x.
0, 1
Let s be 7/(-56)*-2 - 22/(-40). Find c such that -4/5*c - 1/5*c**2 - s = 0.
-2
Let n(i) be the second derivative of -i**6/6 - 3*i**5/4 + 25*i**4/4 - 85*i**3/6 + 15*i**2 - 27*i. Let n(g) = 0. What is g?
-6, 1
Let d(w) = -55*w**2 + 1210*w - 6655. Let g(n) = -5*n**2 + 110*n - 605. Let t(b) = 4*d(b) - 45*g(b). Let t(a) = 0. What is a?
11
Let y(s) be the first derivative of 3/8*s**4 + 1/8*s**2 + 0*s - 1/3*s**3 - 6 + 1/24*s**6 - 1/5*s**5. What is w in y(w) = 0?
0, 1
Let p(b) be the second derivative of -b**5/300 - b**4/30 - b**3/10 + b**2 + 2*b. Let a(m) be the first derivative of p(m). Suppose a(k) = 0. What is k?
-3, -1
Let c(r) be the third derivative of -r**5/360 - r**4/72 - r**3/36 + r**2. Factor c(m).
-(m + 1)**2/6
Let a(l) be the second derivative of -4/3*l**2 - 34/9*l**3 - 101/18*l**4 - 271/60*l**5 - 11/6*l**6 + 0 + 5*l - 2/7*l**7. Find z, given that a(z) = 0.
-2, -1, -2/3, -1/4
Let r = 82415/41 + -2010. Let f = 271/205 - r. Factor -2/5*k**2 - 4/5 + f*k.
-2*(k - 2)*(k - 1)/5
Let y(a) = 3*a + 4. Let w be y(-4). Let l be (9/(-12))/(5/w). What is t in 14/5*t - 4/5 - 16/5*t**2 + l*t**3 = 0?
2/3, 1
Let u(h) be the first derivative of -2*h**6/3 - 4*h**5/5 + h**4 + 4*h**3/3 + 9. Factor u(j).
-4*j**2*(j - 1)*(j + 1)**2
Factor -2/5*i**4 + 0 - 14/15*i**3 - 2/3*i**2 - 2/15*i.
-2*i*(i + 1)**2*(3*i + 1)/15
Suppose -c = -6*c - 5*p - 40, 2*c - 4*p = 14. Let b be (90/16)/c*-4. Solve -1/2 - 3/4*u + 14*u**3 + b*u**2 = 0.
-1/2, -2/7, 1/4
Let r(c) = -c + 10. Let o(a) = -a**3 + 4*a**2 - 2*a + 4. Let z be o(3). Let y be r(z). Factor 2*v**3 - 2*v**y + 2*v**3 - 2*v**2.
2*v**2*(v - 1)
Let w(a) be the first derivative of -a**4/12 + a**3/9 + a**2/6 - a/3 + 1. Factor w(m).
-(m - 1)**2*(m + 1)/3
Let o(l) = 2*l + 17 + 6*l + l**2 + 5*l. Let z be o(-12). Determine m so that 0*m**3 + m + 4*m**3 - 2*m**z - 3*m = 0.
-1, 0, 1
Find c such that 0 + 1/3*c + 11/6*c**2 = 0.
-2/11, 0
Let v(h) be the first derivative of -25*h**3/12 - 5*h**2/2 - h + 12. Factor v(r).
-(5*r + 2)**2/4
Let f(q) = q + 1. Suppose -3*y - 3 + 0 = 0. Let u be f(y). Factor -1/2 + u*m + 1/2*m**2.
(m - 1)*(m + 1)/2
Let g(f) = f**4 - f**3 - f**2 + f - 1. Let l(q) = 4*q**4 + 2*q**3 - 8*q**2 + 12*q - 12. Let u(j) = 12*g(j) - l(j). Find v, given that u(v) = 0.
-1/4, 0, 2
Let k = 961/60 + -16. Let p(m) be the second derivative of -m + k*m**4 + 0 + 0*m**2 - 1/30*m**3. Find j such that p(j) = 0.
0, 1
Let o = 269/2 + -130. Find s, given that 0 - 3*s + o*s**3 - 3/2*s**2 - 3/2*s**5 + 3/2*s**4 = 0.
-1, 0, 1, 2
Let 33/8*c + 3/8*c**2 + 15/4 = 0. Calculate c.
-10, -1
Let u be (9/6)/(1/(4/9)). Determine p so that u + 0*p - 2/3*p**2 = 0.
-1, 1
Suppose -2*t + 5*h = 41 + 10, 4*t + 81 = 3*h. Let n be (4/10)/(t/(-30)). Factor 2/3*o**2 + n*o**4 + 0 + 4/3*o**3 + 0*o.
2*o**2*(o + 1)**2/3
Let x(n) be the first derivative of -n**3 + 3*n - 6. Solve x(d) = 0.
-1, 1
Let y be (-6 + (-355)/(-60))*(-32)/6. Find v, given that y*v**3 - 2/9*v**5 + 4/9*v**2 - 2/9*v - 2/9 - 2/9*v**4 = 0.
-1, 1
Let c(o) = -6*o**5 + 14*o**4 - 2*o**3 - 6*o**2 - 6. Let j(m) = m**5 + m**4 - m**3 - m**2 - 1. Let v(a) = c(a) - 6*j(a). Factor v(w).
-4*w**3*(w - 1)*(3*w + 1)
Let n = 91/190 - -2/95. Factor 0 + 1/2*z**3 + n*z**2 + 0*z.
z**2*(z + 1)/2
Determine z so that -4 + 1 - 17 + 3*z**2 + 2*z**2 = 0.
-2, 2
Let k(c) be the second derivative of 0*c**3 + 1/66*c**4 + 3*c + 0 + 0*c**2. Factor k(b).
2*b**2/11
Let j(o) = o**4 - o**2 + o - 1. Let y(q) = -7*q**4 + 11*q**2 - 3*q - 1. Let h(w) = 3*j(w) + y(w). What is x in h(x) = 0?
-1, 1
Let y(q) = -q - 1. Let s(x) = 3*x**2 - 4*x - 7. Let b = -11 - -7. Let j(f) = b*y(f) + s(f). Factor j(t).
3*(t - 1)*(t + 1)
Let d(u) be the second derivative of 5*u**7/42 + 2*u**6/3 + 3*u**5/4 - 5*u**4/3 - 10*u**3/3 + 3*u. Let d(r) = 0. Calculate r.
-2, -1, 0, 1
Let a(h) be the second derivative of -1/60*h**4 + 0 - 1/30*h**3 + h + 1/5*h**2. Factor a(q).
-(q - 1)*(q + 2)/5
Suppose 0 = -6*s + 2*s - 12. Let h = s + 5. Suppose 2*k**3 - h*k**2 + k**5 + 2*k**2 - 3*k**3 = 0. Calculate k.
-1, 0, 1
Let k(h) be the first derivative of -h**4/24 + h**3/18 + h**2/12 - h/6 - 6. Factor k(x).
-(x - 1)**2*(x + 1)/6
Let g be (-18)/(-14) + -1 - (-1048)/(-5040). Let d(x) be the second derivative of g*x**5 + 0 - 2*x + 0*x**2 + 5/54*x**4 - 2/27*x**3. Factor d(s).
2*s*(s + 1)*(7*s - 2)/9
Let 0 + 0*t + 2/7*t**2 + 2/7*t**3 = 0. Calculate t.
-1, 0
Determine t, given that 30*t**2 - 30*t**2 + 2*t - t**3 - t = 0.
-1, 0, 1
Suppose -75*u + 74*u = 0. Solve -1/2*t**3 + u*t + 0 - 1/4*t**2 + 3/4*t**4 = 0 for t.
-1/3, 0, 1
Let u(h) be the first derivative of 0*h - 1/6*h**2 + 1/18*h**3 + 5 + 1/24*h**4. Solve u(v) = 0 for v.
-2, 0, 1
Let y(b) be the first derivative of 2*b**5/15 + b**4/9 - 2*b**3/3 + 8*b/9 + 1. Determine q, given that y(q) = 0.
-2, -2/3, 1
Factor -32/15*g + 128/15 + 2/15*g**2.
2*(g - 8)**2/15
Suppose -10 = -5*h - 5*f - 85, -65 = 4*h + 5*f. Let t be (4/h)/(11/(-55)). Factor 4/3*o - 2/3 - 2/3*o**t.
-2*(o - 1)**2/3
Suppose p**3 + 9*p**4 - p - 3*p**5 - 9*p**2 + p**3 + 7*p - 5*p**3 = 0. Calculate p.
-1, 0, 1, 2
Let k = -2/277 - -285/1108. Determine a, given that 1/4*a**2 + 0*a - k = 0.
-1, 1
Let o(t) be the first derivative of 2*t**3/27 + t**2/3 + 4*t/9 + 27. Determine w so that o(w) = 0.
-2, -1
Let t = -10 - 7. Let v = t + 19. Solve 4/7*w + 0 + 2/7*w**v = 0.
-2, 0
Let p = -252 - -252. Factor 0*r + 0 + 0*r**4 + 0*r**2 + 1/4*r**5 + p*r**3.
r**5/4
Let p(f) = f**3 - 4*f**2 - 5*f + 3. Let b be p(5). Let k be (-39)/15 - (b + -6). Factor k*w**3 - 2*w**2 + 16/5*w - 8/5.
2*(w - 2)**2*(w - 1)/5
Let z = 585 + -81899/140. Let v(b) be the third derivative of 0*b**3 - 1/42*b**4 + 0 - b**2 - z*b**6 + 1/42*b**5 + 0*b. Factor v(y).
-2*y*(y - 1)*(3*y - 2)/7
Solve 6*t - 9*t**2 - 12*t**3 + 7*t**4 + 2 + 5*t**4 + 1 = 0.
-1/2, 1
Let z = 13 - 6. Factor -z*r**2 + 10*r**4 + r**3 + 3*r**3 + 8 - 4*r**4 - 11*r**2.
2*(r - 1)**2*(r + 2)*(3*r + 2)
Let d(c) = -8*c + 2. Let s be d(-6). Suppose 20 - s = -5*v. Determine i, given that -v*i**4 - i**3 + i**4 + 0*i**5 - 4*i**5 = 0.
-1, -1/4, 0
Let k(y) be the third derivative of y**5/30 + y**4/12 - 3*y**2. Factor k(p).
2*p*(p + 1)
Factor -3/5*i**4 + 0*i**2 + 3/5 + 6/5*i**3 - 6/5*i.
-3*(i - 1)**3*(i + 1)/5
Let n(c) be the second derivative of -c**4/36 - c**3/9 - c**2/6 + 5*c. Factor n(m).
-(m + 1)**2/3
Let w = 20 - 13. Let p be w/(-2) + (7 - 3). Determine u so that -p*u - 1/4*u**4 + 0*u**2 + 1/2*u**3 + 1/4 = 0.
-1, 1
Let z(c) be the first derivative of -4/5*c**5 + 0*c**4 + 3 + 0*c + 0*c**2 + 0*c**3. Suppose z(d) = 0. Calculate d.
0
Suppose -27*s + 42 = -13*s. What is j in -2/7*j**s + 0*j**2 - 1/7*j**4 + 1/7 + 2/7*j = 0?
-1, 1
Let f(c) = c**2 + 3*c - 2. Let d(w) = -3*w**2 - 12*w + 9. Let g(x) = 2*d(x) + 9*f(x). Suppose g(y) = 0. Calculate y.
-1, 0
Let i(y) = y**2 - 7*y. Let m be i(5). Let a(f) = f**2 + 9*f - 8. Let g be a(m). Find b, given that 0 - 1/3*b**5 + 4/3*b**4 - 2*b**3 + 4/3*b**g - 1/3*b = 0.
0, 1
Find k such that -7*k**2 - 5*k**5 + 2 - 3*k**2 + 3 + 2*k + 5*k**4 + 10*k**3 - 7*k = 0.
-1, 1
Find z, given that 3/2 - 5/4*z - 2*z**2 + 7/4*z**3 = 0.
-6/7, 1
Let z(f) = -f**3 - f + 1. Let k(p) = -39*p**3 - 18*p**2 - 18*p + 18. Let l(j) = -k(j) + 18*z(j). Determine q, given that l(q) = 0.
-6/7, 0
Factor -6*y**2 + 2/3 - 2*y - 10/3*y**3.
-2*(y + 1)**2*(5*y - 1)/3
Let w(v) = -v - 2. Suppose o = 6*l - l + 25, -20 = 4*l - o. Let k be w(l). Determine f, given that 21/2*f**k - 1/2*f**2 - f + 0 = 0.
-2/7, 0, 1/3
Let b(x) = -6*x - 8. Let f be b(-2). Let w be (-10)/(-14)*f/10. What is j in 0*j - w*j**4 + 0 + 2/7*j**3 + 0*j**2 = 0?
0, 1
Let n(o) be the first derivative of -3*o**4/16 - 2*o**3 - 6*o**2 - 1. Find g, given that n(g) = 0.
-4, 0
Let n(k) be the first derivative of k**7/140 + k**6/120 - k**5/20 - k**4/8 + 2*k**3/3 + 3. Let i(q) be the third derivative of n(q). Let i(l) = 0. What is l?
-1, -1/2, 1
Let h(p) be the third derivative of -1/36*p**4 + 1/90*p**5 + 0 + 1/36*p**3 - 2*p**2 + 0*p. Let h(j) = 0. Calculate j.
1/2
Let w be 2/6 + (-14)/(-3). Factor 3*g**3 - g - g**3 + 0*g**5 - 3*g**5 + 2*g**w.
-g*(g - 1)**2*(g + 1)**2
Let h(y) be the third derivative of -y**5/75 + y**4/30 + 4*y**3/15 - 6*y**2. Solve h(l) = 0.
-1, 2
Let r(t) be the third derivative of t**7/140 + t**6/40 - t**4/8 - 7*t**3/6 + 3*t**2. Let b(q) be the first derivative of r(q). Solve b(z) = 