15
Suppose 4/15 - 22/15*w - 32/15*w**4 + 14/15*w**5 + 28/15*w**2 + 8/15*w**3 = 0. Calculate w.
-1, 2/7, 1
Let o(m) be the first derivative of -2*m**3/3 + 6*m**2 - 16*m - 48. Factor o(l).
-2*(l - 4)*(l - 2)
Let q = 53/20 - 9/4. Let q*a - 1/5*a**2 - 1/5 = 0. Calculate a.
1
Suppose -3*d - 6 = -2*f - 23, 2*f - 23 = -5*d. Let t = f - -3. Let -g + 0*g**4 - g**5 + t*g**3 + 2*g**2 - 1 + 0 - g**4 = 0. What is g?
-1, 1
Let d(q) be the second derivative of q**5/120 - q**4/72 - q**3/36 + q**2/12 + 19*q. Find a such that d(a) = 0.
-1, 1
Let o(c) be the third derivative of -c**5/48 + 5*c**4/16 + 12*c**2. Let o(v) = 0. Calculate v.
0, 6
Suppose -1/4*t**2 + 1/4*t**4 + 0 + 1/4*t - 1/4*t**3 = 0. Calculate t.
-1, 0, 1
Let i(s) = -5*s**4 + 3*s**3 + s**2 - 3*s + 2. Let j(z) = 6*z**4 - 3*z**3 + 3*z - 3. Let w(o) = 3*i(o) + 2*j(o). Factor w(m).
-3*m*(m - 1)**2*(m + 1)
Let h = -577/5 + 116. Let s = 77 + -77. Factor h*z + s - 3/5*z**3 - 3/5*z**4 + 3/5*z**2.
-3*z*(z - 1)*(z + 1)**2/5
Let v(q) be the third derivative of q**5/300 - q**4/60 + q**3/30 + 7*q**2. Factor v(h).
(h - 1)**2/5
Solve 4 - 14*o + 33*o**3 + 55*o**3 - 60*o**5 - 32*o**4 + 4*o**4 + 24*o**2 - 14*o = 0.
-1, 1/5, 1/3, 1
Let l be ((-6)/(-10))/(-1 - -4). Let y(f) be the second derivative of -l*f**5 - 1/6*f**4 + 0 + 0*f**3 - 1/15*f**6 + 2*f + 0*f**2. Let y(v) = 0. What is v?
-1, 0
Let m(i) be the second derivative of i**7/42 - 2*i**6/15 - i**5/10 + 2*i**4/3 + i**3/6 - 2*i**2 - 5*i. Solve m(d) = 0.
-1, 1, 4
Let s be (-1)/3 + (-52)/(-24). Let f(n) be the first derivative of n**3 + s*n**2 + 2/3*n + 2. Factor f(k).
(k + 1)*(9*k + 2)/3
Let k(r) be the second derivative of r**6/90 - r**5/30 - r**4/3 - 7*r**3/9 - 5*r**2/6 - 39*r. Let k(w) = 0. What is w?
-1, 5
Let k(n) = 3*n**2 - 18*n + 3. Let b(o) = 3*o**2 - 17*o + 4. Let v(w) = 6*b(w) - 5*k(w). Solve v(z) = 0 for z.
1, 3
Let g(s) = -s**2 + 2*s + 10. Let m be g(4). Let t = 9 - 25/3. Factor -t*i**4 - 8/9*i**3 + 2/9*i**m + 0 + 4/9*i.
-2*i*(i + 1)**2*(3*i - 2)/9
Solve -11*s**2 + 10*s**2 + 3*s - 2*s + s = 0.
0, 2
What is y in -2*y**4 + 27/2 - 35/2*y**3 - 99/2*y**2 - 81/2*y = 0?
-3, 1/4
Let u be 16/72*2/((-16)/(-12)). Suppose -3*z**3 + 2/3 - 4*z**2 - u*z = 0. What is z?
-1, -2/3, 1/3
Let a(b) = b**2 - 23*b + 42. Let r be a(21). Let o(q) = -2*q - 6. Let g be o(-5). Let 0*u + 0 + 1/6*u**5 - 1/6*u**3 + 0*u**g + r*u**2 = 0. Calculate u.
-1, 0, 1
Let c = 15 - 43/3. Factor y**3 + c*y**2 + 0 + 1/3*y**4 + 0*y.
y**2*(y + 1)*(y + 2)/3
Solve 0 + 1/4*j**2 + j = 0.
-4, 0
Let b(p) = 27*p**2 + 15*p + 2. Let i be 1/(1*2/(-22)). Let z(s) = -81*s**2 - 45*s - 6. Let q(y) = i*b(y) - 4*z(y). Factor q(o).
(3*o + 1)*(9*o + 2)
Let w = -65 - -133/2. Factor -w*q - 1/2*q**2 + 0.
-q*(q + 3)/2
Solve 5*y**3 + 0 - 5/3*y**5 + 10/3*y - 5/3*y**4 + 25/3*y**2 = 0 for y.
-1, 0, 2
Let g be (-5 + 8 - 6)/(-4). Find w, given that 1/4*w + 1/2 - g*w**2 + 1/4*w**4 - 1/4*w**3 = 0.
-1, 1, 2
Suppose -s = -3 + 1. Factor -c - 2 + 2*c + 2*c**s + 5*c - 6*c**3.
-2*(c - 1)*(c + 1)*(3*c - 1)
Let u = -30 + 32. Suppose -5*s = -2*p - 15, u*s - 6*s = -2*p - 12. Solve 0*y**4 + 1/6*y**5 - 1/6*y**s + 0*y**2 + 0*y + 0 = 0 for y.
-1, 0, 1
Let g(m) = 6*m**4 + 6*m**3 - 16*m**2 - 16*m + 10. Let k(i) = 2*i**4 + 2*i**3 - 5*i**2 - 5*i + 3. Let r(y) = 3*g(y) - 10*k(y). Factor r(v).
-2*v*(v - 1)*(v + 1)**2
Let b(t) be the first derivative of -2*t**5/25 + t**4/5 - 2*t**2/5 + 2*t/5 - 10. Let b(h) = 0. Calculate h.
-1, 1
Let a(o) = -3*o + 15. Let p be a(4). What is k in -3*k - 10/3*k**2 - k**p - 2/3 = 0?
-2, -1, -1/3
Let o(c) be the first derivative of c**3 + 3*c**2/2 - 13. Factor o(u).
3*u*(u + 1)
Suppose -3*p - 29 = -s, -5*s + 89 = -s - 3*p. Suppose -5*c + 5*d + s = 0, 5*c - d + 2*d - 14 = 0. Factor -m + m**2 + 0*m**c - 4*m**2 - 3*m**3 - m**4.
-m*(m + 1)**3
Let y(f) = -7*f**3 - 4*f**2 + 11*f - 6. Let c(r) = 15*r**3 + 8*r**2 - 23*r + 13. Let p(w) = 6*c(w) + 13*y(w). Let p(l) = 0. What is l?
-5, 0, 1
Suppose 4 + 7 = q. Suppose -q - 4 = -3*i. Suppose -4*n**2 + 2*n - 2 + 5*n**2 - 2*n**2 + i*n**2 = 0. What is n?
-1, 1/2
Let i = -3/67 - -337/6030. Let n(o) be the second derivative of 0 + 2/9*o**3 - i*o**6 - 1/6*o**2 + o + 1/15*o**5 - 1/6*o**4. Factor n(a).
-(a - 1)**4/3
Let r(s) be the third derivative of -s**9/15120 + s**7/1400 + s**6/900 - s**3/2 - s**2. Let a(n) be the first derivative of r(n). Factor a(z).
-z**2*(z - 2)*(z + 1)**2/5
Let j(z) be the first derivative of 12*z**5/5 - 3*z**4 - 3*z**3 + 6*z**2 - 3*z - 2. Factor j(r).
3*(r - 1)*(r + 1)*(2*r - 1)**2
Determine l, given that -2*l**2 + 16/15*l**3 + 32/15 - 16/15*l - 2/15*l**4 = 0.
-1, 1, 4
Let y(k) be the second derivative of -k**4/16 + k**3/6 - k**2/8 + 10*k. Solve y(f) = 0.
1/3, 1
Let b(r) = -4*r**2 - 8*r - 19. Let v(z) = -5*z**2 - 8*z - 20. Let l be (-6)/(-8) - (-30)/(-8). Let g(y) = l*v(y) + 4*b(y). Find j such that g(j) = 0.
-4
Suppose 3*o**2 - o**3 - o**4 + 36 + o - 2*o**2 - 36 = 0. What is o?
-1, 0, 1
Let v(d) be the second derivative of 0*d**2 + 0 + 1/30*d**5 - 1/6*d**4 + 0*d**3 - 6*d. Factor v(c).
2*c**2*(c - 3)/3
Let p(c) be the second derivative of -1/15*c**6 + 0 - 1/2*c**2 - 3/4*c**4 - 5*c - 7/20*c**5 - 5/6*c**3. Factor p(o).
-(o + 1)**3*(2*o + 1)
Let l(t) be the third derivative of -t**7/525 + t**5/50 - t**4/30 + 21*t**2. Suppose l(c) = 0. What is c?
-2, 0, 1
Let y(l) = -6*l - l**2 - 2*l**2 + 0 + 5. Let u(p) = 2*p**2 + 4*p - 3. Suppose 25 - 9 = 2*j. Let g(z) = j*u(z) + 5*y(z). Suppose g(i) = 0. What is i?
-1
Let l(f) = 6*f. Let q(h) = 16*h + 16*h + h**2 + 2 - 1 - 7*h. Let a(t) = 9*l(t) - 2*q(t). What is n in a(n) = 0?
1
Suppose 6*n - 3*n - 2*g - 22 = 0, -g = 2*n - 3. Factor -2*h + 5 + 2 - 2*h**3 - n*h + 11 - 10*h**2.
-2*(h - 1)*(h + 3)**2
Let z be (-4)/(5 - 8 - 3). Factor 0 + 0*d + d**5 + 5/3*d**4 + z*d**3 + 0*d**2.
d**3*(d + 1)*(3*d + 2)/3
Let d(g) be the second derivative of -g**7/42 + g**6/15 - 2*g. Factor d(c).
-c**4*(c - 2)
Factor -751*z - z**2 - 20 - 5 + 741*z.
-(z + 5)**2
Let c(a) be the second derivative of a**4/6 - 2*a**3/3 - 7*a. Factor c(l).
2*l*(l - 2)
Let w(q) be the third derivative of -q**5/450 + q**3/45 + 11*q**2. Solve w(p) = 0.
-1, 1
Suppose -39*g**2 + 46*g**5 - 27*g**5 - 6 + 9*g**4 - 25*g**5 + 15*g**3 + 27*g = 0. What is g?
-2, 1/2, 1
Find m, given that -8/3*m + 0 + 20/3*m**2 + 4*m**3 = 0.
-2, 0, 1/3
Let i be (-8368)/(-44) - 4/22. Let r = -371/2 + i. Suppose r*a**2 + 3/2*a**3 - 3/2*a**4 - 3 - 3/2*a = 0. What is a?
-1, 1, 2
Let t(o) be the third derivative of o**5/30 + o**4/12 - 4*o**2. Factor t(d).
2*d*(d + 1)
Let c(u) be the first derivative of -u**5/120 - u**4/24 + u**3/4 + 3*u**2/2 - 8. Let k(y) be the second derivative of c(y). Factor k(p).
-(p - 1)*(p + 3)/2
Solve -32*v**5 + 3*v**4 + 35*v**5 + 9*v - 3*v**2 - 3*v - 9*v**3 = 0.
-2, -1, 0, 1
Let l be 2/3*6*-1. Let p(g) = -8*g**2 + 3*g. Let d(o) = 3*o**2 - o. Suppose -t = t + 22. Let y(n) = l*p(n) + t*d(n). Factor y(j).
-j*(j + 1)
Let f(m) be the third derivative of m**2 + 0*m**4 - 1/60*m**6 + 0 + 1/60*m**5 + 1/210*m**7 + 0*m**3 + 0*m. Determine p so that f(p) = 0.
0, 1
Let t(a) = -a + 5. Let k be t(5). Let w(y) = -y**3 - 3*y**2 - 3*y - 2. Let j be w(-2). Factor k*n**2 - 2/9*n**5 + 4/9*n**3 + j - 2/9*n + 0*n**4.
-2*n*(n - 1)**2*(n + 1)**2/9
Suppose 4*i - 5 = 3*i. Let -21*h**3 + i*h**3 + 4*h + 9*h**4 + 2*h**2 + h**4 = 0. What is h?
-2/5, 0, 1
Let u be 4 + ((-39)/6 - -3). Find b, given that u - 1/4*b**2 - 1/4*b = 0.
-2, 1
Let t(q) = -q**3 - 5*q**2 - q - 5. Let v be t(-5). Factor 0*i + v*i**2 - 2/5*i**5 + 0*i**3 + 0 - 2/5*i**4.
-2*i**4*(i + 1)/5
Let o(a) be the second derivative of -a**8/3360 + a**7/1260 + a**4/6 - a. Let k(v) be the third derivative of o(v). Factor k(p).
-2*p**2*(p - 1)
Find l, given that -30*l**3 - 11*l**4 - 14*l**4 - 2 - 5*l**5 + 2 + 40*l + 20*l**2 = 0.
-2, 0, 1
Let j(h) be the second derivative of -h**7/11340 + h**6/1620 - h**5/540 + h**4/6 - 6*h. Let v(i) be the third derivative of j(i). Factor v(s).
-2*(s - 1)**2/9
Suppose 14 = -127*s + 134*s. Let k be ((-9)/3)/((-1)/1). Find f such that 4/7*f**s + 0 + 0*f + 10/7*f**k = 0.
-2/5, 0
Let x = -10 - -11. Let s be (1/18)/x*4. Suppose -4/9*z + s + 2/9*z**2 = 0. What is z?
1
Let h(i) be the second derivative of -5*i**7/42 + i**6/3 - i**5/4 + 11*i. Factor h(a).
-5*a**3*(a - 1)**2
Let d(l) be the second derivative of -l**6/2340 + l**5/195 