*2
Let k(j) be the second derivative of -5*j**7/42 - 13*j**6/30 + 51*j**5/20 - 43*j**4/12 + 5*j**3/3 + 11*j. Determine u so that k(u) = 0.
-5, 0, 2/5, 1
Let f = 4/19 + 155/76. Factor -f - 1/4*k**2 + 3/2*k.
-(k - 3)**2/4
Factor 3/2*o**2 - 18 + 6*o.
3*(o - 2)*(o + 6)/2
Let x(b) = -5*b**4 + 7*b**3 + 7*b**2 - 7*b + 6. Let k(t) = 5*t**4 - 7*t**3 - 6*t**2 + 7*t - 5. Let f(m) = -4*k(m) - 3*x(m). Factor f(h).
-(h - 1)**2*(h + 1)*(5*h - 2)
Let k(x) be the first derivative of 3*x**5/5 + 6*x**4 + 15*x**3 - 12*x**2 - 48*x + 3. Find r, given that k(r) = 0.
-4, -1, 1
Let b(s) be the first derivative of -2*s**3/5 + 22*s**2/5 - 14*s/5 - 22. Suppose b(f) = 0. Calculate f.
1/3, 7
Let j = -3/11 - -17/22. Let 1/6*u + j*u**2 + 1/2*u**3 + 0 + 1/6*u**4 = 0. Calculate u.
-1, 0
Let q(p) be the second derivative of 16*p**7/399 + 4*p**6/57 - 36*p**5/95 + 37*p**4/114 + 2*p**3/57 - 3*p**2/19 - 24*p. Determine y, given that q(y) = 0.
-3, -1/4, 1/2, 1
Let z = 67 - 401/6. Let j(f) be the first derivative of -3 + 1/6*f**2 + 0*f - z*f**3. Factor j(q).
-q*(3*q - 2)/6
Let j be (-10)/(-4) - (-2)/4. Let a be (2/9)/(2/j). Let 1/3 - 2/3*h + a*h**2 = 0. Calculate h.
1
Let o(p) be the third derivative of p**8/1176 + p**7/735 - p**6/420 - p**5/210 - p**2. Factor o(x).
2*x**2*(x - 1)*(x + 1)**2/7
Let g(c) = -7*c**4 + 4*c**3 - 2*c**2 - 4*c + 3. Let s(h) = -8*h**4 + 4*h**3 - 2*h**2 - 4*h + 3. Let i(a) = -7*g(a) + 6*s(a). Determine j so that i(j) = 0.
-1, 1, 3
Let w(x) = 7*x**5 - 23*x**4 + 11*x**2 + 5*x + 5. Let q(c) = 34*c**4 - 8*c + c - 7 - 11*c**5 - 14*c**2 - 2*c**2. Let u(m) = 5*q(m) + 7*w(m). Factor u(k).
-3*k**2*(k - 1)**2*(2*k + 1)
Let k be (12/18)/((-56)/(-48)). Suppose 0*l - 2/7*l**2 + 0 + 12/7*l**5 + 10/7*l**4 - k*l**3 = 0. Calculate l.
-1, -1/3, 0, 1/2
Let n(t) be the first derivative of -t**7/105 + 2*t**6/75 - t**5/50 + 7*t + 6. Let h(l) be the first derivative of n(l). Determine y so that h(y) = 0.
0, 1
Let d = -15 - -17. Suppose 0 = -d*f + i, -2*f = 3*f + 5*i. Determine c, given that f*c**3 - 2/9*c**2 + 0*c + 2/9*c**4 + 0 = 0.
-1, 0, 1
Let l(x) be the first derivative of -2*x**3/9 + 4*x**2/3 - 8*x/3 + 20. Solve l(w) = 0 for w.
2
Suppose j = 3*j - 6. Factor 17*s**j + 19*s**2 + 3 - 5*s**5 - s - 7 - 3*s**4 + s.
-(s - 2)*(s + 1)**3*(5*s - 2)
Suppose -3*f - 88 = -7*f. Let y = f - 108/5. Factor -6/5*g + y*g**2 + 4/5.
2*(g - 2)*(g - 1)/5
Factor -3*m + 93*m**3 - 90*m**3 + 0*m**4 - 3*m**2 + 3*m**4.
3*m*(m - 1)*(m + 1)**2
Determine d, given that 37*d**2 + 3*d - 2 - 36*d**2 + 4 = 0.
-2, -1
Let f(p) be the first derivative of 2/7*p**3 - 3/7*p**2 - 1/14*p**4 - 4 + 2/7*p. Find w such that f(w) = 0.
1
Let s(v) be the first derivative of v**6/10 - 3*v**5/10 + v**4/4 + 5*v - 9. Let i(j) be the first derivative of s(j). Factor i(a).
3*a**2*(a - 1)**2
Find a, given that 0*a + a - 2*a + 5*a**2 - 4*a**2 = 0.
0, 1
Let b(l) = 11*l**4 - 17*l**3 + 16*l**2 + 2*l + 6. Let k(t) = 12*t**4 - 17*t**3 + 16*t**2 + 3*t + 7. Let q(c) = 7*b(c) - 6*k(c). Factor q(g).
g*(g - 2)*(g - 1)*(5*g - 2)
Let b = -69 - -209/3. Determine x, given that 0 - 2*x**3 - 8/3*x**2 - b*x = 0.
-1, -1/3, 0
Let r(d) = 7*d**4 + 3*d**2. Let a(k) = k**2 - 2*k**4 + k**4 + 2*k**4. Let p(y) = -5*a(y) + r(y). Determine s, given that p(s) = 0.
-1, 0, 1
Let y(o) be the third derivative of o**5/20 + o**4/8 - o**3 - 18*o**2. Factor y(x).
3*(x - 1)*(x + 2)
Let m be -2*(-1)/(-16)*-4. Find c such that -m*c**2 + 0 + 0*c + c**5 - c**3 + 1/2*c**4 = 0.
-1, -1/2, 0, 1
Let h(q) be the first derivative of 7 - 1/2*q**6 - 3/5*q**5 + 0*q**2 + 3/4*q**4 + 0*q + q**3. Let h(m) = 0. What is m?
-1, 0, 1
Let f(q) be the third derivative of -q**5/180 + 5*q**4/36 - 25*q**3/18 + 29*q**2. Determine x, given that f(x) = 0.
5
Let j(b) be the second derivative of 5*b**4/24 + b**3/12 - 23*b. Factor j(d).
d*(5*d + 1)/2
Let p = -14 + 16. Let o(w) be the first derivative of -1/4*w - 1/6*w**3 + 1/8*w**4 + p - 3/8*w**2 + 3/20*w**5 + 1/24*w**6. Let o(c) = 0. Calculate c.
-1, 1
Let h(q) = 5*q**2 + 2*q - 2. Let a be h(1). Suppose -v + a = 4*r, 2*v = -r + v - 1. Determine y, given that -1/4*y**r + 1/4*y + 1/2 = 0.
-1, 2
Let i(r) be the second derivative of r**7/56 + 17*r**6/120 + 33*r**5/80 + 23*r**4/48 - r**2/2 - 7*r. Solve i(u) = 0 for u.
-2, -1, 1/3
Let w = 5 - 2. Solve 1 + 2*d - w*d**5 + 5*d**5 - 4*d**5 - 10*d**2 + 7*d**4 + 2 = 0.
-1, -1/2, 1, 3
Let f = -13 + 14. Suppose -2*n + 4*n**2 + 2*n**5 - 1 + f - 28*n**4 + 24*n**4 = 0. What is n?
-1, 0, 1
Suppose 20/3*i - 1/3*i**2 - 100/3 = 0. Calculate i.
10
Factor -3*h**2 + 4*h**2 + 111 - 105 - 5*h.
(h - 3)*(h - 2)
Let s = -13 + 17. Solve -16*f**2 + 2*f**5 - 3*f**3 + 2*f**5 - 2*f**5 + 27*f**3 - 12*f**s = 0.
0, 2
Suppose z - 3 = -1. Suppose -6 = -z*a - 4*r, -4*r = a - 0*r - 5. Find w such that -w**3 + 1 - a + w = 0.
-1, 0, 1
Find w, given that 32/5*w - 16/5 - 4*w**2 + 4/5*w**3 = 0.
1, 2
Let u = 83/730 + -1/73. Let s(o) be the second derivative of 1/3*o**3 - 1/6*o**4 + o + o**2 - u*o**5 + 0. Suppose s(n) = 0. Calculate n.
-1, 1
Let y(m) = 12*m**2 + 6*m - 8. Let g(k) = k**2 + k - 1. Let t(u) = 10*g(u) - y(u). Factor t(w).
-2*(w - 1)**2
Factor 4/3 + 8*i**2 - 6*i - 10/3*i**3.
-2*(i - 1)**2*(5*i - 2)/3
Factor -9/2*d**4 - 3/2*d**2 + 0*d - 9/2*d**3 + 0 - 3/2*d**5.
-3*d**2*(d + 1)**3/2
Suppose 10*v - v - 18 = 0. Determine k so that 1/6*k**3 + 1/3 + 0*k**v - 1/2*k = 0.
-2, 1
Let k(d) be the third derivative of d**5/48 - d**4/32 - d**3/12 + 22*d**2. Determine i so that k(i) = 0.
-2/5, 1
Let o(p) be the second derivative of p**3 - 1/6*p**4 + 0 + p**2 - 3/10*p**5 + 8*p. Factor o(a).
-2*(a - 1)*(a + 1)*(3*a + 1)
Let r(a) be the third derivative of a**6/360 - a**5/180 - a**4/72 + a**3/18 - a**2. Factor r(l).
(l - 1)**2*(l + 1)/3
Suppose 6*y - 7*y = 0. Suppose -h - 5 = -2*j, 0 = 5*j - 2*h - h - 15. Factor 0*f**2 - 1/2*f**4 + y - 1/4*f**5 - 1/4*f**3 + j*f.
-f**3*(f + 1)**2/4
Factor 0*j - 2/7*j**4 + 2/7*j**3 + 0*j**2 + 0.
-2*j**3*(j - 1)/7
Let l(k) = -2*k**2 - 23*k - 58. Let f be l(-4). Let -1/3*h**f + 0*h + 1/3 = 0. Calculate h.
-1, 1
Let g(n) be the third derivative of -n**6/120 - n**5/30 - n**4/3 - 2*n**3/3 + n**2. Let l(m) = m**3 + m**2 + 7*m + 3. Let k(r) = -4*g(r) - 5*l(r). Factor k(q).
-(q - 1)**3
Factor 20/3*y + 135*y**3 + 60*y**2 + 0.
5*y*(9*y + 2)**2/3
Let r(b) be the third derivative of 0*b + 0 + 0*b**5 + 0*b**3 - 3*b**2 - 1/120*b**6 + 1/24*b**4. Factor r(i).
-i*(i - 1)*(i + 1)
Let x be -6 + 205/30 + (-1)/2. Solve -2/3 - x*b + 1/3*b**2 = 0 for b.
-1, 2
Let n(m) = -6*m**3 + 41*m**2 - 25*m. Let x(d) = 3*d**3 - 21*d**2 + 12*d. Let v(i) = -3*n(i) - 5*x(i). Factor v(p).
3*p*(p - 5)*(p - 1)
Let s = 20 + -14. Let u be 28/(-21)*s/(-4). Solve 0 + 0*k + 2/7*k**3 + 0*k**u = 0.
0
Let q = -53/5 - -179/15. Factor 4 - 28/3*w + 20/3*w**2 - q*w**3.
-4*(w - 3)*(w - 1)**2/3
Let z(g) be the first derivative of 0*g - 7 + 0*g**2 - 2/15*g**3 - 2/25*g**5 - 1/5*g**4. Suppose z(x) = 0. Calculate x.
-1, 0
Let w(k) be the second derivative of -24/5*k**5 + 0*k**2 + 0 + 17/6*k**4 - 4*k + 3*k**6 - 2/3*k**3. Factor w(d).
2*d*(3*d - 1)**2*(5*d - 2)
Let v(i) be the third derivative of -i**7/420 + i**5/60 + 4*i**3/3 + 4*i**2. Let p(u) be the first derivative of v(u). Determine m so that p(m) = 0.
-1, 0, 1
Let g(a) be the first derivative of a**6/18 - 2*a**5/15 + 2*a**3/9 - a**2/6 - 9. Solve g(l) = 0 for l.
-1, 0, 1
Suppose -2/3*y**2 - 4/3 - 2*y = 0. Calculate y.
-2, -1
Let z(m) = m**3 - 3*m**2 + 2. Let k be z(3). Factor -3*d + 8 + d**2 - 5*d**k + 4*d + 3*d.
-4*(d - 2)*(d + 1)
Let u = 2 - 3. Let q(n) = -3*n**3 - n**2 - n - 1. Let b be q(u). Find x, given that -2/5 + 0*x**b - 4/5*x + 4/5*x**3 + 2/5*x**4 = 0.
-1, 1
Let h = 8166/11 - 742. Find x, given that 0 + h*x + 2/11*x**3 - 6/11*x**2 = 0.
0, 1, 2
Factor -4/15*u - 2/5 + 26/15*u**2 - 16/15*u**3.
-2*(u - 1)**2*(8*u + 3)/15
Factor 3*y**3 + y**3 - 16*y**2 - 4*y**3 + 32*y + 2*y**3.
2*y*(y - 4)**2
Let f(x) = 2*x - 3 + 1 - 5 + 2 - 8*x**2. Let u(k) = -33*k**2 + 9*k - 21. Let c(y) = 21*f(y) - 5*u(y). Determine b so that c(b) = 0.
-1, 0
Let q = 6 - 4. Suppose -q*a = a. Factor a*w + 0*w**2 + 1/3*w**3 + 1/3*w**4 + 0.
w**3*(w + 1)/3
Let x be 14/3 + 13/39. Let r(b) be the third derivative of 0*b + 0 - 2*b**2 - 4/27*b**3 - 1/270*b**x + 1/27*b**4. Determine m, given that r(m) = 0.
2
Let u(t) = -t**2 - 12*t - 15. Suppose h + 10 = -0*h. Le