + 2)
Let t(g) be the second derivative of -g**4/42 + 2*g**3/21 - g**2/7 - 3*g. Factor t(f).
-2*(f - 1)**2/7
Let n = 14/11 + -17/22. Factor l**2 + n*l + 0 + 1/2*l**3.
l*(l + 1)**2/2
Let s(n) be the third derivative of 7*n**6/160 + n**5/16 - n**4/16 + 17*n**2. Solve s(d) = 0.
-1, 0, 2/7
Suppose 5*m = 4*t + 1 + 15, 0 = 5*m + 2*t - 22. Determine j so that 3*j**m - 10*j**4 - 6*j**2 + 9*j**3 + 4*j**4 = 0.
0, 1, 2
Let t be 8/(((-28)/(-6))/7). Let o be (3/12)/(1/t). Suppose 1/3*r**4 + 0 + 0*r + 2/3*r**o + 1/3*r**2 = 0. What is r?
-1, 0
Factor 4/7*z - 2/7*z**3 + 0 - 2/7*z**2.
-2*z*(z - 1)*(z + 2)/7
Let a(k) = 4*k**3 - 4*k - 5. Let p(b) = -3*b**3 + 3*b + 5. Let f(w) = 2*a(w) + 3*p(w). Let i be f(0). Factor i*l - l**3 + 3*l**3 + 3*l + 8*l**2.
2*l*(l + 2)**2
Let a(c) be the third derivative of -c**8/112 - c**7/70 + 14*c**2. Find d, given that a(d) = 0.
-1, 0
Let v(x) = x**4 - x**3 - x**2 - 1. Let z(f) = -2*f**4 + 14*f**3 - 22*f**2 + 15*f + 5. Let n(g) = 5*v(g) + z(g). Factor n(k).
3*k*(k - 1)**2*(k + 5)
Factor -1/2 + 1/2*r**2 - 1/4*r + 1/4*r**3.
(r - 1)*(r + 1)*(r + 2)/4
Let g(u) = -u**3 - 2*u + 9. Let l be g(0). Factor -10*v - 3*v**2 + 4*v + 2 + l*v**2 - 2*v**3.
-2*(v - 1)**3
Suppose 9*x - 13*x + 8 = 0. Let d(s) be the first derivative of -2/25*s**5 + 0*s**x + 0*s**4 + 0*s + 2/15*s**3 + 1. Let d(w) = 0. What is w?
-1, 0, 1
Let t(m) = -4*m**3 + 4*m**2 - 4*m. Let k(j) = 3*j**3 - 3*j**2 + 4*j. Let a(q) = -6*k(q) - 5*t(q). Suppose a(f) = 0. Calculate f.
-1, 0, 2
Let z be 7/2 - (-5)/(-10). Factor -4*w**z - 6*w - 6*w**3 + 2*w**3 + 21*w**2 - 4*w**3 - 3.
-3*(w - 1)**2*(4*w + 1)
Let i(j) be the first derivative of 0*j**2 + 2*j + 1/20*j**4 + 1/5*j**3 - 3. Let s(p) be the first derivative of i(p). Let s(k) = 0. Calculate k.
-2, 0
Let n(o) be the first derivative of 1/2*o**3 - 3/2*o**2 - 9 + 2*o - 1/16*o**4. Determine x, given that n(x) = 0.
2
Let y(c) be the third derivative of c**7/840 - c**6/120 + c**5/60 + 2*c**2 + 9*c. Let y(x) = 0. Calculate x.
0, 2
Suppose 2 = a - 3*g, 10 = -a + 6*a + g. Solve 1/3*t + 0 + 7/6*t**a = 0 for t.
-2/7, 0
Let o be (-3)/(-6)*-2 + -3. Let x(d) = -2*d**3 + d**2 + 2*d + 5. Let a(g) = -3*g**3 + g + 6. Let p(t) = o*x(t) + 3*a(t). Solve p(m) = 0 for m.
-2, -1
Let z(o) be the second derivative of 0*o**2 - 1/12*o**4 - o - 1/6*o**3 + 0. Factor z(l).
-l*(l + 1)
Let y(k) be the third derivative of -7*k**5/270 + k**4/54 + k**2. Factor y(u).
-2*u*(7*u - 2)/9
Let v(f) be the second derivative of -f**5/16 - 5*f**4/24 - 5*f**3/24 - 24*f. Factor v(a).
-5*a*(a + 1)**2/4
Let u(p) be the second derivative of -1/2*p**4 - 1/2*p**3 - 3*p + 3/2*p**2 + 0. Factor u(q).
-3*(q + 1)*(2*q - 1)
Let p(d) be the second derivative of d**6/1980 - d**5/220 + d**4/66 - 2*d**3/3 - 4*d. Let x(a) be the second derivative of p(a). Factor x(t).
2*(t - 2)*(t - 1)/11
Let o(r) be the first derivative of 0*r**4 - 1/3*r**3 + 0*r**2 - 5 + 0*r + 1/5*r**5. Determine a, given that o(a) = 0.
-1, 0, 1
Let h(t) be the first derivative of -6*t**5/5 - 11*t**4/2 - 4*t**3 + 12*t**2 + 16*t - 4. Let h(c) = 0. Calculate c.
-2, -2/3, 1
Let l(t) = -t**3 - 4*t**2 - 3*t. Let m(o) = 2*o**3 + 4*o**2 + 4*o. Suppose 0*g + i = 5*g + 26, -i = 4*g + 19. Let u(p) = g*l(p) - 4*m(p). Factor u(d).
-d*(d - 1)*(3*d - 1)
Let y = 37/110 - 3/22. Let t(v) be the second derivative of y*v**2 + 0 - v + 1/15*v**3 - 1/50*v**5 - 1/30*v**4. Factor t(x).
-2*(x - 1)*(x + 1)**2/5
Let n = -2468 - -7324/3. Let v = n - -27. Factor -v - c**2 + 1/3*c**3 + c.
(c - 1)**3/3
Let a(n) be the third derivative of -n**8/672 + n**7/84 - n**6/30 + n**5/30 + 5*n**2. Let a(c) = 0. What is c?
0, 1, 2
Let i = -77/6 - -13. Let u(k) be the second derivative of -2*k**2 + 2*k + 0 - i*k**4 - k**3. Factor u(v).
-2*(v + 1)*(v + 2)
Factor 9*x**5 + 54 + 12*x - 22*x**3 + 27*x**2 - 66 + 16*x**3 - 27*x**3 - 3*x**4.
3*(x - 1)**3*(x + 2)*(3*x + 2)
Let l = 3 - 1. Suppose -3*t = 2 + 1. Let k(g) = g**3 + g**2 + g. Let r(s) = 3*s**3 + 3*s**2 + s - 1. Let y(z) = l*k(z) + t*r(z). Factor y(x).
-(x - 1)*(x + 1)**2
Factor 196/3 - 28/3*j + 1/3*j**2.
(j - 14)**2/3
Let f = 12 - 6. Factor 4*s**3 - 15*s + f*s**4 - 10*s**5 + 15*s.
-2*s**3*(s - 1)*(5*s + 2)
Let l(m) = m**3 - m**2 + 3*m - 3. Let z(f) = 2*f**3 - 2*f**2 + 8*f - 8. Let n(w) = -8*l(w) + 3*z(w). Find q, given that n(q) = 0.
0, 1
Let a(d) be the first derivative of 2*d**3/3 - d**2 - 4*d + 39. Determine b, given that a(b) = 0.
-1, 2
Let t(h) = -2*h - 40. Let n be t(-20). Let d(a) = a**2 + 8*a + 9. Let v be d(-7). Factor -8/3 + v*z**2 - 2/3*z**3 + n*z.
-2*(z - 2)**2*(z + 1)/3
Factor -6*i**2 - 3*i**2 + 6*i**2 + 15*i.
-3*i*(i - 5)
Suppose -5*v + 6 + 4 = 0. Suppose v + 10*r**2 + 12*r + 2*r**2 + 2*r**4 + 8*r**3 - 4*r = 0. What is r?
-1
Let y(r) be the third derivative of -r**7/210 + r**5/60 + 9*r**2. Factor y(i).
-i**2*(i - 1)*(i + 1)
Suppose -1 + 1/2*j**2 + 1/2*j = 0. Calculate j.
-2, 1
Factor 1/4*a + 0*a**2 + 0 - 1/4*a**3.
-a*(a - 1)*(a + 1)/4
Let f(a) = a**3 - 4*a**2 + a + 1. Let o be f(2). Let x be (4 - 1) + 13/o. Factor 0 - x*c**2 - 2/5*c.
-2*c*(c + 1)/5
Let b(w) = 3*w**2 - w - 1. Let a be b(2). Suppose 3*s = -j + a, s = 5*s + j - 11. Factor 2/7*g**s + 18/7 - 12/7*g.
2*(g - 3)**2/7
Let w(n) be the third derivative of n**5/510 + n**4/102 - 51*n**2. Factor w(x).
2*x*(x + 2)/17
Let z = 4 - 0. Suppose -z*b + 4 + 4 = 0. Factor -2*v**3 + 1 + v**3 + 3*v**b + v - 4*v**2.
-(v - 1)*(v + 1)**2
Let n be 176/32 + (-1)/2. Suppose -2*j + j - 2 = d, 6 = n*j - 3*d. Let 0*v - 2*v**2 + 3/2*v**4 + j - 9/2*v**5 + 4*v**3 = 0. What is v?
-1, 0, 2/3
Suppose 2*g - 5 = -3*g - s, 3*g - 1 = -s. Let c(b) be the first derivative of 0*b + 1 + 1/12*b**3 + 1/8*b**g. Factor c(x).
x*(x + 1)/4
Let m(x) = -x. Let n be m(-9). Let l be 2/n - 5/(-18). Suppose 1/2*s**5 + 0*s + 0 - l*s**2 + 3/2*s**3 - 3/2*s**4 = 0. What is s?
0, 1
Let g(c) = c**2 - c + 4. Let f(n) = -2*n**2 + n - 7. Let s = 4 + -7. Let i(z) = s*f(z) - 5*g(z). Factor i(j).
(j + 1)**2
Let w(x) be the third derivative of 0 + 0*x - 1/24*x**4 - 3*x**2 + 1/24*x**3 - 1/240*x**5 + 1/120*x**6. Find p, given that w(p) = 0.
-1, 1/4, 1
Let d(k) = k - 4. Let p be d(4). Let y be 36/20 + 2/10. Determine t, given that 2*t**y + 3*t**3 - t**2 - 2*t**3 + p*t**3 = 0.
-1, 0
Let t(q) be the third derivative of q**9/5040 - q**8/1120 - q**7/840 + q**6/120 - q**4/12 - 3*q**2. Let i(j) be the second derivative of t(j). Factor i(g).
3*g*(g - 2)*(g - 1)*(g + 1)
Let c be ((-44)/16)/((-1)/8). Let x(z) = 2*z**2 + z - 3. Let j(g) = -7*g**2 - 3*g + 11. Let u(f) = c*x(f) + 6*j(f). Factor u(w).
2*w*(w + 2)
Suppose 15 = 7*s - 2*s + g, 0 = 5*g. Let 0 + 0*y**2 + 4/11*y**s + 0*y - 2/11*y**4 = 0. Calculate y.
0, 2
Let x(o) = 8*o + 59. Let n be x(-7). Factor -1/2 - 3/4*f**n - 23/4*f**2 - 13/4*f + 9/4*f**4.
(f - 2)*(f + 1)*(3*f + 1)**2/4
Let c be -82*1/30 + 3. Let g(s) be the first derivative of -2 - 1/10*s**4 - 1/5*s**2 + 0*s + c*s**3. Let g(k) = 0. What is k?
0, 1
Let f(h) be the second derivative of -h**6/210 + h**4/42 - 5*h**2 - 3*h. Let y(v) be the first derivative of f(v). Factor y(k).
-4*k*(k - 1)*(k + 1)/7
Let p be 1*(-178)/(-110) - (-14)/77. Factor 0*k - p*k**3 + 3/5*k**2 - 3/5*k**5 + 9/5*k**4 + 0.
-3*k**2*(k - 1)**3/5
Let v be -4 - (0 + -1 - -2). Let f = 8 + v. Suppose 2/3*c**2 + 0*c + 0 + 2/3*c**f = 0. What is c?
-1, 0
Let g(v) be the second derivative of -1/20*v**5 - v + 1/6*v**4 - 1/6*v**3 + 0*v**2 + 0. Factor g(x).
-x*(x - 1)**2
Let x(u) be the third derivative of u**9/52920 - u**7/4410 + u**5/420 + u**4/12 - u**2. Let g(n) be the second derivative of x(n). Factor g(v).
2*(v - 1)**2*(v + 1)**2/7
Let w = 5 - 3. Suppose -4 = -w*d - 0*d. Factor -4/5*n - 2/5*n**d - 2/5.
-2*(n + 1)**2/5
Let i(b) be the first derivative of b**6/27 + 2*b**5/45 - 5*b**4/18 + 2*b**3/9 - 7. Factor i(n).
2*n**2*(n - 1)**2*(n + 3)/9
Let v(a) = a**3 + 2*a**2 - 4*a + 2. Let x be v(2). Suppose 0 = 6*q - q - x. Factor -o**2 + o**2 - 2*o**2 + q*o.
-2*o*(o - 1)
Let z = 9 + -12. Let w be -4*3/