6). Determine i, given that b + 0*i - 2/9*i**2 = 0.
0
Let t(x) be the first derivative of 2*x**3/15 - 2*x**2/5 + 2*x/5 - 324. Factor t(m).
2*(m - 1)**2/5
Suppose 5*n - 35 = -10. Let c(i) be the third derivative of -1/180*i**n - 1/360*i**6 + 0*i**4 + 0*i**3 + 0 + 11*i**2 + 0*i. Factor c(h).
-h**2*(h + 1)/3
Let k(t) be the third derivative of t**7/35 + t**6/30 - 19*t**5/30 + t**4/2 + 19*t**2 + 7*t. What is u in k(u) = 0?
-3, 0, 1/3, 2
Let a(p) be the second derivative of -p**4/4 - 11*p**3 + 72*p**2 - 490*p. Factor a(y).
-3*(y - 2)*(y + 24)
Let q(j) = -j**2 + j + 1. Let f(x) = 13*x + 9*x**2 - 13*x - 9 - 6. Let y(l) = -f(l) - 6*q(l). Find b such that y(b) = 0.
-3, 1
Let q(b) be the first derivative of b**5/5 - b**4/2 - 13*b**3/3 - 5*b**2 - 105. Determine m so that q(m) = 0.
-2, -1, 0, 5
Suppose -2*h = -3*n + 5, -2*n - 12*h = -11*h - 15. Let y(b) be the third derivative of 0*b + 0*b**4 - 1/60*b**6 - 4*b**2 + 0*b**3 + 1/30*b**n + 0. Factor y(x).
-2*x**2*(x - 1)
Let b be 73/(85410/25812) - (-12)/(-26). Suppose b*h + 2/5*h**4 + 4*h**3 + 72/5*h**2 + 54/5 = 0. Calculate h.
-3, -1
Let q(m) be the second derivative of -m**5/20 + m**4/2 + 7*m**3/6 - 606*m. Let q(b) = 0. Calculate b.
-1, 0, 7
Let d(n) = 19*n + 250. Let o be d(-13). Factor 6/5*i**2 + 8/5*i**o - 2/5*i + 0.
2*i*(i + 1)*(4*i - 1)/5
Solve -1458 + 2*u**3 + 0*u**3 - 67*u**2 - 750*u + 659*u + 577*u + 13*u**2 = 0 for u.
9
Let v(x) be the first derivative of -3 + 1/3*x**3 + 1/60*x**5 + 1/8*x**4 + 0*x + 7/2*x**2. Let w(m) be the second derivative of v(m). Factor w(s).
(s + 1)*(s + 2)
Let f(r) be the third derivative of r**5/60 + 6*r**4 + 143*r**3/6 - 477*r**2. Solve f(o) = 0 for o.
-143, -1
Let y(m) = 4*m + 22. Let u be y(-5). Let 14*x**u + 5*x**3 + 22*x - 17*x - 4*x**2 = 0. Calculate x.
-1, 0
Let p = 471/4 + -1409/12. Let k(w) be the first derivative of -2/3*w + 10/9*w**3 - p*w**2 - 1/2*w**4 - 5. Find l, given that k(l) = 0.
-1/3, 1
Let n(g) be the third derivative of -g**10/30240 - g**9/30240 + g**8/4032 + g**7/2520 + g**5/6 + 7*g**2. Let i(r) be the third derivative of n(r). Factor i(k).
-k*(k - 1)*(k + 1)*(5*k + 2)
Let s = -12 + 24. Let 20*y + s*y**2 + 3*y**5 - 7*y**5 - 135*y**3 + 6 + 119*y**3 - 18*y**4 = 0. Calculate y.
-3, -1, -1/2, 1
Factor 196/5*x**3 + 1332/5*x + 648/5 + 896/5*x**2.
4*(x + 2)*(7*x + 9)**2/5
Let x be 3/18*1/3. Let j(c) be the second derivative of 1/2*c**3 - 3/20*c**5 - 1/3*c**2 - 5*c + x*c**4 + 0. Factor j(s).
-(s - 1)*(s + 1)*(9*s - 2)/3
Let q = 102 - 99. Suppose 4*o - 6 - 2 = 0. Factor 1/2*y**o + 1/2*y**q - 1/2 - 1/2*y.
(y - 1)*(y + 1)**2/2
Let a = -47 - -52. Factor -5*c**2 + a*c**3 + 6*c - 11*c + 9*c**4 - 4*c**4.
5*c*(c - 1)*(c + 1)**2
Let i be (-12)/7*42/(-4). Suppose -6 + i = 6*c. Solve 12/7*h + 0 + 16/7*h**c + 4/7*h**3 = 0.
-3, -1, 0
Let h(k) be the second derivative of 1/12*k**3 + 1/12*k**4 + 0 + 13*k + 0*k**2 + 1/40*k**5. What is u in h(u) = 0?
-1, 0
Let k = 39040 - 39038. Factor 7/2*y**4 + 0*y + 0*y**k + 5/6*y**3 + 0 + 2/3*y**5.
y**3*(y + 5)*(4*y + 1)/6
Determine z, given that -33/2*z - 39/2*z**2 + 3/2*z**4 + 33/2*z**3 + 18 = 0.
-12, -1, 1
Let t be (847/(-55) - -16) + (1 - 186/135). Find y, given that t*y**2 + 20/9*y + 50/9 = 0.
-5
Let m be 0/2 + 10 + 5. Let t(r) = -21*r**2 - 147*r + 15. Let j(k) = 3*k**2 + 21*k - 2. Let z(n) = m*j(n) + 2*t(n). Find v such that z(v) = 0.
-7, 0
Let a(n) = -45*n**3 - 560*n**2 + 590*n - 145. Let w(k) = 68*k**3 + 840*k**2 - 885*k + 217. Let r(y) = 8*a(y) + 5*w(y). Let r(d) = 0. Calculate d.
-15, 1/2
Let m(k) be the third derivative of -k**7/1960 - k**6/120 - 3*k**5/56 - 9*k**4/56 - 8*k**3/3 + 17*k**2. Let j(y) be the first derivative of m(y). Factor j(c).
-3*(c + 1)*(c + 3)**2/7
Let q(c) be the second derivative of c**5/140 + c**4/28 - 2*c**2/7 + 112*c. Determine l so that q(l) = 0.
-2, 1
Factor 0 - 14/3*k**3 + 200/3*k**2 - 56/3*k.
-2*k*(k - 14)*(7*k - 2)/3
Let u(x) be the second derivative of 0 + 1/30*x**3 + 1/20*x**4 - 1/100*x**5 - 8*x - 3/10*x**2. Suppose u(l) = 0. Calculate l.
-1, 1, 3
Let -68/7*u**2 + 10/7*u**5 + 106/7*u**3 - 8/7*u - 8*u**4 + 16/7 = 0. Calculate u.
-2/5, 1, 2
Let o(b) = 17*b**3 + b**2 - 4*b + 2. Let v be o(1). Let a be (-3)/((-576)/40) - (-2)/v. Determine f so that a + 1/3*f**2 - 2/3*f = 0.
1
Let q(j) be the first derivative of j**5/48 - 53*j**4/96 - 11*j**3/12 + 26*j**2 + 56. Let x(i) be the second derivative of q(i). Factor x(u).
(u - 11)*(5*u + 2)/4
Let q(g) = -g**2 - 4*g - 33. Let o be q(-8). Let a be ((-26)/o)/((-16)/(-50)). Factor -a*x**2 + 5/2*x + 15/4.
-5*(x - 3)*(x + 1)/4
Let w(c) be the first derivative of -c**5/210 + 4*c**3/21 - 7*c**2/2 - 15. Let i(d) be the second derivative of w(d). Factor i(v).
-2*(v - 2)*(v + 2)/7
Let z(j) = -j**3 - 12*j**2 - 2*j - 12. Let c be z(-12). Let k be ((-14)/(-88) - 3/c)*-14. Factor -4/11 + k*v - 10/11*v**2.
-2*(v - 1)*(5*v - 2)/11
Let r(d) = d**3. Let v(c) = -5*c**3 + 4*c**2 + 4*c + 5. Let o(w) = -4*r(w) - v(w). Let b be o(5). Factor -2/5*g**2 + 2/5*g**3 + 2/5*g**4 + b - 2/5*g.
2*g*(g - 1)*(g + 1)**2/5
Suppose -34 = -36*v + 38. Let g(r) be the second derivative of v*r + 1/36*r**4 + 1/18*r**3 - 1/90*r**6 + 0 + 0*r**2 - 1/60*r**5. Suppose g(f) = 0. What is f?
-1, 0, 1
Factor -s**5 - 10*s**4 + 7*s**4 - 13*s**4 - 5*s**4 - 2*s**5.
-3*s**4*(s + 7)
Let q = 1692 + -1686. Let k(a) be the third derivative of 1/8*a**4 - 1/4*a**5 + 0 + 0*a + 3*a**2 + 1/2*a**3 + 3/40*a**q. Suppose k(m) = 0. What is m?
-1/3, 1
Let g(m) be the second derivative of 19*m**4/22 + 59*m**3/33 + 2*m**2/11 - 37*m. Suppose g(y) = 0. What is y?
-1, -2/57
Let m(v) be the third derivative of -1/6*v**4 + 0*v + 2/3*v**3 - 1/20*v**5 - 1/210*v**7 - 40*v**2 + 1/30*v**6 + 0. Factor m(u).
-(u - 2)**2*(u - 1)*(u + 1)
Suppose 57*j = -12*j - 119*j + 2820. What is g in 0 - 10*g - j*g**3 - 45/2*g**2 - 5/2*g**4 = 0?
-4, -1, 0
Let h(y) be the first derivative of y**5/5 + 5*y**4/2 + 32*y**3/3 + 16*y**2 - 60. Factor h(x).
x*(x + 2)*(x + 4)**2
Let o(s) be the third derivative of s**6/420 + s**5/7 + 51*s**4/28 - 1156*s**3/21 - 22*s**2 - 6*s. Factor o(x).
2*(x - 4)*(x + 17)**2/7
Suppose 102*i + 18 = 18. What is v in i - 21/2*v**5 + 24*v**4 + 6*v - 24*v**2 + 9/2*v**3 = 0?
-1, 0, 2/7, 1, 2
Let i be -3 + (3 - 0) - -3. Suppose -d + i*d = 40. Factor -3*s**4 - 45*s + 17*s + 0*s**4 - d*s**3 - 8 - 36*s**2 - s**4.
-4*(s + 1)**3*(s + 2)
Let o(m) be the third derivative of m**8/2800 + m**7/700 - m**6/600 - m**5/100 + 7*m**3/6 + 7*m**2. Let p(y) be the first derivative of o(y). Factor p(q).
3*q*(q - 1)*(q + 1)*(q + 2)/5
Let c(u) = -12*u**3 + 12*u**2 + 7*u - 34. Let y(f) = 2*f**3 - 2*f**2 - f + 6. Let g(m) = 6*c(m) + 34*y(m). Factor g(k).
-4*k*(k - 2)*(k + 1)
Factor 3/5*s**2 - 24/5 - 6/5*s.
3*(s - 4)*(s + 2)/5
Let t be (-3)/(-45)*342/(-24). Let p = t + 11/5. Factor 1/2*n**2 + p*n**3 + 0*n + 0 + 1/4*n**5 + n**4.
n**2*(n + 1)**2*(n + 2)/4
Let x(o) be the second derivative of -o**8/6720 + o**7/840 - o**6/360 + 3*o**4/2 - 32*o. Let y(a) be the third derivative of x(a). Factor y(u).
-u*(u - 2)*(u - 1)
Suppose g + 2*v - 7 - 62 = 0, -2*g + 138 = 3*v. Solve -g*h**2 + h**3 - h**5 + 69*h**2 + 0*h**5 = 0.
-1, 0, 1
Suppose 3*v + 2*b = -b + 264, -3*v + 260 = 2*b. Let t be 8/7*(-49)/v*-2. Factor -2*y + 2/3*y**5 + t*y**2 - 2*y**4 + 2/3 + 4/3*y**3.
2*(y - 1)**4*(y + 1)/3
Determine v, given that v - 12*v**2 - 40 - 13*v + 13*v**3 + v**4 + 3*v**4 - 56*v + 7*v**3 = 0.
-5, -1, 2
Suppose j - 16 = -3*j. Factor -j*q - 177*q**3 - 5*q**4 - 40*q**2 + 147*q**3 + 15*q + 45 + 19*q.
-5*(q - 1)*(q + 1)*(q + 3)**2
Suppose 5*h + 9 = 8*h. Suppose 0 = h*o - 0 - 6. Factor -12/7*z - 2/7*z**o - 18/7.
-2*(z + 3)**2/7
Let d(l) be the first derivative of -l**5/15 + 5*l**4/12 - l**3 + 7*l**2/6 - 2*l/3 + 22. Let d(c) = 0. Calculate c.
1, 2
Factor -3*t**2 + 10/3*t - 1/3*t**3 + 0.
-t*(t - 1)*(t + 10)/3
Let i(m) be the second derivative of -4/21*m**4 + 4/21*m**3 + 0 + 6/7*m**2 + 28*m + 2/105*m**6 - 2/35*m**5. Determine h, given that i(h) = 0.
-1, 1, 3
Let p(n) = -2*n - 2. Let o be p(-4). Suppose 0 = -3*i - 0*i + o, 22 = 4*b + 3*i. Factor 0*g + 0*g**3 - 3/2*g**2 + 3/2*g**b + 0.
3*g**2*(g - 1)*(g + 1)/2
Factor 4*c - 1/3*c**2 - 12.
-(c - 6)**2/3
Suppose 0 = -63*x + 65*x - 70. Determine u, given that -28*u - 26*u + 19*u - 245 - 5*u**2 - x*u = 0.
-7
Suppose 3 + 5 = 3*z - 2*o, 3*z - 4 = -2*o. Le