- q. Factor n(h).
2*h*(h - 1)*(h + 1)*(h + 2)/7
Let k = -10 - -10. Let r be (0 + k)*6/(-6). Find q, given that 1/2*q**4 + r - 1/4*q**3 - 1/2*q**2 + 1/4*q = 0.
-1, 0, 1/2, 1
Let k = -6/23 + 35/46. Let i(c) be the first derivative of 0*c**2 - k*c**4 + 0*c**3 - 2/5*c**5 + 0*c + 1. Find a such that i(a) = 0.
-1, 0
Let r(k) be the third derivative of 0*k**5 + 1/168*k**8 + 0*k + 0*k**3 + 0 - 1/30*k**6 + 0*k**4 - 3*k**2 - 1/105*k**7. Factor r(h).
2*h**3*(h - 2)*(h + 1)
Suppose b + 12 = 4*n, 5*n - 4*b = -1 + 27. Solve -y + 3/5*y**n - 2/5 = 0.
-1/3, 2
Let j(s) = -14*s**2 + 7*s - 8. Let k(g) = -27*g**2 + 15*g - 15. Suppose -3*w + 41 - 14 = 0. Let l(t) = w*j(t) - 5*k(t). Factor l(r).
3*(r - 1)*(3*r - 1)
Let r(w) be the first derivative of w**3 + 9*w**2/2 + 7*w + 1. Let d be r(-6). Let -4 + 28*s - d*s**2 - s**4 + 20*s**3 - 8*s**4 + 22*s**3 = 0. What is s?
1/3, 2
Let s(v) be the third derivative of -v**8/252 + v**7/45 - 2*v**6/45 + v**5/45 + v**4/18 - v**3/9 - 6*v**2. Factor s(r).
-2*(r - 1)**4*(2*r + 1)/3
Let n(b) be the first derivative of 7*b**7/1020 + 7*b**6/765 + b**5/255 + 4*b**3/3 + 5. Let l(a) be the third derivative of n(a). Let l(v) = 0. Calculate v.
-2/7, 0
Suppose 0*b + b**4 + 3/4*b**3 - 1/4*b**2 + 0 = 0. Calculate b.
-1, 0, 1/4
Let v(r) = r - 3. Let d be v(3). Factor d*p**2 + 2*p + 4*p**2 - 6*p**2.
-2*p*(p - 1)
Let s(j) be the first derivative of j**6/180 - j**4/3 + 8*j**3/3 - 4. Let a(i) be the third derivative of s(i). Suppose a(n) = 0. What is n?
-2, 2
Suppose -5*s**4 + 12*s**2 + 9*s**2 + 19*s**2 - 80 = 0. What is s?
-2, 2
Factor -3*s + 3/4*s**2 + 9/4.
3*(s - 3)*(s - 1)/4
Let t(q) be the third derivative of 0*q**3 + 0*q - 1/60*q**5 - 1/120*q**6 - 4*q**2 + 0*q**4 + 0. Determine k, given that t(k) = 0.
-1, 0
Let d be (-5 + 0)*(-8)/20. Let i + 0 + 0*i - d*i**3 + i**5 + 0 = 0. Calculate i.
-1, 0, 1
Suppose 33*x + 8 = 37*x. Find p such that -8/7*p**x + 0 + 6/7*p**3 + 8/7*p**4 - 8/7*p + 2/7*p**5 = 0.
-2, -1, 0, 1
Let n(f) = -f**3 + 6*f**2 - 2*f + 5. Let g be n(5). Suppose -5*d + 0*d = -g. Factor 8/3*t**2 + 8/3*t**d + 0 + 4*t**3 + 2/3*t**5 + 2/3*t.
2*t*(t + 1)**4/3
Let q(w) = 8*w**2 - 2*w. Let t(r) = 7*r**2 - r - 1. Let s(h) = 5*q(h) - 6*t(h). Suppose s(y) = 0. What is y?
-3, 1
Let s(f) be the second derivative of -32*f**6/15 + 36*f**5/5 - 97*f**4/12 + 3*f**3 - f**2/2 + 39*f. Solve s(q) = 0 for q.
1/8, 1
Let y(t) be the second derivative of 5*t**7/28 + 11*t**6/10 - 33*t**5/20 - 4*t**4 + 17*t**3/4 + 15*t**2/2 + t - 21. Suppose y(i) = 0. Calculate i.
-5, -1, -2/5, 1
What is o in 2/9*o**5 + o**3 + 0 + 7/9*o**4 + 5/9*o**2 + 1/9*o = 0?
-1, -1/2, 0
Let i(r) be the first derivative of 1 + r**2 + 1/6*r**4 - 2*r - 2/3*r**3. Let n(q) be the first derivative of i(q). Find d such that n(d) = 0.
1
What is p in 272/7*p + 508/7*p**3 + 32/7 + 696/7*p**2 + 16*p**4 = 0?
-2, -2/7, -1/4
Factor -192 + 3*w**3 + 16*w + 19*w**2 - 55*w**2 + 83*w + 45*w.
3*(w - 4)**3
Factor -2/5*a**2 - 4/5*a - 2/5.
-2*(a + 1)**2/5
Suppose p - 18 + 21 = -5*o, -4*o = p + 3. Factor 0 + 3/7*x**2 + o*x.
3*x**2/7
Let f = 109 + -109. Let x(o) be the second derivative of f*o**2 + 1/12*o**3 - 1/48*o**4 + 4*o - 1/80*o**5 + 0. Factor x(g).
-g*(g - 1)*(g + 2)/4
Let s(g) be the first derivative of g**3/5 + 3*g**2/10 - 1. Factor s(n).
3*n*(n + 1)/5
What is c in 24/5*c**4 + 27/5*c**3 - 3*c**5 - 24/5*c**2 + 0 - 12/5*c = 0?
-1, -2/5, 0, 1, 2
Let x(b) = -9*b**4 + 3*b**3 - 6*b - 6. Let l(y) = -26*y**4 + 9*y**3 + y**2 - 17*y - 17. Suppose 4*c + 30 = -c. Let o(i) = c*l(i) + 17*x(i). Factor o(j).
3*j**2*(j - 2)*(j + 1)
Suppose -2*f - 10 = -7*f. Suppose 0 = -f*j - 0*j + 20. Factor -2 - 30*m + j*m - 53*m**2 + 3*m**2.
-2*(5*m + 1)**2
Suppose 2*s = -5*r + 8, 3 = -s + 2*r + 7. Factor 2*m + m**3 + m**3 + s*m**2 - 5*m**2 - 3*m**2.
2*m*(m - 1)**2
Let b(s) = 9*s**4 + s**3 - 12*s**2 - s + 8. Let n(o) = 26*o**4 + 2*o**3 - 36*o**2 - 2*o + 24. Let i(d) = 14*b(d) - 5*n(d). Suppose i(q) = 0. Calculate q.
-1, 1, 2
Let o = 2/11977 + -284028/11977. Let p = 24 + o. Find k, given that p*k**5 - 8/7*k**4 + 0 + 12/7*k**3 + 2/7*k - 8/7*k**2 = 0.
0, 1
Suppose g - 7 = 3*u, 4*u + g - 2*g + 10 = 0. Let k be ((-4)/(-5))/(u/(-15)). Determine s, given that 2/3*s**2 + 4/9*s**3 - 8/9*s - 2/9*s**k - 8/9 = 0.
-1, 2
Factor -4*y**3 - 36*y**3 + 3*y**4 - 28*y**4 - 5*y**5 - 20*y**2.
-5*y**2*(y + 1)*(y + 2)**2
Let z be ((-2)/24)/(2/(-4)). Let x(a) be the second derivative of z*a**4 + 2*a + a**2 + 0 - 2/3*a**3. Factor x(w).
2*(w - 1)**2
Let t = -6 - -10. Suppose t*l = 4*b + 8, -4*b + 17 = 2*l - l. Factor d**4 - 2*d**b + 2*d**3.
d**4
Let h be 23/(-506) - 6/(-4). Find a, given that -2/11*a**3 - 8/11 - h*a - 10/11*a**2 = 0.
-2, -1
Let p(j) = j**2 - 6*j + 2. Let y be p(6). Determine v, given that -v**3 - 2*v**3 + y*v**3 = 0.
0
Let z(o) be the first derivative of o**5 - 5*o**4/4 - 5*o**3 + 25*o**2/2 - 10*o - 26. Suppose z(w) = 0. What is w?
-2, 1
Let y(u) = u**5 - u**4 + u**3 - 1. Let o(z) = z**5 - 2*z**4 + 4*z**3 - z - 2. Let m(r) = -3*o(r) + 6*y(r). Factor m(t).
3*t*(t - 1)**2*(t + 1)**2
Factor 0 - 2/9*w - 2/9*w**2.
-2*w*(w + 1)/9
Factor 0*u**2 + 0 + 0*u + u**4 - 1/2*u**3 - 1/2*u**5.
-u**3*(u - 1)**2/2
Let f(m) be the second derivative of -m**7/70 + 9*m**5/100 + m**4/10 + 7*m. Factor f(z).
-3*z**2*(z - 2)*(z + 1)**2/5
Let b(o) = -3*o + 15. Let s be b(4). Let u(y) be the first derivative of 3/4*y**2 - 4 - 1/4*y**s - 3/16*y**4 + 0*y. Factor u(h).
-3*h*(h - 1)*(h + 2)/4
Let r(d) be the second derivative of -d**6/25 - 7*d**5/50 - d**4/10 + d**3/5 + 2*d**2/5 + 38*d. Find f, given that r(f) = 0.
-1, 2/3
What is b in -2/3*b**2 - 8/3*b + 0 = 0?
-4, 0
Suppose -3*d = -k - 10, 2*k + 2*d + 15 = 7*d. Suppose 3 = -z, 2*f - 3*z = -k*z + 4. Find n, given that 8/7*n**4 + 10/7*n**3 + 0 + 2/7*n**f + 4/7*n**2 + 0*n = 0.
-2, -1, 0
Let q(o) = o + 1. Let w be q(6). Determine m so that -w*m**2 + 2*m + 2*m**3 - 6*m**3 + 9*m**3 = 0.
0, 2/5, 1
Let t = 29 + -57/2. Let v(c) be the second derivative of 0 - t*c**2 + 1/4*c**3 + 0*c**4 + c - 1/40*c**5. Factor v(r).
-(r - 1)**2*(r + 2)/2
Factor 5*j**2 + 8*j**2 + 0*j**2 - 3*j**2 - 5*j**3.
-5*j**2*(j - 2)
Let s(l) be the second derivative of -2*l**6/45 - l**5/6 - 2*l**4/9 - l**3/9 + 6*l. What is j in s(j) = 0?
-1, -1/2, 0
Let x(f) be the third derivative of 2*f**2 - 2/105*f**7 + 0 - 1/15*f**5 + 0*f**4 + 0*f**3 - 1/12*f**6 + 0*f. Determine u so that x(u) = 0.
-2, -1/2, 0
Let i(k) = 4*k**2 - 5*k - 2. Let s(l) = l + 1. Let x(d) = i(d) + 2*s(d). Factor x(g).
g*(4*g - 3)
Find d such that 8/13*d**2 - 10/13*d - 2/13*d**3 + 4/13 = 0.
1, 2
Suppose 7*c - 13 = 8. Solve -3/2*d**3 + 0 + 0*d - c*d**2 = 0.
-2, 0
Suppose p + 2 = 10. Suppose -3*b + 3*j = -22 + 1, 2*j + p = -b. Factor -2/3*u + 4/3*u**3 + 0*u**4 + 0 - 2/3*u**5 + 0*u**b.
-2*u*(u - 1)**2*(u + 1)**2/3
Let d(o) = o**2 - 1. Let b(v) = 3*v - 3. Let r(p) = p**2 - 2*p - 5. Let t be r(4). Let u(j) = t*d(j) - b(j). Factor u(a).
3*a*(a - 1)
Let d = 11 + -25. Let u be (3/d)/((-16)/168). Factor 1/4*v**2 - 3/2*v + u.
(v - 3)**2/4
Let m(d) be the third derivative of -1/120*d**6 + 0 + 0*d + 1/24*d**4 + 0*d**3 - 1/210*d**7 + 1/60*d**5 + 2*d**2. Factor m(b).
-b*(b - 1)*(b + 1)**2
Let j = -530/3 - -177. Factor -10/3*x**3 - 1/3*x**5 + 10/3*x**2 + j + 5/3*x**4 - 5/3*x.
-(x - 1)**5/3
Suppose -2*p - p - 9 = 3*j, -29 = -2*p + 5*j. Let c be 28/10 + 1/5. Determine w, given that 1 + w**2 + 3*w**p + 6*w**c - 1 + 2*w**4 = 0.
-2, -1, 0
Suppose 0*k = -4*k + 12. Suppose z = -k + 7. Factor 0 + 0*v**3 + 0*v + 6/5*v**z - 4/5*v**5 - 2/5*v**2.
-2*v**2*(v - 1)**2*(2*v + 1)/5
Let j(l) be the third derivative of -l**8/7560 + l**6/405 + l**3/2 + 5*l**2. Let k(o) be the first derivative of j(o). What is i in k(i) = 0?
-2, 0, 2
Let x be 10/8*8/40. Solve 1/4*s**3 + x*s**2 - 1/4*s - 1/4 = 0 for s.
-1, 1
Let h(p) be the second derivative of -p**7/210 - p**6/150 + p**5/100 + p**4/60 - 3*p + 2. Factor h(d).
-d**2*(d - 1)*(d + 1)**2/5
Let d(y) = 10*y**4 - 30*y**3 - 2*y**2 + 38*y - 16. Let c(l) = -3*l**4 + 10*l**3 + l**2 - 13*l + 5. Let g(r) = -16*c(r) - 5*d(r). Factor g(f).
-2*f*(f - 1)*(f + 3)**2
Let m(b) be the third derivative of b**5/15 - 5*b**4/3 + 50*b**3/3 - 4*b**2. Factor m(j).
4*(j - 5)**2
Let q(h) be the third derivative of 1/735*h**7 + 0*h**3 - 1/84*h**4 + 1/420*h**6 + 0*h - 1/210*h**5 + 0 - 3*h**2. Let q(v) = 0. Calculate v