10). Let h = 33 + -98/3. Factor 2/3*w - q*w**2 - h.
-(w - 1)**2/3
Let f(m) = -4*m**3 + 3*m**2 + 7*m - 3. Let t(h) = -8*h**3 + 5*h**2 + 13*h - 5. Let w(n) = 5*f(n) - 3*t(n). Find d such that w(d) = 0.
-1, 0, 1
Let l = 6 - 2. Factor 5*q**5 - l*q**3 + 4*q**4 - 3*q**5 + q**4 - 3*q**4.
2*q**3*(q - 1)*(q + 2)
Let d(c) be the first derivative of 5*c**3/6 + 5*c**2/2 - 15*c/2 - 15. Solve d(y) = 0.
-3, 1
Let f = -1478 + 1480. What is r in 0 + 2/3*r**3 - 1/3*r**4 + 0*r + 0*r**f = 0?
0, 2
Let p(w) be the third derivative of w**6/24 + w**5/12 - 5*w**4/6 - 10*w**3/3 + 51*w**2. Solve p(z) = 0 for z.
-2, -1, 2
Suppose -5*k + 27 = -4*v, 3 = 4*k + 3*v - 0. Let u(o) be the first derivative of -o**2 + 0*o - k + 4/3*o**3 - 1/2*o**4. Determine m so that u(m) = 0.
0, 1
Let u(s) = 3*s**3 - 15*s**2 + 15. Let x(a) = 9*a**3 - 44*a**2 - a + 44. Let d(j) = 8*u(j) - 3*x(j). Factor d(o).
-3*(o - 4)*(o - 1)*(o + 1)
Let y(w) = 7*w**3 - 9*w**2 - 3*w. Let j be 1/(0 - 3/(-15)). Let z(n) = -10*n**3 + 13*n**2 + 4*n. Let i(b) = j*z(b) + 7*y(b). Factor i(p).
-p*(p - 1)**2
Let m(l) = 8*l**5 + 20*l**4 + 22*l**3 + 10*l**2 + 2. Let s(n) = -33*n**5 - 79*n**4 - 87*n**3 - 41*n**2 - 9. Let y(c) = -18*m(c) - 4*s(c). Solve y(u) = 0.
-2, -1, -2/3, 0
Let x(z) be the first derivative of -2*z**7/735 - z**6/420 + z**5/210 + z**2/2 + 3. Let f(r) be the second derivative of x(r). Factor f(h).
-2*h**2*(h + 1)*(2*h - 1)/7
Let m(y) be the second derivative of y**5/45 - 5*y**4/72 + y**3/18 + 3*y**2/2 + y. Let v(f) be the first derivative of m(f). What is l in v(l) = 0?
1/4, 1
Factor -1/3*l**2 - 2 + 5/3*l.
-(l - 3)*(l - 2)/3
Let x(c) = 18*c**2 + 38*c + 32. Let y(z) = -7*z**2 - 15*z - 13. Let l(n) = -5*x(n) - 12*y(n). Suppose l(t) = 0. What is t?
-1, -2/3
Let i(h) be the third derivative of 7*h**7/3 + 287*h**6/60 + h**5/5 - 11*h**4/3 - 8*h**3/3 + 2*h**2. Determine n so that i(n) = 0.
-1, -2/7, 2/5
Let c = 12 + -10. Factor -20*k**3 - 5*k + 10*k**4 + 4*k**2 - 2*k**5 - c*k + 2 + 16*k**2 - 3*k.
-2*(k - 1)**5
Let g(z) be the first derivative of z**5/15 + 3*z**4/8 - z**3/3 - 5*z**2/12 - 45. Suppose g(r) = 0. What is r?
-5, -1/2, 0, 1
Let b = -7 + 9. Let -1/4*h**2 - 2*h**3 + 1 - 3/4*h**4 + b*h = 0. Calculate h.
-2, -1, -2/3, 1
Let r(z) be the first derivative of -z**5/300 + z**4/60 + z**2/2 - 2. Let i(v) be the second derivative of r(v). Factor i(c).
-c*(c - 2)/5
Factor -4/9*h**3 + 2/9*h**5 + 0*h + 0*h**2 + 2/9*h**4 + 0.
2*h**3*(h - 1)*(h + 2)/9
Let s be 14/3*45/6. Suppose 5*h - 15 = 3*g, h + 5*g - 10 = -s. Determine z so that h*z**4 - z**4 + 0*z**4 + z**3 = 0.
0, 1
Let o(c) be the first derivative of -c**4/12 + c**2/2 - 3*c + 1. Let j(u) be the first derivative of o(u). Find h, given that j(h) = 0.
-1, 1
Let l(d) be the third derivative of d**11/332640 + d**10/151200 + d**5/30 - d**2. Let q(p) be the third derivative of l(p). Suppose q(s) = 0. Calculate s.
-1, 0
Let b(i) be the second derivative of -i**5/120 + i**4/48 + i**2 + 2*i. Let u(h) be the first derivative of b(h). Factor u(c).
-c*(c - 1)/2
Suppose c + 2*b = 4 + 3, 0 = -2*c + 4*b - 2. Solve -3/4*k + 3/4*k**c - 3/4*k**2 + 3/4 = 0.
-1, 1
Let w be (-2)/10 + 68/(-60). Let q = -5/6 - w. Factor -q*s**3 + 0 + s - 1/2*s**2.
-s*(s - 1)*(s + 2)/2
Let d(c) be the third derivative of -c**5/90 + c**4/18 + 8*c**3/9 - 27*c**2. Suppose d(s) = 0. What is s?
-2, 4
Let c(a) be the first derivative of a**4/4 - a**2/2 - 6. Factor c(f).
f*(f - 1)*(f + 1)
Let g(y) be the second derivative of -y**6/105 + y**5/70 + 6*y. Factor g(i).
-2*i**3*(i - 1)/7
Let r(k) be the third derivative of -1/6*k**4 + 0*k - 7*k**2 + 1/30*k**6 + 0 - 1/15*k**5 + 2/3*k**3. Determine f so that r(f) = 0.
-1, 1
Let k(a) be the second derivative of a**6/60 - a**5/30 - a**4/6 - 2*a**2 + 5*a. Let r(t) be the first derivative of k(t). Factor r(n).
2*n*(n - 2)*(n + 1)
Suppose -a - 4*b - 16 = 0, -4*a = -2*a + 3*b + 7. Let f(c) = 2*c - 6. Let n be f(a). Factor 0 + 2/3*p**3 + 2/3*p**n - 2/3*p - 2/3*p**4.
-2*p*(p - 1)**2*(p + 1)/3
Let o(s) = -s**3 - 5*s**2 + 6*s + 4. Let w be o(-6). Suppose -10 + w = -3*v. Find j, given that 0 - 1/4*j - 1/2*j**v - 1/4*j**3 = 0.
-1, 0
Let d(j) = -7*j**5 + 2*j**4 + j**3 - 8*j**2 - 6*j. Let s(r) = -6*r**5 + 2*r**4 + r**3 - 7*r**2 - 5*r. Let m(w) = -5*d(w) + 6*s(w). Factor m(y).
-y**2*(y - 2)*(y - 1)*(y + 1)
Suppose 0 = 5*w - 0*w. Let b(u) be the third derivative of 1/210*u**5 + 2*u**2 - 1/84*u**4 - 2/21*u**3 + 0 + w*u. Factor b(t).
2*(t - 2)*(t + 1)/7
Let f(t) be the third derivative of t**6/360 + t**5/60 - t**3/2 - 5*t**2. Let k(q) be the first derivative of f(q). Factor k(w).
w*(w + 2)
Let q = -428/3 - -143. Let p**2 + q*p + 0 + 1/3*p**4 + p**3 = 0. Calculate p.
-1, 0
Solve 5/3*z**4 + 13/3*z**3 - 2/3 + 3*z**2 - 1/3*z = 0 for z.
-1, 2/5
Let d(x) be the first derivative of 1/3*x**3 + 1/4*x**4 + 0*x**2 + 0*x + 3. Factor d(v).
v**2*(v + 1)
Let g(j) be the first derivative of 4*j**5/5 + 13*j**4/2 + 4*j**3 + 23. Let g(d) = 0. Calculate d.
-6, -1/2, 0
Let u(d) be the third derivative of 0*d**7 + 0*d + 0*d**5 - 1/12*d**4 + 1/30*d**6 + 0*d**3 + 0 - 1/168*d**8 - 3*d**2. Factor u(i).
-2*i*(i - 1)**2*(i + 1)**2
Let r(b) be the second derivative of b**6/240 + b**5/40 + b**4/16 + b**3/12 - b**2/2 - 2*b. Let k(p) be the first derivative of r(p). What is y in k(y) = 0?
-1
Let p(h) be the third derivative of -h**7/42 - 7*h**6/120 - h**5/30 + 20*h**2. Factor p(t).
-t**2*(t + 1)*(5*t + 2)
Suppose b - 4*t - 14 = 0, 4*t - 2 + 22 = 4*b. Solve 6*i**b + 7 - 9*i**4 - 9*i - 4*i**3 + 3*i**5 + 10*i**3 - 4 = 0 for i.
-1, 1
Solve -81*u**4 + 26*u**2 + 8*u + 87*u**4 + 12*u**2 + 28*u**3 - 8 = 0 for u.
-2, -1, 1/3
Let j(g) be the first derivative of 2*g**4 - 4*g**3 + 2*g**2 + 6. Factor j(o).
4*o*(o - 1)*(2*o - 1)
Let r(f) be the first derivative of -2*f**3/3 - 9*f**2 - 24. Factor r(g).
-2*g*(g + 9)
Let y be (0/1)/(-3)*(-4 + 3). Suppose 1/2*d**5 + 0 - d**3 + 1/2*d + 0*d**2 + y*d**4 = 0. Calculate d.
-1, 0, 1
Let a = -3 + 6. Factor 8*f**a + 6*f**4 - 4*f**4 - 3*f**2 + 11*f**2.
2*f**2*(f + 2)**2
Let t = -18 - -21. Let 17*w - 9*w**t + 11*w**2 - 7*w**3 - 25*w + 25*w**2 = 0. Calculate w.
0, 1/4, 2
Factor -t + 0*t + 2*t**2 - 2 - t**3 + 2*t**3.
(t - 1)*(t + 1)*(t + 2)
Suppose 0 = 4*y - 22 + 6. Let s = y - 4. Factor -2*g**5 - g + 4*g**4 - 4*g**2 + 3*g + s*g**5.
-2*g*(g - 1)**3*(g + 1)
Let d(u) be the second derivative of 0 - 1/50*u**5 - 3*u - 1/15*u**4 + 0*u**2 - 1/15*u**3. Solve d(b) = 0.
-1, 0
Let h(y) be the second derivative of y**4/42 + 4*y**3/21 + 4*y**2/7 - 51*y. Factor h(u).
2*(u + 2)**2/7
Let 2*c**3 + 5*c**3 - 5*c**3 + 2*c**4 = 0. Calculate c.
-1, 0
Let u(d) be the third derivative of 1/36*d**4 + 0 + 0*d - 1/9*d**3 - d**2 + 1/90*d**5 - 1/180*d**6. Solve u(s) = 0 for s.
-1, 1
Let f(d) be the third derivative of d**6/540 - 7*d**5/270 + 5*d**4/36 - d**3/3 + 8*d**2. Suppose f(a) = 0. What is a?
1, 3
Find f such that f**3 + f**3 + 3*f - 4*f**3 - f = 0.
-1, 0, 1
Let f(k) be the first derivative of -1/2*k**2 + 0*k**3 + 0*k + 0*k**4 + 1 + 1/60*k**5. Let w(n) be the second derivative of f(n). Factor w(l).
l**2
Let k = 15 - -1. Suppose 4*r - 8*r**4 - 12 - 3*r**3 + 4 + k*r**2 - 5*r**3 + 4*r**5 = 0. Calculate r.
-1, 1, 2
Factor x**2 - 35*x - 15*x**3 - 72 + 62 - 41*x**2.
-5*(x + 1)**2*(3*x + 2)
Let t(j) = j**5 - j**3 + j - 1. Let m(u) = -2*u**4 - 2*u**3 + u - 1. Let r = -22 - -21. Let s(i) = r*m(i) + t(i). Factor s(z).
z**3*(z + 1)**2
Let f be (-3)/(-8) + -1 - 0. Let c = -3/56 - f. Determine d so that 4/7*d - 2/7*d**4 + 2/7 + 0*d**2 - c*d**3 = 0.
-1, 1
Suppose 5*q - 18 = k, 0*k + 3 = -3*q - 4*k. Factor -q*a**3 - 2*a + 4*a - 2 - a + 2*a**2 + 2*a**3.
-(a - 2)*(a - 1)*(a + 1)
Let n(x) be the first derivative of 1/3*x**3 - 3 + 3/8*x**4 + 0*x + 0*x**2. Factor n(a).
a**2*(3*a + 2)/2
Factor -3/2*f**3 - 2 + 4*f - 1/2*f**2.
-(f - 1)*(f + 2)*(3*f - 2)/2
Let d(p) = -5*p**4 + 6*p**3 + 4*p**2 - 5. Let s be (-2)/4 - 63/14. Let j(g) = -4*g**4 + 5*g**3 + 3*g**2 - 4. Let h(z) = s*d(z) + 6*j(z). Factor h(c).
(c - 1)**2*(c + 1)**2
Let c(o) = 6*o - 3. Let r be c(-3). Let d be (-56)/r - 2/(-3). Factor -8/3 + 16/3*h + 2/3*h**3 - d*h**2.
2*(h - 2)**2*(h - 1)/3
Suppose -f = -117 + 114. Let k(x) be the third derivative of -3*x**2 + 0*x + 0 + 1/84*x**4 - 1/105*x**5 + 0*x**f. Factor k(p).
-2*p*(2*p - 1)/7
Let l(n) be the third derivative of -n**10/1