 4. Let k(d) = 4*g(d) + n(d). Factor k(v).
4*v**3*(v - 1)*(4*v - 1)
Let z be (-26)/(-8) - 12/(-16). Let k(t) be the second derivative of 0*t**3 + 1/90*t**6 + 0*t**z + 0 + 0*t**2 + 2*t - 1/30*t**5. Solve k(l) = 0.
0, 2
Let z = 9 + -25/2. Let u = z - -4. Let 1/4*v**2 + u + 3/4*v = 0. Calculate v.
-2, -1
Let x(u) be the first derivative of 3*u**5/5 - 9*u**4/4 + 2*u**3 + 10. Determine b, given that x(b) = 0.
0, 1, 2
Let y(p) be the first derivative of p**8/336 + p**7/210 - p**6/120 - p**5/60 + 3*p**2/2 - 5. Let q(t) be the second derivative of y(t). What is j in q(j) = 0?
-1, 0, 1
Let u be (1 - 5)/2*(-10)/48. Let z(l) be the first derivative of 2/3*l**2 + 8/9*l**3 + 1 + 1/15*l**5 + u*l**4 + 0*l. Factor z(x).
x*(x + 1)*(x + 2)**2/3
Let q(r) be the first derivative of r**4/8 + r**3/3 + 23. Factor q(j).
j**2*(j + 2)/2
Let m be 6*3*(-2)/(-30). What is c in 2/5*c + 0 - m*c**3 - 8/5*c**2 + 28/5*c**4 - 16/5*c**5 = 0?
-1/2, 0, 1/4, 1
Let u(c) = c + 17. Let k be u(-14). Let m(b) be the first derivative of 2*b - 5*b**2 + 20/3*b**k - 1/3*b**6 + 2*b**5 - 1 - 5*b**4. Let m(i) = 0. What is i?
1
Suppose 23 = 2*w - 3*a, 0 = 2*w + w - 4*a - 32. Factor -3/4*l**w + 0*l + 3/4*l**3 + 3/4*l**2 + 0 - 3/4*l**5.
-3*l**2*(l - 1)*(l + 1)**2/4
Suppose 3*z - 3*u + 2 = -4, -4*z = 5*u - 19. Suppose 25 = 2*m + 19. Let -5/2*p**m - 9/2*p - z - 6*p**2 = 0. Calculate p.
-1, -2/5
Let m(f) = 9*f**2 - 13*f + 9. Let v(x) = 28*x**2 - 40*x + 28. Suppose 4*w = w + 48. Let a(t) = w*m(t) - 5*v(t). Factor a(n).
4*(n - 1)**2
Suppose 8 - 16*y**3 + 25*y + 70*y**2 - 72*y**2 - 6*y**4 - 9*y = 0. What is y?
-2, -1, -2/3, 1
Suppose -3 + 0 = -q. Solve -12 + 3*z**q + 24*z - 2*z**3 + 2*z**3 - 15*z**2 = 0 for z.
1, 2
Determine d so that 1152*d - 243/2*d**4 - 1296*d**2 - 384 + 648*d**3 = 0.
4/3
Solve -4*a**2 + 8*a - 16/3 + 2/3*a**3 = 0.
2
Suppose 5*u - 2 = 13. Determine a, given that 1 - 3 + a**4 - 3*a + a**2 - 3*a**u + 6*a = 0.
-1, 1, 2
Let z = -8 - -10. Let n(j) be the third derivative of -1/840*j**7 - 1/240*j**6 + j**z + 0 - 1/240*j**5 + 0*j**4 + 0*j + 0*j**3. Factor n(i).
-i**2*(i + 1)**2/4
Let k be 1 + 8/20*5. Let c be k/(-4 - (-9 + 4)). Find v, given that 24/5*v - 8/5 - 24/5*v**c + 22/5*v**2 - 14/5*v**4 = 0.
-2, -1, 2/7, 1
Let r(x) = 6*x**3 - 4*x**2 + 4*x - 4. Let u(f) = 7*f**3 - 5*f**2 + 5*f - 5. Suppose -20 = -3*p - p. Let l(n) = p*r(n) - 4*u(n). Factor l(s).
2*s**3
Let a(c) = -c**2 - 4*c + 7. Let p be a(-6). Let b(y) = -y**2 - 4*y + 8. Let v be b(p). What is s in s**2 - 2/3*s + 0 + s**v + s**5 - 7/3*s**4 = 0?
-2/3, 0, 1
Suppose 3 = -3*i - 4*x, 2*x - 2 = -2*i - 4. Let c be i/(-2) - (-3)/2. Factor -c*b + 8*b**2 - 11*b**2 + 0*b**3 - b**3.
-b*(b + 1)*(b + 2)
Let a = 22 - 22. Let b(d) be the first derivative of -1/14*d**4 - 1/7*d**2 + 3 + a*d + 4/21*d**3. Factor b(v).
-2*v*(v - 1)**2/7
Let s(k) = -k - k + 3*k. Let m be s(3). Factor -c + m*c - 5*c**2 + 4 + 3*c**2.
-2*(c - 2)*(c + 1)
Let q(b) be the third derivative of b**7/1470 - b**6/840 - b**5/420 + b**4/168 - 6*b**2 - 2. Factor q(n).
n*(n - 1)**2*(n + 1)/7
Suppose -4*u = -5*v + 19, -3 = -2*v - 4*u + 27. Let n be -4 + ((-72)/v)/(-2). Factor -2/7*z**2 - n*z - 8/7.
-2*(z + 2)**2/7
Suppose 3*x + 4*l - 38 = 0, 0*x = -2*x - 2*l + 22. Let c be (x/7)/(2 + -1). Determine h, given that -4/7 + c*h - 2/7*h**2 = 0.
1, 2
Let j be 2 + 5 + (-6)/(-3). Let q = j + -7. Suppose 1/4*v**4 + 0 + 0*v - 1/4*v**q + 0*v**3 = 0. What is v?
-1, 0, 1
Let y = 29 - 21. Let b = -5 + y. Determine d so that 0 + 0*d + 0*d**2 + 2/7*d**5 + 4/7*d**b - 6/7*d**4 = 0.
0, 1, 2
Let x(t) be the third derivative of -t**5/30 - 3*t**4/2 - 27*t**3 + 14*t**2. Factor x(n).
-2*(n + 9)**2
Let z = -22433/3360 - -187/28. Let k(w) be the third derivative of 1/96*w**4 - 1/240*w**5 - z*w**6 + 0*w + 3*w**2 + 0 + 1/24*w**3. Factor k(y).
-(y - 1)*(y + 1)**2/4
Let i be 3/1 + -2 + 4. Let q be i + -3 + (1 - 0). Factor -2*x + 5*x - 4*x - x**5 + 0*x**q + 2*x**3.
-x*(x - 1)**2*(x + 1)**2
Let n(l) be the third derivative of 1/12*l**4 - 1/60*l**5 + 0 + 0*l**3 + 2*l**2 + 0*l. Factor n(p).
-p*(p - 2)
Let w(k) be the third derivative of -k**5/30 - k**4/6 - k**3/3 - 2*k**2. Factor w(d).
-2*(d + 1)**2
Let q = 31 + 15. Find h, given that 44*h + 2*h**2 - q*h - 2*h**4 + 0*h**2 + 2*h**3 = 0.
-1, 0, 1
Let v(k) be the first derivative of k**4/60 - k**3/15 - 2*k + 7. Let z(a) be the first derivative of v(a). Factor z(x).
x*(x - 2)/5
Let j be (-2)/((-1)/3 + 40/(-6)). Let v(w) be the first derivative of 5 - 3/14*w**2 + 6/7*w - j*w**3 + 3/28*w**4. Factor v(x).
3*(x - 2)*(x - 1)*(x + 1)/7
Let x be (-1)/(6/(-5) + 1). Suppose 0 = -x*a - 5 + 20. What is s in -s**2 - s**3 - 2*s**4 - a*s**3 + s**4 - 3*s**2 = 0?
-2, 0
Let k(i) be the second derivative of 0*i**4 - 3*i + 0 - 1/168*i**7 + 0*i**3 + 0*i**2 + 0*i**5 - 1/120*i**6. Suppose k(b) = 0. What is b?
-1, 0
Suppose 5*o = 4*f + 2 - 4, 0 = -3*f - 4*o + 17. Let r(q) be the first derivative of 1/4*q**4 + q - 1/2*q**2 - 1/3*q**f - 2. Factor r(a).
(a - 1)**2*(a + 1)
Let s(z) be the third derivative of 7*z**5/180 + 41*z**4/36 - 4*z**3/3 + 5*z**2 + 4. Find c, given that s(c) = 0.
-12, 2/7
Let q = 76/3 + -374/15. Factor -q*f**3 + 2/5*f + 0*f**2 + 0.
-2*f*(f - 1)*(f + 1)/5
Suppose -t + 4*f = 13, -5*t + 0*t + 5*f = 5. Let c(p) be the first derivative of -2*p**2 + 2*p - 3 + 2/3*p**t. Solve c(l) = 0.
1
Let a be ((-24)/200)/(1 + (-6)/5). Find i, given that 3/5*i**2 - a*i**4 - 3/5*i**5 + 0*i + 3/5*i**3 + 0 = 0.
-1, 0, 1
Let t(y) be the second derivative of -y**7/168 - y**6/30 - y**5/16 - y**4/24 + 5*y. Factor t(g).
-g**2*(g + 1)**2*(g + 2)/4
Let a(l) = -5*l. Let y be a(1). Let j = y + 5. Determine h, given that -2/7*h - 6/7*h**2 - 4/7*h**3 + j = 0.
-1, -1/2, 0
Factor -5/4*a**4 - 1/2*a - 9/4*a**3 + 0 - 1/4*a**5 - 7/4*a**2.
-a*(a + 1)**3*(a + 2)/4
Factor o**3 + 0*o**3 - 5*o + 4*o.
o*(o - 1)*(o + 1)
Let g(o) be the third derivative of 0*o - 1/70*o**5 - 1/28*o**4 - 1/420*o**6 + 0 - 1/21*o**3 + 3*o**2. Factor g(y).
-2*(y + 1)**3/7
Let w(f) be the second derivative of -1/10*f**4 + 3*f + 3/100*f**5 + 3/5*f**2 + 0 - 1/10*f**3. Factor w(x).
3*(x - 2)*(x - 1)*(x + 1)/5
Let o(t) be the second derivative of 1/78*t**4 + 0 + 0*t**2 + 0*t**3 - 1/130*t**5 - 2*t. Factor o(s).
-2*s**2*(s - 1)/13
Let n = -3/116 - -125/348. Find m such that 4/3 - 4/3*m + n*m**2 = 0.
2
Let q(a) be the third derivative of a**5/30 + a**4/2 - 16*a**3/3 + 21*a**2. Find y, given that q(y) = 0.
-8, 2
Let t(m) = 2*m**2 + 8*m + 7. Let c be t(-1). Determine y so that y + 1/4*y**2 + c = 0.
-2
Let x(o) be the second derivative of -o**8/20160 + o**7/2520 - o**6/1080 - o**4/3 - 2*o. Let j(q) be the third derivative of x(q). Find u, given that j(u) = 0.
0, 1, 2
Factor -4/7 - 6/7*q + 0*q**2 + 2/7*q**3.
2*(q - 2)*(q + 1)**2/7
Let w(d) be the third derivative of 1/18*d**3 + 0*d + 0 - 1/24*d**4 + 1/60*d**5 - 2*d**2 - 1/360*d**6. Let w(r) = 0. What is r?
1
Find u, given that 1/4*u**5 + 7/4*u**3 - 2*u - 1/4*u**2 - 1 + 5/4*u**4 = 0.
-2, -1, 1
Let h(i) be the third derivative of 3*i**2 + 1/12*i**4 + 7/60*i**5 + 0 + 0*i**3 + 0*i. Factor h(k).
k*(7*k + 2)
Factor 3/4*n**2 - 9/2*n + 27/4.
3*(n - 3)**2/4
Find u such that 5/3*u**2 - u**3 - 1/2*u**4 + 3/2 + 1/6*u**5 + 7/2*u = 0.
-1, 3
Let q(l) be the first derivative of l**5/10 + l**4/12 - 3*l**2/2 - 5. Let r(c) be the second derivative of q(c). Factor r(g).
2*g*(3*g + 1)
Let n(u) be the second derivative of 0 - 2/15*u**4 - 3*u + 1/5*u**3 + 1/5*u**2. Factor n(r).
-2*(r - 1)*(4*r + 1)/5
Factor 0*y + 0*y**3 + 8/3*y**2 + 2/3*y**5 + 0 - 2*y**4.
2*y**2*(y - 2)**2*(y + 1)/3
Find n such that -101 - 16*n**3 + 101 - 4*n + 20*n**2 = 0.
0, 1/4, 1
Suppose -i - 2*l = 0, -4*i + l + 3*l + 24 = 0. Determine r so that 0*r**i - 16*r**5 + 16*r**3 + 4*r**2 + 0*r**4 - 4*r**4 = 0.
-1, -1/4, 0, 1
Let c(l) be the second derivative of 5*l**7/399 + 4*l**6/95 + 9*l**5/190 + l**4/57 + 6*l. Suppose c(a) = 0. What is a?
-1, -2/5, 0
Let s = 6 - 1. Let a(d) be the second derivative of -1/90*d**6 + 1/18*d**4 + 0*d**3 - 1/6*d**2 + 0 + 0*d**s + d. Factor a(p).
-(p - 1)**2*(p + 1)**2/3
Determine v so that 0*v + 7/10*v**3 + 3/10*v**2 + 1/2*v**4 + 0 + 1/10*v**5 = 0.
-3, -1, 0
Let x(z) be the third derivative of 0*z**3 + 1/20*z**5 + 1/40*z**6 + 0 + 0*z - 1/4*z**4 - 7*z**2. Factor x(l).
3*l*(l - 1)*(l + 2)
Suppose 45 = c - i - 8, -5*i + 23 = c. Suppose