. Let b = f - 8. Solve -2*c**2 + b*c**2 - 3*c**2 = 0.
0
Let r(d) be the second derivative of 5*d**4/4 + 5*d**3/3 - 11*d + 1. Factor r(u).
5*u*(3*u + 2)
Let z(y) be the third derivative of -3/56*y**4 + 0*y + 0*y**5 - 8*y**2 + 1/280*y**6 + 1/7*y**3 + 0. Let z(r) = 0. What is r?
-2, 1
Let j(h) = h**3 - 8*h**2 + h - 4. Let o be j(8). Factor 3*d**3 - 5*d**3 + o*d**3 + 2*d**2.
2*d**2*(d + 1)
Suppose 0 = -14*k - 10*k + 48. Factor -6/5*s - 2/5 + 8/5*s**k.
2*(s - 1)*(4*s + 1)/5
Let a = 5 + -5. Suppose -2*h = -4*u + 6, 0*u + u - 3 = a. Determine v so that -h*v**4 - 5*v + 2*v**5 + 4*v**2 - v**4 + 3*v = 0.
-1, 0, 1
Let f(c) be the second derivative of c**8/1344 - c**6/240 + c**4/96 + 3*c**2/2 + 2*c. Let k(w) be the first derivative of f(w). Factor k(o).
o*(o - 1)**2*(o + 1)**2/4
Let h(m) = 7*m + 1. Let u be h(-1). Let q be ((-1)/u)/(2/4). Suppose 0 - q*t - 1/3*t**2 = 0. Calculate t.
-1, 0
Determine t, given that 6*t + 0 - 3*t**2 - 3/2*t**3 + 3/4*t**4 = 0.
-2, 0, 2
Suppose 0*b - 2 = -b. Let o = b + 0. Let -9*m**2 + 0*m**3 - 2*m**3 + m**2 + o*m + 8*m**4 = 0. What is m?
-1, 0, 1/4, 1
Factor q**3 + 2 - q**4 + 2*q**3 + 3*q**4 + 5*q**3 + 12*q**2 + 8*q.
2*(q + 1)**4
Let 5*r**4 + 5*r + 5*r**2 + 0*r - 10*r**2 - 5*r**3 = 0. What is r?
-1, 0, 1
Let o(x) be the second derivative of x**6/6 - 5*x**4/12 - 4*x. Determine a, given that o(a) = 0.
-1, 0, 1
Let c(v) be the third derivative of v**8/336 - v**7/35 + 13*v**6/120 - v**5/5 + v**4/6 + 7*v**2. Suppose c(u) = 0. What is u?
0, 1, 2
Let t be (-3 - -2) + 1 + 3. Suppose t*d = -4*m + 5*m + 8, 5*m + 10 = 0. Factor d*s**2 - 18/7*s + 4/7.
2*(s - 1)*(7*s - 2)/7
Let z(m) = m**2 + 7*m - 13. Let n be z(-9). Suppose 0 = -n*u + 10. Factor 0 + 3/5*v**u + 3/5*v.
3*v*(v + 1)/5
Let h(a) be the third derivative of a**8/13440 - a**7/1680 + 7*a**4/24 + a**2. Let k(b) be the second derivative of h(b). Let k(w) = 0. Calculate w.
0, 3
Let p = -15 - -17. Let k(y) be the second derivative of -1/75*y**6 + 0 - 1/5*y**2 + 1/15*y**4 + 0*y**5 - p*y + 0*y**3. Let k(t) = 0. Calculate t.
-1, 1
Let f(r) be the second derivative of r**6/45 + r**5/6 + 7*r**4/18 + r**3/3 + 35*r. What is v in f(v) = 0?
-3, -1, 0
Let q be (-1155)/(-297) - 1/(-9). Let c(d) be the first derivative of 4/15*d**6 + 0*d**2 - 14/25*d**5 + 3 + 0*d + 1/5*d**q + 2/15*d**3. Factor c(i).
2*i**2*(i - 1)**2*(4*i + 1)/5
Let k be -2 + 1 + (-218)/(-216). Let m(n) be the third derivative of 0*n + 1/90*n**5 - k*n**4 - 2/27*n**3 - 3*n**2 + 0. Determine q, given that m(q) = 0.
-2/3, 1
Let t be -8*6/(-60) - (0 + 0). Find v, given that 6/5*v + t + 2/5*v**2 = 0.
-2, -1
Let p(w) be the second derivative of -w**7/14 + w**6/15 - 10*w. What is h in p(h) = 0?
0, 2/3
Determine d, given that -8*d**5 - 42*d**2 - 4*d**5 + 3*d**4 + 9*d**5 + 33*d - 2 - 7 + 18*d**3 = 0.
-3, 1
Suppose 6*o + 128 = 2*o. Let j be o/(-14) - (-2)/(-7). Factor -1 - 1 + 4*w - 8*w - 2*w**j.
-2*(w + 1)**2
Let r(i) be the second derivative of 0 - 1/3*i**4 + 0*i**2 - i + 2/3*i**3. Factor r(h).
-4*h*(h - 1)
Suppose 20*o + 17 - 57 = 0. Suppose -2*i - 3 - 1/3*i**o = 0. What is i?
-3
Let g be 3/4 + (-1)/2. Let v be 5 + ((-8)/12 - (-49)/(-12)). Determine q so that -g*q + v*q**2 + 0 = 0.
0, 1
Let r(w) be the third derivative of w**5/150 + w**4/10 + 22*w**2. Factor r(k).
2*k*(k + 6)/5
Suppose 0 = -3*t - 2*i + 7, 5*i = 3*t + t - 17. Let g(u) be the first derivative of -4*u**2 + 2 - 6*u**t - 8/9*u. Solve g(d) = 0 for d.
-2/9
Let t = -33 - -37. Let y(g) be the first derivative of -1/4*g**t + 0*g + 8/9*g**3 - 2/3*g**2 - 2. What is m in y(m) = 0?
0, 2/3, 2
Let h be -2 - (-4 - (-2 + -4 + 4)). Factor 0*v - 1/4*v**2 + h.
-v**2/4
Let r = 178/3 - 59. Factor -2/3*y**3 + 1/3*y**4 + 0*y + 0 + r*y**2.
y**2*(y - 1)**2/3
Let f(c) be the second derivative of c**6/120 + 8*c. Determine z so that f(z) = 0.
0
Suppose 0*z + 5*t + 32 = 4*z, -2*t + 7 = 5*z. Let -7*d**4 + 2*d**5 + 0*d**4 + d**2 + 2*d**z + 2*d**5 = 0. What is d?
-1/4, 0, 1
Let x(o) be the second derivative of -o**6/195 - o**5/65 + o**4/78 + 2*o**3/39 - 19*o. Determine c, given that x(c) = 0.
-2, -1, 0, 1
Let q(g) be the second derivative of g**7/21 - g**6/5 + 3*g**5/10 - g**4/6 + 4*g. Factor q(c).
2*c**2*(c - 1)**3
Let d(h) be the second derivative of h**6/45 - h**5/15 + h**4/18 + 11*h. Solve d(f) = 0 for f.
0, 1
Let -243*o**5 - 15*o + 41*o**4 - 39*o**3 + 127*o**2 + 3*o - 419*o**4 - 43*o**2 = 0. Calculate o.
-1, 0, 2/9
Let c(k) = 15*k**4 - 36*k**3 + 29*k**2 - 4*k. Let t(d) = 15*d**4 - 36*d**3 + 30*d**2 - 3*d. Suppose -9*o + 6*o = 9. Let j(i) = o*c(i) + 2*t(i). Factor j(w).
-3*w*(w - 1)**2*(5*w - 2)
Let f be (4 + -1)/((-2)/(-2)). Find t such that -t**3 + t**3 + t**5 + 2*t**4 + 4*t**3 - f*t**3 = 0.
-1, 0
Let p(w) be the first derivative of -2*w**5/35 + 4*w**3/21 - 2*w/7 - 9. Find s such that p(s) = 0.
-1, 1
Factor 2/3*h**5 - 10/3*h**4 + 2 + 4/3*h**2 + 4*h**3 - 14/3*h.
2*(h - 3)*(h - 1)**3*(h + 1)/3
Factor 15*y**4 - 78 + 13*y + 2*y - 5*y**5 - 10*y**2 - 10*y**3 + 73 + 0*y.
-5*(y - 1)**4*(y + 1)
Let v(z) be the third derivative of -z**8/2184 + z**7/1365 - 8*z**2. Factor v(t).
-2*t**4*(t - 1)/13
Let l(d) = d**4 + d**3 - d + 1. Let f(t) = t**4 + 16*t**3 - 10*t**2 - 56*t + 41. Let a(c) = -f(c) - 4*l(c). Suppose a(m) = 0. Calculate m.
-3, 1
Factor 4/9*s**2 + 2/9*s - 2/9*s**4 + 2/9*s**5 - 2/9 - 4/9*s**3.
2*(s - 1)**3*(s + 1)**2/9
Let d(j) = -3*j**3 - 3*j**2 - 3*j. Let y be d(-2). Let w be 1/3 - 6/y. Factor w + 1/5*f**3 + 3/5*f**2 + 2/5*f.
f*(f + 1)*(f + 2)/5
Factor 44*k**2 + 49*k**2 - 118*k**2 + 35*k + 5*k**3 - 19 + 4.
5*(k - 3)*(k - 1)**2
Let k(b) be the third derivative of -b**7/3780 + b**4/24 - 2*b**2. Let y(a) be the second derivative of k(a). Find o such that y(o) = 0.
0
Let a(d) = d**2 + 21*d + 42. Let j be a(-19). Determine k, given that 0 - 2/9*k - 2/9*k**j + 2/9*k**2 + 2/9*k**3 = 0.
-1, 0, 1
Let g = -5 - -29. Suppose p - 3*y = -9, 3*y + 0*y = -4*p + g. Find x, given that -6 - 5*x**3 + 9*x + x**3 + 2*x**3 - x**p = 0.
-2, 1
Let y = 3 - 3. Let z be 3 - 13/5 - y. Factor -2/5*r**2 - 4/5*r**3 + 0*r - z*r**4 + 0.
-2*r**2*(r + 1)**2/5
Let f be 2*(10/4 - 0). Factor -2*y**2 - 3*y - 1 + 3*y**5 + 3 - 4*y**f + 4*y**3.
-(y - 1)**3*(y + 1)*(y + 2)
Suppose 0 = -0*o - 3*o + 9. Suppose 0 = -5*j + 8*j - 15. Let -3*a**4 + 3*a**3 - 5*a**5 - 2*a**5 + 2*a**j - a**o = 0. What is a?
-1, 0, 2/5
Factor 1/7*u**3 + 1/7*u**2 + 0 - 2/7*u.
u*(u - 1)*(u + 2)/7
Let c be (0 - -1)/(0 + 1). Suppose 1 + c = l. Factor 4*h**l - 3*h - h**3 - h**2 + 0*h + 1.
-(h - 1)**3
Let x(f) be the first derivative of -f - 1 - 1/30*f**4 - 1/15*f**3 + 0*f**2. Let q(d) be the first derivative of x(d). Suppose q(u) = 0. Calculate u.
-1, 0
Factor 0 + 1/5*n**5 + 2/5*n**2 - 1/5*n - 2/5*n**4 + 0*n**3.
n*(n - 1)**3*(n + 1)/5
Let j(b) = -b**3 - 2*b**2 - 2*b - 3. Let u be j(-2). Let r = 3 - u. Let 3 - 4 + r*a + 0*a - a**2 = 0. Calculate a.
1
Let w be 3*(2 + -3) + 5 + -2. Let z(v) be the third derivative of 1/15*v**3 + 0 + w*v**4 - v**2 - 1/150*v**5 + 0*v. Let z(t) = 0. What is t?
-1, 1
Let w(s) be the second derivative of s**6/30 - s**5/10 + s**3/3 - s**2/2 - 6*s. Factor w(q).
(q - 1)**3*(q + 1)
Let b = 0 + 2. Determine f so that -13*f**3 - 4*f - 27*f**4 - 12*f**b + 23*f**4 + 7*f**3 - 6*f**3 = 0.
-1, 0
Let s = -15 + 11. Let a be s/(-42)*3*7. Factor -1/4 + 1/2*m + 3/4*m**a.
(m + 1)*(3*m - 1)/4
Let d(k) be the second derivative of -k**6/12 + k**5/8 - 10*k. Determine x so that d(x) = 0.
0, 1
Let p(d) = -20*d**4 + 14*d**3 - 17*d + 17. Let n = 0 - -4. Let i(k) = 7*k**n + 6*k - 6 - 5*k**3 + 0*k**3 + 0. Let q(c) = -17*i(c) - 6*p(c). Factor q(r).
r**3*(r + 1)
Suppose 2*l - 9 = -3*j, -3*j = -4*l - 0*l + 9. Let -12 + 12 + l*c**2 = 0. Calculate c.
0
Let y be (-4)/(-3) + (-6)/(-9). Solve 1 + 6*b**y - 4*b**3 + 4*b - 3*b**2 + b**4 - 5 = 0.
-1, 1, 2
Let r(b) be the first derivative of -b**6/6 + 4*b**5/5 - 3*b**4/4 - 4*b**3/3 + 2*b**2 - 8. Find u, given that r(u) = 0.
-1, 0, 1, 2
Let f(s) be the second derivative of -s**6/540 + s**5/90 - s**4/36 + s**3/6 + 3*s. Let n(m) be the second derivative of f(m). Find r, given that n(r) = 0.
1
Let z(l) = 4*l**2 - 5*l + 4. Let u(i) = i**2. Let o(s) = -3*u(s) + z(s). Let k be o(4). Factor 0 - 2/7*p**3 - 2/7*p**2 + k*p.
-2*p**2*(p + 1)/7
Let g be (-294)/(-30) - 8 - 0. Find w, given that 3/5*w**2 - g*w + 6/5 = 0.
1, 2
Factor -146*l**2 + 294*