What is f?
3
Let r(b) be the third derivative of -b**7/420 - b**6/30 - b**5/6 - b**4/3 + 2*b**2 + 576*b. Solve r(s) = 0.
-4, -2, 0
Let z be -2*(4 - 0) + (-29)/(-3). Determine b so that -5/3*b**2 + 0*b + z*b**5 + 0 + 5/3*b**4 - 5/3*b**3 = 0.
-1, 0, 1
Let c(q) = 21 - 821*q - q**2 + 831*q + 3. Let f be c(12). Find t such that -2/13*t**2 - 4/13*t + f = 0.
-2, 0
Let o(q) = -2*q**4 - q**3 + 5*q**2 + 12*q + 5. Let b(k) = k**4 + 2*k**2 + k + 1. Let g(p) = 5*b(p) + 5*o(p). Suppose g(n) = 0. Calculate n.
-2, -1, 3
Determine q so that -14/5*q**2 - 188/5 + 662/5*q = 0.
2/7, 47
Let n(w) be the second derivative of -11*w**6/6 + 27*w**5/4 + 15*w**4/2 - 18*w. Factor n(r).
-5*r**2*(r - 3)*(11*r + 6)
Let y(s) be the second derivative of 1/5*s**3 + 3/100*s**5 + 0*s**2 - 1/10*s**6 + 1/4*s**4 + 0 - 3/70*s**7 - 26*s. Determine h so that y(h) = 0.
-1, -2/3, 0, 1
Let z(s) be the first derivative of -s**4/10 + 44*s**3/15 - 121*s**2/5 - 66. What is g in z(g) = 0?
0, 11
Suppose 0 = -2*b - 0*b - 2*y, -b - 20 = 5*y. Let x(w) be the third derivative of 1/140*w**b + 3/56*w**4 + 0 + w**2 + 1/7*w**3 + 0*w. Factor x(p).
3*(p + 1)*(p + 2)/7
Let f(r) be the first derivative of -10 - 1/2*r**3 + 0*r - 3/4*r**2. Factor f(s).
-3*s*(s + 1)/2
Let x(b) = -b**2 + b + 1. Let a(v) = v**3 + 7*v**2 - 14*v - 18. Let r(z) = 5*a(z) + 30*x(z). Factor r(n).
5*(n - 3)*(n + 2)**2
Suppose -8*u + 6 = -6*u. Factor -9*y**2 + 10*y + u*y + 6 - 16*y.
-3*(y + 1)*(3*y - 2)
Let g(r) = -r**2 + 5*r + 28. Let i be g(8). Determine x so that -2/9 + 2/3*x - 4/9*x**3 - 4/9*x**2 + 2/3*x**i - 2/9*x**5 = 0.
-1, 1
Let -20 - 60*f - 165/4*f**4 + 50*f**2 + 35/4*f**5 + 40*f**3 = 0. Calculate f.
-1, -2/7, 2
Factor 72*w - 40*w + 0*w**5 + 68*w**2 + 48*w**3 + w**5 + 13*w**4.
w*(w + 1)*(w + 2)**2*(w + 8)
Let c(h) be the first derivative of 3 + 4/3*h**3 + 0*h + 4/7*h**2. Factor c(w).
4*w*(7*w + 2)/7
Let d(m) = -7*m**3 - 20*m**2 + m + 18. Let g(j) = -j**3 - 2*j - 1. Let z(w) = -d(w) + 2*g(w). Determine r, given that z(r) = 0.
-4, -1, 1
Let i(d) = d + 2. Suppose 4 - 23 = -4*y - 3*p, 0 = -3*y + 5*p + 36. Let n be i(y). Let 3 - 1 + n*q**2 - 2 + 12*q + 3 = 0. What is q?
-1, -1/3
Let w(h) be the second derivative of h**6/180 + h**5/30 - 7*h**4/72 - 5*h**3/18 - 214*h. Factor w(s).
s*(s - 2)*(s + 1)*(s + 5)/6
Let p(m) = -43*m**2 + 9*m**2 - 6*m**2 + 21 + 24*m. Let j(g) = -20*g**2 + 12*g + 11. Let a(z) = 5*j(z) - 3*p(z). Solve a(h) = 0 for h.
-2/5, 1
Let h(o) = -o**3 - 44*o**2 + 193*o + 50. Let x be h(-48). Factor 4/3*u**x - 4 + 8/3*u.
4*(u - 1)*(u + 3)/3
Suppose 0 = -2*w + 3*c + 3 - 45, 88 = -4*w + 4*c. Let p = w - -28. Factor -1/2 - 1/4*u**3 + 3/4*u**2 - 1/4*u**p + 1/4*u.
-(u - 1)**2*(u + 1)*(u + 2)/4
Factor 8/7*x**3 + 1/7*x**4 + 9/7 + 24/7*x + 22/7*x**2.
(x + 1)**2*(x + 3)**2/7
Let d(k) = 3*k**4 + 15*k**3 - 30*k**2 - 140*k - 124. Let f(a) = -2*a**4 - 15*a**3 + 30*a**2 + 140*a + 126. Let r(p) = 3*d(p) + 2*f(p). Factor r(y).
5*(y - 3)*(y + 2)**3
Let f = -3056/3 - -1019. Let v(o) be the first derivative of 10 + f*o**3 - o**4 + 7/15*o**5 + 1/3*o**2 + 0*o. Factor v(c).
c*(c - 1)**2*(7*c + 2)/3
Let k be ((-13)/4 + 3)/((-4)/(-1352)). Let x = -84 - k. Find a, given that 3/4*a**3 - x*a**4 + 0 + 0*a**2 - 1/4*a = 0.
-1/2, 0, 1
Let g be (0 + 7)/((-2)/(-6)). Suppose -4*c = x - g, 5*c - 23 = -0*x + 2*x. Find q, given that 3*q - 10*q**4 - 19*q**2 + 18*q**3 + 7*q**2 + 3*q**c - 2*q**4 = 0.
0, 1
Let f be 841/52 + (22 - (-1425)/(-65)). Factor f*i + 15/2 + 5/4*i**3 + 10*i**2.
5*(i + 1)**2*(i + 6)/4
Let x(v) = -15*v**3 - 8*v**2 + 53*v + 38. Let b(y) = -64*y**2 - 18*y - 13 - 68*y**2 + 135*y**2 + 5*y**3. Let m(j) = -8*b(j) - 3*x(j). Factor m(a).
5*(a - 2)*(a + 1)**2
Let m be 42/9*(-3)/(-2). Let y = m - 5. Determine x, given that 3*x**5 + 3*x**4 - 9*x**y + 23*x**3 - 6*x**2 - 6*x - 32*x**3 + 0*x**4 = 0.
-1, 0, 2
Suppose -219*a + 1045 = -124*a. Let n(o) be the first derivative of -4*o**3 - 22/5*o**5 + o**6 - o**2 + 7*o**4 + 2*o - a. Factor n(t).
2*(t - 1)**4*(3*t + 1)
Let o = 65777/75 + -877. Let b(x) be the third derivative of -x**2 + 0*x**3 - o*x**5 + 0*x + 1/25*x**6 + 1/75*x**7 + 0 + 0*x**4. Factor b(v).
2*v**2*(v + 2)*(7*v - 2)/5
Let q(c) = c**4 + 2*c**3 + 4*c**2 + 3*c. Let f be 2/4*(-4 - -2). Let d(u) = 0*u + u**4 - 2*u**4 + 2*u**4 + u. Let h(m) = f*q(m) + 3*d(m). Factor h(g).
2*g**2*(g - 2)*(g + 1)
Factor 8*d + 12/5*d**2 + 0 - 24/5*d**3 + 4/5*d**4.
4*d*(d - 5)*(d - 2)*(d + 1)/5
Let i(a) be the first derivative of -2*a**5/45 - 4*a**4/3 - 44*a**3/27 + 8*a**2/3 + 46*a/9 + 79. Suppose i(x) = 0. What is x?
-23, -1, 1
Let l(s) be the second derivative of s**10/151200 - s**9/75600 - 11*s**4/12 + 3*s. Let g(k) be the third derivative of l(k). Suppose g(m) = 0. Calculate m.
0, 1
Find w, given that 12/7*w**2 + 2/7*w**3 + 18/7*w + 0 = 0.
-3, 0
Factor -173*m - 3*m**2 - 67*m**2 + 238*m - 3*m**3 + 8*m**3.
5*m*(m - 13)*(m - 1)
Let z = -100 + 1587/16. Let t = z + 155/112. Factor 2/7*k - t*k**2 + 2/7.
-2*(k - 1)*(2*k + 1)/7
Find b, given that -5/4*b**2 + 0 + 0*b + 1/4*b**3 = 0.
0, 5
Let v(c) = c**3 + 16*c**2 + 58*c + 38. Let g be v(-11). Let -4/11*z**2 + 0*z - 6/11*z**g - 16/11*z**4 + 0 - 14/11*z**3 = 0. Calculate z.
-1, -2/3, 0
Solve 1/3*a**2 + 98/3*a + 2401/3 = 0.
-49
Let d(b) be the first derivative of -b**6/1440 + b**5/160 + b**4/24 + 5*b**3 + 12. Let n(f) be the third derivative of d(f). Let n(u) = 0. What is u?
-1, 4
Let m(g) be the first derivative of -11*g**5/15 - 5*g**4/2 - 8*g**3/3 + 4*g**2 + 34. Let z(v) be the second derivative of m(v). Factor z(j).
-4*(j + 1)*(11*j + 4)
Let z(o) be the first derivative of -3*o**5/20 - o**4/2 + o**3/2 + 3*o**2 + 10*o + 4. Let b(h) be the first derivative of z(h). Suppose b(q) = 0. Calculate q.
-2, -1, 1
Let x(k) be the third derivative of k**8/20160 + k**7/5040 - k**6/360 + k**5/10 + 10*k**2. Let f(r) be the third derivative of x(r). Factor f(w).
(w - 1)*(w + 2)
Let b(r) = -2*r**5 - 19*r**4 - 14*r**3 + 5*r**2 - 5. Let x(f) = f**5 + 10*f**4 + 6*f**3 - 3*f**2 + 3. Let c(t) = 3*b(t) + 5*x(t). Find o, given that c(o) = 0.
-4, -3, 0
Suppose 5*z = 8*z - 75. Let h = 25 - z. Factor h*m + 0 + 3/5*m**4 + 3/5*m**2 + 6/5*m**3.
3*m**2*(m + 1)**2/5
Let c be 5/9*19/(380/12). Suppose r - 4/3 + c*r**2 = 0. Calculate r.
-4, 1
Let x(d) be the first derivative of 121*d**6/3 + 154*d**5/5 - 20*d**4 + 8*d**3/3 + 430. Factor x(o).
2*o**2*(o + 1)*(11*o - 2)**2
Suppose -6 = -6*a + a + 2*h, 0 = 4*a - 4*h. Let d(k) be the first derivative of -4 + 3/2*k - 1/6*k**3 - 1/2*k**a. Factor d(q).
-(q - 1)*(q + 3)/2
Let g(v) = v + 5. Let q be g(-3). Suppose -q*l = -3*l. Factor 0*y - 2*y**3 - 2*y**2 + l*y**4 + 5*y - 3*y + 2*y**4.
2*y*(y - 1)**2*(y + 1)
Factor 2/9 + 2/3*q**5 - 29/9*q**4 + 5/9*q + 49/9*q**3 - 11/3*q**2.
(q - 2)*(q - 1)**3*(6*q + 1)/9
Let p(c) = -3*c**4 + 15*c**3 - 36*c**2 - 24. Let w(v) = -v**3 - v**2 - 2. Let i(s) = -p(s) + 12*w(s). Determine f, given that i(f) = 0.
0, 1, 8
Let 5*q**3 + 245*q + 3*q**2 - 245*q - 13*q**2 = 0. Calculate q.
0, 2
Suppose -47*r + 50*r = 0. Let a(q) be the third derivative of 0 - 1/4*q**4 + 6*q**2 + 0*q + 1/20*q**5 + r*q**3. Let a(m) = 0. Calculate m.
0, 2
Suppose i - 1 = 5*s, -6*i + 4*i = -4*s - 8. Suppose 5*y = -3*v + 4, y - v - i = -y. Factor 12/5 + 3/5*c**3 - 21/5*c + 6/5*c**y.
3*(c - 1)**2*(c + 4)/5
Let v(y) be the second derivative of 0 - 1/3*y**6 + 0*y**5 - 5/6*y**3 + 5/42*y**7 + 4*y + 5/6*y**4 + 0*y**2. Determine t so that v(t) = 0.
-1, 0, 1
Let u(g) be the third derivative of -3*g**2 + 1/60*g**6 - 1/12*g**4 + 0*g + 0 + 1/3*g**3 - 1/30*g**5. Determine z so that u(z) = 0.
-1, 1
Factor 132/13 - 2/13*y**2 + 10/13*y.
-2*(y - 11)*(y + 6)/13
Factor 0*z + 6/11*z**3 - 6/11*z**4 + 2/11*z**5 + 0 - 2/11*z**2.
2*z**2*(z - 1)**3/11
Let p(i) be the third derivative of i**7/336 + 7*i**6/240 + 11*i**5/160 + i**4/96 - i**3/6 + 510*i**2. Suppose p(x) = 0. Calculate x.
-4, -1, 2/5
Let c(w) = -2*w**3 + 2*w**2 + 3*w + 2. Let l be c(-1). Solve 133*d**5 - 5*d**5 + 224*d**4 + 5*d + 26*d**2 - l*d + 100*d**3 + 20*d**3 = 0 for d.
-1, -1/4, 0
Let v(h) be the first derivative of -7*h**6/120 - h**5/30 - 13*h**2/2 - 17. Let b(y) be the second derivative of v(y). Factor b(p).
-p**2*(7*p + 2)
Factor -3*g**2 + 0 - 3/4*g + 15/4*g**3.
3*g*(g - 1)*(5*g + 1)/4
Let f(c) = -c**3 - c**2 - 1. Let x be 1088/48 - (-4)/(-6). Let m(z) = 11*z**3 - 15*z**2