hat is n in d(n) = 0?
-1, 0, 1
Factor -2/7*m + 8/7*m**2 - 12/7*m**3 + 8/7*m**4 - 2/7*m**5 + 0.
-2*m*(m - 1)**4/7
Let s(l) be the first derivative of 3/5*l + 4/5*l**3 + 3 + 3/2*l**2. Factor s(k).
3*(k + 1)*(4*k + 1)/5
Suppose -8 = -u - 28. Let g be ((-2)/(-5))/((-2)/u). Suppose 0*p + 6*p**2 + 27*p**3 + 2*p + 7*p**5 + 7*p**2 + 22*p**g + p**4 = 0. Calculate p.
-1, -2/7, 0
Suppose t + 4*t - 30 = 0. Let c be 2/t - (-5)/21. Factor 0 + c*p + 2/7*p**2.
2*p*(p + 2)/7
Let v be (-6 + 8)*(-2)/(-4). Let d be 0/(2*v/2). Factor d*x + 0*x**2 + 3/4*x**3 + 0.
3*x**3/4
Suppose 0 = -10*d - 2*d + 72. Let k(l) be the second derivative of -1/10*l**d + 0*l**4 + 2*l + 0 - l**3 + 3/10*l**5 + 3/2*l**2. Suppose k(n) = 0. Calculate n.
-1, 1
Suppose -5*a - f = 3*f - 22, -3*a + 5*f = -28. Let h be (1/a)/(1/4). Solve 1/3 + 4/3*k + 1/3*k**4 + 4/3*k**5 - h*k**2 - 8/3*k**3 = 0.
-1, -1/4, 1
Let b = 565/2 - 282. Find j, given that 1/2*j**4 - 1/2*j**5 + 0 + 0*j + b*j**3 - 1/2*j**2 = 0.
-1, 0, 1
Let d(h) = -2*h + 14. Let m be d(7). Suppose 4*u + 2*g - 10 = m, -13 = -2*u - 5*g - 4. Factor -4/7*a**u + 4/7 - 6/7*a + 6/7*a**3.
2*(a - 1)*(a + 1)*(3*a - 2)/7
Let g be 2 - 6 - (-1 - -1). Let d be g + ((-12)/(-21) - -4). Solve 0*s - 2/7*s**4 + 0 + d*s**3 - 2/7*s**2 = 0 for s.
0, 1
Let r = -5 + -4. Let w be 1*1*r/(-3). Factor 0*i**2 - 4*i**3 - 2*i**2 + 2*i**w.
-2*i**2*(i + 1)
Let n(j) be the third derivative of 9*j**8/112 + j**7/70 - j**6/6 + j**5/15 + 31*j**2. Suppose n(p) = 0. What is p?
-1, 0, 2/9, 2/3
Let s = -7 - -11. Factor 3*t**3 + t**4 + 2*t**2 + t**3 + 0*t**s + t**4.
2*t**2*(t + 1)**2
Let j(n) be the first derivative of n**5/80 + n**4/24 + n**3/24 + 3*n + 1. Let r(b) be the first derivative of j(b). Factor r(s).
s*(s + 1)**2/4
Determine t, given that 9*t + 3*t**2 - 7 + 1 + 6 + 6 = 0.
-2, -1
Find i, given that -1/2*i**2 + 0 - 1/4*i**3 - 1/4*i = 0.
-1, 0
Let g(v) be the second derivative of -v**7/147 + 4*v**6/105 - 2*v**5/35 - v**4/21 + 5*v**3/21 - 2*v**2/7 - 9*v. Find d such that g(d) = 0.
-1, 1, 2
Let b(c) be the first derivative of c**4/22 - 2*c**3/11 + 3*c**2/11 - 2*c/11 + 11. Find j, given that b(j) = 0.
1
Let h(j) be the third derivative of j**9/105840 + j**8/17640 + j**7/8820 - j**5/15 + 11*j**2. Let r(v) be the third derivative of h(v). Factor r(a).
4*a*(a + 1)**2/7
Let d(v) be the second derivative of 1/24*v**4 + 0 + 0*v**2 - 1/80*v**5 - 7*v + 0*v**3. Find f, given that d(f) = 0.
0, 2
Let v(k) = -13 + 4*k + 5 - k - 2*k. Let f be v(10). Factor -f - 4*o + 2*o**2 + o**2 - 5*o**2.
-2*(o + 1)**2
Suppose 33/5*f + 3/5*f**3 - 18/5 - 18/5*f**2 = 0. What is f?
1, 2, 3
Let n(q) be the first derivative of -q**5/10 + q**3 - 2*q**2 + 3*q/2 + 24. Find i, given that n(i) = 0.
-3, 1
Suppose 0 = -g - 0 + 2. Let b = -1 - -3. Factor -d**3 + 5*d**3 + b*d**5 - 6*d + 2*d**4 - 4*d**g + 4*d**4 - 2.
2*(d - 1)*(d + 1)**4
Factor 6 - 2 + 2*w**3 + 2*w - 8*w + 0*w.
2*(w - 1)**2*(w + 2)
Let y = -15 - -18. Let h(w) be the first derivative of -y + 2/9*w**3 + 8/3*w - 4/3*w**2. Factor h(t).
2*(t - 2)**2/3
Let w(t) be the third derivative of t**6/420 - 2*t**5/35 + 4*t**4/7 - 64*t**3/21 + 6*t**2. Factor w(r).
2*(r - 4)**3/7
Let b(a) = -a + 1. Let j be b(8). Let k(c) = c**2 + 5*c - 10. Let o be k(j). Let o*l - 2*l + 2*l**2 - 4*l - 2*l**4 + 2*l**3 = 0. What is l?
-1, 0, 1
Let w(r) be the first derivative of r**5/80 + r**4/16 + r**3/8 + r**2/8 - 3*r + 1. Let m(j) be the first derivative of w(j). Let m(k) = 0. What is k?
-1
Let n(l) = -l**2 + 5*l - 2. Let w be ((-6)/4)/((-3)/8). Let t be n(w). Factor 2*x**2 - x**2 + x**2 + x**t + 5*x + 2.
(x + 1)*(3*x + 2)
Suppose 26 = h - 5*j, -4*h + 21 = -3*h - 4*j. Let b(i) = 3*i**3 - 3*i**2 - 6. Let x(o) = -o**3 + 1. Let w(c) = h*b(c) + 6*x(c). Suppose w(n) = 0. What is n?
-1, 0
Suppose -6*z - 4*z = -20. Find f such that 2/3*f**4 + 1/2*f**3 + 0 + 1/6*f**5 - 2/3*f - 2/3*f**z = 0.
-2, -1, 0, 1
Let z(x) be the third derivative of -x**6/960 + x**5/480 + x**4/192 - x**3/48 + 15*x**2. Factor z(w).
-(w - 1)**2*(w + 1)/8
Let f = 14/17 - 123/170. Let c(x) be the first derivative of -4/5*x + 3/5*x**2 + 3 + 0*x**3 - f*x**4. Solve c(a) = 0.
-2, 1
Let 8 + 9*x - 4*x**4 - 9*x**3 + x**4 - 2 - 3*x**2 = 0. What is x?
-2, -1, 1
Let y(h) be the first derivative of 0*h**2 + 0*h**4 + 0*h**3 - 1/126*h**7 - 1 + 0*h**5 + h - 1/90*h**6. Let v(g) be the first derivative of y(g). Factor v(z).
-z**4*(z + 1)/3
Let n = 3366/7 - 474. Factor n*o**3 + 44/7*o**2 + 2/7 + 18/7*o**4 + 16/7*o.
2*(o + 1)**2*(3*o + 1)**2/7
Let q(i) be the third derivative of i**7/945 + i**6/270 + i**5/270 + 5*i**2. Factor q(h).
2*h**2*(h + 1)**2/9
Let l(c) be the first derivative of -c**7/210 - c**6/180 - c**3/3 + 3. Let t(p) be the third derivative of l(p). Let t(z) = 0. Calculate z.
-1/2, 0
Let x be 1*(0/4)/2. Find w such that 0*w**3 - 1/4*w**4 + 1/4*w**2 + x*w + 0 = 0.
-1, 0, 1
Suppose 5*i = -5*n + 35, -4*i - 5 = -3*i - 3*n. Let b(k) be the third derivative of 0 + 0*k**3 + 0*k**5 - k**2 + 0*k**i + 1/60*k**6 + 0*k. Factor b(v).
2*v**3
Let i(s) = s + s + 0 + 9 - s. Let k be i(-7). Factor 4*t**k - 2 + 0*t**2 - 3*t**2 + t.
(t - 1)*(t + 2)
Let c = 2/93 - -176/465. Let -2*b**4 + 2/5*b**5 + 2*b - c - 4*b**2 + 4*b**3 = 0. What is b?
1
Let w(x) be the second derivative of -x**7/8820 + x**5/420 + x**4/3 + 4*x. Let y(q) be the third derivative of w(q). Let y(b) = 0. What is b?
-1, 1
Solve 3/5*u - 1/5*u**2 + 0 = 0.
0, 3
Let g(i) be the third derivative of i**9/10800 - i**8/6720 - i**7/6300 + i**4/12 + 5*i**2. Let d(s) be the second derivative of g(s). Factor d(k).
k**2*(k - 1)*(7*k + 2)/5
Let c(y) = y**2 + 2*y - 8. Let l be c(-4). Let b(w) be the second derivative of l + 0*w**3 - 4*w - 1/6*w**4 + w**2. Factor b(i).
-2*(i - 1)*(i + 1)
Let w(x) be the third derivative of -x**5/150 + x**3/15 + 5*x**2. Solve w(p) = 0 for p.
-1, 1
Factor -4*l - 11*l**2 + 2*l**2 + 10*l**2.
l*(l - 4)
Let w(y) = 2*y**2 - 11*y - 13. Let l be w(6). Let o be 4 + 10/l + -2. Factor -o*i - 2/7*i**2 + 2/7*i**3 + 0.
2*i*(i - 2)*(i + 1)/7
Determine u, given that 12*u**5 - 44*u**4 - 4*u + 0*u**2 - 19*u**2 - 16*u**2 + 56*u**3 + 11*u**2 + 4 = 0.
-1/3, 1
Let d(p) = -5*p**4 - 5*p**3 - 6*p**2 + 5*p - 11. Let j(a) = -a**4 - a**3 - a**2 + a - 2. Let b(z) = 4*d(z) - 22*j(z). Solve b(c) = 0.
-1, 0, 1
Let z(m) = 0*m**2 + m - 2*m + m**2. Let t(w) = 5*w - 9. Let v(d) = -t(d) + z(d). Factor v(a).
(a - 3)**2
Factor 0*t + 6/7*t**3 - 4/7*t**2 + 0 - 2/7*t**4.
-2*t**2*(t - 2)*(t - 1)/7
Let o be -3*(-2)/2 - 1. Let d be (-1)/2*o*-4. Let -8*f + 32*f**d + 7*f - 16*f**3 - 19*f - 78*f**2 - 4 - 14*f = 0. Calculate f.
-1, -1/4, 2
Let a(c) = -c**5 + c. Let k(o) = -10*o**5 + 4*o**4 + 8*o**3 - 4*o**2 + 2*o. Let y(b) = -4*a(b) + k(b). Let y(r) = 0. What is r?
-1, -1/3, 0, 1
Suppose -12/5*d**2 - 3/5*d**4 - 12/5*d**3 + 0 + 0*d = 0. Calculate d.
-2, 0
Let n(r) = 5*r**5 - r**4 - 14*r**3 - 19*r**2 + 11. Let s(i) = -i**5 + 3*i**3 + 4*i**2 - 2. Let j(x) = -2*n(x) - 11*s(x). Determine g, given that j(g) = 0.
-3, -1, 0, 2
Let c = 36 - 11. Suppose -c*h**4 + 44*h**3 - 4*h**2 - 12*h**3 + 16 - 32*h + 13*h**4 = 0. Calculate h.
-1, 2/3, 1, 2
Factor 4/9 - 2/3*c + 2/9*c**2.
2*(c - 2)*(c - 1)/9
Let g(z) = -4*z**5 + 2*z**4 + 6*z**3 + 4*z**2 - 2*z - 3. Let l(n) = 11*n**5 - 5*n**4 - 17*n**3 - 11*n**2 + 6*n + 8. Let r(o) = 8*g(o) + 3*l(o). Factor r(a).
a*(a - 1)**2*(a + 1)*(a + 2)
Suppose -z = -3 + 6. Let i be z/(-1)*2/3. Factor 1 + 0 + 0*h**i - h**2.
-(h - 1)*(h + 1)
Let k(x) = -5*x**5 - 30*x**4 - 50*x**3 - 75*x**2 - 20*x + 15. Let m(j) = -j**3 + j**2 - 1. Let b(p) = k(p) + 15*m(p). Factor b(n).
-5*n*(n + 1)**2*(n + 2)**2
Let t = 4 - 2. Let s be (-1)/t + 10/4. Let -3*p**3 - 2 + 5*p**3 - 2*p + 0 + 2*p**s = 0. Calculate p.
-1, 1
Let x be (-1 - 5 - (-580)/44) + -7. Factor 2/11*b**2 + 0*b - x.
2*(b - 1)*(b + 1)/11
Let l(t) be the third derivative of 0 + 1/150*t**5 + 1/15*t**4 + 0*t - 2*t**2 + 4/15*t**3. Factor l(v).
2*(v + 2)**2/5
Let y = 2/9 + 17/45. Let u = 1266/5 - 252. Factor -6/5*c**3 + 3/5*c + y*c**4 + 3/5 - u*c**2 + 3/5*c**5.
3*(c - 1)**2*(c + 1)**3/5
Suppose -1/3*i**2 + 4*i - 12 = 0. What is i?
6
Factor 0 - 3/7*h**2 + 0*h + 3/7*h**4 - 3/7*h**5 + 3/7*h**3.
-3*h**2*(h - 1)**2*(h + 1)/7
Let w(s) be the first derivative of s**6/15 + 8*s**5/25 + 3*s**4/10 + 5. Determine n, given that w(n) = 0.
-3, -1, 0
Let -15/7*v + 58/7*v**