0 + d**4/54 + d**2 - 2. Let u(p) be the second derivative of l(p). Determine h so that u(h) = 0.
-1, 0, 2
Find k, given that -5*k + 3*k**3 - 6*k**2 + 2*k + 4*k + 2*k = 0.
0, 1
Let s(c) be the second derivative of c**4/72 - 2*c**3/9 + 7*c**2/12 + 35*c. Factor s(y).
(y - 7)*(y - 1)/6
Let z be -6 - (2 - 522/63). Solve -z*l**2 - 4/7*l + 2/7*l**4 + 0 + 4/7*l**3 = 0 for l.
-2, -1, 0, 1
Factor -3/2*p**5 - 3/2 + 3*p**2 - 3/2*p - 3/2*p**4 + 3*p**3.
-3*(p - 1)**2*(p + 1)**3/2
Let q(s) be the first derivative of 1 + 0*s - s**2 + 1/2*s**4 + 0*s**3. Factor q(n).
2*n*(n - 1)*(n + 1)
Let z be 7/(-14)*(-2)/90. Let f(j) be the third derivative of -1/9*j**3 + 0*j + 1/18*j**4 + 0 - z*j**5 + 3*j**2. Factor f(p).
-2*(p - 1)**2/3
Suppose -1 = -3*p + 5*f, -4*p + 0*f = 3*f - 11. Let t = 0 + p. Find c such that -6*c**3 + 1 - 2*c - 2*c**4 + 1 - 6*c**2 - t = 0.
-1, 0
Let u = 3 + -2. Let y(l) = l**3 - l**2 - 2*l. Let m(n) = 2*n**3 + 4*n**3 + n - 3*n**3 - 4*n**3. Let q(g) = u*y(g) + 2*m(g). Find i, given that q(i) = 0.
-1, 0
Let v be (2/9)/(1/195). Let r = v - 43. Factor -4/3*g**2 + 5/3*g - r.
-(g - 1)*(4*g - 1)/3
Let p be 0/1 - (-6 - (-102)/18). Let v(h) be the second derivative of 9/10*h**5 + 3*h + 0*h**2 - 2/3*h**6 + 0 + 0*h**3 - p*h**4. Find y, given that v(y) = 0.
0, 2/5, 1/2
Let b be (-117)/(-36) + 2/(-8). Find w, given that 32*w**2 - 20*w**b - 1 - 4*w - 10 - 1 + 4 = 0.
-2/5, 1
Let j(b) be the first derivative of 1/5*b**2 - 2/15*b**3 + 4 + 0*b. Find z such that j(z) = 0.
0, 1
Let p = -8 - -8. Let k(x) be the third derivative of -1/420*x**6 + 0*x - 1/84*x**4 + 1/105*x**5 + 2*x**2 + p + 0*x**3. Determine d, given that k(d) = 0.
0, 1
Let n(b) be the second derivative of -b**7/210 + b**6/150 + 3*b**5/100 - b**4/12 + b**3/15 + 11*b. Factor n(i).
-i*(i - 1)**3*(i + 2)/5
Let s(j) be the second derivative of -4*j - 1/60*j**6 + 0 + 0*j**4 + 1/20*j**5 + 0*j**2 + 0*j**3. Factor s(n).
-n**3*(n - 2)/2
Let v(h) be the second derivative of h**9/7560 - h**8/3360 - h**7/630 + h**4/4 - 6*h. Let b(x) be the third derivative of v(x). Factor b(s).
2*s**2*(s - 2)*(s + 1)
Let t be (9/6)/(-3)*0. Let d(b) be the third derivative of 1/105*b**7 + 1/3*b**3 + 1/15*b**6 - 3*b**2 + 1/5*b**5 + 1/3*b**4 + 0 + t*b. Let d(n) = 0. What is n?
-1
Let n(p) = 49*p**2 - 96*p - 13. Let w(c) = 344*c**2 - 672*c - 92. Let v(g) = -20*n(g) + 3*w(g). Factor v(u).
4*(u - 2)*(13*u + 2)
Let f(k) be the first derivative of 0*k + 1/4*k**4 + k**3 + k**2 - 3. What is d in f(d) = 0?
-2, -1, 0
Suppose -1 = 2*d - 5. Let n = d + 1. Factor 13*m**2 - 48*m + 12 + 10*m**2 + n*m**2 - 5*m**2.
3*(m - 2)*(7*m - 2)
Let a = 4/15 + 2/105. Find w, given that -2/7*w**2 + 0*w + a = 0.
-1, 1
Suppose 15*n**3 - 5*n + 9 - 10*n + 25*n**4 - 35*n**2 + 1 = 0. Calculate n.
-1, 2/5, 1
Solve 0 + 3/2*j**2 + 3/2*j = 0.
-1, 0
Let u be 0/(-1 - 2) + 11. Let l(m) = -3*m**2 - 5*m - 3. Let s(n) = -n**2 - 2*n - 1. Let f(y) = u*s(y) - 4*l(y). Suppose f(g) = 0. What is g?
1
Factor -9/7*n - 6/7 + 0*n**2 + 3/7*n**3.
3*(n - 2)*(n + 1)**2/7
Suppose 0 = -4*m + 1 + 7. Suppose 0 = -4*g + 6 + 2. Solve 6*t**2 - 2*t**2 - 2*t**g - m*t = 0.
0, 1
Let s = 3/7 - 5/28. Let y(g) be the second derivative of 2*g + 1/24*g**4 + 0 + 1/40*g**5 - 1/12*g**3 - s*g**2. Solve y(w) = 0 for w.
-1, 1
Suppose -2*c + 5*l = 15 - 2, -l = -2*c - 1. Let a be (c/2)/((-4)/(-16)). Find j such that -a*j**3 - 8/3*j**2 + 4/3 + 2/3*j = 0.
-1, 2/3
Factor -4/7*i + 0*i**3 - 8/7*i**4 + 0 + 8/7*i**2 + 4/7*i**5.
4*i*(i - 1)**3*(i + 1)/7
Let q(s) be the second derivative of -s**4/12 + s**3 - 5*s**2/2 - 3*s. Let k be q(5). Factor -2/7*j**4 - 2/7*j - 6/7*j**2 + k - 6/7*j**3.
-2*j*(j + 1)**3/7
Let y(r) = r**3 - r**2. Suppose 1 = d - 3. Let p(t) = -3*t**3 - 2*t**2 + 2*t**2 + 3*t**2. Let j(v) = d*p(v) + 11*y(v). Factor j(k).
-k**2*(k - 1)
Let g = 2 - 0. Let u = 0 - 0. Determine b, given that u*b**3 + 2*b**3 - b**3 + g*b**2 = 0.
-2, 0
Let v(r) = 2*r + 1. Let t be v(1). Find y such that 4/7*y**4 - 4/7*y**2 + 2/7*y + 0 - 2/7*y**t = 0.
-1, 0, 1/2, 1
Let z be (-474)/10*(-8)/504. Let g = z + -7/15. Factor 4/7*b**3 - g*b - 2/7 + 4/7*b**2 - 2/7*b**4 - 2/7*b**5.
-2*(b - 1)**2*(b + 1)**3/7
Let s(g) be the first derivative of g**6/9 - 4*g**5/15 - g**4/3 + 16*g**3/9 - 7*g**2/3 + 4*g/3 - 4. What is q in s(q) = 0?
-2, 1
Let j be 12/(-16) + 62534/168. Let b = 1123/3 - j. Factor -4/7 + b*z**2 + 2/7*z.
2*(2*z + 1)*(5*z - 2)/7
Let b = 34 + -28. Let q(u) be the second derivative of 0 + 4/15*u**3 - 1/5*u**2 + 3*u - 1/75*u**b - 1/5*u**4 + 2/25*u**5. Factor q(i).
-2*(i - 1)**4/5
Let n be 6 - 1 - (-5 + 6). Factor 3 + 2*s - 15*s**2 + 14*s**2 - n.
-(s - 1)**2
Let j(k) be the second derivative of -k**6/90 + k**4/36 - 7*k. Suppose j(u) = 0. Calculate u.
-1, 0, 1
Let d be 42/9 + (-6)/9. Factor -v - 7*v - 5*v + v + 8 + d*v**2.
4*(v - 2)*(v - 1)
Let l(c) be the third derivative of -c**7/336 - c**6/240 + c**5/120 + c**3/6 + c**2. Let m(u) be the first derivative of l(u). Suppose m(j) = 0. What is j?
-1, 0, 2/5
Let h(p) = p**3 - 7*p**2 + 10*p + 2. Let b be h(5). Determine t so that 2/15*t**b + 0 - 2/15*t = 0.
0, 1
Let u be (-12)/3*(-9)/4. Find d, given that -3*d**3 - 3 + 6*d - u*d + 3*d**2 + 6*d = 0.
-1, 1
Factor 3*s**5 - 3*s**4 - 2*s**3 - s**5 + 3*s**4.
2*s**3*(s - 1)*(s + 1)
Let k(l) be the second derivative of 1/3*l**6 + 5*l + 0 + 3/2*l**4 - 13/10*l**5 - 2*l**2 + 1/3*l**3. Let k(q) = 0. What is q?
-2/5, 1
Let z(q) = 1. Let m(w) = w**2 + w + 3. Let j(d) = -2*m(d) + 6*z(d). Find t such that j(t) = 0.
-1, 0
Suppose -13 = -4*y - u + 16, 4*u - 20 = 0. Suppose 4*i + 6 = y*i. What is j in -i*j**2 - 1/2*j + 12*j**4 - 8*j**5 - 1/2*j**3 + 0 = 0?
-1/4, 0, 1
Let w(o) = -o**2 + o - 1. Let f(k) = 9*k**2 + 6. Let x(b) = f(b) + 6*w(b). Factor x(c).
3*c*(c + 2)
Let o be -1 + 3/(108/34). Let x = 5/9 + o. Find u, given that 0*u - 1/2 + x*u**2 = 0.
-1, 1
Let f be 12/(-176) - ((-11)/(-4) + -3). Factor 0*t**2 + 0*t**3 + 0*t - f*t**4 + 0.
-2*t**4/11
Let h(o) = -o**5 + o**3 + o**2 - o. Let k(y) = -10*y**5 + 7*y**4 + 3*y**3 + 5*y**2 - 5*y. Let b(m) = -5*h(m) + k(m). Suppose b(z) = 0. What is z?
0, 2/5, 1
Suppose u = -2*s, 2*u = -0*u + s. Let x(w) be the second derivative of 0*w**3 + u*w**2 + 0 - 2*w + 0*w**4 - 1/40*w**5. Find a such that x(a) = 0.
0
Let u = 425/12 + -139/4. Factor 0*o**2 - 1/3*o**3 - u*o**4 + 0*o - 1/3*o**5 + 0.
-o**3*(o + 1)**2/3
Let m = 50 - 47. Factor 0 + 0*v**2 + 0*v + 1/4*v**4 + 0*v**m.
v**4/4
Let l be (2/(-4))/1 + 1. Let d(t) = -t**2 - 17*t - 30. Let z be d(-15). Determine h, given that 1/2*h**4 + 0*h**2 + z + 0*h - l*h**3 = 0.
0, 1
Determine c, given that 9/4*c**3 - 31/4*c + 3/2 + 4*c**2 = 0.
-3, 2/9, 1
Let u(g) be the first derivative of -2*g**5/75 - g**4/30 + 2*g**3/15 + g**2/3 + 4*g/15 + 3. Suppose u(s) = 0. What is s?
-1, 2
Let y(c) = 21*c**3 + 6*c**2 - 21*c. Let o(j) = 21*j**3 + 6*j**2 - 21*j - 1. Let q(v) = 6*o(v) - 5*y(v). Determine a, given that q(a) = 0.
-1, -2/7, 1
Let q be (-43)/(-4) + 6 + -11. Let g be 1/2*(-14)/(-4). Factor g*t**3 - 1 - q*t**2 + 5*t.
(t - 2)*(t - 1)*(7*t - 2)/4
Let f = 91 + -91. What is b in -1/2*b + f - 1/2*b**2 = 0?
-1, 0
Let k(c) be the second derivative of c**7/35 - c**6/60 - c**5/6 + c**4/12 + 2*c**3/3 - 3*c**2 - 7*c. Let b(v) be the first derivative of k(v). Factor b(l).
2*(l - 1)**2*(l + 1)*(3*l + 2)
Let f(r) = -r**2 - r - 1. Let i(a) = -3*a**3 - 12*a**2 - 12*a - 18. Let y be (15/(-5))/(1/(-5)). Let q(t) = y*f(t) - i(t). Let q(w) = 0. Calculate w.
-1, 1
Let r(b) = -b**5 - 4*b**4 + 6*b**3 - 2*b**2 - 5*b. Let z(i) = i**5 + 3*i**4 - 5*i**3 + 2*i**2 + 4*i. Let y(f) = 5*r(f) + 6*z(f). What is g in y(g) = 0?
-1, 0, 1
Let p(b) be the third derivative of b**5/30 - b**4/24 - 9*b**2. What is z in p(z) = 0?
0, 1/2
Suppose -641*c - 6 = -643*c. Solve -3/5*b**2 - 1/5*b**c - 1/5 - 3/5*b = 0 for b.
-1
Let x(f) be the third derivative of -f**7/70 + 3*f**5/20 - f**4/4 + 12*f**2. Find i, given that x(i) = 0.
-2, 0, 1
Factor -h**4 + 0*h**4 + h**3 - 3*h**3 + 0*h**2 - h**2.
-h**2*(h + 1)**2
Let i be 0 - (1 - -2)/(-1). Factor -9*p**i + 6*p**2 - 3*p - 15*p**2 + 0*p**3 - 3*p**4.
-3*p*(p + 1)**3
Suppose -n + 17 = -0*n. Let p = n - 15. Suppose 4/3 - 2*x + 2/3*x**p = 0. Calculate x.
1, 2
Factor 0 - 3/8*x**2 + 0*x + 3/8*x**5 + 9/8*x**3 - 9/8*x**4.
3*x**2*(x - 1)**3/8
Let s(h) be the second derivative of h**4/60 - h**3/10 - 34*h. F