5 - -17. Find r, given that g*r**2 + 0*r**3 - 3*r**3 - 9*r + 0*r**3 + 7*r**2 + 3 = 0.
1
Let f(n) be the second derivative of n**6/75 - 11*n**5/50 - 2*n**4/5 + 190*n + 2. Let f(b) = 0. Calculate b.
-1, 0, 12
Let k(f) = f**3 - 2*f**2 - 31*f + 64. Let a be k(2). Factor 8/7*b**3 + 10/7*b**a + 0 + 2/7*b.
2*b*(b + 1)*(4*b + 1)/7
Suppose -3*l - 3 = -15. Factor 203 + l*u**2 - 105 - 110 + 8*u.
4*(u - 1)*(u + 3)
Let d(g) be the third derivative of 0 + 4*g**2 - 1/105*g**5 + 8/21*g**3 + 1/21*g**4 + 0*g - 1/420*g**6. Factor d(y).
-2*(y - 2)*(y + 2)**2/7
Let z(v) be the first derivative of -v**2/2 + v + 7. Let u be z(-3). Factor -24*f + 16 + 20*f**5 - 6*f + 65*f + 61*f + 108*f**u + 212*f**2 + 220*f**3.
4*(f + 1)**3*(f + 2)*(5*f + 2)
Let m = -3 - -3. Suppose -z - y + 7 = m, 2*z = -0*z - 5*y + 29. Determine s so that -6*s - 4*s**2 + 7*s**3 + 2*s**3 - 7*s**4 - s**2 + 7*s + z*s**5 = 0.
0, 1/2, 1
Let y(v) be the first derivative of -v**5/30 + 2*v**4/3 - 31*v**3/9 + 20*v**2/3 - 11*v/2 + 163. Suppose y(s) = 0. What is s?
1, 3, 11
Suppose 35 = -9*o + 476. Let y be 385/o + -1 + -6. Factor -2/7*q**4 + 0 + y*q**3 + 0*q - 4/7*q**2.
-2*q**2*(q - 2)*(q - 1)/7
Let z(o) be the first derivative of 3*o**2 - 3/5*o**5 + o**3 - 4 + 0*o - 3/2*o**4. Determine m, given that z(m) = 0.
-2, -1, 0, 1
Let g(l) be the first derivative of l**6/4 - 69*l**5/20 - 3*l**4/8 + 23*l**3/4 - 461. Solve g(k) = 0.
-1, 0, 1, 23/2
Let a(o) be the first derivative of 0*o**2 + 5/3*o**4 - 16/15*o**5 + 2/9*o**6 + 0*o - 1 - 8/9*o**3. Factor a(g).
4*g**2*(g - 2)*(g - 1)**2/3
Let u(m) be the first derivative of -3/2*m - 1/4*m**2 + 1/8*m**4 + 1/2*m**3 - 5. Factor u(p).
(p - 1)*(p + 1)*(p + 3)/2
Suppose d + 2*x = -x + 11, 3*x - 17 = -4*d. Suppose a = -d*m + 2, -a - 4*m = -5*a - 4. Factor 0*s + a*s**2 + 0 + 4/7*s**5 + 0*s**3 + 4/7*s**4.
4*s**4*(s + 1)/7
Let q(v) = -v**2 + 45*v - 40. Let x(g) = 12*g**2 - 585*g + 519. Let c(u) = 27*q(u) + 2*x(u). Factor c(t).
-3*(t - 14)*(t - 1)
Let t(k) = 4*k**3 - 15*k**2 + 3. Let j(n) = 4*n**3 - 14*n**2 + 2. Let c(r) = -r**2 - 8*r - 12. Let h be c(-5). Let o(y) = h*j(y) - 2*t(y). Factor o(u).
4*u**2*(u - 3)
Let s = -159 - -1117/7. Suppose -2*t + 6 + 0 = 0. Factor 8/7*p**t + 0 + s*p**2 + 1/7*p**5 + 0*p + 5/7*p**4.
p**2*(p + 1)*(p + 2)**2/7
Let z(k) be the second derivative of -1/30*k**4 + 4 - 6*k + 14/15*k**2 - 19/45*k**3. Suppose z(g) = 0. Calculate g.
-7, 2/3
Suppose 3*y - 11 = -23. Let h be (-1)/3 + (y - (-78)/18). Factor 3/2*o**2 + 0 + 3*o**3 + h*o + 3/2*o**4.
3*o**2*(o + 1)**2/2
Solve 0 + 0*m - 32/9*m**2 - 4/9*m**3 = 0 for m.
-8, 0
Let d be 6/504*8 + 366/126. Determine m so that 1/2*m**d - m**4 + 0*m**2 + 0*m + 1/2*m**5 + 0 = 0.
0, 1
Let j(r) be the third derivative of -r**7/105 - r**6/12 - 4*r**5/15 - r**4/3 - 6*r**2 - 9*r. Factor j(n).
-2*n*(n + 1)*(n + 2)**2
Solve 10 - 98*s**2 + 16*s - 111*s + 143*s**2 = 0.
1/9, 2
Factor -2*m**4 + 0*m + 4*m**4 - 2478*m**3 - 4*m + 13*m**2 + 2467*m**3.
m*(m - 4)*(m - 1)*(2*m - 1)
Let l(d) = -d**2 + 16*d - 13. Let a be l(15). Factor i**2 - 7 - 3 - a*i + 11.
(i - 1)**2
Let w(n) = 74*n**2 + 76*n - 6. Let l(p) = -15*p**2 - 15*p + 1. Suppose 4*b - 9 = 3. Let v be 84/35 + (-4)/10 + 14. Let y(k) = b*w(k) + v*l(k). Factor y(u).
-2*(3*u + 1)**2
Let d = 6935/1221528 + 2/7271. Let a(i) be the third derivative of -1/120*i**5 + 0*i**3 - 3*i**2 + 0 - d*i**7 + 0*i + 0*i**4 + 7/480*i**6. Factor a(f).
-f**2*(f - 1)*(5*f - 2)/4
Suppose -1/6*u**2 - 43/6*u + 0 = 0. Calculate u.
-43, 0
Let q be 7 + (14 + -15)*(1 + 2). Let 16*o - 26 - q*o + 16 - 2*o**2 = 0. Calculate o.
1, 5
Suppose 22 = 5*z + 2. Let r(t) be the first derivative of 5/16*t**z + 0*t - 6 + 1/5*t**5 + 1/12*t**3 + 0*t**2. Let r(k) = 0. Calculate k.
-1, -1/4, 0
Let q be (-25)/6 + 4 - 1/(-4). Let s = 1/3 - q. Factor -b - 1 - s*b**2.
-(b + 2)**2/4
Let r be 306/1326 - (-1)/(78/86). Let i(q) = -q**2 - 4*q + 7. Let j be i(-5). Suppose -r*p - 2/3*p**j + 0 = 0. Calculate p.
-2, 0
Let n(f) = -92*f + 7. Let h be n(-1). Let z be (h/(-12))/(-3) - 1/(-4). Suppose 2/7*q**4 + 0 + 0*q**z + 2/7*q**5 + 0*q**2 + 0*q = 0. Calculate q.
-1, 0
Let v(h) be the second derivative of h**5/80 + h**4/8 + 77*h. Solve v(t) = 0 for t.
-6, 0
Let t(f) be the third derivative of -5*f**2 + 0*f**3 + 0*f + 1/270*f**5 + 0 + 1/54*f**4. Find i such that t(i) = 0.
-2, 0
Let l(m) be the first derivative of -5*m**4/8 + 5*m**3/3 + 65*m**2/4 + 25*m - 485. Factor l(a).
-5*(a - 5)*(a + 1)*(a + 2)/2
Factor -13722888/7*o**4 + 13970892/7*o**3 - 249498/7*o**2 + 1497/7*o - 3/7.
-3*(o - 1)*(166*o - 1)**3/7
Let v = -951 + 10463/11. Find i such that -6/11*i - v*i**2 + 0 = 0.
-3, 0
Let n = -80 - -82. Determine y, given that -10*y**2 + 23*y**n + 4*y - 9*y**2 - 6*y**2 = 0.
0, 2
Let c(t) be the second derivative of t**4/72 - 5*t**3/18 + 3*t**2/4 + t - 1. Find o, given that c(o) = 0.
1, 9
Let y(l) be the third derivative of 0*l - 5/24*l**6 + 7/12*l**5 - 5*l**3 - 1/42*l**7 + 0 - 24*l**2 + 25/24*l**4. Factor y(k).
-5*(k - 1)**2*(k + 1)*(k + 6)
Factor 43 + 2*t**2 + 18*t - 40 + 25.
2*(t + 2)*(t + 7)
Factor 530*i**3 - 9*i - 7*i - 528*i**3 - 2*i**2 + 24.
2*(i - 2)**2*(i + 3)
Let f(n) be the third derivative of n**9/20160 - n**8/6720 - n**7/1680 + n**6/240 + n**5/6 + 8*n**2. Let s(g) be the third derivative of f(g). Factor s(d).
3*(d - 1)**2*(d + 1)
Let w(l) be the second derivative of -37/60*l**5 + 0*l**2 + 1/18*l**7 - 29*l - 31/36*l**4 - 1/18*l**6 + 0 - 1/3*l**3. Find m such that w(m) = 0.
-1, -2/7, 0, 3
Let o(b) be the third derivative of 0*b**3 - 1/12*b**4 - 1/15*b**6 - 2*b**2 - 1/6*b**5 + 0 + 0*b. Factor o(j).
-2*j*(j + 1)*(4*j + 1)
Let y(h) be the third derivative of -h**5/160 + 11*h**4/64 + 3*h**3/4 + 10*h**2. Factor y(g).
-3*(g - 12)*(g + 1)/8
Let n(x) be the first derivative of -3*x**7/14 - 53*x**6/72 - 19*x**5/24 - 5*x**4/12 + x**3 - 2. Let m(s) be the third derivative of n(s). Factor m(q).
-5*(q + 1)*(4*q + 1)*(9*q + 2)
Let c(x) be the second derivative of -1/12*x**4 - 1/4*x**2 + 9*x + 1/20*x**5 - 7/24*x**3 + 0. Factor c(r).
(r - 2)*(2*r + 1)**2/4
Factor -15/4 - 13/8*j + 1/8*j**2.
(j - 15)*(j + 2)/8
Let q be 5*(-30)/25*8/(-6). Suppose -2*t - 2 = -2*p - q, -3*t - 5*p = 15. Solve 5*g**4 + 0 - 11/3*g**3 + 2/3*g**2 + t*g = 0 for g.
0, 1/3, 2/5
Let l(k) be the second derivative of 7*k**7/18 + 28*k**6/15 + 22*k**5/15 - 8*k**4/3 + 8*k**3/9 + k + 11. What is f in l(f) = 0?
-2, 0, 2/7
Let t(w) be the third derivative of w**11/133056 + w**10/30240 - 7*w**5/30 - 14*w**2. Let u(k) be the third derivative of t(k). Solve u(l) = 0 for l.
-2, 0
Find u such that 0*u - 1/2*u**5 + 1/2*u**3 + 0 + 7/2*u**2 - 7/2*u**4 = 0.
-7, -1, 0, 1
Suppose -h = h. Factor -2*x**3 + h*x + 2*x - 2*x**2 - 2*x.
-2*x**2*(x + 1)
Let q(f) be the first derivative of -f**5/5 + f**4/2 - f**3/3 - 43. Solve q(a) = 0.
0, 1
Let r be (6 - 4) + 2 + -2. Factor 35*h**4 + 2*h**3 - 36*h**4 - h + h - h**r.
-h**2*(h - 1)**2
What is g in 135/2*g**3 - 489*g**2 + 72*g**4 + 15/2*g**5 + 450*g - 108 = 0?
-6, 2/5, 1
Let c(o) = 2*o**2 + 3*o - 3. Let g(x) = 3*x**2 + 5*x - 5. Let w(l) = 5*c(l) - 3*g(l). Let j(p) = 3*p**2 + 3*p. Let m(s) = -j(s) + 4*w(s). Factor m(b).
b*(b - 3)
Suppose -5*b = 3*j - 7, -3*j - 2*b = -4*j - 16. Let z be (j/(-50))/(-6*2/(-60)). Factor 4/5*c - 1/5 - z*c**2.
-(c - 1)*(3*c - 1)/5
Solve -2/5*t**3 - 6/5 - 2/5*t**2 + 2*t = 0.
-3, 1
Let n(i) = -i**3 - 25*i**2 + 8*i + 200. Let c be n(-25). Factor -b**2 + c - 1/2*b.
-b*(2*b + 1)/2
Let i(k) be the third derivative of -11*k**2 - 1/630*k**7 + 0 + 0*k + 0*k**4 + 0*k**3 - 1/90*k**5 - 1/120*k**6. Factor i(s).
-s**2*(s + 1)*(s + 2)/3
Solve -1/4*n**2 + 3/2*n + 0 = 0 for n.
0, 6
What is i in 492*i + 12545 - 4*i**2 - 1759 + 14183 + 7*i**2 - 4797 = 0?
-82
Let s(q) be the second derivative of -q**5/20 - q**4/6 + 7*q**3/6 - q**2/2 - 37*q. Let c be s(-4). Factor 0*t + 0 + 1/5*t**c + 0*t**2.
t**3/5
Let c(j) = 9*j**4 - 9*j**3 + 15*j**2 + 106*j - 144. Let f(s) = 5*s**4 - 3*s**3 + 7*s**2 + 54*s - 72. Let u(y) = 3*c(y) - 5*f(y). Factor u(h).
2*(h - 3)**2*(h - 2)*(h + 2)
What is r in 4*r - 5 - 4*r**2 - 3 - 16*r = 0?
-2, -1
Find q, given that 12*q**2 + 224*q + 46*q - 8*q**2 + 146*q = 0.
-104, 0
Let o(t) be the third derivative of -1/20*t**5 + 19*t**2 + 0*t + 0 + 5/8*t**4 + 3*t**3. Factor o(z).
-3*(z - 6)*(z + 1)
Let j(a) be the first derivative of -a**5/80 + a**3/8 +