 10 - 8. Let g(j) be the second derivative of -1/84*j**7 - 1/12*j**3 - 3/20*j**5 + 1/15*j**6 + 0*j**d + 0 + 1/6*j**4 - 2*j. Solve g(u) = 0 for u.
0, 1
Let w(d) = 3*d + 3. Let p(q) = 8*q + 8. Let n(l) = 5*p(l) - 14*w(l). Let g be n(-1). Factor -1/3*a**2 + g + 1/3*a.
-a*(a - 1)/3
Let j(u) be the second derivative of u**6/6 - u**5 + 5*u**4/2 - 10*u**3/3 + 5*u**2/2 + 28*u. Factor j(n).
5*(n - 1)**4
Let t be (-194)/(-10) + (-2)/5. Suppose 0 = 2*g + 5*u - t, 11 = 3*g - 2*g + 3*u. Factor 3*b + b - 2*b + 2*b**g.
2*b*(b + 1)
Solve 2*o**3 + 8*o**5 - 11*o**5 - 7*o**3 + 2*o**3 - 6*o**4 = 0.
-1, 0
Let y(b) = -b**3 + 4*b**2 + b - 2. Let w be y(4). Suppose a = w*m - 3*a - 16, 5*m = -a + 18. Determine t so that 0*t + 0 + t**3 - t**2 - 1/4*t**m = 0.
0, 2
Let u(t) be the third derivative of -t**7/525 + t**6/150 - t**4/30 + t**3/15 - 3*t**2. Determine k so that u(k) = 0.
-1, 1
Let l(i) be the third derivative of i**7/210 + i**6/60 - i**5/60 - i**4/12 + i**2. Factor l(m).
m*(m - 1)*(m + 1)*(m + 2)
Let z(i) be the second derivative of -i**6/105 - 3*i**5/70 - i**4/21 - 5*i. Factor z(d).
-2*d**2*(d + 1)*(d + 2)/7
Let -2/7*p**2 + 8/7*p - 8/7 = 0. Calculate p.
2
Let v(p) be the first derivative of -p**7/14 + p**6/5 - 3*p**5/20 + 2*p - 4. Let z(n) be the first derivative of v(n). Determine q so that z(q) = 0.
0, 1
Find x such that 0*x**3 + 0*x - 4/9*x**2 + 2/9*x**4 + 2/9 = 0.
-1, 1
Factor -4*h - 1/3*h**4 + 8/3 + 2/3*h**2 + h**3.
-(h - 2)**2*(h - 1)*(h + 2)/3
Let f(r) = -r**3 - 2*r**2 + 16*r + 9. Let h be f(-5). Suppose -6/7*t**2 - 2*t + 2*t**3 - 4/7 + 10/7*t**h = 0. What is t?
-1, -2/5, 1
Find f, given that 4*f**4 + 2*f**2 + f**2 + 11*f**3 - 3*f**3 + f**2 = 0.
-1, 0
Let x be 11/(-4)*-2*12. Let p be 5*(x/15 - 4). Suppose -1/2*m - 1 + 1/2*m**p = 0. What is m?
-1, 2
Let h(m) be the first derivative of m**4/20 + 7*m**3/15 + 3*m**2/2 + 9*m/5 + 3. Find q such that h(q) = 0.
-3, -1
Let i(r) be the third derivative of -r**5/75 + r**4/30 + 7*r**2. Suppose i(u) = 0. What is u?
0, 1
Let i(x) be the first derivative of -1/3*x**6 + 0*x - 5/2*x**4 + 0*x**2 + 4/3*x**3 + 8/5*x**5 + 3. Factor i(k).
-2*k**2*(k - 2)*(k - 1)**2
Suppose -1 = n - 3. Let j(q) be the first derivative of -1/3*q + 14/9*q**3 + 1 - 1/12*q**n. Let j(p) = 0. Calculate p.
-1/4, 2/7
Find k such that 4/3*k**2 - 92/3*k**3 + 92/3*k + 8 - 28/3*k**4 = 0.
-3, -1, -2/7, 1
Suppose -4 = -4*o + 8. Suppose -o*h + 6 = 3*s, s - 2*h + h + 2 = 0. Factor 0*r**2 + 2/9*r**4 + s*r + 0 + 4/9*r**3.
2*r**3*(r + 2)/9
Let x = -41/39 - -5/13. Let y = 1/12 - x. Find g, given that -y*g**2 + 0 - 3/4*g = 0.
-1, 0
Let h(w) be the first derivative of 5*w**3/6 - 5*w**2 + 15*w/2 + 5. Factor h(c).
5*(c - 3)*(c - 1)/2
Let g(v) be the second derivative of v**6/40 + v**5/10 + v**4/8 + v**2/2 - 8*v. Let l(x) be the first derivative of g(x). Factor l(y).
3*y*(y + 1)**2
Let a = 14 + -10. Suppose -a*f = -20, -4*f + 35 = -2*b + 7*b. Factor 10*l**b + 0*l**2 + 7*l**2 - 3*l**2 + 6*l**4.
2*l**2*(l + 1)*(3*l + 2)
Let u be (-6)/(-16)*1/90. Let b(q) be the third derivative of 0 - u*q**6 + 0*q**3 + 0*q + 3*q**2 + 1/120*q**5 + 0*q**4. Suppose b(t) = 0. Calculate t.
0, 1
Let y(z) be the first derivative of 2*z**5/15 + 2*z**4/9 - 14*z**3/27 - 4*z**2/9 + 8*z/9 + 1. Determine q so that y(q) = 0.
-2, -1, 2/3, 1
Let u(v) be the first derivative of v**5/15 + v**4/6 + 6. Suppose u(r) = 0. What is r?
-2, 0
Let n(u) be the third derivative of 0*u**3 + 1/15*u**5 + 0 + 1/3*u**4 + 0*u - 1/15*u**6 - 6*u**2 - 2/105*u**7. What is f in n(f) = 0?
-2, -1, 0, 1
Let g(s) be the third derivative of -5*s**8/588 + 23*s**7/1470 + 19*s**6/840 - 5*s**5/84 + s**4/168 + s**3/21 - 39*s**2. Find n such that g(n) = 0.
-1, -1/4, 2/5, 1
Let i(w) = 504*w**4 - 904*w**3 - 1556*w**2 - 688*w - 92. Let r(s) = 505*s**4 - 905*s**3 - 1555*s**2 - 688*s - 91. Let j(l) = 5*i(l) - 4*r(l). Factor j(a).
4*(a - 3)*(5*a + 2)**3
Let k(q) = 5*q**3 - 9*q**2 + 7*q - 3. Let m = -26 + 11. Let t(u) = -11*u**3 + 19*u**2 - 15*u + 7. Let w(s) = m*k(s) - 6*t(s). Factor w(x).
-3*(x - 1)**2*(3*x - 1)
Suppose q + 6*q = 126. Let z be (-60)/q + 1*4. Determine o, given that -2/3*o**2 + 1/3*o**3 + z - 1/3*o = 0.
-1, 1, 2
Let i(d) be the first derivative of -d**4/2 - 4*d**3/3 + 3*d**2 + 16. Factor i(s).
-2*s*(s - 1)*(s + 3)
Let o = -2 - -5. Determine z so that 21*z + 7*z**4 - 24*z**2 + 11*z**3 + 4*z**3 - o*z**2 - 10*z**4 - 6 = 0.
1, 2
Let v be -1 + (128/36 - -1). Factor -v + 16/9*z - 2/9*z**2.
-2*(z - 4)**2/9
Let b = -18 - -20. Solve 14*x**b - 4*x - 2 - 12*x**2 + 2 = 0.
0, 2
Suppose 5*l - 1 = -16. Let t be 1/(2/(7 - l)). Factor -4*q**3 + 13*q + 8 + 2*q**4 + 0*q**3 - t*q - 6*q**2.
2*(q - 2)**2*(q + 1)**2
Suppose -12*m = -7*m - 100. Let a be (6/m)/((-36)/(-150)). Factor 1/2*c**2 + 0 + 0*c - a*c**3 + 3/4*c**4.
c**2*(c - 1)*(3*c - 2)/4
Factor 4 + 6*z**2 + 0*z**2 - 9*z - 1.
3*(z - 1)*(2*z - 1)
Let t(a) be the first derivative of -a**5/5 - a**4/2 + 7*a**3/3 - 2*a**2 - 20. Let t(p) = 0. Calculate p.
-4, 0, 1
Let a = -45 + 48. Suppose -3*m + 2 = -4. Factor -1/2*h + 0*h**m - 1/4*h**4 + 1/2*h**a + 1/4.
-(h - 1)**3*(h + 1)/4
Let m(i) be the first derivative of i**4/18 - 8*i**3/27 + i**2/3 + 2. Solve m(s) = 0.
0, 1, 3
Let v(b) be the first derivative of -27*b**5/20 - 21*b**4/4 - 8*b**3 - 6*b**2 + 4*b + 3. Let w(d) be the first derivative of v(d). Find u, given that w(u) = 0.
-1, -2/3
What is q in 2/9*q**3 - 2/3*q**2 + 0 + 4/9*q = 0?
0, 1, 2
Let k = 641 - 1281/2. Determine u so that -5/3*u + 2/3*u**3 + 3/2*u**2 - k = 0.
-3, -1/4, 1
Let p be (-42)/35*(-32)/72. Solve p + 54/5*a**3 + 16/3*a + 78/5*a**2 = 0 for a.
-1, -2/9
Let s(w) = w**4 + w**3 + w. Let d(b) = -2*b**4 - b**3 + b**2 - b. Let c(i) = -d(i) - s(i). Factor c(l).
l**2*(l - 1)*(l + 1)
Let w(c) = c**2 - 7*c - 16. Let n be w(-2). Let o(u) be the first derivative of -u**n - 2/9*u**3 - 4/3*u + 4. Factor o(p).
-2*(p + 1)*(p + 2)/3
Factor -1/2*x**3 + 3/2*x - 1 + 0*x**2.
-(x - 1)**2*(x + 2)/2
Suppose 0 = 3*x - n - 3*n - 19, 5*x - 26 = n. Suppose x*u = 3*u. Factor 0*y**3 + 0 - 2/3*y**4 + 0*y - 2/3*y**5 + u*y**2.
-2*y**4*(y + 1)/3
Let v = 0 + 0. Let u(s) = s**2 + 7*s + 3. Let x be u(-7). Factor -2*k**x - 2 + v + 2.
-2*k**3
Let g = 12 - 5. Let s be g + (-3 - 0)/1. Factor -2*h**4 + 4*h**3 + 5*h**3 - 5*h**s - 2*h**2.
-h**2*(h - 1)*(7*h - 2)
Let c(y) = y**2 - 4*y - 12. Let o be c(6). Factor 6/5*i**3 + 0 + o*i - 3/5*i**2 - 3/5*i**4.
-3*i**2*(i - 1)**2/5
Let t(c) be the first derivative of -2/15*c**3 + 1/15*c**6 - 1/10*c**4 + 0*c + 0*c**2 + 2/25*c**5 - 5. Factor t(a).
2*a**2*(a - 1)*(a + 1)**2/5
Let 3*h**2 + 0*h**2 - 3*h**2 + 2*h**2 + 2*h = 0. What is h?
-1, 0
Let c(i) = 26*i**2 - 2*i + 2. Let m be c(1). Let x = m + -24. Determine q, given that 7/4*q**x + 0 + 1/2*q - 7/4*q**4 - 1/2*q**3 = 0.
-1, -2/7, 0, 1
Suppose 5*j = -3*c, 4*j + 0*c = -5*c - 13. Find x such that 72*x - 27*x**2 + 3*x**j - 48 - 2*x**3 + 2*x**3 = 0.
1, 4
Suppose -4*l = -l - 21. Let j = -5 + l. Factor -s - s**j - s**2 - 3*s.
-2*s*(s + 2)
Suppose h + 0*h = 3. Suppose -1 = 3*n - 2*w + 1, 14 = n + h*w. Let n*j**2 - j**3 - j**3 + 0*j**3 = 0. Calculate j.
0, 1
Let b(p) be the third derivative of -p**5/60 + 7*p**4/24 - 30*p**2. Factor b(v).
-v*(v - 7)
Let r(p) be the first derivative of -3*p**4/4 + p**3 + 15*p**2/2 + 9*p + 6. Solve r(o) = 0 for o.
-1, 3
Factor -2 - 4*z**2 - 21 - 41 + 32*z.
-4*(z - 4)**2
Let d(w) = w - 1. Let b(n) = -3*n**2 - 14*n + 15. Let l(v) = 5*v**2 + 27*v - 29. Let c(r) = -7*b(r) - 4*l(r). Let p(m) = 2*c(m) + 22*d(m). Solve p(u) = 0 for u.
-1, 0
Suppose -l - 23 = -5*p, -3*p + 0 + 3 = 3*l. Suppose -14 = -p*j - 6. Find o such that -6*o**j - o**3 + 2*o**2 + 3*o**2 = 0.
-1, 0
Factor 4/5*t**2 - 2/5 - 2/5*t.
2*(t - 1)*(2*t + 1)/5
Let v(i) be the first derivative of -i**4/18 + 2*i**3/27 + 4*i**2/9 - 8*i/9 + 6. Factor v(d).
-2*(d - 2)*(d - 1)*(d + 2)/9
Suppose 49/5*k**3 - 48/5 + 68*k - 616/5*k**2 = 0. Calculate k.
2/7, 12
Solve 4/19*s**2 - 10/19*s**4 + 6/19*s**5 + 6/19 + 22/19*s - 28/19*s**3 = 0.
-1, -1/3, 1, 3
Let t be -9 + 138/(-30)*-2. Determine a, given that -1/5*a**3 + 3/5*a**2 - t*a**4 - 2/5 + 1/5*a = 0.
-2, -1, 1
Factor -3/2*i**2 - 9/2*i - 3.
-3*(i + 1)*(i + 2)/2
Suppose 0*d - 4 = -3*v + 5*d, -4*v + 5*d = -7. Let b(t) be the third derivative of -1/36*t**4 - 1/180*t**6 - t**2 + 0*t**v + 0*t + 1/45*t**5 + 0. Factor b(h).
-