4. Let o(g) = 0. What is g?
1, 2
Let q be 3/(-30) + (-963)/(-630). Factor 4/7 + 8/7*i**3 + q*i - 22/7*i**2.
2*(i - 2)*(i - 1)*(4*i + 1)/7
Let 5*f - 2*f**2 - 125 + 45*f - 3*f**2 = 0. Calculate f.
5
Let t(k) be the first derivative of -1/140*k**6 - 1/2*k**2 + 0*k**3 + 0*k - 1/210*k**5 + 3 + 0*k**4. Let v(c) be the second derivative of t(c). Factor v(n).
-2*n**2*(3*n + 1)/7
Let p(l) be the second derivative of -l**7/21 + 2*l**6/15 + l**5/10 - l**4/3 - 32*l. Suppose p(q) = 0. Calculate q.
-1, 0, 1, 2
Let p(s) be the third derivative of s**6/150 + 2*s**5/25 + 4*s**4/15 - 7*s**2. Factor p(i).
4*i*(i + 2)*(i + 4)/5
Suppose -2*t + z + 6 = 3, z = 3. Find w such that -4/5*w**2 + 2/5*w + 2/5*w**t + 0 = 0.
0, 1
Suppose -2*y = -9 + 1. Let m(s) be the second derivative of 0*s**2 + 0 + 2*s + 1/40*s**5 + 0*s**3 - 1/24*s**y. Factor m(j).
j**2*(j - 1)/2
Let y(q) = 6*q + 2 + q - 8*q. Let d be y(0). Factor 2/5*n**d + 8/5 - 8/5*n.
2*(n - 2)**2/5
What is j in 4/5 - 8/5*j**3 + j**4 + 8/5*j - 9/5*j**2 = 0?
-1, -2/5, 1, 2
Determine x so that x + 2*x - 9*x - 31*x**2 + 34*x**2 = 0.
0, 2
Let w(k) be the third derivative of k**6/120 - k**5/60 - k**4/24 + k**3/6 + k**2. Determine l, given that w(l) = 0.
-1, 1
Let q(l) be the third derivative of l**8/336 - 2*l**7/315 - l**6/90 + l**5/30 + l**4/72 - l**3/9 + 6*l**2. Solve q(c) = 0 for c.
-1, -2/3, 1
Determine w, given that 6/5*w**4 + 4/5*w**2 - 9/5*w**3 + 0*w - 1/5*w**5 + 0 = 0.
0, 1, 4
Let g(o) be the third derivative of 0*o + 1/15*o**5 + 0 + 1/3*o**3 - 3*o**2 + 1/4*o**4. Factor g(l).
2*(l + 1)*(2*l + 1)
Let z = 0 + 3. Factor -2*m**2 + 3*m**z + 3*m**2 - 2*m**2 + 3*m + 7*m**2.
3*m*(m + 1)**2
Factor 0*w + 7/4*w**4 - 4*w**3 + w**2 + 0.
w**2*(w - 2)*(7*w - 2)/4
Let d(n) be the second derivative of n**5/20 - n**3/6 + 3*n. Factor d(t).
t*(t - 1)*(t + 1)
Let g(b) be the third derivative of -b**7/1260 - b**3/6 - 3*b**2. Let u(k) be the first derivative of g(k). Let u(c) = 0. What is c?
0
Let n(i) be the first derivative of 0*i**3 + 0*i + 1/195*i**5 + 1/780*i**6 + 1/156*i**4 - 1 - 1/2*i**2. Let k(u) be the second derivative of n(u). Factor k(v).
2*v*(v + 1)**2/13
Let h(s) be the second derivative of 0*s**3 + 0 - 1/12*s**4 - 3*s + 0*s**2. Factor h(u).
-u**2
Let b(i) be the second derivative of -i**7/14 + i**6/5 - i**4/2 + i**3/2 - 2*i. Factor b(t).
-3*t*(t - 1)**3*(t + 1)
Let q(g) be the second derivative of 1/48*g**4 + 1/4*g**3 + 9/8*g**2 - 2*g + 0. Factor q(f).
(f + 3)**2/4
Let v(t) = -2*t**4 - 9*t**3 - 27*t**2 - 5*t + 5. Let c(g) = -6*g**4 - 28*g**3 - 80*g**2 - 16*g + 14. Let p(b) = -5*c(b) + 14*v(b). Factor p(j).
2*j*(j + 1)**2*(j + 5)
Determine p, given that 24 + 21*p - 2*p**2 + 7 - p - 9 = 0.
-1, 11
Let n be 9/20 - (-5 - (-63)/12). Let v(f) be the third derivative of -4/25*f**5 + 7/200*f**6 + 0*f + 11/40*f**4 + f**2 - n*f**3 + 0. Factor v(z).
3*(z - 1)**2*(7*z - 2)/5
Let u(g) be the second derivative of 0 - 1/30*g**4 - 9/5*g**2 + 2/5*g**3 + 2*g. Let u(r) = 0. Calculate r.
3
Let j(p) be the second derivative of -p**7/70 - p**6/50 + 3*p**5/20 + p**4/4 - 2*p**3/5 - 6*p**2/5 + p. Suppose j(c) = 0. What is c?
-2, -1, 1, 2
Let j(c) = c**2 - 9*c - 4. Let p be j(10). Let y = p - 4. Factor -y*w - w**3 + 2*w**2 + 3*w**3 - 4*w**4 + 2*w**4.
-2*w*(w - 1)**2*(w + 1)
Let n(c) be the third derivative of c**7/1050 + c**6/300 + c**5/200 + 5*c**4/24 + 5*c**2. Let p(t) be the second derivative of n(t). Factor p(z).
3*(2*z + 1)**2/5
Let j(f) be the second derivative of -1/30*f**5 - 2*f - f**2 + 0*f**3 + 0 + 1/12*f**4. Let l(v) be the first derivative of j(v). Factor l(y).
-2*y*(y - 1)
Let r(w) be the first derivative of 12/5*w**5 - 1/2*w**6 - 5 + 0*w - 3/2*w**2 + 4*w**3 - 9/2*w**4. Factor r(f).
-3*f*(f - 1)**4
Factor -y + 12*y - 1 - 4*y - 11*y - 6*y**2 - y**4 - 4*y**3.
-(y + 1)**4
Let d = 5 - 3. Factor 5*k**3 - 2*k**3 + 9*k**2 - d*k + 8*k.
3*k*(k + 1)*(k + 2)
Let k be (-1)/((-1 - 3)/16). Factor 3 + 4*u**3 + 2*u**2 - 2*u**4 - 2*u**2 - k*u - 1.
-2*(u - 1)**3*(u + 1)
Factor 7*m**2 + 11*m**3 - 4*m**3 - 5*m**2.
m**2*(7*m + 2)
Factor 3*z**2 + 46 + 22 - 104 - 8*z - 4*z.
3*(z - 6)*(z + 2)
Let v(t) = t**3 - 2*t**2 + 2. Let l be v(2). Let q be 656/36 + (-4)/18. Factor q*f - 28*f**l - 2*f**2 + 18*f - 8 - 25*f**3.
-(f + 2)*(5*f - 2)**2
Find r such that -8/5 + 8/5*r**2 + 4/5*r - 4/5*r**3 = 0.
-1, 1, 2
Let z be ((-36)/15)/(39/(-20)). Let q = 196/117 - z. What is j in q*j + 2/9 + 2/9*j**2 = 0?
-1
Let d be (10 + -2)*5/10. Factor d*v - 1 + 4 + 2*v**2 - v**2 + 0*v**2.
(v + 1)*(v + 3)
Factor 4/5*p + 0 + 2/5*p**2.
2*p*(p + 2)/5
Let h(z) = z**4 + 34*z**3 + 13*z**2 - 41*z + 7. Let p(n) = -n**4 - 16*n**3 - 7*n**2 + 20*n - 4. Let o(q) = -4*h(q) - 7*p(q). Let o(y) = 0. Calculate y.
-1, 0, 1, 8
Let t(c) be the second derivative of c**8/1680 + c**7/630 - c**4/12 + 6*c. Let g(l) be the third derivative of t(l). Determine m so that g(m) = 0.
-1, 0
Suppose -4*p = 2*z - z - 28, p = 4. Factor 6*n**2 - 2*n**4 + 4*n**4 - z*n**2 + 4*n.
2*n*(n - 1)**2*(n + 2)
Suppose -5*r + 32 = -8. Let n = 8 - r. Let -2/5*s**3 + n + 0*s**2 + 2/5*s = 0. What is s?
-1, 0, 1
Let b(m) = -12*m**2 - 36*m - 16. Let r(v) = -4*v**2 - 12*v - 5. Let t(i) = 3*b(i) - 8*r(i). Determine s so that t(s) = 0.
-2, -1
Let r = -3 + -4. Let o(s) = 7*s**2 - 3*s. Let p(b) = -10*b**2 + 4*b. Let i(x) = r*o(x) - 5*p(x). Find f such that i(f) = 0.
-1, 0
Let q(a) = 2*a**5 - 3*a**3 - a**2 + a + 1. Let s(r) = -3*r**5 + 4*r**3 + 2*r**2 - r - 2. Let t(i) = -8*q(i) - 5*s(i). Solve t(b) = 0 for b.
-2, -1, 1
Let x(p) be the third derivative of -p**8/784 + 3*p**7/490 + 9*p**6/280 + p**5/28 + 17*p**2 + 2. Find o such that x(o) = 0.
-1, 0, 5
Suppose -3*c - 2*b = 0, -4*c = -3*b + 2 + 15. Let t be (15/(-12))/(c/8). Factor -t*s**4 + 3*s**3 - 3*s + s**2 + 0*s**4 + 1 + 3*s**4.
-(s - 1)**2*(s + 1)*(2*s - 1)
Determine g so that -2/3*g**2 - 6/5*g - 8/15 = 0.
-1, -4/5
Let m be 1/(-2)*(1 + -1). Suppose m*v - v = -3. Let -v*x + 4*x**2 + 7*x - 3*x - 3*x**2 = 0. What is x?
-1, 0
Let a be 5/((-220)/8) + 82/88. Factor -1/4*v**4 + 0 + 5/4*v**2 + a*v**3 + 1/2*v - 1/4*v**5.
-v*(v - 2)*(v + 1)**3/4
Let r(p) = -2*p**3 - 22*p**2 - 146*p - 344. Let d(l) = -l**3 - l**2 + l - 1. Let m(y) = d(y) - r(y). Factor m(j).
(j + 7)**3
Let s(a) = -15*a**2 + 27*a - 6. Let i(r) = r**2. Let x(k) = 3*i(k) + s(k). Factor x(z).
-3*(z - 2)*(4*z - 1)
Let k be (-2)/(-21)*(4 + 15/(-9)). Factor k*a - 4/9 + 2/9*a**2.
2*(a - 1)*(a + 2)/9
Suppose 0*h - 6 = -2*h. Suppose -5*k = 2*p - 6*p + 18, h*k + 16 = 5*p. Factor -p*g + 0*g**2 - 2*g**2 + 0*g**2.
-2*g*(g + 1)
Let f(w) be the third derivative of -w**6/360 + w**5/45 - 5*w**4/72 + w**3/9 - w**2. Find u, given that f(u) = 0.
1, 2
Let t(q) be the first derivative of q**5/50 + q**4/15 + q**3/15 + 3*q - 1. Let p(g) be the first derivative of t(g). Solve p(b) = 0 for b.
-1, 0
Let s(h) be the second derivative of 1/6*h**2 - 1/18*h**3 - 11/60*h**5 - 1/4*h**4 - 9*h - 2/45*h**6 + 0. Factor s(i).
-(i + 1)**3*(4*i - 1)/3
Let -2/11*w**4 + 2/11*w**2 + 0*w + 2/11*w**3 - 2/11*w**5 + 0 = 0. Calculate w.
-1, 0, 1
Factor 8/5*k + 2/5*k**2 - 2/5*k**3 - 8/5.
-2*(k - 2)*(k - 1)*(k + 2)/5
Suppose -1 = g - 3. Let 4*c**g + 6*c - 3*c + 3*c + 12 + 10*c = 0. Calculate c.
-3, -1
Let c be 77/(-3) + 2/(-6). Let s = 53/2 + c. Factor -s*t**4 + 0*t**2 - t + t**3 + 1/2.
-(t - 1)**3*(t + 1)/2
Let x(z) = 14*z - 70. Let i be x(5). Solve -6/5*d**4 - 6/5*d**3 - 2/5*d**2 + 0 - 2/5*d**5 + i*d = 0.
-1, 0
Let u(w) be the third derivative of w**8/112 - 3*w**6/40 + w**5/10 + 10*w**2. Solve u(p) = 0 for p.
-2, 0, 1
Let l = -5279/24 + 220. Let b(p) be the third derivative of 0 + 1/120*p**6 + 0*p**3 + 1/210*p**7 - l*p**4 - 1/60*p**5 + 0*p - p**2. Find a such that b(a) = 0.
-1, 0, 1
Let c be 1/4 - 4/16. Let i(h) = -h**3 - h + 3. Let w be i(c). Factor 4 - b - 4 + w*b**2.
b*(3*b - 1)
Solve -3*k + 2*k**3 - 7 + 82*k**3 + 80*k**2 - 1 - 9*k = 0 for k.
-1, -2/7, 1/3
Let -37/8*z**2 - 21/8*z**3 - 1/2*z**4 - 3*z - 1/2 = 0. What is z?
-2, -1, -1/4
Suppose -3*f + 2*f - l + 8 = 0, f - 13 = -2*l. Solve -1/2*p**4 - 1/2*p**2 + 0 - p**f + 0*p = 0 for p.
-1, 0
Let a(x) be the second derivative of -x**5/30 - x**4/6 - x**3/3 - x**2/2 - 3*x. Let r(c) be the first derivative of a(c). What is n in r(n) = 0?
-1
Suppose 0 = 4*c + 6*d - 5*d + 3, d + 3 = 0. Let k(x) be the second derivative of 0*x**2 + 1/9*