lculate d.
-3, 5/2
Factor 8*o - 15*o**2 + 39*o**2 + 13*o + o**3 - 56 + 10.
(o - 1)*(o + 2)*(o + 23)
Let u(k) = k**3 + 15*k**2 - 5*k - 35. Let f be u(-15). Suppose -f*n = -35*n - 10. Factor 1/2*o**4 - o**2 - n*o**3 + 6*o + 9/2.
(o - 3)**2*(o + 1)**2/2
Let a(x) be the first derivative of x**3/2 + 39*x**2/2 + 75*x/2 - 75. Factor a(h).
3*(h + 1)*(h + 25)/2
Let b(r) be the first derivative of -2/3*r**3 + 0*r + 42 - 3*r**2. Let b(s) = 0. What is s?
-3, 0
Suppose 2*w + 9 + 0 = z, 2*w + 4*z = -24. Let p be 2/w*(-15 + 3). Let -p*x**2 - 9*x - 6 + 0*x**2 + x**2 = 0. What is x?
-2, -1
Let x = 611/721 - -1/103. Factor 3/7*u**2 + 9/7*u + x.
3*(u + 1)*(u + 2)/7
Let b(j) = -j**2 - 16. Let i(m) be the second derivative of -m**4/3 - 24*m**2 + 12*m. Let n(k) = 16*b(k) - 5*i(k). Find c such that n(c) = 0.
-2, 2
Let 2/13*z**2 - 4/13*z + 2/13 = 0. Calculate z.
1
Suppose 4*a - 192 = 2*a. Solve a*l**3 + 144*l**3 + 448*l**4 - 18*l**2 + 256*l**5 + 4*l + 70*l**2 = 0.
-1, -1/4, 0
Let r(l) = 26*l**4 - 106*l**3 + 155*l**2 - 59*l - 48. Let z(j) = -9*j**4 + 36*j**3 - 52*j**2 + 20*j + 16. Let t(y) = -4*r(y) - 11*z(y). Factor t(a).
-(a - 2)**3*(5*a + 2)
Let d(y) be the second derivative of 2*y + 0*y**3 - 8/45*y**6 + 1/3*y**5 + 2/63*y**7 + 0 + 0*y**2 - 2/9*y**4. Determine w so that d(w) = 0.
0, 1, 2
Let c(j) = j**3 - 12*j**2 + 22*j - 17. Let v be c(10). Let g(k) be the first derivative of 3 + k + 2/3*k**2 + 1/9*k**v. Factor g(u).
(u + 1)*(u + 3)/3
Let q(j) be the second derivative of -1/54*j**4 + 0 + 1/27*j**3 + 2/9*j**2 + 11*j. Factor q(s).
-2*(s - 2)*(s + 1)/9
Let o be 639/3692 + (3 - (-114)/(-117)*3). Let m = 1205/4 - 299. Suppose 0 + 3/2*b**2 + o*b**3 + m*b = 0. Calculate b.
-3, 0
Determine u, given that -1/6*u**4 + 1/2*u**3 - 1/2*u**2 + 1/6*u + 0 = 0.
0, 1
Factor 1/6*a**2 - 8*a + 96.
(a - 24)**2/6
Factor 45/8*k - 3/8*k**3 + 9/4*k**2 - 75/2.
-3*(k - 5)**2*(k + 4)/8
Factor -3*w**3 + 4376 - 42*w**3 + 340*w - 210*w**2 - 4496.
-5*(w + 6)*(3*w - 2)**2
Let n = 3 + 193. Determine v, given that 0*v**2 + 6*v**2 - 10*v**2 - n + 56*v = 0.
7
Suppose -205 + 205 = 23*p. Factor p*n + 1/3*n**2 + 0.
n**2/3
Let g be -3 + 3564/(-21) - -2. Let h = g - -171. Factor 0*o**2 - 2/7*o**3 + h*o + 0.
-2*o*(o - 1)*(o + 1)/7
Let j(i) = i + 6 - 4 - 4*i. Let o be j(-1). Factor g + 12*g**4 + 20*g**3 + 0*g**4 - o*g + 4*g**2.
4*g*(g + 1)**2*(3*g - 1)
Factor 47914 - 47914 + y**3 + 3*y**2 - 54*y.
y*(y - 6)*(y + 9)
Factor 2/9*w**4 + 170/9*w**2 - 28/3*w - 88/9*w**3 + 0.
2*w*(w - 42)*(w - 1)**2/9
Let p be ((-2)/(-25))/(-22 - 4862/(-220)). Factor p*k - 2/5*k**2 - 2/5*k**3 + 0.
-2*k*(k - 1)*(k + 2)/5
Determine n so that 3/2*n**2 + 2*n + 1/4*n**3 + 0 = 0.
-4, -2, 0
Determine i so that 0 + 2/3*i**5 - 2/3*i**2 + 2/3*i**4 - 2*i**3 + 4/3*i = 0.
-2, -1, 0, 1
Let t(p) = 2*p. Let l be 1*(-3 + 1)*-2. Let q be t(l). Factor -q*g**2 + 8*g - 5*g**2 - 8 + 11*g**2.
-2*(g - 2)**2
Let r(a) be the first derivative of -2/45*a**5 + 10/27*a**3 + 13 - 2/9*a**2 + 1/27*a**6 + 0*a - 1/6*a**4. Factor r(v).
2*v*(v - 1)**3*(v + 2)/9
Let m = -4 + 8. Solve -4 + 3*i**2 + 14*i**2 + 32*i**3 + 18*i**m - 6*i**4 + 7*i**2 = 0.
-1, 1/3
Let o(f) = -f**3 + 2*f + 2. Let v(k) = 56*k**3 - 88*k**2 + 19*k - 20. Let y(p) = -33*o(p) - 3*v(p). Suppose y(b) = 0. What is b?
-2/45, 1
Let c be (-4 + 270/63)*5/10. Determine s so that 1/7*s**2 - 1/7*s**4 + 0*s + 0 + c*s**3 - 1/7*s**5 = 0.
-1, 0, 1
Factor 21*j + 18 + 30*j + 9*j**2 + 12*j**2.
3*(j + 2)*(7*j + 3)
Factor 29/2*s - 841/4 - 1/4*s**2.
-(s - 29)**2/4
Let t(r) = r**4 + 10*r**3 + 39*r**2 + 42*r + 16. Let h(s) = 3*s**4 + 29*s**3 + 118*s**2 + 126*s + 48. Let b(n) = 2*h(n) - 7*t(n). Factor b(m).
-(m + 1)**2*(m + 2)*(m + 8)
Let j(y) be the second derivative of -y**5/150 - y**4/9 - 11*y**3/15 - 12*y**2/5 + 5*y - 7. Find w, given that j(w) = 0.
-4, -3
Let x(c) be the second derivative of c**5/30 + c**4/4 - 3*c**2 - 15*c. Let a(k) be the first derivative of x(k). Factor a(g).
2*g*(g + 3)
Let z(h) be the second derivative of 0 - 3/11*h**2 - 3/22*h**4 + 27/110*h**5 - 5/11*h**3 + 7*h. Factor z(n).
6*(n - 1)*(3*n + 1)**2/11
Factor 2/11*w**2 + 16/11 + 18/11*w.
2*(w + 1)*(w + 8)/11
Determine f so that -8/7*f**4 + 0 + 12/7*f**3 - 4/7*f**5 + 0*f + 0*f**2 = 0.
-3, 0, 1
Let d(a) = a + 7. Let n be d(-3). Factor 41 + 8*x + 12*x - 49 - 16*x**2 + n*x**3.
4*(x - 2)*(x - 1)**2
Let o(f) be the first derivative of 10*f**2 - 5/3*f**3 - 6 + 25*f. Factor o(t).
-5*(t - 5)*(t + 1)
Factor 0 + 4/7*z - 2/7*z**2.
-2*z*(z - 2)/7
Let j = 21 + -21. Suppose -5*v + 20 = j, 2*v + v = 5*m + 2. Factor -15*i**3 + 26*i**3 - 4*i**4 - 7*i**3 - 4*i + 4*i**m.
-4*i*(i - 1)**2*(i + 1)
Let m(t) be the first derivative of -2883*t**4/16 - 930*t**3 + 369*t**2/2 - 12*t - 459. Suppose m(g) = 0. Calculate g.
-4, 2/31
Let p(n) be the first derivative of n**6/39 - 2*n**5/65 + 120. Suppose p(v) = 0. Calculate v.
0, 1
Let m(b) = -b**2 - 1. Let u(j) = -3*j**3 - 2*j**2 - 1. Let x(n) = 3*m(n) - 3*u(n). Factor x(a).
3*a**2*(3*a + 1)
Let q = 16553/17 - 973. Let h(r) be the first derivative of 26/51*r**3 - 1 + 2/85*r**5 - 3/17*r**4 - q*r**2 + 8/17*r. Let h(g) = 0. What is g?
1, 2
Let r = -1276 - -6398/5. Determine h, given that -12/5*h + r + 2/5*h**2 = 0.
3
Suppose -5*m = 5*i - 40, 1692 - 1684 = -2*m + 2*i. Factor 2/15*o**m + 2/5*o**4 - 2/5*o**3 - 2/15*o**5 + 0*o + 0.
-2*o**2*(o - 1)**3/15
Let h(w) be the second derivative of w**7/560 - w**5/80 + 5*w**3/3 - 13*w. Let t(x) be the second derivative of h(x). Determine k, given that t(k) = 0.
-1, 0, 1
Let p be (4 + -3)*(-1)/2*-10. Let w be (3 - p/10)*18/15. Factor 0*v**w + 0*v - 4/11*v**2 + 2/11*v**4 + 2/11.
2*(v - 1)**2*(v + 1)**2/11
Suppose 5*c - 6*c + 4 = 0. Factor 4 - 9*f + c*f + f**2 + 9*f.
(f + 2)**2
Let q = -53 - -64. Suppose 2*s - 15 = -q. Factor -1/3*z - 1/6*z**s + 1/3*z**3 + 0 + 1/6*z**4.
z*(z - 1)*(z + 1)*(z + 2)/6
Let v(j) be the first derivative of 2*j**3/9 - 68*j**2 + 6936*j - 997. Factor v(d).
2*(d - 102)**2/3
Factor 23/5*f**3 - 11/5*f**2 + 0 + 0*f + 1/5*f**5 - 13/5*f**4.
f**2*(f - 11)*(f - 1)**2/5
Let n(i) be the second derivative of -i**8/30240 + i**7/11340 + 11*i**4/4 - 3*i. Let j(x) be the third derivative of n(x). Find d such that j(d) = 0.
0, 1
Let x = -10 - -15. Suppose -4*f - 3*y + 8 = -5*y, -f + x*y = -2. Factor 0*g**2 + 0*g**f - 6*g**2 + 2*g**2 + 4.
-4*(g - 1)*(g + 1)
Suppose -2*y + 3*y = -3*x + 112, -x - 2*y + 44 = 0. Factor -x*s**3 - 52*s - 80*s**2 - 3 - 3 - 2 + 0.
-4*(s + 1)**2*(9*s + 2)
Let n(q) be the third derivative of 0 - 1/9*q**6 - 11/60*q**5 - 8/315*q**7 - 5/36*q**4 + 0*q + 2*q**2 - 1/18*q**3. Suppose n(k) = 0. Calculate k.
-1, -1/4
Suppose a = -a - 2, 5*p + 5*a - 70 = 0. Solve -120*i - 4*i**2 - 10*i**3 + 45 + 54*i**2 + p*i**2 = 0.
1/2, 3
Let y(h) = -40*h**2 + 1360*h + 3780. Let a(t) = -3*t**2 + 97*t + 270. Let v(c) = 55*a(c) - 4*y(c). Solve v(u) = 0.
-18, -3
Let d(p) = p**2 - 15*p + 17. Let o be d(14). Determine c so that -3*c**4 + c**3 + o*c**5 - 4*c**5 - c**2 - 4*c**3 = 0.
-1, 0
Suppose 2*b + 2*b = -168. Let y be (b/(-36) - 2)*3/(-5). Determine t so that 1/2*t**2 + y*t + 0 = 0.
-1, 0
Factor -44*h - 3*h**2 + 3*h**2 - 2*h**2 - 4*h**2 - 12 - h**2.
-(h + 6)*(7*h + 2)
Let q = 41 - 8. Let f be 6/(-33) - (-138)/q. Let 4*v**f - 4 + 5*v**3 - 8*v + 3*v**3 + 0*v = 0. What is v?
-1, 1
Let n(v) be the third derivative of v**8/1512 + 46*v**7/945 + 673*v**6/540 + 1304*v**5/135 - 1856*v**4/27 + 4096*v**3/27 - v**2 + 44*v. Factor n(p).
2*(p - 1)**2*(p + 16)**3/9
Let i = -34 + 71. Solve 15*j**3 - i*j**3 + 5*j**5 + 17*j**3 = 0.
-1, 0, 1
Let c(a) be the first derivative of 2*a**6/21 - 36*a**5/35 + 24*a**4/7 - 80*a**3/21 + 114. Factor c(g).
4*g**2*(g - 5)*(g - 2)**2/7
Let y(d) be the first derivative of -9 + 59/9*d**3 + 23/12*d**4 + 19/2*d**2 + 6*d + 1/5*d**5. Factor y(b).
(b + 1)*(b + 3)**2*(3*b + 2)/3
Suppose 20*a = -44*a. Factor a*h**3 + 2/5*h**4 + 2/5 + 0*h - 4/5*h**2.
2*(h - 1)**2*(h + 1)**2/5
Suppose -2 = -3*m + 2*m. Let c be ((-112)/(-40))/((-4)/(-10)). Factor -c*k - 10*k**3 + m*k + 5*k - 5*k**4 - 5*k**2.
-5*k**2*(k + 1)**2
Let q be -13 - -4 - (12 - 19) - (-76)/14. Factor -12/7*n**2 - q*n - 2/7*n**3 - 16/7.
-2*(n + 2)**3/7
Let p**3 - 3*p + 4*p**2 - 17*p**2 + 11*p**2 = 0. What is p?
-1, 0, 3
Suppose -517 = 6*d + 473. Let c = 499/3 + d. Factor c + 1/3*n**5 - 1/3*n**4 - 5/3*n**3 + 1/3*n**2 + 8/3*n.
(n - 2)