*3/3 + 21*l**2. Let g(o) = -1. Let f(v) = c(v) + 2*g(v). Determine w so that f(w) = 0.
-4, -2/5
Let d(o) be the first derivative of -o**4/12 + 14*o**3/3 + 29*o**2/2 + 44*o/3 - 492. Factor d(j).
-(j - 44)*(j + 1)**2/3
Let w(b) be the second derivative of b**7/630 - b**6/90 - 17*b**4/12 - 15*b. Let h(r) be the third derivative of w(r). Find v, given that h(v) = 0.
0, 2
Suppose -2*i - 1 = 9. Let p(b) = 2 + b**2 - 3 + 0*b**2. Let m(a) = 3*a**2 + 4*a - 5. Let r(q) = i*p(q) + m(q). Factor r(z).
-2*z*(z - 2)
Let d(w) = -w**2 - 7*w - 4. Let n be d(-6). Suppose 0 = -3*y - n*y + 45. Factor -6*z**4 + 0*z**4 - 6*z**2 + 3 + y*z**4.
3*(z - 1)**2*(z + 1)**2
Let t = 78 + -75. Let n(k) be the first derivative of 1/6*k**2 - t + 0*k + 1/9*k**3. Suppose n(x) = 0. What is x?
-1, 0
Let v(p) be the second derivative of p**8/15120 - p**7/2835 - p**6/405 + 4*p**5/135 + p**4/2 + 13*p. Let u(o) be the third derivative of v(o). Factor u(x).
4*(x - 2)**2*(x + 2)/9
Let n(r) = -r + 9. Let j be n(-10). Suppose 4*o**4 - 36*o**2 - 44*o - j*o**3 + 20*o**3 - 16 - 5*o**3 = 0. What is o?
-1, 4
Let n(a) be the second derivative of a**6/72 - 5*a**4/72 + 13*a**2/2 + 13*a. Let v(g) be the first derivative of n(g). Factor v(o).
5*o*(o - 1)*(o + 1)/3
Let w(y) be the first derivative of y**6/12 - 124. Factor w(m).
m**5/2
Let r be (6/(-3))/((-75)/(-39) - 2). Let -20 - 25*o - 31*o**2 - r*o**2 + 52*o**2 = 0. Calculate o.
-4, -1
Let w(a) be the third derivative of a**5/60 - 35*a**4/12 + 1225*a**3/6 - 2*a**2 + 93. Factor w(o).
(o - 35)**2
Let v(a) be the third derivative of -2*a**3 - 11*a**2 - 1/30*a**5 + 5/12*a**4 + 0*a + 0. Factor v(b).
-2*(b - 3)*(b - 2)
Determine z, given that 40/3*z - 113/3*z**2 + 112/3 + 1/3*z**5 - 41/3*z**3 + 1/3*z**4 = 0.
-4, -1, 1, 7
Factor 12/5*n**3 + 0 + 94/5*n**2 - 16/5*n.
2*n*(n + 8)*(6*n - 1)/5
Suppose 5*i - 21*i = -15*i - 40*i. Find w such that -9/4*w + i + 3/8*w**2 = 0.
0, 6
Suppose 18/11*d**4 - 12*d**3 + 68/11*d + 14/11 + 32/11*d**2 = 0. Calculate d.
-1/3, 1, 7
Let s(x) = 6*x**3 - 4*x**2 - 9*x - 9. Let v be (3 + -13)/((-4)/(-2)). Let i(o) = o**3 - o**2 - o - 1. Let p(g) = v*i(g) + s(g). Let p(q) = 0. What is q?
-2, -1, 2
Let u(b) be the third derivative of b**5/270 - 19*b**4/54 - 13*b**3/9 - 14*b**2 - 9. Factor u(g).
2*(g - 39)*(g + 1)/9
Let j be -12*(3/(-1))/(-30). Let h = -9/20 - j. Factor h*d**3 + 3/4*d**5 + 0*d**2 + 3/2*d**4 + 0*d + 0.
3*d**3*(d + 1)**2/4
Suppose -3*f = j, 2*j + 0*j = 5*f. Suppose -10 = -j*d - 2*d. Determine y, given that y**3 + 0*y**2 + y**2 + 7*y**4 - 12*y**4 - y**d + 4*y**4 = 0.
-1, 0, 1
Let b(o) = 14*o**4 + 178*o**3 + 400*o**2 + 11. Let n(d) = 3*d**4 + 36*d**3 + 80*d**2 + 2. Let y(q) = 2*b(q) - 11*n(q). Factor y(r).
-5*r**2*(r + 4)**2
Suppose 0 = -8*g + 3*g + 35. Factor 6*p**2 - 4*p**3 + g*p**2 - 13*p**2 - p**2 - p**4 + 6*p.
-p*(p - 1)*(p + 2)*(p + 3)
Let z be 50/(-2)*4/(-4). Solve 56 + 57 - z*r**2 - 133 + 5*r**3 + 40*r = 0.
1, 2
Let q(l) = -7*l**2 - 16*l + 56. Let x(v) = -2*v**2 - 1. Let j(o) = q(o) - 4*x(o). Let k be j(6). Factor -1/3*b**3 + 1/3*b**4 + 0*b**2 + 0*b + k.
b**3*(b - 1)/3
Let p be ((-14)/30)/(1785/(-765)). Factor 0*j + 1/5*j**2 + p*j**3 - 1/5*j**5 - 1/5*j**4 + 0.
-j**2*(j - 1)*(j + 1)**2/5
Solve 0 - 1/7*j**2 - 12/7*j = 0 for j.
-12, 0
Find f, given that 85 - 56 - 32*f**3 + 33*f + 8*f**4 - 64*f**2 + 99 + 31*f + 4*f**5 = 0.
-2, 2
Factor -28*h - 732*h**2 + 364*h**2 + 366*h**2.
-2*h*(h + 14)
Let z(m) be the second derivative of 0 + 5/48*m**3 + 1/8*m**2 + 1/160*m**5 + 3*m + 1/24*m**4. Let z(v) = 0. Calculate v.
-2, -1
Let k(f) be the third derivative of f**6/24 - 7*f**5/12 + 5*f**4/3 + 40*f**3/3 - 2*f**2 + 23*f. Suppose k(u) = 0. What is u?
-1, 4
Let j(n) be the third derivative of 0*n**3 - 1/240*n**6 + 0*n + 1/48*n**4 - 25*n**2 + 0 - 1/240*n**5 + 1/840*n**7. Factor j(a).
a*(a - 2)*(a - 1)*(a + 1)/4
Let b be 5 + -12*(-32)/2112*(-94)/4. Find d such that b - 8/11*d + 2/11*d**2 = 0.
2
Suppose 5*z - 11 = 54. Factor 0*a + 7*a + 0*a**3 + z*a**3 + 1 + 4*a**4 + 15*a**2.
(a + 1)**3*(4*a + 1)
Let h(o) = 28 - 621*o - 5 - o**2 + 603*o. Let d(t) be the first derivative of 2*t**3 + 63*t**2 - 162*t - 1. Let r(s) = -4*d(s) - 27*h(s). What is v in r(v) = 0?
3
Suppose 2*q + 0*q = 6. Let l be (-18)/9*q/(-2). Factor -2*u**l - u**3 + 9*u + 10 - 16.
-3*(u - 1)**2*(u + 2)
Let r(d) = -143*d**2 + 4 + 142*d**2 - d - 3. Let b(f) = -25*f**2 - 50*f + 45. Let t(y) = b(y) - 30*r(y). Factor t(p).
5*(p - 3)*(p - 1)
Let p = 2360/9 - 262. Let y(b) be the second derivative of 0 + 6*b + p*b**4 - 4/9*b**3 + 1/3*b**2. Solve y(q) = 0 for q.
1/2
Factor -2/15*m**5 + 0*m**4 + 2/15*m**3 + 0*m**2 + 0*m + 0.
-2*m**3*(m - 1)*(m + 1)/15
Let k(w) be the first derivative of 2*w**3/3 - 2*w**2 - 6*w - 93. Solve k(z) = 0.
-1, 3
Suppose -m - 3*q + 11 = 0, -606 = -m - 5*q - 589. Factor 2/7*p**m + 0 - 2/7*p.
2*p*(p - 1)/7
What is w in 3/8*w**2 - 33/8*w - 9/2 = 0?
-1, 12
Let r(u) be the second derivative of u**6/10 - 3*u**4 + 8*u**3 - 41*u - 1. Find c such that r(c) = 0.
-4, 0, 2
Let 6*h**3 + 8*h - 76*h**2 + 4*h**4 - 6*h**5 + 60*h**2 + 4*h**5 = 0. What is h?
-2, 0, 1, 2
Let x(j) be the second derivative of j**6/50 - 6*j**5/25 + 6*j**4/5 - 16*j**3/5 + 24*j**2/5 - 134*j - 1. Factor x(o).
3*(o - 2)**4/5
Let z(i) = -3*i**5 + 98*i**4 - 693*i**3 + 1782*i**2 - 1272*i - 642. Let m(b) = b**3 - b + 2. Let o(f) = -3*m(f) + z(f). Factor o(d).
-(d - 24)*(d - 3)**3*(3*d + 1)
Determine k, given that -49/2 - 1/2*k**2 - 7*k = 0.
-7
Let a(k) be the second derivative of -3*k**5/80 - 3*k**4/16 + 3*k**2/2 - 151*k - 1. Factor a(c).
-3*(c - 1)*(c + 2)**2/4
Let c be -18*(-1 - 6/12). Suppose 0 = j + 4*t - 3, -c + 12 = -5*j - 2*t. Factor 6*q**3 + 6*q**4 - j*q**2 - 15/2*q - 3 + 3/2*q**5.
3*(q - 1)*(q + 1)**3*(q + 2)/2
Let r(p) = -p**3 - 14*p**2 + 15*p + 9. Let u be r(-15). Suppose 0 = 10*c - u*c - 2. Factor -3*s**c - s**2 - 3 - 5*s - s + s**2.
-3*(s + 1)**2
Solve -6*q**5 - 15/2*q + 9/4 + 27/2*q**3 - 3*q**4 + 3/4*q**2 = 0 for q.
-3/2, -1, 1/2, 1
Let z = -64538/5 + 12910. Factor -z*k + 4/5*k**3 + 0 - 8/5*k**2.
4*k*(k - 3)*(k + 1)/5
Let y(m) be the first derivative of -m**7/1120 - m**6/1440 + m**5/160 + m**4/96 - 2*m**3/3 - 1. Let k(z) be the third derivative of y(z). Factor k(b).
-(b - 1)*(b + 1)*(3*b + 1)/4
Let y be (-85)/51 - 40/(-6). Solve y + 2*i + 1/5*i**2 = 0 for i.
-5
Factor 8 + 4*k**2 - 6 + 10 - 16*k.
4*(k - 3)*(k - 1)
Let j be (1 - 1 - -1)*3. Factor 22*s**j - 18*s**3 - 12*s**2 + 5*s + 3*s.
4*s*(s - 2)*(s - 1)
Suppose -4*c - 12 = 10*v - 6*v, -2*c + v + 9 = 0. Let -o**4 + 1868*o**2 - 3*o**3 - 1871*o**c + 6*o**3 + o = 0. Calculate o.
0, 1
Suppose -18*q + 6*q = 31*q. Let 0 - 6/5*v**2 + q*v - 8/5*v**3 - 2/5*v**4 = 0. What is v?
-3, -1, 0
Let r(b) be the second derivative of 5*b**7/42 + b**6/3 - 3*b**5/4 - 5*b**4/3 + 10*b**3/3 + 59*b - 1. Factor r(u).
5*u*(u - 1)**2*(u + 2)**2
Let o(b) = -10*b**3 - 7*b**2 + 37*b + 16. Let y(i) = -5*i**3 - 3*i**2 + 18*i + 8. Let v(h) = 4*o(h) - 9*y(h). Factor v(q).
(q - 2)*(q + 1)*(5*q + 4)
Let y(a) = -2*a**2 + 3*a - 1. Let j(k) = 3*k**2 - 6*k + 3. Suppose -3 = 8*o - 7*o. Let z(p) = o*j(p) - 5*y(p). Solve z(q) = 0 for q.
-4, 1
Let c(n) = 13*n + 52. Let j be c(-4). Let w be (j - -4) + (-783)/203. Factor 2/7*o + 0 + w*o**2.
o*(o + 2)/7
Let v be 3 - (0 - 12)/(-3). Let n be 10/8 + v - (-35)/(-140). Factor 1/4*a**4 + 1/4*a**5 + 0*a**2 + n*a**3 + 0*a + 0.
a**4*(a + 1)/4
Factor -25*p**4 + 10*p**3 + 9/4*p + 51/4*p**2 + 0.
-p*(p - 1)*(10*p + 3)**2/4
Let l(d) be the third derivative of d**8/84 + 4*d**7/105 - d**6/10 - 4*d**5/15 + 2*d**4/3 + 135*d**2. Factor l(z).
4*z*(z - 1)**2*(z + 2)**2
Let w = -3386 + 13545/4. Let w*r + 1/4*r**2 - 1/4*r**3 + 0 - 1/4*r**4 = 0. What is r?
-1, 0, 1
Let p(y) be the first derivative of 7*y**2 - 2*y**5 + 4/3*y**3 + 15 + 6*y - 3*y**4 - 1/3*y**6. Determine m so that p(m) = 0.
-3, -1, 1
Let i = -3529658/2095 - -8424/5. Let a = 25166/27235 + i. Let a*n**2 + 2/13 + 8/13*n**3 + 2/13*n**4 + 8/13*n = 0. What is n?
-1
Let d(a) = -a - 3. Let b = 13 + -18. Let k be d(b). Factor -163*z**2 + 161*z**2 + 0*z + k + 0*z.
-2*(z - 1)*(z + 1)
Suppose 4*q - 45 = 5*f, f + 17 = 2*q + 2. Factor 6*c**3 + 12*c**4 - 3*c**q - 13*c**3 - 2*c**3.
-3*c**3*(c - 3)*(c - 1)
Suppose -l + 6 = 2*l. Suppose -j - j = -4. Factor -2*d**j + 3*d - 4*d**2 + 4*d**l + d**2.
-d*(d - 3)
Let x(l) 