he first derivative of 2 - 7/5*f**2 + 2/5*f**5 - 4/5*f + 7/10*f**c - 2/5*f**3. Find m such that b(m) = 0.
-1, -2/5, 1
Let q(x) be the first derivative of x**6/2 + 21*x**5/5 + 45*x**4/4 + 9*x**3 - 8. Factor q(c).
3*c**2*(c + 1)*(c + 3)**2
Suppose 0 = 3*h - 5*h + 8. Let u(v) be the first derivative of -1/9*v**3 + 0*v**2 + 0*v + 1/12*v**h + 2. Factor u(m).
m**2*(m - 1)/3
Let k(a) be the third derivative of -1/120*a**6 + 0*a**3 - 2*a**2 + 0*a**5 + 0 + 0*a**4 + 1/70*a**7 + 0*a. Factor k(w).
w**3*(3*w - 1)
Let g(r) be the first derivative of 4*r**3/9 + 55*r**2/6 - 14*r/3 - 25. Factor g(v).
(v + 14)*(4*v - 1)/3
Suppose 9*q = 64 + 17. Suppose -4*y + 1 - q = -4*x, -y = -4*x + 17. Solve 3/2*a**4 + y + 3/2*a**3 - 9/2*a**2 - 3/2*a = 0 for a.
-2, -1, 1
Let s(y) = 5*y**5 - 5*y**4 + 10*y**3 - y**2 - 3*y + 3. Let r(q) = -6*q**5 + 4*q**4 - 10*q**3 + 4*q - 4. Let b(f) = 3*r(f) + 4*s(f). Factor b(n).
2*n**2*(n - 2)*(n - 1)**2
Let y be (0/(-2))/(-3) + 8. Suppose 2*u = -0*u + y. Factor 0 + 0*q**3 + 1/5*q**u - 1/5*q**2 + 0*q.
q**2*(q - 1)*(q + 1)/5
Let o(p) = p**2 + 5*p - 6. Let d(h) = -h + 1. Let u(y) = 6*d(y) + o(y). Let n be u(2). Factor w**5 + 0*w**5 - 4*w**3 + 2*w - 4*w**n + 2*w**4 + w**5 + 2.
2*(w - 1)**2*(w + 1)**3
Let r = 18 - 52/3. Solve 2/3 - 2*i**4 + 4/3*i**2 + 2*i - r*i**5 - 4/3*i**3 = 0.
-1, 1
Solve 4*a - 2*a**2 + a**2 - a**2 = 0.
0, 2
Let r(g) be the first derivative of -g**4/14 + 4*g**3/21 + 3*g**2/7 - 9. What is w in r(w) = 0?
-1, 0, 3
Let f(l) = -l - 5. Let n be f(-9). Let q(g) be the first derivative of -2/3*g - 1/12*g**n + 1/2*g**2 - 1 + 0*g**3. Factor q(h).
-(h - 1)**2*(h + 2)/3
Let r(b) be the third derivative of b**8/84 - 2*b**7/35 + b**6/30 + b**5/5 - b**4/3 + 25*b**2. Factor r(y).
4*y*(y - 2)*(y - 1)**2*(y + 1)
Factor -4/3*c**3 + 0 - 8/3*c - 4*c**2.
-4*c*(c + 1)*(c + 2)/3
Suppose -278*z + 277*z = -5. Suppose 1/4*o**z - o - o**2 + o**4 + 3/4*o**3 + 0 = 0. Calculate o.
-2, -1, 0, 1
Let w(f) be the first derivative of -f**6/180 + f**4/12 + f**3/3 - 2. Let y(o) be the third derivative of w(o). Find t such that y(t) = 0.
-1, 1
Let p = 114 + -111. Let -2*i + 2*i**p - 2/3*i**4 + 4/3 - 2/3*i**2 = 0. Calculate i.
-1, 1, 2
Let d = -39 + 45. Let c(l) be the second derivative of 1/12*l**5 + 0*l**2 - l - 1/18*l**4 + 1/126*l**7 + 0 - 2/45*l**d + 0*l**3. Determine k so that c(k) = 0.
0, 1, 2
Factor 22/3*p**3 - 100/3 - 1/3*p**4 - 47*p**2 + 220/3*p.
-(p - 10)**2*(p - 1)**2/3
Let d = 8 - 8. Let o(p) be the second derivative of d - 2*p - 1/24*p**4 - 1/2*p**2 - 1/4*p**3. Factor o(c).
-(c + 1)*(c + 2)/2
Let x(i) be the second derivative of 49*i**5/10 - 49*i**4/2 - 4*i**3/3 + 12*i**2 + 5*i. Factor x(l).
2*(l - 3)*(7*l - 2)*(7*l + 2)
Let p(v) be the first derivative of 2*v**5/45 + v**4/18 - 2*v**3/27 - v**2/9 + 2. Find b, given that p(b) = 0.
-1, 0, 1
Suppose 5*u = 7 + 8. Suppose 3*y + y + 4 = 4*v, -u*y + v - 1 = 0. Factor -1/3*w**2 + y + 0*w.
-w**2/3
Let n = 11 - 9. Let a = 7 - n. Solve -4/3*c**4 + 2*c**3 + 4/3*c**2 + 0*c - 2*c**a + 0 = 0 for c.
-1, -2/3, 0, 1
Let h = -1/495 - -63859/1980. Let d = h + -32. Factor 0 + 1/2*t + d*t**2.
t*(t + 2)/4
Let m = 12 - 10. Factor 4 - 14*y**2 + m - 10*y - 2.
-2*(y + 1)*(7*y - 2)
Suppose 0 = 2*z + 2*z - d - 20, 28 = 2*z - 5*d. Let b(w) be the first derivative of 1/10*w**z + 1/5*w + 0*w**3 + 1 - 1/25*w**5 - 1/5*w**2. Factor b(h).
-(h - 1)**3*(h + 1)/5
Suppose 100 = -10*s + 5*s. Let m be (0 + -12)*s/75. Find h such that -m*h**2 + 21/5*h**3 + 4/5*h + 0 - 9/5*h**4 = 0.
0, 2/3, 1
Determine g so that 1/5*g**4 + 0 + 2/5*g**3 + 0*g + 0*g**2 = 0.
-2, 0
Let r(d) be the third derivative of -d**8/50400 + d**6/1800 - d**5/20 + d**2. Let g(q) be the third derivative of r(q). Factor g(a).
-2*(a - 1)*(a + 1)/5
Let l(n) = -n**4 + n**2 - 1. Let a = 18 - 8. Let q(h) = 8*h**4 - 4*h**3 - 4*h**2 + 8*h + 2. Let u(b) = a*l(b) + q(b). What is t in u(t) = 0?
-2, 1
Factor 6*m**2 - 9 + 3/2*m**3 + 3/2*m.
3*(m - 1)*(m + 2)*(m + 3)/2
Suppose 5*v + 4*u + 3 = -5, 5*v + 17 = -u. Let f be (-3)/2*v/6. Let -f - 4*h**3 - h**3 + 0 - 3*h**2 + 4*h**3 - 3*h = 0. What is h?
-1
Let n(f) = f - 1. Let c be n(4). Suppose 0 = 2*s - c*s. Determine k, given that 2*k**3 - 6*k**4 + s*k + 0 + 4/3*k**2 = 0.
-1/3, 0, 2/3
Let d(z) be the first derivative of z**5/2 - 4*z**4/3 + z**3/3 + 2*z**2 - 2*z - 1. Let l(c) be the first derivative of d(c). Find v such that l(v) = 0.
-2/5, 1
Let m(s) = -3*s**2 - 21*s + 28. Let a(y) = 12*y**2 + 84*y - 111. Let b(q) = 4*a(q) + 15*m(q). Factor b(n).
3*(n - 1)*(n + 8)
Let 3/5*q - 12/5*q**4 + 0 - 12/5*q**2 + 18/5*q**3 + 3/5*q**5 = 0. What is q?
0, 1
Suppose s = -5*a - 10, 98*s - 96*s + 10 = -5*a. Solve 4/13*o**4 - 4/13*o**2 - 2/13*o + s*o**3 + 2/13*o**5 + 0 = 0.
-1, 0, 1
Let o be 1320/576 + 9/24*1. Find a such that 2/3*a**4 + 10/3*a**2 + o*a**3 + 4/3*a + 0 = 0.
-2, -1, 0
Let o(w) be the first derivative of -w**4/36 - 7. Factor o(m).
-m**3/9
Factor -2/17*i + 2/17 - 2/17*i**2 + 2/17*i**3.
2*(i - 1)**2*(i + 1)/17
Find x such that -2/15*x**5 - 4/15*x**4 + 0*x**2 + 0 + 0*x - 2/15*x**3 = 0.
-1, 0
Let g(h) be the third derivative of -h**7/315 - 4*h**6/45 - 13*h**5/15 - 28*h**4/9 - 49*h**3/9 - 8*h**2 - h. Suppose g(v) = 0. What is v?
-7, -1
Let b(n) = n**3 - 2*n**2 - n - 3. Let g be b(3). Suppose 3*u - 18 = -w - 1, -4*w = g*u - 23. Factor q**w - q**3 + 4 - 4.
-q**2*(q - 1)
Let x(c) be the first derivative of c**7/1680 - c**6/360 + c**5/240 + c**3 - 2. Let v(g) be the third derivative of x(g). Factor v(t).
t*(t - 1)**2/2
Let l(f) be the third derivative of f**6/30 + 4*f**5/15 + 13*f**4/24 + f**3/2 + 10*f**2. Let l(b) = 0. Calculate b.
-3, -1/2
Find s, given that -1/11*s**3 + 2/11*s**2 + 0 - 1/11*s = 0.
0, 1
Determine c so that 2*c**2 - c**5 - c - c**4 + 1 + 0*c**5 + 2*c**3 + 0*c**4 - 2 = 0.
-1, 1
What is s in 3 + 1 - 2*s + 8*s - 4*s**4 - 8*s**3 + 2*s = 0?
-1, 1
Let k(y) be the third derivative of -2*y**2 - 1/2*y**4 + 0*y + 4/3*y**3 + 0 + 1/10*y**5 - 1/120*y**6. Determine g so that k(g) = 0.
2
Let x(l) = -4*l**2 - 2*l - 4. Suppose -10 = 2*n + 3*n. Let q(g) = -g**2 - 1. Let s(v) = n*x(v) + 10*q(v). Determine a, given that s(a) = 0.
1
Determine t so that 36/7*t - 4/7*t**3 - 20/7 - 12/7*t**2 = 0.
-5, 1
Suppose 4*p + 4*q - 14 - 10 = 0, 0 = 4*p - 4*q. Let n(j) be the first derivative of 0*j**2 + 0*j - 1/6*j**p - 1/16*j**4 + 1. Factor n(d).
-d**2*(d + 2)/4
Let l be (1 + 1)*2/2. Let y(b) be the first derivative of -1/10*b**5 - 1/2*b**3 - 1 + 3/8*b**4 + 1/4*b**l + 0*b. Find p such that y(p) = 0.
0, 1
Let b = -121 + 124. Let c(w) be the second derivative of -w - 1/6*w**4 + 2/3*w**3 + 0 + b*w**2. Let c(t) = 0. What is t?
-1, 3
Suppose -16 = -4*q, -3*a + 2*a = 5*q - 23. Factor -2/3*u + 2/3*u**2 + 2/3*u**a - 2/3.
2*(u - 1)*(u + 1)**2/3
What is s in 0 - 2/11*s**5 + 14/11*s**2 - 4/11*s - 18/11*s**3 + 10/11*s**4 = 0?
0, 1, 2
Suppose -31 = -2*r - 27. Let b(q) be the second derivative of 0 - 1/10*q**5 + 0*q**4 + 0*q**3 + 0*q**2 + r*q. What is z in b(z) = 0?
0
Let r = -2/1975 - -477968/17775. Let x = 304/9 + -296/9. Suppose -r*y**2 - 88/9*y - x = 0. What is y?
-2/11
Suppose 6*v - 8*v = 0. Factor 5*n**4 + n**4 + n**5 + 5*n**3 - 2*n**4 + v*n**5 + 2*n**2.
n**2*(n + 1)**2*(n + 2)
Let d(x) be the third derivative of x**5/60 + x**4/8 - 5*x**3/6 + x**2. Let c be d(-5). Determine n so that 2*n**c - 4*n**3 + 6*n**3 + 0*n**5 - 4*n**4 = 0.
0, 1
Let o(k) = 4*k**5 + 9*k**4 - 4*k**3 - 9*k**2 + 9*k + 9. Let l(d) = -d**5 - 2*d**4 + d**3 + 2*d**2 - 2*d - 2. Let b(t) = -9*l(t) - 2*o(t). Factor b(h).
h**3*(h - 1)*(h + 1)
Let k(a) be the third derivative of -a**6/120 - a**5/20 + 5*a**4/24 + a**3 + a**2. Let p be k(-4). Factor -4/7*l - p*l**4 - 22/7*l**2 + 0 - 32/7*l**3.
-2*l*(l + 1)**2*(7*l + 2)/7
Factor -3/7*u**3 + 9/7 + 3/7*u**2 + 15/7*u.
-3*(u - 3)*(u + 1)**2/7
Let q(d) = -d**3 + 9*d**2 - 9*d + 12. Let n be q(8). What is x in 6*x**4 - n*x**4 - x**5 + 118*x**3 - 119*x**3 = 0?
0, 1
Let g(j) be the first derivative of -2*j**3/21 + 2*j**2/7 + 1. Determine r, given that g(r) = 0.
0, 2
Let p = -74/11 + 540/77. Factor p*u**2 + 0*u - 2/7.
2*(u - 1)*(u + 1)/7
Factor -1/6*n**2 - 1/3*n - 1/6.
-(n + 1)**2/6
Let t(d) be the second derivative of d**7/13860 + d**6/3960 + d**4/4 + 4*d. Let v(x) be the third derivative of t(x). What is f in v(f) = 0?
-1, 0
Suppose 8*m - 4*m + 8 = 0. Let c be 1*3/m*-8. Fac