15. Let p = t + 2/3. Determine r, given that 1/3*r + 4/3*r**2 + 0 + 4/3*r**4 + p*r**5 + 2*r**3 = 0.
-1, 0
Let u(r) be the second derivative of r**5/90 + r**4/54 - 18*r. Factor u(i).
2*i**2*(i + 1)/9
Let i(z) be the third derivative of z**5/60 + z**4/6 + 2*z**3/3 + 3*z**2. Let i(p) = 0. What is p?
-2
Let x(w) = 9*w**2 - w. Let k(g) be the first derivative of 4*g**3/3 - 2. Let u = 0 + 2. Let i(v) = u*x(v) - 5*k(v). Factor i(r).
-2*r*(r + 1)
Let d(m) = m**3 + 6*m**2 - 2*m - 7. Let v be d(-6). Suppose u = -5*g + 6 + 11, 0 = v*u + g - 13. Factor 6/5*i - 2*i**u + 4/5.
-2*(i - 1)*(5*i + 2)/5
Let n(g) be the third derivative of 0*g**4 + 0 + 4*g**2 + 0*g**3 + 1/420*g**7 + 0*g - 1/120*g**6 + 1/120*g**5. Factor n(y).
y**2*(y - 1)**2/2
Let y(m) be the third derivative of m**6/120 - m**4/8 - m**3/3 - 3*m**2. Solve y(b) = 0 for b.
-1, 2
Let k(s) = 9*s**3 + 36*s**2 + 33*s - 6. Let n(g) = g**3 + g**2 + 1. Let t(p) = -k(p) - 12*n(p). Factor t(u).
-3*(u + 1)**2*(7*u + 2)
Let g = 52 - 36. Suppose 32*w**2 - 24*w - 8*w**3 + 8*w**4 + 8 - 4*w - g*w**4 + 8*w**5 - 4*w**5 = 0. What is w?
-2, 1
Let d(f) be the first derivative of 6*f**5/35 - f**4/7 + 10. Determine u, given that d(u) = 0.
0, 2/3
Let a(w) be the second derivative of -w**7/14 - 4*w**6/5 - 18*w**5/5 - 17*w**4/2 - 23*w**3/2 - 9*w**2 + 26*w. Factor a(x).
-3*(x + 1)**3*(x + 2)*(x + 3)
Suppose -26 + 6 = -4*q, 5*g - 4*q - 40 = 0. Factor -108*o**4 + 32*o + 14*o**4 - 198*o**3 - g*o**2 - 8*o - 95*o**4.
-3*o*(3*o + 2)**2*(7*o - 2)
Let f(q) = q**2 + 8*q - 6. Let b be f(-9). What is r in r**2 + b - 7 + 4 - 3*r = 0?
0, 3
Let r(n) be the first derivative of -5*n**3/3 - 60*n**2 - 720*n + 5. Suppose r(p) = 0. What is p?
-12
Let v(w) = 7*w**3 + 26*w**2 + 3*w - 3. Let s(k) = -14*k**3 - 51*k**2 - 7*k + 5. Let c(b) = -3*s(b) - 5*v(b). Factor c(g).
g*(g + 3)*(7*g + 2)
Let o(d) be the first derivative of -5*d**3/3 - 5*d**2 - 18. Determine v, given that o(v) = 0.
-2, 0
Let g(k) be the third derivative of 0*k**4 + 0*k + 0 + 1/180*k**6 - 1/60*k**5 + 2*k**2 + 1/3*k**3. Let y(w) be the first derivative of g(w). Factor y(d).
2*d*(d - 1)
Let m = -8 + 10. Let q be 1 + ((-12)/(-4) - m). Factor -j**q + 1/2 + 1/2*j**4 + 1/2*j + 1/2*j**5 - j**3.
(j - 1)**2*(j + 1)**3/2
Let q(d) = -5*d**2 - 4*d - 9. Let p(n) = -n**2 - n - 2. Let z(w) = 9*p(w) - 2*q(w). Factor z(y).
y*(y - 1)
Let o(s) be the third derivative of -s**5/12 - 5*s**4/12 + 5*s**3/2 + 6*s**2. Factor o(k).
-5*(k - 1)*(k + 3)
Let q(r) be the third derivative of r**7/42 - r**6/60 - r**5/12 + r**4/12 - 12*r**2. Factor q(l).
l*(l - 1)*(l + 1)*(5*l - 2)
Suppose -3*j**2 + j + 7*j**3 + j - 6*j**3 = 0. What is j?
0, 1, 2
Factor 17*z**5 + 6*z**3 + z**2 - 8*z**5 + 6*z**4 + z**2 - 7*z**5.
2*z**2*(z + 1)**3
Let d(b) be the third derivative of -b**8/1176 - b**7/735 + b**6/210 + b**5/105 - b**4/84 - b**3/21 - 7*b**2. Factor d(w).
-2*(w - 1)**2*(w + 1)**3/7
Let r(n) be the third derivative of n**9/30240 - n**8/13440 - n**7/5040 + n**6/1440 + n**4/6 + 5*n**2. Let u(q) be the second derivative of r(q). Factor u(x).
x*(x - 1)**2*(x + 1)/2
Let 2/3 - 1/3*b**2 + 1/3*b = 0. What is b?
-1, 2
Let n = -1 + 4. Let m be 12*(-3 - (-10)/n). Find h, given that 2/3*h**m + 0*h**3 + 0 + 0*h - 2/3*h**2 = 0.
-1, 0, 1
Factor 0*l**3 - 2/3*l**2 + 0*l + 0 + 2/3*l**4.
2*l**2*(l - 1)*(l + 1)/3
Let l(g) be the first derivative of -3*g**5/35 + 11*g**4/28 - 5*g**3/7 + 9*g**2/14 - 2*g/7 - 11. Suppose l(a) = 0. What is a?
2/3, 1
Let o(s) be the second derivative of s**6/5 - 27*s**5/20 + 9*s**4/4 + s**3/2 - 9*s**2/2 + 10*s. Factor o(q).
3*(q - 3)*(q - 1)**2*(2*q + 1)
Let k be (0 - 10/(-2)) + -3. Let d(h) be the third derivative of 5/36*h**4 - 1/36*h**6 + 0 - 1/45*h**5 + 2/9*h**3 - h**k + 0*h. Factor d(l).
-2*(l - 1)*(l + 1)*(5*l + 2)/3
Let h(r) be the first derivative of r**5/240 - r**4/32 + r**3/12 - 2*r**2 - 1. Let d(o) be the second derivative of h(o). Factor d(q).
(q - 2)*(q - 1)/4
Let a = 12 + -7. Let c(p) be the second derivative of 1/30*p**4 - 1/15*p**3 + 1/50*p**a - 3*p - 1/5*p**2 + 0. Factor c(i).
2*(i - 1)*(i + 1)**2/5
Let z(x) be the second derivative of -2*x**6/3 + 22*x**5/5 + 17*x**4/3 - 20*x**3/3 + 2*x - 1. Factor z(r).
-4*r*(r - 5)*(r + 1)*(5*r - 2)
Let b(f) be the third derivative of f**6/360 - f**5/60 - 35*f**2. Find w such that b(w) = 0.
0, 3
Let y(a) = a**2 + 4*a - 2. Let v be y(-6). Let z = v - 6. Let -3*d**2 + d**2 + 0*d**2 - 2 - z*d = 0. Calculate d.
-1
Let z = -29 + 30. Let n be (z/(-6))/(10/(-20)). Let 4/3*p**4 + 0 + 4/3*p**2 + 2*p**3 + 1/3*p**5 + n*p = 0. What is p?
-1, 0
Let s = 18 + -14. Let b(d) be the third derivative of -1/96*d**s + d**2 + 0*d - 1/120*d**5 + 0*d**3 + 0. Factor b(k).
-k*(2*k + 1)/4
Let v(y) be the first derivative of -1/10*y**5 - 2 + 0*y**3 + 0*y**4 + 3*y + 0*y**2. Let m(b) be the first derivative of v(b). Solve m(s) = 0.
0
Let s(h) = h - 9. Let m be s(8). Let g be m*5/((-35)/2). Factor 2/7 - 2/7*k - g*k**2 + 2/7*k**3.
2*(k - 1)**2*(k + 1)/7
Let 0 - 14/19*q**3 - 2/19*q - 10/19*q**2 - 6/19*q**4 = 0. Calculate q.
-1, -1/3, 0
Solve 0*v**2 + 0 + 0*v - 2/15*v**4 + 4/15*v**5 - 2/15*v**3 = 0.
-1/2, 0, 1
Let l = 6 + -4. Let z = 7 - 5. Factor -3/2*j**l - z - 1/4*j**3 - 3*j.
-(j + 2)**3/4
Find x such that 0 - 4/5*x - x**2 - 1/5*x**3 = 0.
-4, -1, 0
Suppose -12*p**2 - 9*p**4 + 0*p**3 + 3*p**4 + p**5 + 17*p**3 - 4*p**3 + 4*p = 0. Calculate p.
0, 1, 2
Suppose 0*n**4 - 3*n + 7/4*n**3 + 2 - 1/4*n**5 - 1/2*n**2 = 0. Calculate n.
-2, 1, 2
Let y = -119 - -122. Factor 2/3*f + f**y + 0 + 5/3*f**2.
f*(f + 1)*(3*f + 2)/3
Let q(u) be the first derivative of u**7/168 - u**6/120 - u**5/80 + u**4/48 - 2*u - 1. Let k(b) be the first derivative of q(b). Find n, given that k(n) = 0.
-1, 0, 1
Suppose -2*a = -a - 9. Let l(s) = 3*s**3 + 9*s**2 - 21*s. Let k(c) = c**3 + 2*c**2 - 5*c. Let o(i) = a*k(i) - 2*l(i). Factor o(z).
3*z*(z - 1)*(z + 1)
Let j(y) = 3*y**3 - 3*y**2 - y + 1. Suppose 4 - 2 = -f. Let b(a) = a**4 - 10*a**3 + 9*a**2 + 3*a - 3. Let n(c) = f*b(c) - 7*j(c). Factor n(g).
-(g - 1)*(g + 1)**2*(2*g - 1)
Let a be ((-6)/4)/((-3)/10). Let h be 1/5 - 1/a. Factor -1/4*z**3 + h*z**2 - z**5 + 0*z + 0 - 5/4*z**4.
-z**3*(z + 1)*(4*z + 1)/4
Let p be 169/65 + (-2)/(-5). Find r, given that -2/7*r**5 + 4/7*r**4 + 0*r + 0*r**2 + 0 - 2/7*r**p = 0.
0, 1
Let k = 7 - 5. Factor -11*v**4 - 2*v**2 - 3*v**4 + 16*v**4 - k*v**3 + 2*v**5.
2*v**2*(v - 1)*(v + 1)**2
Let k be (-5)/4*228/(-190). Factor -1 - 1/2*u**2 - k*u.
-(u + 1)*(u + 2)/2
Let k be ((-2)/189)/(22/(-33)). Let d(q) be the second derivative of 0*q**2 - k*q**7 + 0*q**5 + 2/45*q**6 + 0 - 1/9*q**4 - q + 1/9*q**3. Factor d(v).
-2*v*(v - 1)**3*(v + 1)/3
Let v(t) = -5*t**2 - 5*t + 4. Let f(z) = -4*z**2 - 4*z + 3. Let s(q) = 4*f(q) - 3*v(q). Suppose s(c) = 0. What is c?
-1, 0
Let z be (10/(-30))/((-1)/15). Let m = 3 + -1. Factor -r**z - r**3 + 4*r**3 + m*r**4 - 4*r**3.
-r**3*(r - 1)**2
Let s(x) = -5*x**4 - 30*x**3 - 40*x**2 + 24*x + 39. Let n(k) = 5*k**4 + 30*k**3 + 40*k**2 - 25*k - 40. Let m(a) = -6*n(a) - 5*s(a). Suppose m(l) = 0. What is l?
-3, -1, 1
Let x(m) = m**2 - m - 12. Let s be x(-3). Let l(g) be the third derivative of -2*g**2 + 1/12*g**3 - 1/120*g**5 + 0 + 0*g**4 + s*g. Factor l(c).
-(c - 1)*(c + 1)/2
Let n(p) be the second derivative of p**7/294 + p**6/105 - p**5/70 - p**4/21 + p**3/42 + p**2/7 - 6*p. What is x in n(x) = 0?
-2, -1, 1
Let m(o) be the second derivative of -o**7/5040 - o**6/480 - o**5/120 - o**4/3 + 4*o. Let d(v) be the third derivative of m(v). Factor d(u).
-(u + 1)*(u + 2)/2
Let q(w) be the second derivative of w**6/60 - 9*w**5/40 + w**4 - 4*w**3/3 + 3*w. What is x in q(x) = 0?
0, 1, 4
Let i = -5 + 9. Let s be i + (2 - 4) - -1. Factor 0*n**2 - 2*n**s + n**3 + n**2.
-n**2*(n - 1)
Let n(y) be the second derivative of -y**2 - 1/420*y**6 + 0*y**5 + y + 1/84*y**4 + 0*y**3 + 0. Let u(l) be the first derivative of n(l). Factor u(r).
-2*r*(r - 1)*(r + 1)/7
Suppose -2*z = -4*x - 11 + 3, 5 = -5*x. Solve 5/2*c**2 + z - 8*c + 25/2*c**3 = 0.
-1, 2/5
Let v(h) = -h**3 - h**2 - h. Let n(b) = 10*b**3 - 42*b**2 + 90*b - 40. Let w(x) = -n(x) - 6*v(x). Factor w(i).
-4*(i - 10)*(i - 1)**2
Let a(v) = -v**2 - 2. Let l(y) = 0*y**2 + 1 - 2*y + y**2 + y. Let r(k) = -a(k) - 3*l(k). Solve r(p) = 0.
1/2, 1
Let 8/7 - 12/7*d + 6/7*d**2 - 1/7*d**3 = 0. What is d?
2
Factor 5/