ppose 2*g - 9 = -g. Let f(o) = o**2 + 3*o - 7. Let n be f(-5). Find s, given that 54 - 3*s**3 - 34*s - s**g - 20*s + 2*s**n + 18*s**2 = 0.
3
Let o(x) be the second derivative of -x**7/280 + x**6/120 - x**3/3 + 2*x. Let q(v) be the second derivative of o(v). Determine r so that q(r) = 0.
0, 1
Find u, given that -6/7*u**3 + 0*u + 0 + 6/7*u**5 - 2/7*u**4 + 2/7*u**2 = 0.
-1, 0, 1/3, 1
Let v(d) be the first derivative of d**7/420 + d**6/45 + d**5/12 + d**4/6 + 2*d**3/3 + 1. Let p(i) be the third derivative of v(i). Suppose p(k) = 0. What is k?
-2, -1
Let m(w) = w**3 + 6*w**2 - 6*w + 7. Let q be m(-7). Factor 1 + 5*b**3 + q*b**4 - 5*b - 15*b**3 + 5*b**4 + 10*b**2 - b**5.
-(b - 1)**5
Suppose 12*n = 7*n + 10. Find r, given that 7*r - 48 - 12*r**3 - 163*r - 80*r**n - 24 = 0.
-3, -2/3
Let v(q) be the third derivative of -1/120*q**6 + 4*q**2 + 0*q + 0 + 1/672*q**8 + 0*q**3 + 0*q**5 + 0*q**7 + 1/48*q**4. What is d in v(d) = 0?
-1, 0, 1
Let o be (4*2/(-48))/((-2)/4). Find n, given that n**2 - o*n**3 + 1/3 - n = 0.
1
Let r(k) = k**3 + 2*k**2 - 3. Let g be r(-3). Let w be g/15*5/(-11). Let -2/11*v**5 + 0 + 4/11*v**4 + 2/11*v - w*v**2 + 0*v**3 = 0. Calculate v.
-1, 0, 1
Find k such that 0*k + 3*k - 4*k + 9*k + 12 - 4*k**2 = 0.
-1, 3
Factor 0 + 2/9*m**4 + 0*m - 4/9*m**2 + 2/9*m**3.
2*m**2*(m - 1)*(m + 2)/9
Let c = 245/9 - 27. Let g(z) be the first derivative of 1/15*z**5 + 0*z**4 - c*z**3 + 0*z**2 + 1 + 1/3*z. Suppose g(m) = 0. Calculate m.
-1, 1
Let a(n) be the second derivative of -n**7/12600 + n**5/600 + n**4/12 - 4*n. Let z(b) be the third derivative of a(b). Determine g so that z(g) = 0.
-1, 1
Let i be (14/(-3) - -4)*-3. Suppose 4*n - 8 = -i*o + 8, -2*n = -3*o - 8. Factor -1/3 + 2/3*y**3 + 0*y**2 - 2/3*y + 1/3*y**n.
(y - 1)*(y + 1)**3/3
Factor -2/5*i + 4/5*i**2 - 4/5 + 2/5*i**3.
2*(i - 1)*(i + 1)*(i + 2)/5
Let d be (22/26)/(4 + (-92)/24). Factor -92/13*r**2 - 18/13*r**4 - 18/13 + 60/13*r**3 + 2/13*r**5 + d*r.
2*(r - 3)**2*(r - 1)**3/13
Let k be -2 - ((-8570)/858)/5. Let i = 5141/3003 - k. Factor -165/7*z**2 + 12/7*z + i - 300/7*z**3.
-3*(4*z - 1)*(5*z + 2)**2/7
Let k(a) be the second derivative of -a**6/1800 - a**5/600 + 2*a**3/3 + a. Let w(b) be the second derivative of k(b). Let w(r) = 0. What is r?
-1, 0
Suppose -20 = -6*l + l. Solve h**l + 12/7*h**3 + 0*h - 4/7*h**2 + 0 = 0.
-2, 0, 2/7
Let m(u) be the third derivative of u**8/70560 - u**7/8820 + u**6/2520 - u**5/30 + 2*u**2. Let q(w) be the third derivative of m(w). Factor q(c).
2*(c - 1)**2/7
Let i = 26 - 24. Factor -i*x**2 + 12*x - 2*x**2 - 14 + 6.
-4*(x - 2)*(x - 1)
Let h(i) be the third derivative of -i**6/30 - i**5 - 21*i**4/2 - 98*i**3/3 - 22*i**2. Determine r so that h(r) = 0.
-7, -1
Determine r, given that 0 + 0*r - 2/3*r**2 - 2/9*r**3 = 0.
-3, 0
Let f(m) be the third derivative of -m**8/140 + 9*m**7/350 - 3*m**6/100 + m**5/100 - 8*m**2. Solve f(k) = 0 for k.
0, 1/4, 1
Let j be 18/14 - (-4 + 10 + -5). Factor 8/7 - 8/7*r + j*r**2.
2*(r - 2)**2/7
Let t(w) = 3*w - 1. Let b be t(6). Suppose -l = 5*u - b, 0 = 2*l + l - 2*u. Factor -56/3*m - 98/3*m**l - 8/3.
-2*(7*m + 2)**2/3
Let k(i) = 8*i**4 - 4*i**2 - 6*i + 8. Let g(u) = -u**4 + u - 1. Let n(x) = -6*g(x) - k(x). Factor n(y).
-2*(y - 1)**2*(y + 1)**2
Suppose 0*s - 2*s = 12. Let w(u) = u + 8. Let o be w(s). Factor -v**3 - 2*v**5 + 3*v**3 - 2*v**o + 3*v**4 + 0*v**3 - v**4.
-2*v**2*(v - 1)**2*(v + 1)
Factor 2*n**2 + 0*n + 0 - 3/2*n**3 - 1/2*n**4.
-n**2*(n - 1)*(n + 4)/2
Let t(s) be the third derivative of s**6/60 - s**5/42 - 4*s**4/21 - 4*s**3/21 + 2*s**2. Factor t(j).
2*(j - 2)*(j + 1)*(7*j + 2)/7
Factor -11/2*a**3 + 0 + 2*a**4 + a + 5/2*a**2.
a*(a - 2)*(a - 1)*(4*a + 1)/2
Let c(x) = x**4 - 4*x**3 + 4*x + 5. Let i(g) = -4*g**4 + 12*g**3 - 12*g - 16. Let w(v) = 10*c(v) + 3*i(v). Find r, given that w(r) = 0.
-1, 1
Let m(g) be the first derivative of -27/25*g**5 + 3 + 2/5*g**3 - 21/20*g**4 + 0*g**2 + 0*g. Find q such that m(q) = 0.
-1, 0, 2/9
Let t = -8369/30 - -279. Let n(u) be the third derivative of -1/9*u**3 + 0*u - t*u**5 + 1/12*u**4 + 0 + 1/180*u**6 + u**2. Factor n(h).
2*(h - 1)**3/3
Let o(d) be the first derivative of 3*d**4/16 - 3*d**2/8 + 5. Solve o(s) = 0 for s.
-1, 0, 1
Let x = 8 - 7. Let m(u) be the first derivative of 2/3*u**3 + 0*u + x + 0*u**2. What is h in m(h) = 0?
0
Let g(l) be the second derivative of -l**5/20 + l**4/12 + l**3/6 - l**2/2 + 2*l. Factor g(p).
-(p - 1)**2*(p + 1)
Let i(a) be the second derivative of a**6/360 - a**5/90 + a**4/72 - 3*a**2/2 - 2*a. Let f(s) be the first derivative of i(s). Solve f(o) = 0 for o.
0, 1
Let b(p) be the third derivative of p**8/2184 - p**7/1365 - p**6/390 + p**5/195 + p**4/156 - p**3/39 + 30*p**2. Factor b(o).
2*(o - 1)**3*(o + 1)**2/13
Let c(m) = -m**2 - 10*m + 4. Let p(i) = 9*i - 3. Let k(f) = 3*c(f) + 4*p(f). Factor k(n).
-3*n*(n - 2)
Suppose -f + 5*f + 40 = -4*h, -3*f - 34 = 5*h. Let n = 18 + f. Factor -n*c**3 - 14*c - 10*c**2 - 3*c**4 + c**4 + 3*c**2 - 4 - 11*c**2.
-2*(c + 1)**3*(c + 2)
Let m(x) be the second derivative of 3*x**6/10 - 3*x**5/10 - x**4/4 + 5*x. Factor m(t).
3*t**2*(t - 1)*(3*t + 1)
Let k(l) be the second derivative of 0*l**2 + 0 + 0*l**3 - 3/80*l**5 - 3*l - 1/48*l**4 - 1/60*l**6. Solve k(a) = 0.
-1, -1/2, 0
Let b(i) be the first derivative of 0*i**2 + 2/9*i**3 + 1 - 2/3*i. Let b(c) = 0. Calculate c.
-1, 1
Let w(b) be the first derivative of b**5/10 + b**4/8 - b**3/6 - b**2/4 - 25. Solve w(r) = 0 for r.
-1, 0, 1
Let b(v) = v**2 + 5*v. Let x(c) = c. Let q(m) = b(m) - 4*x(m). Determine o so that q(o) = 0.
-1, 0
Suppose 0 = -4*w - 5*w + 27. Factor -1/3*z - 2/3*z**2 + 0 - 1/3*z**w.
-z*(z + 1)**2/3
Let n(i) be the third derivative of -2*i**2 + 0*i - 1/630*i**7 + 0*i**4 + 0 + 0*i**3 - 1/180*i**6 - 1/180*i**5. Factor n(w).
-w**2*(w + 1)**2/3
Let v(m) be the first derivative of m**6/6 - 2*m**5/3 + 3*m**4/4 - 2*m**3/9 + 3. Let v(s) = 0. What is s?
0, 1/3, 1, 2
Let x = -1525/2 - -763. Factor x*l**2 - 1/2*l**4 - 1/2*l**3 + 0 + 1/2*l.
-l*(l - 1)*(l + 1)**2/2
Let s = -4353/13 + 335. Determine y so that 0*y - s*y**2 + 2/13 = 0.
-1, 1
Factor -1 + k + 2*k + 3*k**2 + 1.
3*k*(k + 1)
Let l(b) be the first derivative of 1/21*b**6 + 1/7*b**2 + 0*b**3 + 0*b + 3 - 1/7*b**4 + 0*b**5. Solve l(g) = 0.
-1, 0, 1
Let t = 9 + 1. Suppose -4 = 2*a - t. Factor h + 2*h - 4*h - h**5 + 2*h**a.
-h*(h - 1)**2*(h + 1)**2
Let v = 266/1035 - 4/115. Let y = 248 + -2230/9. Find w, given that v*w**4 - y*w**3 + 2/9*w - 2/9*w**2 + 0 = 0.
-1, 0, 1
Suppose -12/5 + 18/5*r**2 + 6/5*r = 0. What is r?
-1, 2/3
Let n(g) be the second derivative of 0*g**2 + 3*g - 1/168*g**7 + 1/120*g**6 + 0*g**4 + 0*g**5 + 0 + 0*g**3. Factor n(b).
-b**4*(b - 1)/4
Let s(t) be the second derivative of 9/5*t**5 - t - 2*t**4 + 0 + 0*t**2 - 8/15*t**6 + 2/3*t**3. Factor s(k).
-4*k*(k - 1)**2*(4*k - 1)
Let t be (-8)/2 + (-246)/(-41). Factor -5/2*o**t - 3*o - 1/2.
-(o + 1)*(5*o + 1)/2
Let l be (-2 + 12 + -4)*-2. Let j be 13 + l - 1/5. Factor 2/5*g**2 + j*g + 2/5.
2*(g + 1)**2/5
Let g(l) be the first derivative of l**4/8 + 4*l**3/3 + 4*l**2 + 15. Factor g(z).
z*(z + 4)**2/2
Suppose -3 = -2*l - l - 3*f, -5*l + 8 = 2*f. Let k(o) be the second derivative of l*o - 2/15*o**6 + 0*o**2 + 0 - 7/20*o**5 + 1/6*o**3 - 1/6*o**4. Factor k(n).
-n*(n + 1)**2*(4*n - 1)
Let a be 3 - (-2 - (-1 - -2)). Let i = 1 + a. Factor -12*g**4 + i*g**4 - 4*g**2 + 7*g**3 - 2*g**2 + 4*g**2.
-g**2*(g - 1)*(5*g - 2)
Let d(x) be the third derivative of -x**11/95040 + x**10/60480 + x**9/60480 + x**5/30 + 9*x**2. Let s(a) be the third derivative of d(a). Factor s(q).
-q**3*(q - 1)*(7*q + 2)/2
Let f(t) be the first derivative of 0*t + 1/5*t**5 - 1/6*t**6 - 5/3*t**3 - 6 + 3/4*t**4 + t**2. Solve f(d) = 0 for d.
-2, 0, 1
Let k = -11 + 13. Let i(z) be the first derivative of -1/4*z + 1/8*z**k + 1/12*z**3 - 1/16*z**4 - 4. Factor i(m).
-(m - 1)**2*(m + 1)/4
Let i(b) = b**2 - 9*b - 14. Let c be i(11). Factor -7*q + 4 + 3*q - 4*q**5 + 4*q**3 + 4*q**3 + 0*q**3 + 4*q**4 - c*q**2.
-4*(q - 1)**3*(q + 1)**2
Let h(o) = o**3 - 5*o**2 - o + 7. Let z be h(5). What is k in 11*k**2 - 4*k + 4*k**2 - k**z = 0?
0, 2/7
Solve 0*v**3 + 0*v**2 - 2/3*v**4 + 0*v + 0 + 1/3*v**5 = 0.
0, 2
Let 0*j**2 - 4*j**2 + 93*j - 109*j + 3*j**2 - 64 = 0. What is j?
-8
Suppose 2/15*g**5 + 0 - 2/15*g**4 - 2/15*g**3 + 2/15*g**2 + 