 12. Determine i so that a(i) = 0.
-4, 1
Let s be 5*18/15*2. Let f be 1/((s/(-4))/(-21)). Factor -m - 2*m - 2 + m**3 + 2*m**2 + f*m - 5*m.
(m - 1)*(m + 1)*(m + 2)
Factor -80 + a**2 + 40*a + a**2 - 16*a**2 + 9*a**2.
-5*(a - 4)**2
Let n(r) be the second derivative of 5*r**4/12 + 80*r**3/3 + 150*r**2 - 376*r. Factor n(g).
5*(g + 2)*(g + 30)
Let f be 2/(51/45 - 1). What is k in -21*k**3 + 16 + f*k - 16*k**4 + 23*k**2 - 14 - 3*k**3 = 0?
-2, -1/4, 1
Factor 1948*z**4 + 2*z**3 - 1 + 12*z**2 + 1 - 1950*z**4.
-2*z**2*(z - 3)*(z + 2)
Let j(q) be the second derivative of -q**4/42 - 2*q**3/21 - 16*q + 11. Let j(a) = 0. Calculate a.
-2, 0
Suppose 3*w - 12 + 3 = 0. Suppose 2*i + x = 7*i - 13, -3*i - 3*x = w. Find d such that -14/5*d**i - 6/5*d**5 - 8/5 - 18/5*d**3 + 24/5*d + 22/5*d**4 = 0.
-1, 2/3, 1, 2
Let i(b) be the first derivative of 2*b**7/147 + 2*b**6/105 - 4*b - 11. Let w(k) be the first derivative of i(k). Factor w(d).
4*d**4*(d + 1)/7
Suppose 12*p - 13*p + 2 = 0. Let n be ((-36)/(p - 0))/(-5). Find z, given that 10*z**2 + n - 12*z = 0.
3/5
Let m(y) = 96*y + 1637. Let x be m(-17). Factor -1/2*r + 0 + x*r**2.
r*(10*r - 1)/2
Let o(z) = 11*z**4 + 7*z**3 - 37*z**2 + 19*z. Let h(i) = 6*i**4 + 3*i**3 - 18*i**2 + 9*i. Let v(x) = -5*h(x) + 3*o(x). Solve v(r) = 0 for r.
-4, 0, 1
Let q(b) be the third derivative of -7*b**2 + 0*b - 10/3*b**4 + 0*b**3 - 2/3*b**5 - 1/24*b**6 + 0. Factor q(i).
-5*i*(i + 4)**2
Let b be ((0*(-8)/48)/1)/3. Let q(l) be the third derivative of 1/2*l**6 - 5/42*l**7 + 5/12*l**4 + 0*l**3 - 3/4*l**5 + 0 + b*l - 4*l**2. Factor q(k).
-5*k*(k - 1)**2*(5*k - 2)
Let h(u) be the second derivative of u**7/70 - u**6/50 - 3*u**5/20 + u**4/20 + 4*u**3/5 + 6*u**2/5 - 62*u. Factor h(t).
3*(t - 2)**2*(t + 1)**3/5
Let y(h) = 6*h**3 + 6*h**2 + h + 1. Suppose -2*j - 8 = -4. Let d(f) = f**3 + f**2. Let b(o) = j*y(o) + 14*d(o). Solve b(n) = 0 for n.
-1, 1
Let p(g) be the second derivative of g**5/20 - g**4/2 + 2*g**3 - g**2/2 - 7*g. Let d(t) be the first derivative of p(t). Find o such that d(o) = 0.
2
Let u(m) be the second derivative of -m**5/60 + m**4/36 - 52*m. Find k, given that u(k) = 0.
0, 1
Let c be 7*(920/5152 + (-2)/(-8)). Solve 12/5 + 6/5*v**2 + 21/5*v - 3/5*v**c = 0 for v.
-1, 4
Let b be (3 - 36/20)*210/63. Let f(a) be the third derivative of 8*a**2 + a**b + 0*a + 6*a**3 + 0 + 1/15*a**5. Suppose f(l) = 0. What is l?
-3
Let x = -18 - -21. Let b = -14/5 - -33/10. Factor -13/2*i**2 - b*i**4 + x*i**3 - 2 + 6*i.
-(i - 2)**2*(i - 1)**2/2
Let v be (-18)/27 - -4 - 5 - 71/(-21). Solve -v*c + 9/7*c**5 + 3*c**3 - 30/7*c**4 + 0 + 12/7*c**2 = 0 for c.
-2/3, 0, 1, 2
Let r(d) = 31*d + 4. Let s be r(0). Let b(i) = -i**2 + 3*i - 2. Let v be b(2). Let -2*n**3 + n**4 - 3*n**4 + v*n**s = 0. Calculate n.
-1, 0
Factor 32/7 - 2/7*x**2 - 12/7*x.
-2*(x - 2)*(x + 8)/7
Let g(b) = -3*b - 9. Let j be g(-11). Factor 32*k**2 - 14*k**2 - 16 + 12 + 3*k**4 - 17 + 24*k**3 - j*k.
3*(k - 1)*(k + 1)**2*(k + 7)
Let i be ((-7)/5)/((-238)/(-35) - 7). Let d(l) be the first derivative of -2/15*l**3 - i + 4/5*l**2 - 8/5*l. Factor d(h).
-2*(h - 2)**2/5
Suppose -2*t = 3*y + 3, -4*t - 2 = -0*y + 2*y. Let z(j) be the third derivative of 1/30*j**5 + 0*j**4 + t - 1/3*j**3 + 4*j**2 + 0*j. Factor z(o).
2*(o - 1)*(o + 1)
Let j(g) be the first derivative of -3*g**5/5 + 27*g**4/4 - 24*g**3 + 30*g**2 - 460. Let j(f) = 0. What is f?
0, 2, 5
Suppose 2*g - 18 = 6. What is k in -15*k**2 - 24*k**3 - g + 50*k + 33*k**4 - 14*k + 6*k**5 - 24*k**4 = 0?
-2, 1/2, 1
Let b(y) be the third derivative of 0*y + 1/15*y**5 + 0 + 5/6*y**4 + 6*y**2 + 8/3*y**3. Factor b(o).
4*(o + 1)*(o + 4)
Let m(v) be the third derivative of v**5/90 - 14*v**4/9 + 784*v**3/9 + 6*v**2 - 3*v. Find a, given that m(a) = 0.
28
Let m be 36/30*(100/(-6))/(-5). Solve 3/2*a - 5*a**2 + 7/3*a**m + 2/3*a**3 + 0 + 1/2*a**5 = 0 for a.
-3, 0, 1/3, 1
Let m(r) be the second derivative of -r**4/2 - 4*r**3/3 - 4*r**2/3 - 5*r. Find y such that m(y) = 0.
-2/3
Let m(k) = 2*k**3 - 13*k**2 + 14*k - 6. Let o(f) = f**2. Let i(g) = g**2. Let q(x) = -7*i(x) + 6*o(x). Let y(r) = m(r) - 3*q(r). Find t such that y(t) = 0.
1, 3
Let b(j) be the third derivative of -j**5/60 - 33*j**4/4 - 3267*j**3/2 - 38*j**2. Let b(i) = 0. What is i?
-99
Let l(y) be the second derivative of -y**6/20 + 207*y**5/20 - 4621*y**4/8 - 2415*y**3 - 3675*y**2 + 850*y. Determine s so that l(s) = 0.
-1, 70
Let u be 3/(-20) + (-78)/(-120). Suppose 11/4*w + 3/4*w**2 - u*w**3 - 3/2 = 0. What is w?
-2, 1/2, 3
Determine m, given that 0*m**2 + 10*m**2 - 19*m**2 + 10*m**2 - 13 + 12*m = 0.
-13, 1
Let p(j) be the first derivative of -27 + 0*j + 0*j**2 - 4/3*j**3. Solve p(d) = 0 for d.
0
Find n, given that -60835/3 + 5/3*n**3 + 2645*n - 115*n**2 = 0.
23
Suppose -1988*m + 64*m + 499*m**3 + 4*m - 159*m**3 - 25*m**5 + 680*m**2 + 640 - 90*m**4 = 0. Calculate m.
-4, 2/5, 2
Let u(q) = -3*q + 19. Let o be u(5). Let f be ((-14)/(-20) - 0) + 2/o. Solve 2/5*g**5 - 4/5*g**2 + 4/5*g**3 - f*g + 6/5*g**4 - 2/5 = 0.
-1, 1
Let q be 2/(-8) - (-182)/56. Factor 16*t**2 - 28*t**4 - 35*t**5 - 64*t + 1 - 1 + 48*t**q + 39*t**5.
4*t*(t - 4)*(t - 2)**2*(t + 1)
Let y(p) = -17*p**4 - 5*p**3 + 41*p**2 - 19*p - 61. Let x(f) = 4*f**4 + f**3 - 10*f**2 + 5*f + 15. Let v(k) = -26*x(k) - 6*y(k). Solve v(i) = 0 for i.
-2, -1, 2, 3
Let h(y) be the first derivative of -7/2*y**2 - 1/720*y**6 + 1/180*y**5 + 0*y**3 - 1/144*y**4 + 0*y - 6. Let s(z) be the second derivative of h(z). Factor s(c).
-c*(c - 1)**2/6
Suppose -5*t + 6*t = 4. Suppose -8 = -3*b + 2*c, -t*c = 4*b - 3*b + 2. Find w such that -w - 2*w**b - 1/5*w**5 - 1/5 - 2*w**3 - w**4 = 0.
-1
Let k(v) = 73*v**2 + 10*v - 6. Let b(p) = 144*p**2 + 18*p - 11. Let a(q) = 6*b(q) - 11*k(q). Factor a(x).
x*(61*x - 2)
Solve 93/8*o**2 + 29791/8 + 1/8*o**3 + 2883/8*o = 0 for o.
-31
Let q(a) be the third derivative of a**10/14400 - 23*a**9/40320 + a**8/2240 - a**5/20 - 8*a**2. Let i(s) be the third derivative of q(s). Factor i(x).
3*x**2*(x - 3)*(7*x - 2)/2
Let o be (0 - 0)/((-104)/(-52)). Let n(h) be the third derivative of -1/180*h**5 + 0*h**3 + o*h - h**2 + 0 + 1/72*h**4. Factor n(q).
-q*(q - 1)/3
Let t be (16/14)/((-238)/(-357)). Determine f, given that -16/7*f**3 + 4/7*f**2 + 8/7*f + 0 - t*f**4 = 0.
-1, 0, 2/3
Factor 25/4*m + 40*m**2 + 0 + 64*m**3.
m*(16*m + 5)**2/4
Let f(x) = x**2 + 3*x. Let h be f(-4). Factor 4*c**2 - 4*c + c + 6*c**3 + h*c + 4*c**4 + c**5.
c*(c + 1)**4
Let k(j) be the first derivative of j**7/1960 + j**6/210 + j**5/56 + j**4/28 + 10*j**3/3 - 31. Let u(b) be the third derivative of k(b). Factor u(d).
3*(d + 1)**2*(d + 2)/7
Let s(t) = -t**3 + 36*t**2 - 39*t + 140. Let x be s(35). Factor -1/2*i**2 + x - 1/2*i.
-i*(i + 1)/2
Let x be (-28)/(-20) + -1 - 18/45. Let q(s) be the second derivative of -1/9*s**3 - 7*s + x*s**2 + 0*s**6 + 0 + 1/15*s**5 - 1/63*s**7 + 0*s**4. Factor q(i).
-2*i*(i - 1)**2*(i + 1)**2/3
Let u(q) be the first derivative of q**3/33 + q**2 - 23*q/11 + 129. Determine z so that u(z) = 0.
-23, 1
Suppose -1677 = 29*x - 1735. Let -12/5*k**x - 18/5 - 15*k = 0. Calculate k.
-6, -1/4
Let c be 465/868 + (-2)/(-8) + (-2)/4. Suppose -2/7*s**4 - c*s + 0 + 2/7*s**3 + 2/7*s**2 = 0. Calculate s.
-1, 0, 1
Suppose o + 5*w + 62 = 12*o, -3*o + 14 = -w. Find h, given that 1/3*h**3 + 2/3*h**o + 0*h + 0 = 0.
-2, 0
Factor -5*m**3 + 46 + 40*m - 29*m**2 - 12*m**2 + 194 + 16*m**2.
-5*(m - 3)*(m + 4)**2
Solve u**4 + 28*u**2 - 26*u**2 - 3 - 4*u**3 + u**4 - u**4 + 4*u = 0.
-1, 1, 3
Let s be 64/30 + -4 + (-208)/(-240) + 3. Factor 2/3*l**4 + 0*l + 0*l**s + 0 - 4/3*l**3.
2*l**3*(l - 2)/3
Let p(g) be the second derivative of -3*g**7/49 - 13*g**6/21 - 88*g**5/35 - 36*g**4/7 - 16*g**3/3 - 16*g**2/7 - 3*g - 9. Let p(a) = 0. Calculate a.
-2, -1, -2/9
Factor 49*b - 130*b**2 + 80 - 169*b - 5*b**3 + 175*b**2.
-5*(b - 4)**2*(b - 1)
Suppose -3*v + 12 = 60. Let q be ((-5)/(50/v))/((-9)/(-5)). Solve 8/9*r + 0 + 2/9*r**3 + q*r**2 = 0 for r.
-2, 0
Let d(c) be the first derivative of -c**3/21 + 7*c**2/2 - 48*c/7 + 104. Let d(j) = 0. What is j?
1, 48
Let y = 6 + -184. Let p = y + 178. Factor 0 + 0*m - 2/9*m**3 + 0*m**2 + p*m**4 + 2/9*m**5.
2*m**3*(m - 1)*(m + 1)/9
Let b(o) be the first derivative of -o**3/21 + 3*o**2/7 + o + 189. Solve b(u) = 0 for u.
-1, 7
Let d(l) = -l. Let t = -3 + 4. Let b(m) = 4*m**2.