2546/45 - 501. Let s(f) be the second derivative of 2/9*f**3 - 3*f + 0*f**2 + 0 + 1/6*f**4 - b*f**6 + 0*f**5. Let s(a) = 0. What is a?
-1, 0, 2
Let v(x) be the second derivative of -x**5/60 - x**4/9 - 2*x**3/9 + 5*x. Find l such that v(l) = 0.
-2, 0
Factor 0*u**4 + 0 - 1/3*u**3 + 1/3*u**5 + 0*u + 0*u**2.
u**3*(u - 1)*(u + 1)/3
Suppose -40*l + 15 - 5*l**4 - 125*l**3 + 125*l**3 + 30*l**2 = 0. What is l?
-3, 1
Suppose -6 - 2 = -4*t. Let h(b) be the first derivative of -1/4*b**4 + 10*b**3 - t*b - 1 - 28/5*b**5 + 1/2*b**2. What is a in h(a) = 0?
-1, -2/7, 1/4, 1
Let s = 1141/6 + -190. Factor s + 1/3*g**4 - 7/6*g**3 - 5/6*g + 3/2*g**2.
(g - 1)**3*(2*g - 1)/6
Let j(y) = 6*y. Let w be j(3). Suppose -p + 3*g + 3 = 3*p, -5*p - g = -w. Factor -3*u**3 + 5*u**3 + 2*u**2 - p*u + u - 2*u**4.
-2*u*(u - 1)**2*(u + 1)
Let j(g) = -g**3 + g**2 + 1. Suppose 0 = -5*t - 3 + 8. Let z(y) = 6*y**3 + 3*y**2 + 3*y - 3. Let b(c) = t*z(c) + 3*j(c). Suppose b(f) = 0. What is f?
-1, 0
Let k = 5 - 3. Suppose 8 - 9 - 2*o**4 + o**4 + k*o**2 = 0. What is o?
-1, 1
Let a(m) = -47*m**4 - 77*m**3 - 34*m**2 - 4*m. Let z(r) = 46*r**4 + 77*r**3 + 35*r**2 + 4*r. Let q(v) = 6*a(v) + 4*z(v). Solve q(u) = 0 for u.
-1, -2/7, 0
Let j be (1/(-1))/(2/(-2)). Let m be j*(1 - 2 - -2). Factor 2*h**2 + 5 - m - 6.
2*(h - 1)*(h + 1)
Find l such that 2/19*l**3 + 0 + 0*l + 2/19*l**4 + 0*l**2 = 0.
-1, 0
Let y(c) be the second derivative of 25*c**4/48 + 5*c**3/4 + 9*c**2/8 - 19*c. Factor y(r).
(5*r + 3)**2/4
Let k(q) = 5*q**4 - 4*q**3 - 10*q**2 - 6*q + 3. Let g(p) = 4*p**4 - 3*p**3 - 11*p**2 - 6*p + 2. Let m(l) = -3*g(l) + 2*k(l). Determine f so that m(f) = 0.
-2, -1/2, 0, 3
Factor 1/2*y**5 - 6*y**2 + 0 - 4*y + 3/2*y**4 - y**3.
y*(y - 2)*(y + 1)*(y + 2)**2/2
Let a(h) be the third derivative of -h**5/360 + h**4/72 - h**3/36 + 6*h**2. What is u in a(u) = 0?
1
Let w = 130/193 + -4/579. Suppose w*q + 0 + 1/3*q**2 - 3*q**3 - 4/3*q**4 + 4/3*q**5 = 0. Calculate q.
-1, -1/2, 0, 1/2, 2
Let k(m) = -15*m**3 - 21*m**2 - 5*m + 1. Let n(o) = -45*o**3 - 64*o**2 - 15*o + 4. Let p(y) = -11*k(y) + 4*n(y). Factor p(c).
-5*(c + 1)**2*(3*c - 1)
Let v(r) be the third derivative of -r**7/2520 + r**6/1080 + r**5/360 - r**4/72 - r**3/6 - 2*r**2. Let i(s) be the first derivative of v(s). Factor i(m).
-(m - 1)**2*(m + 1)/3
Let h(m) = -m**4 - 2*m. Let i(p) = 3*p**4 + 7*p**3 - 27*p**2 + 33*p - 10. Let w(n) = 2*h(n) + i(n). Solve w(g) = 0 for g.
-10, 1
Let -49*z - 24 + 23*z + 4*z**2 + 22*z = 0. Calculate z.
-2, 3
Let f = -3/22 - 181/44. Let d = -15/4 - f. Factor -d*i - 1/2*i**2 + 1.
-(i - 1)*(i + 2)/2
Let o(c) be the third derivative of c**6/30 + 2*c**5/15 - c**4/2 + 9*c**2. Factor o(s).
4*s*(s - 1)*(s + 3)
Let i(t) be the second derivative of t**4/30 - t**2/5 - 8*t. Suppose i(n) = 0. What is n?
-1, 1
Let m be (5 + -1)*(-18)/(-24). Let a(c) be the second derivative of -1/12*c**4 + c + 0*c**m + 0 + 0*c**2. Solve a(h) = 0.
0
Let y(q) be the second derivative of -2*q**7/7 + 2*q**6/15 + 23*q**5/15 + 13*q**4/9 + 4*q**3/9 + 4*q. Suppose y(p) = 0. Calculate p.
-1, -1/3, 0, 2
Let i(y) be the second derivative of 0*y**5 + 0*y**3 - 1/6*y**4 - 2*y + 0 + 0*y**2 + 1/15*y**6. Factor i(n).
2*n**2*(n - 1)*(n + 1)
Let y(v) be the third derivative of -5*v**2 + 1/9*v**4 - 1/3*v**3 + 0*v + 0 - 1/90*v**5. Solve y(p) = 0 for p.
1, 3
Factor -2/5*d**4 + 0 + 2/5*d**2 + 4/5*d**3 - 4/5*d.
-2*d*(d - 2)*(d - 1)*(d + 1)/5
Solve -3/11*x**3 + 1/11*x**5 - 1/11*x**4 + 5/11*x**2 - 2/11*x + 0 = 0 for x.
-2, 0, 1
Suppose 0 + 0*n + 4/3*n**2 + 4/3*n**3 = 0. What is n?
-1, 0
Let u(n) be the third derivative of n**5/30 - n**4/8 - n**3/3 + 5*n**2. Let u(p) = 0. What is p?
-1/2, 2
Determine l, given that -1/2*l**4 + 2*l + 7/2*l**2 + 0 + l**3 = 0.
-1, 0, 4
Factor -3/5 + 1/2*p + 1/10*p**2.
(p - 1)*(p + 6)/10
Suppose -13*s = -21*s - 27*s. Let -14/3*c**3 + 16/3*c**2 + s - 8/9*c - 98/9*c**4 = 0. What is c?
-1, 0, 2/7
Let d(u) be the first derivative of u**4/4 + u**3/3 - u - 3. Let h(b) = b. Let v(i) = -2*d(i) + 2*h(i). Suppose v(p) = 0. What is p?
-1, 1
Let z(m) be the third derivative of -m**5/360 - 5*m**4/72 - 25*m**3/36 + 11*m**2. Let z(d) = 0. Calculate d.
-5
Factor 3/7*g**2 + 3/7*g**3 - 3/7*g**4 - 3/7*g**5 + 0 + 0*g.
-3*g**2*(g - 1)*(g + 1)**2/7
Find k, given that 72*k**2 + 23*k**3 + 4*k - 4 - 116*k**2 - 7*k**5 + 73*k**2 - 5*k**4 = 0.
-1, 2/7, 2
Let x(j) be the first derivative of j**5 + 3*j**4 - 11*j**3/3 - 3*j**2 + 19. Factor x(c).
c*(c - 1)*(c + 3)*(5*c + 2)
Let r(x) be the second derivative of x**6/60 - 3*x**5/40 + x**4/12 + 23*x. Determine c, given that r(c) = 0.
0, 1, 2
Let a = -7 + 6. Let h = 1 - a. Factor -2*d - 3*d**3 - d**2 - d**5 - 3*d**4 + h*d + 0*d.
-d**2*(d + 1)**3
Let m(j) = 56*j**4 - 100*j**3 + 24*j**2 + 8*j + 8. Let q(r) = 19*r**4 - 33*r**3 + 8*r**2 + 3*r + 3. Let a(h) = 3*m(h) - 8*q(h). Let a(s) = 0. What is s?
0, 1/4, 2
Let u(m) be the second derivative of -1/9*m**3 + 1/18*m**4 + 0 - 2/3*m**2 + 2*m. Factor u(s).
2*(s - 2)*(s + 1)/3
Let m(w) be the first derivative of -w**4/36 - 14. Factor m(z).
-z**3/9
Factor 0*q + 0 - 2/7*q**3 - 6/7*q**2.
-2*q**2*(q + 3)/7
Let y(z) be the first derivative of 2*z**6/21 + 12*z**5/35 + 2*z**4/7 - 8*z**3/21 - 6*z**2/7 - 4*z/7 + 30. Let y(j) = 0. Calculate j.
-1, 1
Let d(w) be the first derivative of -4*w**3/9 + 68*w**2/3 - 1156*w/3 - 76. Find j such that d(j) = 0.
17
Let j = 8 - 4. Let n(w) = w**3 + 4*w**2 - 2*w - 4. Let f be n(-4). What is q in 2*q**4 - q + 2*q**2 - 3*q**f - q**j + q**5 = 0?
-1, 0, 1
Let z(p) = p**3 - 15*p**2 - 16*p. Let j be z(16). Let t(o) = -o**3 + 5*o**2 - 5*o. Let q be t(2). Factor j*a**q + 2/7*a - 2/7*a**3 + 0.
-2*a*(a - 1)*(a + 1)/7
Let l be (-3)/(-12)*-6 - (-1677)/182. Factor -54/7 + l*u + 2/7*u**3 - 18/7*u**2.
2*(u - 3)**3/7
Let i(k) = -2*k**3 - 4*k**2 - 2*k. Let d be i(-2). Factor -2*c - 4*c**3 + 0*c**4 + 2*c**d + 6*c**2 + 2*c**3 - 4*c**3.
2*c*(c - 1)**3
Find z, given that 5 - 7*z - 1 + 4*z - 4*z**2 + 4*z**3 - z = 0.
-1, 1
Let w be (0 + 5/6)*(-5)/(-1000). Let m(f) be the third derivative of 0*f + f**2 + 0 - 1/24*f**3 + w*f**5 + 0*f**4. Let m(b) = 0. Calculate b.
-1, 1
Let f = 22 + -22. Factor -2/5*o + 6/5*o**2 + f.
2*o*(3*o - 1)/5
Let s(o) be the second derivative of -o**7/126 + o**6/30 - o**5/20 + o**4/36 - 13*o. Solve s(z) = 0.
0, 1
Let o = -3/25 - -46/175. Factor -3/7*t + o - 4/7*t**2.
-(t + 1)*(4*t - 1)/7
Factor 4/5 + 6/5*h + 2/5*h**2.
2*(h + 1)*(h + 2)/5
Suppose -1 = 3*m - 7. Let k = -12/7 + 50/21. Factor -4/3*n - k*n**m - 2/3.
-2*(n + 1)**2/3
Let b(i) be the third derivative of 0*i + 0 - 1/60*i**4 - 2*i**2 + 0*i**3 - 1/100*i**6 - 1/525*i**7 - 1/50*i**5. Suppose b(k) = 0. What is k?
-1, 0
Let r(s) = s**3 + 5*s**2 - s - 3. Let i(h) = h - 1. Let q be i(-4). Let y be r(q). Factor 2 + x**2 + y*x**3 - 3*x**2 + 4*x - 6*x.
2*(x - 1)**2*(x + 1)
Let z(h) = 7*h**2 + 8*h + 1. Let s(r) = -64*r**2 - 72*r - 8. Let x(o) = 3*s(o) + 28*z(o). Factor x(g).
4*(g + 1)**2
Let t(i) = -2*i**5 + 5*i**4 - 2*i**2 - i + 3. Let s(z) = z**5 - z**4 - 1. Let f be (-112)/18 + (-2)/(-9). Let k(g) = f*s(g) - 2*t(g). Factor k(w).
-2*w*(w - 1)*(w + 1)**3
Suppose 0 = t + 1 + 1. Let r be 0/(2 + -2 - t). Let 4*l**2 - 2*l**3 + 3*l + r*l - 5*l = 0. What is l?
0, 1
Let w(g) = g**2 - g. Let v be w(2). Let r(t) be the first derivative of 5/6*t**4 - 4/15*t**5 - 3 + 1/3*t**v - 8/9*t**3 + 0*t. Factor r(d).
-2*d*(d - 1)**2*(2*d - 1)/3
Let w(y) = y**3 + 11*y**2 + 9*y - 3. Let z be w(-10). Let o(f) = f - 5. Let m be o(z). Determine i, given that 0*i + 4 - 2*i - 4*i**2 + m*i**2 = 0.
-2, 1
Let u be 0/12*(-1)/(-2). Let g be 0/14*(u + 1). Determine b so that -1/3*b**2 + g + 1/3*b = 0.
0, 1
Suppose -5*f + 6 = -9, -2*k = 3*f - 9. Let y(n) be the third derivative of -1/8*n**4 + k + 1/20*n**5 + 0*n - n**3 + 4*n**2. What is j in y(j) = 0?
-1, 2
Let f(g) = g + 8. Let s be f(-6). Suppose 3*k = -s*k. Factor -1/2*t - 1/2*t**2 + k.
-t*(t + 1)/2
Let k(x) be the first derivative of x**6/6 + 2*x**5/5 - x**4/2 - 4*x**3/3 + x**2/2 + 2*x + 7. Factor k(j).
(j - 1)**2*(j + 1)**2*(j + 2)
Let c be (-1)/((-1 - -4)/12). Let w be (-2)/(-10) - (4 + c). Solve 0*m**3 - w*m**2 + 0*m + 1/5*m**4 + 0 = 0.
-1, 0, 1
What is z in -5/2*z**3 - 7/2*z - 21/4*z**2 - 3/4 = 0?
-1, -3/5, -1/2
Let o(s) be the second derivative of -s**6/5 + s**5/2 + 7*s**4/9 - 4*s**3/3 - 8*s**2/3 - s. 