- 15*h**3 - 9*h**2 - 9*h - 9. Let c(p) = -5*p**4 - 4*p**3 - 2*p**2 - 2*p - 2. Let v(w) = 9*c(w) - 2*o(w). Let v(s) = 0. Calculate s.
-2, 0
Let i(h) = 36*h**3 - 16*h**2 + 4*h - 8. Let x(y) = -y**2 + 1. Let t(z) = -i(z) - 8*x(z). What is r in t(r) = 0?
0, 1/3
Let q(s) = s**3 - 4*s**2 + 7*s - 4. Let n(l) = -5*l**3 + 9*l + 31*l**2 - 34*l - 11*l - 11*l**2 + 21. Let x(t) = 2*n(t) + 11*q(t). Find z, given that x(z) = 0.
1, 2
Let r(s) = s - 4. Let u be r(4). Suppose 0*m + 2*m = u. Factor -1/3*i**3 + 1/3*i**2 + m*i + 0.
-i**2*(i - 1)/3
Factor -10*a**2 + 5*a**3 + 29*a - 56*a + 32*a.
5*a*(a - 1)**2
Let k = -1433 - -1438. Determine t, given that -100/3*t**4 + 50*t**k + 32*t - 208*t**3 + 416/3*t**2 - 64/3 = 0.
-2, -2/5, 2/5, 2/3, 2
Let k = 15 - 11. Suppose 0 = -h + g, 2*h = -k*g + 5*g + 2. Factor -t**3 + 3*t**3 - t**3 + h*t**4 - 3*t**4.
-t**3*(t - 1)
Let r(q) be the first derivative of -2*q**5/7 - 3*q**4/7 - 2*q**3/21 - 20. Factor r(l).
-2*l**2*(l + 1)*(5*l + 1)/7
What is x in 1/4*x**4 - 1/4*x**2 + 1/2*x + 0 - 1/2*x**3 = 0?
-1, 0, 1, 2
Let k(o) be the third derivative of 0*o**4 + 0*o**3 + 1/180*o**5 + 13/720*o**6 - 3*o**2 + 1/224*o**8 + 0*o + 0 + 2/105*o**7. Factor k(f).
f**2*(f + 2)*(3*f + 1)**2/6
Let b be (-2)/11 - 501/(-33). Suppose -d = -6*d + b. Factor -2/3 + 2/3*i - 2/3*i**d + 2/3*i**2.
-2*(i - 1)**2*(i + 1)/3
Let y(l) be the first derivative of -l**5/5 + 5*l**4/4 - 3*l**3 + 7*l**2/2 - 2*l + 8. Find d such that y(d) = 0.
1, 2
Let g be ((-155)/(-50) - 3)*16. Factor -g*m - 24/5*m**2 + 14/5*m**3 + 0.
2*m*(m - 2)*(7*m + 2)/5
Let f be 34/(-238) + (-1 - (-438)/224). Let j(s) be the first derivative of 11/8*s**2 - 2 + f*s**4 + 1/2*s + 3/20*s**5 + 19/12*s**3. Solve j(r) = 0.
-2, -1, -1/3
Let d be ((-40)/(-15))/((-27)/(-3) - 3). Let w be 1/((6/4)/3). Factor 2/9*q**3 + d*q - 2/3*q**w + 0.
2*q*(q - 2)*(q - 1)/9
Let q(m) = 2*m - 2. Let p be q(3). Factor -4 - 4*s**3 - 2*s**3 + 4 - 3*s**p.
-3*s**3*(s + 2)
Let m(p) be the third derivative of p**5/90 + p**4/9 + 4*p**3/9 + p**2. Factor m(i).
2*(i + 2)**2/3
Let j(r) be the second derivative of 0*r**2 - 1/10*r**6 + 0*r**3 + 0*r**4 - 1/20*r**5 + 0 + 4*r + 2/21*r**7. Determine h, given that j(h) = 0.
-1/4, 0, 1
Let y(g) be the first derivative of g**3/18 + 27. Factor y(a).
a**2/6
Let u(c) = c**3 - c**2 - c + 1. Let i(d) = -45*d**3 + 50*d**2 + 35*d - 40. Let m(t) = i(t) + 30*u(t). Factor m(k).
-5*(k - 1)**2*(3*k + 2)
Let i be (45 + 0)*(4 + -3). Let n be 38/i + (-4)/10. Factor 2/9*z**2 + 2/9*z - n.
2*(z - 1)*(z + 2)/9
Let m(s) be the third derivative of -s**6/20 + s**5/15 + 20*s**2. Factor m(t).
-2*t**2*(3*t - 2)
Let j = -78 - -81. Factor -2*x**j + 0 - 4/5*x**2 + 0*x.
-2*x**2*(5*x + 2)/5
Let a(x) be the first derivative of -x**8/1344 + x**7/840 + x**6/480 - x**5/240 - x**2/2 - 1. Let l(r) be the second derivative of a(r). Factor l(q).
-q**2*(q - 1)**2*(q + 1)/4
Let w(q) be the third derivative of 0*q**3 + 0*q + 1/84*q**4 + 5*q**2 + 0 + 1/210*q**5. Determine t, given that w(t) = 0.
-1, 0
Let i = 32 - 33. Let r(j) = j + 11*j**5 - 4*j - 3 - 2*j**4 + 3*j**2 - 5*j**4. Let v(f) = f**5 + f**4 - f**2 + f + 1. Let y(l) = i*r(l) - 3*v(l). Factor y(u).
-2*u**4*(7*u - 2)
Let b be 4 + (-1)/((-1)/(-2)). Factor -b*u - 2*u - 2*u**2 + 0 + 0.
-2*u*(u + 2)
Let a = 46 - 33. Let a*v**2 + 10*v**2 + 4*v**4 + 2*v**5 - 2*v - 27*v**2 = 0. What is v?
-1, 0, 1
Let m(h) be the third derivative of -h**7/630 - h**6/45 - 11*h**5/90 - h**4/3 - h**3/2 - 10*h**2. Factor m(o).
-(o + 1)**2*(o + 3)**2/3
Let d = -1 + 1. Factor -2/7*g + 0*g**4 + 4/7*g**3 + d*g**2 - 2/7*g**5 + 0.
-2*g*(g - 1)**2*(g + 1)**2/7
Suppose 4*n + p = 6 - 0, -2*n + 4*p + 12 = 0. Factor -3/5*l + 0 + 6/5*l**n - 3/5*l**3.
-3*l*(l - 1)**2/5
Let i be (-1)/(6/(-1)) + (-15)/(-45). Factor 0*n - 1/2*n**4 + i*n**2 + 0 + 0*n**3.
-n**2*(n - 1)*(n + 1)/2
Factor 0 + 2/5*i**3 - 2/5*i**5 + 2/5*i**2 - 2/5*i**4 + 0*i.
-2*i**2*(i - 1)*(i + 1)**2/5
Let d(k) be the first derivative of -k**6/6 + 2*k**5/5 - 2*k**3/3 + k**2/2 - 15. Find v, given that d(v) = 0.
-1, 0, 1
Solve -24*l**2 + 63*l**3 - 101*l**3 + 56*l**3 - 3*l**4 = 0 for l.
0, 2, 4
Let z(v) = -65*v**4 + 209*v**3 - 222*v**2 + 79*v - 12. Let l(t) = 22*t**4 - 70*t**3 + 74*t**2 - 26*t + 4. Let p(r) = -11*l(r) - 4*z(r). Factor p(m).
2*(m - 2)*(m - 1)*(3*m - 1)**2
Suppose -1 = v - 4. Find z such that 3*z + 1 + 2*z**2 - 2*z**2 - z**2 - v = 0.
1, 2
Let k(p) be the second derivative of -p**5/150 - 2*p**4/45 - p**3/9 - 2*p**2/15 - 10*p. Determine y, given that k(y) = 0.
-2, -1
Let p be 452/8*(0 - -2). Factor -i + i - p*i**3 + 2*i**2 + 118*i**3.
i**2*(5*i + 2)
Find w, given that 2*w + 0 + 1/2*w**5 - 2*w**2 - 3/2*w**3 + w**4 = 0.
-2, 0, 1
Suppose 0 = 9*g - 14 - 4. Suppose -3*d + 25 - 7 = 0. Solve d*q**3 - 2*q + q**2 + 3*q**g + 0*q = 0.
-1, 0, 1/3
Let h(b) be the first derivative of 5*b**3/3 - 15*b**2 + 45*b + 46. What is i in h(i) = 0?
3
Let v(h) = 11*h**2 + 17*h - 17. Let d(y) = -2*y**2 - 3*y + 3. Let o(j) = -34*d(j) - 6*v(j). Suppose o(g) = 0. Calculate g.
0
Suppose -27*m = -24*m - 15. Suppose -20 = -m*u - l, -u - 2*l = -5*l + 12. Suppose 9/5*o**u - 3/5*o**4 - 9/5*o**2 + 3/5*o + 0 = 0. What is o?
0, 1
Let i(r) be the first derivative of -3*r**4/10 + 7*r**3/15 + 2*r**2/5 - 7*r - 3. Let z(b) be the first derivative of i(b). Factor z(u).
-2*(u - 1)*(9*u + 2)/5
Factor -2*r**4 + 6*r**3 - r**4 + 20*r**2 - 22*r**4 + 34*r**3.
-5*r**2*(r - 2)*(5*r + 2)
Determine b so that -4/5 - 2/5*b**3 + 2/5*b + 6/5*b**2 - 2/5*b**4 = 0.
-2, -1, 1
Solve 2/7*m**2 + 0 + 0*m = 0 for m.
0
Let k be 8/(-10)*25/(-10). Let i(o) be the second derivative of 0*o**4 + 0 - 2/15*o**6 - 2*o - 1/21*o**7 - 1/10*o**5 + 0*o**3 + 0*o**k. Solve i(l) = 0 for l.
-1, 0
Let n(m) be the second derivative of 2*m - 3/20*m**5 + 0*m**3 + 1/4*m**4 + 0*m**2 + 0. Let n(r) = 0. What is r?
0, 1
Let w(i) be the second derivative of -i**5/20 - 3*i**4/8 - i**3 - 3*i**2/2 - 3*i. Let d(f) be the first derivative of w(f). Factor d(c).
-3*(c + 1)*(c + 2)
Let w(r) = 2*r - 1. Let k be w(5). Factor 3*n**3 - n**3 + 2*n + k*n + 5*n**3 + 2 + 16*n**2.
(n + 1)**2*(7*n + 2)
Let n(f) be the first derivative of -2*f**4 - 14*f**3/3 + 2*f**2 + 3. Determine s, given that n(s) = 0.
-2, 0, 1/4
Let w = 49 - -109. Factor -158*p + 2*p**4 + p**3 + p**3 + w*p.
2*p**3*(p + 1)
Factor -172*w**2 - 224*w**4 - 124*w**5 - 44*w - 4 + 60*w**5 - 180*w**3 - 112*w**3 + 0.
-4*(w + 1)**3*(4*w + 1)**2
Suppose -r + 5 = 3. Suppose 2*t - 4 + 6*t - 2*t**2 - r*t = 0. Calculate t.
1, 2
Determine j so that -9/5*j**2 - 1/5*j**4 - 4/5*j + 6/5*j**3 + 12/5 = 0.
-1, 2, 3
Let m be ((-4)/12)/((-2)/12). Factor 24/5*v**3 + 1/5*v + 16/5*v**4 + 9/5*v**m + 0.
v*(v + 1)*(4*v + 1)**2/5
Factor -2*n**3 - 4*n**3 + 10*n**3 - 4*n**5.
-4*n**3*(n - 1)*(n + 1)
Let c = 4 - 6. Let d be c/12 - (-1)/2. Find t, given that -4/3*t**3 - d + 7/3*t**2 - 2/3*t = 0.
-1/4, 1
Let r = 137 + -134. Factor -2/3*w**2 + 2*w**r + 0*w + 0 - 2*w**4 + 2/3*w**5.
2*w**2*(w - 1)**3/3
Let m(q) be the second derivative of -4*q**2 + 0 - 1/6*q**4 - 4/3*q**3 - q. Factor m(w).
-2*(w + 2)**2
Let i(x) be the second derivative of -x**4/84 + 11*x. Factor i(l).
-l**2/7
Let l(b) be the first derivative of -b**5/15 + b**3/9 + 10. Determine w so that l(w) = 0.
-1, 0, 1
Let k(w) = 4*w**4 + 10*w**3 - 50*w**3 - 40*w + 17 + 64*w**2 + 3. Let s(n) = n**4 - 13*n**3 + 21*n**2 - 13*n + 7. Let u(x) = -3*k(x) + 8*s(x). Factor u(a).
-4*(a - 1)**4
Let c be 3 - (-6)/(-285) - 3. Let h = 99/190 + c. Factor 1/2*o**2 - h - 1/2*o + 1/2*o**3.
(o - 1)*(o + 1)**2/2
Let j(n) be the second derivative of -n**8/336 + n**6/30 + n**5/30 - n**4/8 - n**3/3 - 3*n**2/2 - 6*n. Let h(a) be the first derivative of j(a). Factor h(q).
-(q - 2)*(q - 1)*(q + 1)**3
Let k = -10 + 12. Factor -4*m + 9*m**3 + 0*m**4 + k*m**2 - m**3 - 6*m**4.
-2*m*(m - 1)**2*(3*m + 2)
Let v be (-726)/(-187) - (-4)/34. Let j(o) be the first derivative of 4/3*o**3 - 2/5*o**5 + o**2 + 1/3*o**6 - o**v - 2*o - 4. Suppose j(t) = 0. What is t?
-1, 1
Let x(p) be the first derivative of -3 - 1/2*p**3 + 1/4*p**4 + 0*p**2 - 2*p. Let r(v) be the first derivative of x(v). Factor r(k).
3*k*(k - 1)
Let l(s) be the first derivative of -4 + 2/3*s**3 - 1/3*s**4 + 1/15*s**5 - 2/3*s**2 + 1/3*s. Factor l(j).
(j - 1)**4/3
Let k(i) be the first derivative of -1/2*i**2 - 2/3*i**3 + 1 + i. Factor k(p).
-(p + 1)*