actor m(r).
-(r + 1)*(2*r - 1)*(3*r - 2)/4
Determine z, given that -582/7*z + 28227/7 + 3/7*z**2 = 0.
97
Let q(n) be the second derivative of -n**6/30 + n**4/4 - n**3/3 - 4*n - 12. Find c such that q(c) = 0.
-2, 0, 1
Let b(x) = -x**3 + 12*x**2 + 14*x - 11. Let z be b(13). Factor -5*n**4 - 65*n + 65*n**3 + 18*n**2 - z*n**2 - n**2 - 10*n**2 + 0*n**4.
-5*n*(n - 13)*(n - 1)*(n + 1)
Suppose 50*p - 40 = 160. Let o be ((-56)/(-42))/(4/(-3)) + p. Factor 8*m**2 - 13/3*m + 4/3*m**4 + 2/3 - 17/3*m**o.
(m - 2)*(m - 1)**2*(4*m - 1)/3
Let n(c) = -4*c**3 + 6653*c**2 - 2742337*c - 2748954. Let h(g) = -4*g**3 + 6658*g**2 - 2742338*g - 2748952. Let i(q) = -5*h(q) + 6*n(q). Factor i(v).
-4*(v - 829)**2*(v + 1)
Let y(w) = 28*w**3 - 23160*w**2 - 15432*w - 8. Let n(v) = 9*v**3 - 7720*v**2 - 5143*v - 3. Let p(q) = 8*n(q) - 3*y(q). Factor p(x).
-4*x*(x - 644)*(3*x + 2)
Let d(n) be the third derivative of -n**5/690 + n**4/46 - 5*n**3/69 - 4*n**2 + 5*n - 13. Solve d(a) = 0.
1, 5
Let p(f) = -13*f**2 - 6*f - 1. Let j(i) = 74*i**2 + 3768*i + 3742. Let d(w) = j(w) + 6*p(w). Factor d(m).
-4*(m - 934)*(m + 1)
Let q(x) = 39*x - 214. Let l be q(-8). Let r = l + 2638/5. Find h, given that 4*h**4 + 4/5*h**5 + 36/5*h**3 + r*h + 0 + 28/5*h**2 = 0.
-2, -1, 0
Let h(y) be the first derivative of -y**6/2 + 951*y**5/5 - 18960*y**4 + 24964*y**3 - 5927. Factor h(m).
-3*m**2*(m - 158)**2*(m - 1)
Let t(m) be the third derivative of -m**8/1848 + 17*m**7/1155 - 13*m**6/165 - 8*m**5/165 + 56*m**4/33 - 208*m**3/33 + 53*m**2 + m + 5. Solve t(f) = 0.
-2, 2, 13
Let g be ((-5)/(-3) + -3)/(28/63). Let b be g + 8 + -3 + 7 + -6. Find m such that 0 + 3/2*m + 1/2*m**b - 2*m**2 = 0.
0, 1, 3
Let k(q) be the first derivative of -2*q**3/21 + 61*q**2/7 + 2078. Factor k(u).
-2*u*(u - 61)/7
Factor -15*r - 3*r**2 + 3*r - 5*r + r**2 + 3*r.
-2*r*(r + 7)
Let i(s) = -5*s**5 + 22*s**4 + 24*s**3 + 2*s**2 - 27*s - 16. Let o(f) = f**5 - 2*f**4 + 2*f**3 - f. Let p(w) = -3*i(w) - 12*o(w). Let p(z) = 0. What is z?
-1, 1, 16
Let g(q) = -q**3 + 16*q**2 + q + 13. Let r be g(15). Let -5*n**3 - 3*n**2 + r*n**4 + 10 + 13*n + 262*n**4 - 514*n**4 = 0. Calculate n.
-1, 2, 5
Let w(r) = -262*r**2 + 5708*r + 50868. Let c(y) = -8*y**2 + 173*y + 1542. Let h(f) = -196*c(f) + 6*w(f). Factor h(p).
-4*(p - 93)*(p + 8)
Let r be ((-48)/40)/(21/(-7630)). Let m = -432 + r. Factor 0 + 2/3*p**3 + 0*p - 1/3*p**m + 0*p**2.
-p**3*(p - 2)/3
Suppose -123*v + 54 = -192. Let s(b) be the first derivative of -6 - 35/2*b**v - 15*b**3 - 10*b - b**5 - 25/4*b**4. Suppose s(f) = 0. Calculate f.
-2, -1
Suppose -2*k = -2*b - 38, -4*b = 5*k - 5*b - 79. Factor k*a**4 - 11*a**3 - a**3 - 18*a**4 - 7*a**2 - 2*a**2.
-3*a**2*(a + 1)*(a + 3)
Suppose 5895*l = 5879*l. Let n(h) be the third derivative of 1/70*h**7 + 0 + h**3 + 1/40*h**6 + 22*h**2 + l*h - 3/20*h**5 - 1/8*h**4. Factor n(w).
3*(w - 1)**2*(w + 1)*(w + 2)
Let z(j) = 50*j**2 - 1872*j - 1064. Let a be z(38). Factor 1/6*p**4 + a + 1/6*p**3 + 1/2*p - 5/6*p**2.
p*(p - 1)**2*(p + 3)/6
Let x(l) = l - 2. Let z(t) = 6*t + 5. Let f be z(-1). Let q(k) = 20*k**2 + 330*k + 115. Let y(m) = f*q(m) - 15*x(m). Factor y(n).
-5*(n + 17)*(4*n + 1)
Let m(t) be the second derivative of -t**5/15 + 4*t**4/3 + 6*t**3 - 62*t**2 - 172*t. Let i(z) be the first derivative of m(z). What is p in i(p) = 0?
-1, 9
Let a(u) = -10*u**2 - 37*u + 44. Let m(w) = 12*w**2 + 36*w - 44. Let s = -421 + 418. Let g(p) = s*m(p) - 4*a(p). Factor g(d).
4*(d - 1)*(d + 11)
Suppose -f + 17 = -5*f - 5*p, 0 = 2*f + 5*p + 21. Let g(t) = -16*t. Let k(w) = -w**2 + w. Let h(a) = f*g(a) + 4*k(a). Factor h(m).
-4*m*(m + 7)
Let a(f) be the third derivative of -f**7/315 + 23*f**6/540 + 7*f**5/27 + f**4/27 - 40*f**3/27 - 1076*f**2. Suppose a(h) = 0. What is h?
-2, -1, 2/3, 10
Let k be (1 + -1 - 1)*0. Suppose 0 = -4*s - 5*b + 28, k = -s - 3*b + 4 + 10. Factor 5*u + u**3 + 4*u**3 - 17*u**2 - u**s + 8*u**2.
5*u*(u - 1)**2
Suppose 0 = -11*d + 10*d + 14. Let z(v) = v**2 - v - 4. Let k be z(3). Let 5*j**4 - 5*j**5 - 3*j**2 + 0*j**2 - d*j**3 + 19*j**3 - k*j**2 = 0. Calculate j.
-1, 0, 1
Let j = -2/666965 - -897734904/4668755. Factor -176*f + 56 + j*f**2 - 566/7*f**3 - 2/7*f**5 + 62/7*f**4.
-2*(f - 14)**2*(f - 1)**3/7
Let z(p) be the first derivative of p**6/1800 - 3*p**5/200 + 3*p**4/20 - 64*p**3 + 56. Let j(w) be the third derivative of z(w). Factor j(d).
(d - 6)*(d - 3)/5
Let w be (-413)/(-56) - 2/6*(-27)/(-24). Let r(y) be the first derivative of -7/3*y**3 - 11 - 1/4*y**4 + w*y + 1/2*y**2. Factor r(z).
-(z - 1)*(z + 1)*(z + 7)
Let b = 29 - 26. Solve -47*w**2 + 4*w**4 - 33*w**2 + 92*w**2 - 20*w**b + 4*w**5 = 0.
-3, 0, 1
Suppose 40*q - 531 = 31*q. Suppose 84*z = q*z. Factor z + 4/7*d - 2/7*d**3 - 2/7*d**2.
-2*d*(d - 1)*(d + 2)/7
Let v(k) be the second derivative of -3 + 0*k**2 - k + 1/20*k**5 - 1/4*k**4 + 1/3*k**3. Determine w, given that v(w) = 0.
0, 1, 2
Let t(o) be the first derivative of -660*o**3 - 5336*o**2/9 + 4*o/3 - 2234. Factor t(q).
-4*(5*q + 3)*(891*q - 1)/9
Let u(a) be the third derivative of -1/60*a**6 + 0*a**5 + 0*a**4 + 1/525*a**7 + 0*a**3 + 47*a**2 + 0 + 0*a. Factor u(q).
2*q**3*(q - 5)/5
Let g be 6*2/60*4601 + -2. Let j = g - 915. Find r such that -52/5*r**2 + 0 - 12*r**3 - 4/5*r**5 - j*r - 28/5*r**4 = 0.
-4, -1, 0
Let f(k) be the first derivative of k**3/4 - 27*k**2/8 + 15*k + 382. Suppose f(m) = 0. What is m?
4, 5
Let m = -1043 - -893. Let s be (6/(-10))/(-5*(-45)/m). Find o such that -4/5 - s*o**2 - 6/5*o = 0.
-2, -1
Let o = 16 - 11. Let p(g) = g**3 - 4*g**2 - 6*g + 7. Let j be p(o). Factor -3*l - 24 + 2*l**j + 23*l - 4*l**2 + 6*l**2.
4*(l - 1)*(l + 6)
Let j(m) be the second derivative of -5/16*m**4 - 38 - m + 9/80*m**5 - 1/56*m**7 + 1/40*m**6 + 0*m**2 + 1/4*m**3. Factor j(z).
-3*z*(z - 1)**3*(z + 2)/4
Solve 672800*b + 1160*b**2 + 2/3*b**3 + 390224000/3 = 0.
-580
Suppose -3*v - 5*t - 30 = 0, 3*v = t + 5182 - 5176. Factor 0*n - 12/11*n**4 - 16/11*n**2 - 2/11*n**5 - 24/11*n**3 + v.
-2*n**2*(n + 2)**3/11
Suppose 0 = -2*i + 4*m + 8, -4*i - 7*m + 23 = -8*m. Let -36 + 21*t**2 + 3/2*t**5 + 42*t - i*t**4 - 45/2*t**3 = 0. What is t?
-2, 1, 6
Let m be 4/(-14) - 12*15/(-140). Factor -5*n - 9*n**2 - 4*n + m + n.
-(n + 1)*(9*n - 1)
Let u(s) be the second derivative of 5*s**3 + 0 + 3/20*s**5 + 237*s - 7/4*s**4 + 0*s**2. Factor u(y).
3*y*(y - 5)*(y - 2)
Let i(a) be the first derivative of -a**3/24 - 135*a**2/8 + 1508. Determine r, given that i(r) = 0.
-270, 0
Let q(o) = 3*o**5 + 1591*o**4 + 210674*o**3 - 212266*o**2 + 2. Let b(v) = -v**4 + v**3 + v**2 + 1. Let t(h) = 2*b(h) - q(h). Suppose t(w) = 0. Calculate w.
-266, 0, 1
Let y(q) = -260*q**3 + 22770*q**2 - 3228*q + 182. Let r(c) = 6*c**3 - c**2 + c + 3. Let t(z) = 44*r(z) - 2*y(z). Factor t(n).
4*(n - 58)*(14*n - 1)**2
Let a be (-36)/(-180)*(48/(-18) - -6). Factor -a*r**2 - 600 - 40*r.
-2*(r + 30)**2/3
Let x be ((-72792)/(-288))/337 - 474/(-8). Factor 2/3*o**2 + 1350 - x*o.
2*(o - 45)**2/3
Suppose -o + 0 = -3. Suppose -5*t - o*y + 186 = 16, 3*y = 15. Factor -7*k**2 + 15*k + t*k**2 + 3*k**3 + 6 - 12*k**2.
3*(k + 1)**2*(k + 2)
Let w(o) = -79*o**2 - 8*o + 2. Let l(z) = 155*z**2 + 15*z - 5. Let a = -59 - -54. Let v(t) = a*w(t) - 2*l(t). Factor v(j).
5*j*(17*j + 2)
Let w(j) = -4*j - 2. Let x = -117 - -119. Let l(p) = 1287*p**2 + 4*p**3 - 1287*p**x - 3*p**3 + p. Let c(m) = -4*l(m) - 4*w(m). Let c(q) = 0. What is q?
-1, 2
Let r = 20425/3 + -6795. Let i(g) be the second derivative of -r*g**3 + 0 - 7/5*g**5 - 46*g - 16*g**2 - 6*g**4 - 2/15*g**6. Let i(w) = 0. What is w?
-2, -1
Suppose o - 1 - 4 = b, -3*b = 3*o - 3. Let z(d) be the first derivative of -10/3*d**3 + 5/4*d**4 + 5/2*d**2 + 0*d + o. Factor z(n).
5*n*(n - 1)**2
Let z(l) be the first derivative of 0*l - 1/20*l**4 + 87 + 17/15*l**3 - 8/5*l**2. Factor z(f).
-f*(f - 16)*(f - 1)/5
Suppose 47330 = 88*r + 47066. Factor 4 - 4*k**2 - 1/5*k**r + 1/5*k.
-(k - 1)*(k + 1)*(k + 20)/5
Suppose -49*f + 52*f + 3*b = -21, 2*f + 34 = -4*b. Suppose 2/7*d**4 + 0*d + 0 + 2/7*d**2 + 4/7*d**f = 0. Calculate d.
-1, 0
Suppose -4*t - g + 68 + 29 = 0, 3*t - 49 = 4*g. Suppose 68 = 15*o + t. Determine a so that -4*a + 2*a**o + 9*a - 2*a**2 - 9*a = 0.
-1, 0, 2
Let m(t) be the first derivative of 4*t**4/3 - 146*t**3/9 + 73*t**2/3 - 16*t/3 + 116. Factor m(z).
2*(z - 8)*(z - 1)*(8*z - 1)/3
Determi