ve of -p**6/120 + 7*p**5/180 - 2*p**3/9 - 3*p**2/2 - 2*p. Let j(r) be the first derivative of n(r). Determine h so that j(h) = 0.
-2/3, 1, 2
Let f(l) be the first derivative of -l**5/5 - l**4/4 - l + 1. Let y(q) = 4*q**4 + 8*q**3 + 2*q**2 - 2*q + 6. Let r(d) = 6*f(d) + y(d). Factor r(h).
-2*h*(h - 1)**2*(h + 1)
Let b = -23 + 35. Let t be 9/b - (-4)/(-16). Let 1/2 + 0*z - t*z**2 = 0. What is z?
-1, 1
Factor 20/3*f + 40/3*f**3 + 4/3*f**5 - 4/3 - 20/3*f**4 - 40/3*f**2.
4*(f - 1)**5/3
Suppose 0 = r - 5*s - 32, 12 - 76 = -3*r - s. Let j = -20 + r. Factor -1/5*x**j + 0*x**3 + 0 + 0*x + 1/5*x**4.
x**2*(x - 1)*(x + 1)/5
Factor 0*h**2 - 1/3*h - 8/3*h**4 + 2*h**3 + 0 + h**5.
h*(h - 1)**3*(3*h + 1)/3
Solve -8 + 4*y**4 - 4 + 9*y**2 - 12*y - 7*y**4 + 6*y**3 = 0.
-1, 2
Suppose 12 = 2*y - 3*v, -11*y - 4 = -9*y + 5*v. Suppose 2/15*r + 0 + 4/15*r**4 + 0*r**y - 4/15*r**2 - 2/15*r**5 = 0. What is r?
-1, 0, 1
Factor -3/7 + 3/7*g - 3/7*g**3 + 3/7*g**2.
-3*(g - 1)**2*(g + 1)/7
Let w(v) be the second derivative of -v**5/4 - v**4/2 - v**3/6 + 2*v. Let x(d) = -d**3 - d**2. Let c(o) = 2*w(o) - 11*x(o). Solve c(y) = 0 for y.
-1, 0, 2
Let v(u) = -3*u**4 + 8*u**3 - 2*u**2 + 4*u - 7. Let h(n) = 3*n**4 - 9*n**3 + 3*n**2 - 5*n + 8. Let f(j) = 6*h(j) + 7*v(j). Suppose f(x) = 0. Calculate x.
-1, -1/3, 1
Let d be ((-18)/(-24))/((-5)/4). Let u = 14/15 + d. Solve 0 - u*j**2 - 1/3*j = 0.
-1, 0
Let z be (8/24)/((-49)/(-42)). Factor 0*o + 0 + 2/7*o**2 - z*o**3.
-2*o**2*(o - 1)/7
Let l = 76 + -53. Find o such that 0*o**4 + 3*o**4 + l*o**2 - 26*o**2 = 0.
-1, 0, 1
Suppose 4*g - 2 = -12*h + 7*h, -2*h - g = -2. Determine c, given that 0 - 2/7*c**h - 2/7*c = 0.
-1, 0
Let v(p) be the second derivative of -p**6/1620 + p**3/2 + p. Let a(t) be the second derivative of v(t). Factor a(j).
-2*j**2/9
Let v = 24 - 18. Factor 0*m + 1 - 7 + 5*m**3 + v*m**2 - 2*m**3 - 3*m.
3*(m - 1)*(m + 1)*(m + 2)
Let j(w) be the third derivative of w**6/200 + 11*w**5/100 + 3*w**4/5 - 18*w**3/5 - 3*w**2. Factor j(g).
3*(g - 1)*(g + 6)**2/5
Suppose 5 = 5*r, r = -s - 4*r + 5. Determine p so that s - 2/3*p**2 + 4/3*p = 0.
0, 2
Let x = 1 + 5. Factor -4*b**2 - 5*b**2 + 3*b + x + 3*b**2 + 3*b**2.
-3*(b - 2)*(b + 1)
Suppose 5*m + k = -4*k + 25, -2*k = 4*m - 14. Factor 0 + 1/4*c**5 + 1/4*c**4 - 1/4*c**3 + 0*c - 1/4*c**m.
c**2*(c - 1)*(c + 1)**2/4
Let d = 42 + -39. Let p(x) = x**3 + x**2 - 1. Let a(k) = -3 - k**4 + 0 + 3*k**2 + 3*k**3 + k**2. Let f(q) = d*p(q) - a(q). Let f(b) = 0. Calculate b.
-1, 0, 1
Let y(n) be the first derivative of -n**6/6 - 12*n**5/5 - 23*n**4/2 - 20*n**3 - 25*n**2/2 - 11. Solve y(q) = 0.
-5, -1, 0
Let q(j) = -11*j. Let v be q(-1). Suppose 4*f - v - 7 = -2*t, -3*t + 11 = 2*f. Determine m so that 1/2*m**3 - 1/4*m**f + 0*m**2 - 1/2*m + 1/4 = 0.
-1, 1
Let x(m) be the third derivative of 3*m**6/100 + 11*m**5/150 + m**4/30 - 16*m**2. Suppose x(p) = 0. What is p?
-1, -2/9, 0
Let t(w) be the second derivative of -3*w + 0*w**3 - 3/4*w**2 + 1/8*w**4 + 0. Factor t(k).
3*(k - 1)*(k + 1)/2
Let t(s) be the first derivative of -9*s**5/35 + 15*s**4/14 - 4*s**3/3 + 4*s**2/7 - 5. Let t(o) = 0. What is o?
0, 2/3, 2
Let r(f) = f**5 - 1. Let o(u) = -2*u**4 - u**3 - 1. Let h(m) = -o(m) + r(m). Factor h(x).
x**3*(x + 1)**2
Let b(o) = o**2 + 11*o + 12. Let l be b(-10). Suppose 2/3*d**l - 4*d + 6 = 0. Calculate d.
3
Suppose -2 = 3*u - 2*v - 6, 3*v = -u - 6. Let q(f) be the second derivative of 0*f**3 + u - 1/10*f**2 + 1/60*f**4 + 4*f. Let q(g) = 0. Calculate g.
-1, 1
Suppose -4*w + 6 + 18 = 0. Suppose -w*o = -2*o. Determine k so that -2*k**5 + k**2 - 3*k**4 + o*k**5 + 2*k**3 + 2*k**4 = 0.
-1, -1/2, 0, 1
Let s = 31 - 31. Let s + 2/5*w**4 + 0*w**2 - 1/5*w + 3/5*w**3 = 0. Calculate w.
-1, 0, 1/2
Let c(h) be the third derivative of -h**6/180 + h**5/45 - h**4/36 + 3*h**2. Let c(o) = 0. What is o?
0, 1
Let g(n) be the third derivative of 0 - 3*n**2 - 1/480*n**6 + 0*n + 0*n**3 - 1/120*n**5 - 1/96*n**4. Find t such that g(t) = 0.
-1, 0
Let i be 5/(-2) - (-18)/12. Let k be i/(-5) - 4/(-20). Find o, given that k*o**3 - 2/5*o - 2/5*o**2 + 2/5 = 0.
-1, 1
Solve 68*r**2 + 185*r + 10 - 15*r**2 + 4*r**2 + 118*r**2 = 0.
-1, -2/35
Suppose 0 + 0*t - 1/2*t**2 - 3/4*t**3 - 1/4*t**4 = 0. Calculate t.
-2, -1, 0
Let n(v) be the third derivative of -v**7/45 + v**6/90 + 7*v**5/90 - v**4/18 + v**2. What is y in n(y) = 0?
-1, 0, 2/7, 1
Let l(a) be the third derivative of -a**11/83160 - a**10/50400 + a**9/60480 - a**5/60 - 4*a**2. Let u(h) be the third derivative of l(h). Factor u(b).
-b**3*(b + 1)*(4*b - 1)
Let a(t) = -t**2 + 9. Let i be a(3). Let 4/11*w + 2/11*w**2 - 2/11*w**3 + i = 0. Calculate w.
-1, 0, 2
Let d(m) be the third derivative of -m**8/1344 + m**7/210 - m**6/80 + m**5/60 - m**4/96 + 4*m**2. Factor d(n).
-n*(n - 1)**4/4
Let h = 1 + -3. Let w be (-1)/h - 10/(-12). Factor 4/3*j + 0*j**2 + 2/3*j**4 - 2/3 - w*j**3.
2*(j - 1)**3*(j + 1)/3
Let -20*j**2 + 7*j**4 + 5 + 10*j**2 - 2*j**4 = 0. What is j?
-1, 1
Let p be (-6 - -2)*(-3 + 23/8). What is s in 0 + s - p*s**3 + 3/2*s**2 - 1/2*s**5 - 3/2*s**4 = 0?
-2, -1, 0, 1
Factor 28*t**5 + 60*t**3 - 574*t**2 + 1164*t**2 + 76*t**4 - 586*t**2 - 8*t.
4*t*(t + 1)**3*(7*t - 2)
Let x(m) be the third derivative of -m**6/600 + m**4/120 + 4*m**2. Factor x(d).
-d*(d - 1)*(d + 1)/5
Factor -9 + 19*f**2 - 22*f**2 + 10*f + 2*f.
-3*(f - 3)*(f - 1)
Let d(p) be the first derivative of p**5/90 - p**3/27 + 4*p + 3. Let l(s) be the first derivative of d(s). Factor l(g).
2*g*(g - 1)*(g + 1)/9
Let q(s) be the second derivative of -9*s + 13/36*s**4 - 2/3*s**2 + 0 + 1/12*s**5 + 2/9*s**3. Factor q(b).
(b + 1)*(b + 2)*(5*b - 2)/3
Let v = 20 - 12. Let c be 1*1*2/v. Determine j, given that 1/4*j**3 + c*j**4 + 0*j**2 + 0 + 0*j = 0.
-1, 0
Let n = -1 + 4. Factor -b**2 + 4*b**3 - b + 3*b**3 - 1 + 2*b**2 - 6*b**n.
(b - 1)*(b + 1)**2
Let t(c) be the first derivative of 2*c**5/45 + c**4/9 - 14*c**3/27 + 4*c**2/9 + 43. Factor t(a).
2*a*(a - 1)**2*(a + 4)/9
Let o(h) be the third derivative of -h**5/70 + 5*h**4/84 - 2*h**3/21 - 8*h**2. Factor o(z).
-2*(z - 1)*(3*z - 2)/7
Let j be ((-12)/(-16))/((-3)/(-1)). Factor -j*u**3 + 0 - 1/4*u**2 + 0*u.
-u**2*(u + 1)/4
Suppose -f - 4*f = 2*w + 4, 4*w + 8 = 0. Factor 3*y**4 - y**2 + f - 2*y**4 - y**3 + 0 + y.
y*(y - 1)**2*(y + 1)
Let f be (1/3)/((-2)/(-24)). Let j be (f/10)/(2/20). Suppose -s**2 - s**3 - 7*s**j + 3*s**4 + 3*s**3 + 3*s**4 = 0. Calculate s.
0, 1
Let j(w) be the second derivative of 3*w**5/20 - 7*w**4/12 - w**3/6 + w**2 - 5*w. Let s(h) = -3*h**3 + 6*h**2 + h - 2. Let p(z) = 2*j(z) + 3*s(z). Factor p(v).
-(v - 1)**2*(3*v + 2)
Let z = -377/3 + 127. Let q = 14 + -12. Suppose -z*v**q + 2/3 + 7/3*v = 0. Calculate v.
-1/4, 2
Let l be 22/6 - (-2)/(-3). Find s, given that -2*s**4 - 5*s**4 + 7*s**2 - 2*s + 0*s - l*s**3 + 5*s**5 = 0.
-1, 0, 2/5, 1
Let z(g) be the third derivative of -2/3*g**3 + 1/15*g**5 + 0 + 6*g**2 + 0*g**4 + 0*g. Find d such that z(d) = 0.
-1, 1
Factor -15*g + 5*g**2 + 25/3 + 5/3*g**3.
5*(g - 1)**2*(g + 5)/3
Let p be 5*(-4 - 22/(-5)). Find l such that -4*l**3 + 40*l + 4*l**p - 40*l = 0.
0, 1
Let k be 2 + (840/(-66))/7. Factor -k*q**3 - 8/11 - 16/11*q - 10/11*q**2.
-2*(q + 1)*(q + 2)**2/11
Let l(b) be the first derivative of b**5/20 - b**3/6 - 2*b - 3. Let i(h) be the first derivative of l(h). What is j in i(j) = 0?
-1, 0, 1
Let r(b) = -9*b**3 + 31*b**2 - 9*b - 9. Let q(l) = l**3 - l - 1. Let d(c) = c**3 + 8*c**2 + 7*c - 1. Let i be d(-7). Let k(h) = i*r(h) + 5*q(h). Factor k(p).
(p - 2)*(2*p - 1)*(7*p + 2)
Let d be (563/21)/((-6)/4). Let o = d + 166/9. Solve 2/7*s - 2/7*s**2 + o = 0.
-1, 2
Let d(f) be the second derivative of -2*f**6/15 - 19*f**5/60 + f**3/2 + f**2/3 - 5*f. Let d(q) = 0. What is q?
-1, -1/4, 2/3
Suppose 3*x + 2*g - 3 = -5, 5*x = -2*g - 2. Suppose 5*z + x*z = 0. Suppose 2/3*k**3 + z + 2/3*k**2 + 0*k = 0. What is k?
-1, 0
Factor 4 - 8*j + 0*j**2 - 8*j - 9*j**2.
-(j + 2)*(9*j - 2)
Let -7*d**3 - 2 - 1 - 6*d**2 + 10*d**3 - 3*d + 9 = 0. Calculate d.
-1, 1, 2
Let v(i) = 6*i**2 - 38*i + 24. Let h(s) = s**2 + 8 - 13*s - 2*s**2 + 0*s**2 + 3*s**2. Let g(x) = -14*h(x) + 5*v(x). Factor g(n).
2*(n - 2)**2
Let g(w) = -w + 7. Let j be g(5). Let d be (-4)/(-18) - 50/(-18). Factor 0*f - 2/7*f**j - 8/7*f**d + 0.
-2*f**2*(4*f + 1)/7
Let i(t) be the third derivative of t**6/660