k) + t(k). Factor s(d).
(d - 3)*(d + 1)
Factor -71/2*r + 1/4*r**2 + 0.
r*(r - 142)/4
Let j = -1992 - -1994. Solve 3/7*g**j + 0 + 0*g**3 + 2/7*g - 1/7*g**4 = 0.
-1, 0, 2
Factor -12*r**2 - 4*r**3 + 6*r**2 + 3*r**3 + 11*r**2 - 2*r - r**3.
-r*(r - 2)*(2*r - 1)
Factor -3*m + 6*m + 13*m - m**2 + 3*m.
-m*(m - 19)
Let m = 48 - 66. Let r be (3*3/m)/(-1). Factor 1/4*w**5 - 1/4*w**4 - r*w**3 + 0 + 0*w**2 + 0*w.
w**3*(w - 2)*(w + 1)/4
Factor 0 - 6/5*v - 15*v**3 + 81/5*v**2.
-3*v*(v - 1)*(25*v - 2)/5
Let z be (-140)/(-8) + (-1)/(-6)*-3. Let x = z - 15. Factor -2/7 + 0*n + 2/7*n**x.
2*(n - 1)*(n + 1)/7
Let u(d) be the first derivative of -1/190*d**5 + 0*d**2 - 8*d + 0*d**3 + 1/114*d**4 - 11. Let o(m) be the first derivative of u(m). Factor o(h).
-2*h**2*(h - 1)/19
Let i(d) be the third derivative of d**5/180 - 7*d**4/72 + d**3/3 + 402*d**2. Factor i(g).
(g - 6)*(g - 1)/3
Let q = 1652 - 1648. Let a(f) be the second derivative of 0*f**3 + 0*f**5 + 1/3*f**4 - 2/15*f**6 + 0*f**2 - q*f + 0. Factor a(x).
-4*x**2*(x - 1)*(x + 1)
Let t = 10223/21 - 1460/3. Let -3/7*g + t*g**2 + 2/7 = 0. What is g?
1, 2
Let u(w) be the second derivative of -5*w**4/12 + 95*w**3/3 - 180*w**2 + 51*w. Factor u(t).
-5*(t - 36)*(t - 2)
Factor 9/2*s**2 - 1/2*s**4 + 0*s**3 + 2*s - 6.
-(s - 3)*(s - 1)*(s + 2)**2/2
Let x = -6 - -1. Let w be x/(-3) + 1/3. Let 4 + o**2 - 4*o - 2*o**w - 2*o + 3*o**2 = 0. What is o?
1, 2
Determine r, given that 16/5 - 2/5*r**4 - 8/5*r**3 + 28/5*r + 6/5*r**2 = 0.
-4, -1, 2
Let f(k) be the second derivative of 2/15*k**6 + 1/5*k**5 + 5*k - 2/3*k**3 - 1/3*k**4 + 0 + 0*k**2. Solve f(v) = 0.
-1, 0, 1
Let t(p) be the third derivative of p**7/630 + p**6/120 - p**4/18 + 38*p**2. Factor t(f).
f*(f - 1)*(f + 2)**2/3
Suppose -2*r - 2*r + 16 = 0. Let s be (-1)/((-6)/r + 1). Suppose 3 + 6*u + 5*u**5 - 12*u**3 + 4*u**5 - 7*u**2 + 3*u**4 - 3*u**5 + u**s = 0. Calculate u.
-1, -1/2, 1
Let a(p) = -p**3 - 6*p**2 - 15*p. Let s(w) = w. Let u(k) = a(k) + 6*s(k). Determine d so that u(d) = 0.
-3, 0
Let m(l) be the second derivative of -l**7/105 - l**6/25 + 3*l**5/25 + l**4/3 - 7*l**3/5 + 9*l**2/5 - 29*l. Factor m(s).
-2*(s - 1)**3*(s + 3)**2/5
Let y = 4 + -1. Let z be (-3 - (3 - y)) + 6 + -1. Suppose 63/5*v**3 + 0 - 27/5*v**4 - 48/5*v**z + 12/5*v = 0. What is v?
0, 2/3, 1
Suppose 0 = -3*r + 4*d - 20, r - 3*r + 3*d - 12 = 0. Let j = -7 - r. Determine a so that -48*a**2 - 65*a**2 + j*a**2 - 36*a - 3 = 0.
-1/6
Let z(a) = -a**3 - 2*a**2 - 3*a - 4. Let d be z(-2). Factor d*u**5 - 6*u**3 + 3*u**5 - u**5 + 2*u**3.
4*u**3*(u - 1)*(u + 1)
Let k be 37/296 - (-7)/8. Let c(s) be the first derivative of -1/2*s**2 - k - 4/9*s**3 + 1/3*s. Solve c(u) = 0 for u.
-1, 1/4
Let d(h) be the second derivative of h**7/1176 + h**6/1260 - h**5/280 - 2*h**3 - 2*h. Let k(n) be the second derivative of d(n). Factor k(z).
z*(z + 1)*(5*z - 3)/7
Let v(k) be the first derivative of 8*k**6/15 - 36*k**5/25 + 6*k**4/5 - 4*k**3/15 - 136. Suppose v(w) = 0. What is w?
0, 1/4, 1
Factor -1/5*k**2 - 246/5*k - 15129/5.
-(k + 123)**2/5
Let a = 2331/3092 + -3/773. Factor -1/4*n**2 + 1 - a*n.
-(n - 1)*(n + 4)/4
Factor -4*v**3 - 2/9*v**4 - 56/3*v**2 - 304/9*v - 64/3.
-2*(v + 2)**3*(v + 12)/9
Suppose 40 = 2*a + 32. Let 3*v**2 - 4 - a*v**2 - 2*v + 4*v**2 - v**2 = 0. Calculate v.
-1, 2
Let x = 156 + -153. Let b be (-130)/(-50) - x/5. Factor 9/4 + 1/4*t**b - 3/2*t.
(t - 3)**2/4
Suppose -r - 59 + 62 = 0. Suppose x = r*j - 6, j = -2*x + 5*j - 6. Factor 0*o - 1/3*o**x + 4/3 - o**2.
-(o - 1)*(o + 2)**2/3
Factor 40/7*j + 2/7*j**2 + 38/7.
2*(j + 1)*(j + 19)/7
Let o(q) be the third derivative of -q**7/2100 - q**6/300 - q**5/120 - q**4/120 - 201*q**2. Determine p, given that o(p) = 0.
-2, -1, 0
Let j(s) be the first derivative of -s**6/1800 + s**5/600 - 16*s**3/3 - 3. Let c(k) be the third derivative of j(k). Factor c(p).
-p*(p - 1)/5
Let d(m) be the second derivative of -m**4/78 + m**3/3 + 155*m. Find r such that d(r) = 0.
0, 13
Let o(t) be the third derivative of -3*t**7/14 + 239*t**6/4 - 56641*t**5/12 - 23900*t**4/3 - 16000*t**3/3 - 65*t**2. Suppose o(z) = 0. Calculate z.
-1/3, 80
Let f(h) be the third derivative of h**10/75600 - h**9/60480 + 7*h**5/30 + 20*h**2. Let x(m) be the third derivative of f(m). Factor x(w).
w**3*(2*w - 1)
Let 3*w**2 + w**2 + 57*w - 49*w + 72 + 68*w = 0. Calculate w.
-18, -1
Let g(y) be the third derivative of y**5/30 - 37*y**4/6 + 1369*y**3/3 - 87*y**2 - 5. Determine k, given that g(k) = 0.
37
Determine k so that 1089/2 + 1/2*k**2 + 33*k = 0.
-33
Suppose -h + 4*g = h + 6, g = 3*h - 6. Suppose w = 4*f + 59, 3*f - 109 = -h*w - 2*f. Factor -76*d**2 + 3*d + 36*d**2 + w*d**2.
3*d*(d + 1)
Let d = -15 + -15. Let v be (-4)/10 - 12/d. What is p in 2/3*p**3 + v*p - 4/3*p**2 + 0 + 2/3*p**4 = 0?
-2, 0, 1
Let v = -13523/12 + 1126. Let w = v + 19/12. Factor 0 + 0*j**2 + w*j**5 + 0*j + 4/3*j**4 + 2/3*j**3.
2*j**3*(j + 1)**2/3
Let n(a) = a**2 + a - 1. Let g be n(3). Solve -12 + 6 - 5*o**2 - g - 20*o - 3 = 0 for o.
-2
Let s be -2*5/((-10)/(-7)). Let m = s + 9. Let 2*z**2 + 0*z**2 + 2*z - 3*z**m = 0. What is z?
0, 2
Let p(u) = -6*u**2 - 50*u - 24. Let l(q) = 2*q**2 + 16*q + 8. Let k(h) = -10*l(h) - 3*p(h). Factor k(o).
-2*(o + 1)*(o + 4)
Let y(j) be the second derivative of -10/3*j**4 + 0 + 144*j**2 + 8*j**3 - 48*j + 1/5*j**5. Factor y(d).
4*(d - 6)**2*(d + 2)
Let o(n) = -2*n**2 + 30*n + 1090. Let z be o(-17). Factor 32/5*x + 128/5 + 2/5*x**z.
2*(x + 8)**2/5
Suppose l + 46 = 4*y, -3*y + 4*l + 40 = y. Let h be (4 + 3*(-16)/y)/(-1). Suppose -1/3*z + h + 1/6*z**2 = 0. Calculate z.
0, 2
Let z(y) be the third derivative of -22/35*y**7 - 18*y**4 + 18*y**3 - 6/5*y**5 + 8/3*y**6 + 1/21*y**8 + 0*y + 0 - 27*y**2. Find g, given that z(g) = 0.
-1, 1/4, 3
Let x = 32 - 27. Factor -5*a + 2*a**2 + 5*a**3 - x + 6 - 3*a**2.
(a - 1)*(a + 1)*(5*a - 1)
Suppose -73*i - 16*i = 0. Let 0*z**2 + 0*z**4 + 0*z + i*z**3 + 3/4*z**5 + 0 = 0. Calculate z.
0
Factor -10 - 28*p + 257*p**2 - 37*p**3 - 281*p**2 + 33*p**3 + 2*p**4.
2*(p - 5)*(p + 1)**3
Let p(u) be the first derivative of -2*u**7/105 + 2*u**5/25 - 2*u**3/15 + u + 10. Let j(g) be the first derivative of p(g). Solve j(s) = 0.
-1, 0, 1
Factor 5*c**3 + 237*c - 380*c + 223*c - 40*c**2.
5*c*(c - 4)**2
Let d(g) be the second derivative of g**5/120 - 2*g**4/9 - 35*g**3/36 - 3*g**2/2 - 54*g + 2. Determine z so that d(z) = 0.
-1, 18
Suppose 0 = -8*h + 14*h. Let v(k) be the first derivative of -1/2*k**2 - 1/6*k**6 + h*k - 4/3*k**3 - 3/2*k**4 + 3 - 4/5*k**5. What is l in v(l) = 0?
-1, 0
Let 208*i**2 + 0*i**5 - 138 + 96*i - 8*i**3 - 4*i**5 - 156 - 36*i**4 + 38 = 0. Calculate i.
-8, -2, 1, 2
Let w(y) be the second derivative of 3*y**6/80 + y**5/20 + y**4/36 - y**3 + 12*y. Let i(f) be the second derivative of w(f). Let i(p) = 0. Calculate p.
-2/9
Let t be ((-87)/3)/(-18 - -9) + -3. Let m(i) be the second derivative of 1/18*i**4 - 2*i + 0 + 1/3*i**2 - t*i**3. Factor m(o).
2*(o - 1)**2/3
Factor -z**3 + 5284*z + 8*z**2 - 3*z**2 + 13*z**2 - 5200*z + 88.
-(z - 22)*(z + 2)**2
Let f(y) be the second derivative of -y**4/84 - 31*y**3/21 - 61*y**2/14 - 263*y. Factor f(w).
-(w + 1)*(w + 61)/7
Suppose -4*o + 118 = -l, -4*l - 13*o = -9*o + 372. Let t = l + 98. Let h**3 - 1/2*h**4 + t*h + 0 - 1/2*h**2 = 0. Calculate h.
0, 1
Let d = 1427 - 1424. Factor -1/2*j**2 - 1/6 - 5/6*j + 3/2*j**d.
(j - 1)*(3*j + 1)**2/6
Let p = -5 - -1. Let l(k) = -8*k**4 + k**3 + 9*k**2 + 5*k. Let a(r) = 7*r**4 - 2*r**3 - 9*r**2 - 4*r. Let b(f) = p*l(f) - 5*a(f). Suppose b(h) = 0. Calculate h.
-1, 0, 3
Solve -13/4*z**2 - 3/4*z**3 - 4*z - 1 = 0.
-2, -1/3
Let m(h) = h**3 - 5*h**2 + 4*h - 7. Let q be m(5). Let u = q - 10. Factor -t**2 + 3*t + u - 3 + 3*t**4 + 9*t**3 + 10*t**2.
3*t*(t + 1)**3
Let d(j) = -4*j**2 + 4. Let k(o) = 5*o**2 + o - 4. Let w(r) = r + 3. Let p be w(-5). Let m = 8 + p. Let x(l) = m*k(l) + 7*d(l). Factor x(z).
2*(z + 1)*(z + 2)
Let a = -313093/333 + 855/37. Let q = -916 - a. Factor -64/9*r**2 - q*r**5 - 4/9 - 44/9*r**4 - 26/9*r - 76/9*r**3.
-2*(r + 1)**4*(5*r + 2)/9
Find y, given that 48*y**3 + y + y - 4 + 4*y**2 + 45*y**3 - 95*y**3 = 0.
-1, 1, 2
Let u(a) be the first derivative of a**6/135 - a**5/45 + a**4/54 + 7*a - 15. Let m(s) be the first derivative of u(s). Let m(i) = 0. What is i?
0, 1
Let p(q) be the second derivative of -q**7/88