7. Find k such that f*k + 0 - 2/11*k**2 = 0.
0, 1
Let m(d) be the third derivative of 1/40*d**4 - 1/560*d**8 + 1/50*d**5 + 4*d**2 + 0*d**6 + 0*d**3 + 0 - 1/175*d**7 + 0*d. Factor m(h).
-3*h*(h - 1)*(h + 1)**3/5
Let i(v) be the first derivative of v**5/15 + v**4/6 - v**3/9 - v**2/3 - 12. What is g in i(g) = 0?
-2, -1, 0, 1
Suppose 3*h + 0*h**2 + 2 - 2*h**2 - h**2 - 3*h**3 + 1 = 0. What is h?
-1, 1
Let y(p) be the second derivative of 0 - p**2 - 7/240*p**6 - p + 0*p**3 - 1/24*p**5 + 1/24*p**4. Let m(n) be the first derivative of y(n). Factor m(x).
-x*(x + 1)*(7*x - 2)/2
What is a in -12*a**4 - 12*a - 53*a**2 - 71*a**2 + 76*a**3 - 4 + 76 = 0?
-2/3, 1, 3
Let r(l) be the third derivative of -1/3*l**3 + 0*l**4 + 0 + 1/30*l**5 - 3*l**2 + 0*l. Suppose r(s) = 0. Calculate s.
-1, 1
Let b be 1 - (-1 + (-40)/(-25)). Factor -b*u**2 - 4/5 + 6/5*u.
-2*(u - 2)*(u - 1)/5
Let p be (2 - -1) + 7/(-28)*4. Factor -1/6*c**p + 0 - 1/6*c.
-c*(c + 1)/6
Suppose 2*c - 12 = -8. Factor a**4 + 3*a**2 + c*a**3 + a + 3*a**3 - 2*a**3.
a*(a + 1)**3
Let t(x) = 28*x + 254. Let u be t(-9). Let 3/5*q**u - 6/5 - 3/5*q = 0. What is q?
-1, 2
Let f(o) = 18*o - 104. Let r be f(6). Factor 1/3*x**r + 2/3*x**3 - 1/3*x**2 - 2/3*x + 0.
x*(x - 1)*(x + 1)*(x + 2)/3
Let y(m) be the third derivative of m**8/3360 + m**7/1680 - m**6/720 - m**5/240 + m**3/6 + 2*m**2. Let u(q) be the first derivative of y(q). Solve u(t) = 0.
-1, 0, 1
Let a(w) = -2*w**4 - 14*w**3 - 27*w**2 - 21*w - 3. Let p(u) = -18*u**4 - 126*u**3 - 244*u**2 - 188*u - 26. Let c(h) = -52*a(h) + 6*p(h). Solve c(t) = 0 for t.
-3, -1, 0
Let x(t) = 4*t**3 - 5*t**2 - 22*t + 1. Let h(w) = w**3 - 2*w**2 - 7*w. Suppose 1 + 15 = 4*j. Let q(s) = j*x(s) - 14*h(s). Determine p so that q(p) = 0.
-2, -1
Factor -12 + 160*s**2 + 140*s**3 - 4 - 4*s**2.
4*(s + 1)*(5*s + 2)*(7*s - 2)
Factor 19*v**2 - 12*v + 0 - 8 - 7*v**2 - 16*v**2.
-4*(v + 1)*(v + 2)
Let v(f) be the third derivative of -2*f**2 + 1/18*f**4 + 1/9*f**3 + 1/90*f**5 + 0 + 0*f. Factor v(z).
2*(z + 1)**2/3
Let i(x) = -5*x**5 + 15*x**4 + 6*x + 6. Let r(c) = -c - 1. Let z(q) = -i(q) - 6*r(q). Factor z(v).
5*v**4*(v - 3)
Let i = 82695541/18348 + -148708/33. Let f = i + -1/139. Solve -3/4*u**3 + 3/4*u**5 + 0 + 0*u + 3/4*u**2 - f*u**4 = 0.
-1, 0, 1
Let a = 11 + -8. Let p(d) be the third derivative of -2*d**2 + 1/32*d**4 + 1/480*d**6 + 0 + 0*d + 1/80*d**5 + 1/24*d**a. What is g in p(g) = 0?
-1
Find h such that -7/6*h**5 + 20/3*h**2 + 5*h**4 + 1/3 - 5/2*h - 25/3*h**3 = 0.
2/7, 1
Factor 1/3*g**4 - g + 1/3*g**2 + g**3 - 2/3.
(g - 1)*(g + 1)**2*(g + 2)/3
Let x(k) = 2*k**2 + 8*k - 6. Let f(c) = -2*c - 2. Let l be f(-2). Let o(d) = d**3 + 1. Let b(m) = l*o(m) - x(m). What is v in b(v) = 0?
-2, 1, 2
Let o(a) = -a**2 + 3*a + 3. Let m be o(3). Let z be (-2)/15 - (-128)/60. Find s, given that 2*s**3 - s + s**z - m*s**2 + s = 0.
0, 1
Let x(b) be the first derivative of -b**2 - 1/6*b**3 - 1/30*b**6 + 0*b - 1/12*b**4 + 7/60*b**5 + 1. Let h(v) be the second derivative of x(v). Factor h(z).
-(z - 1)**2*(4*z + 1)
Let d(k) be the second derivative of -k**3/6 - 3*k**2 - 2*k. Let z be d(-6). Factor s + 0*s + 0*s**2 + z*s**2 + s**2.
s*(s + 1)
Let p(f) be the third derivative of -1/3*f**3 - 1/30*f**5 + 0*f - 1/6*f**4 + 0 + 2*f**2. Factor p(h).
-2*(h + 1)**2
Let s be (4 + -20)*(-1)/5. Let b be (1 - -5)/((-4)/(-2)). Let -s - 12/5*m**2 + 2/5*m**b + 24/5*m = 0. Calculate m.
2
Let 0 - 1/6*u - 1/6*u**4 - 1/2*u**3 - 1/2*u**2 = 0. What is u?
-1, 0
Let j(x) be the third derivative of x**9/7560 - x**8/1680 + x**7/1260 + x**4/24 + 3*x**2. Let t(a) be the second derivative of j(a). Factor t(z).
2*z**2*(z - 1)**2
Let q = 9 - 9. Let j(p) be the first derivative of q*p + 0*p**3 - 4/5*p**5 + p**2 + 1 - 3/2*p**4. Solve j(g) = 0 for g.
-1, 0, 1/2
Let w(j) be the third derivative of -j**7/1680 - j**6/720 + j**5/240 + j**4/48 + j**3/3 - 3*j**2. Let g(l) be the first derivative of w(l). Solve g(s) = 0.
-1, 1
Let z(v) be the third derivative of v**7/525 - v**6/600 - v**5/150 + v**4/120 + 5*v**2. Factor z(o).
o*(o - 1)*(o + 1)*(2*o - 1)/5
Let o(c) = -c. Let a be o(-5). Let f = a + -2. Factor -6*z**4 - 6*z**5 - 6*z**5 - 6*z**5 + 10*z**f - 2*z**2.
-2*z**2*(z + 1)*(3*z - 1)**2
Let l = 16 + -13. Factor -4*j**4 + 26*j**l + 6*j**2 + 9*j**4 - 9*j**3.
j**2*(j + 3)*(5*j + 2)
Let l(a) be the second derivative of -a**6/240 + a**5/60 - 5*a**2/2 + 4*a. Let w(j) be the first derivative of l(j). Let w(u) = 0. Calculate u.
0, 2
Let i(g) be the first derivative of -2/15*g**3 + 0*g - 1 + 2/5*g**2. Factor i(x).
-2*x*(x - 2)/5
Let p(k) be the third derivative of k**7/420 + k**6/90 - k**5/60 - k**4/6 + 3*k**3/2 + 10*k**2. Let w(r) be the first derivative of p(r). Factor w(b).
2*(b - 1)*(b + 1)*(b + 2)
Let g be 3 + -1 - 6/2. Let c = g + 7. Let j(f) = -f**2 - f + 1. Let d(n) = n**3 + 6*n**2 + 6*n - 2. Let w(i) = c*j(i) + 2*d(i). Solve w(a) = 0.
-1
Suppose u = 26 - 11. Solve 34*p**2 - u*p - 18*p + 5 - 7*p - 8*p**3 + 3 = 0 for p.
1/4, 2
Let l(r) = -12*r + 376. Let d be l(31). Factor -6*c**3 + 4/3*c**2 + 0*c + 0 - 8/3*c**5 + 8*c**d.
-2*c**2*(c - 2)*(2*c - 1)**2/3
Let l be 64/28 + 2*(-1)/(-7). Factor -l*k**3 + 8/7 - 32/7*k + 6*k**2.
-2*(k - 1)*(3*k - 2)**2/7
Let d(x) = 5*x**4 + 4*x**3 + x**2 + 2*x + 4. Let t(p) = -6*p**4 - 5*p**3 - 2*p**2 - 3*p - 5. Let v(n) = -5*d(n) - 4*t(n). Factor v(o).
-o*(o - 2)*(o + 1)**2
Let v be ((-9)/(-2) + -3)/((-6)/(-8)). Factor 1/7*c**v - 2/7*c + 3/7*c**3 + 0.
c*(c + 1)*(3*c - 2)/7
Let v(c) be the second derivative of -c**6/105 - c**5/14 + c**4/42 + 5*c**3/21 + 31*c. Suppose v(j) = 0. Calculate j.
-5, -1, 0, 1
Factor 82 + o**3 - 2*o**3 + 3*o**2 + 9*o - 77.
-(o - 5)*(o + 1)**2
Let x(c) be the third derivative of c**8/110880 - c**7/13860 + c**6/3960 + c**5/60 - 3*c**2. Let p(r) be the third derivative of x(r). Factor p(y).
2*(y - 1)**2/11
Let g(x) be the second derivative of x**4/16 + 7*x**3/8 - 3*x**2 + 4*x. Factor g(h).
3*(h - 1)*(h + 8)/4
Let l(y) be the second derivative of -y**6/840 - 3*y**5/140 - 9*y**4/56 + 2*y**3/3 - 3*y. Let w(f) be the second derivative of l(f). Factor w(g).
-3*(g + 3)**2/7
Let t(a) be the second derivative of 0*a**2 + 0*a**3 - 10*a + 1/60*a**4 + 0. Factor t(o).
o**2/5
Let d(x) be the third derivative of x**8/1008 - x**7/210 + x**6/120 - x**5/180 + 9*x**2. Factor d(l).
l**2*(l - 1)**3/3
Suppose y - 3 = -2*i, 0 = -y - 4 + 1. Let s(n) be the second derivative of 2/3*n**i + 0 - 2*n - 1/12*n**4 - 2*n**2. Suppose s(x) = 0. What is x?
2
Let f(m) = -12*m**2 - 28*m + 1. Let n(u) be the third derivative of 0 + 3*u**2 + 7/24*u**4 + 1/20*u**5 + 0*u + 0*u**3. Let z(b) = 4*f(b) + 18*n(b). Factor z(g).
2*(g + 2)*(3*g + 1)
Let z be (19 - 15)*1/2. Let i(n) be the first derivative of 2 + 7/2*n**z - 2*n - 7/3*n**3 + 1/2*n**4. Let i(m) = 0. Calculate m.
1/2, 1, 2
Let s be 8 - (7 + 9/12). Determine w so that -s*w**4 - w - 1/4 - w**3 - 3/2*w**2 = 0.
-1
Suppose 3 = 2*u - 2*k - 13, -k + 8 = 3*u. Factor 3*a**u + 2*a**2 + a**2 - 5 + 6*a**3 + 5.
3*a**2*(a + 1)**2
Suppose -6 + 11*p**2 + 4 + 11*p - 2*p = 0. What is p?
-1, 2/11
Let i(o) be the first derivative of o**4/12 + o**3 + 9*o**2/2 + 9*o + 7. Factor i(f).
(f + 3)**3/3
Let b(z) = 19*z**4 - 29*z**2 + 31*z + 7. Let h(v) = -13*v**4 + 19*v**2 - 21*v - 5. Let c(l) = 5*b(l) + 7*h(l). Let c(m) = 0. Calculate m.
-2, 0, 1
Determine o, given that 3*o - 5*o**2 + 116 - 126 + 12*o = 0.
1, 2
Let l(i) = 2*i**3 - 4*i**2 + 2. Let d(n) = -n**3 - n**2 + n + 1. Let t(m) = 10*d(m) + l(m). Determine p, given that t(p) = 0.
-2, -3/4, 1
Let x(r) be the third derivative of r**6/420 - r**5/210 - 7*r**2. Factor x(s).
2*s**2*(s - 1)/7
Suppose 5*d + b + 4*b = 25, d + 3*b = 9. Suppose t + 0*t = -2*i + 5, d*i - 2*t - 4 = 0. Factor 0 - 2*c**2 + 0 - i*c.
-2*c*(c + 1)
Factor 2/3*s**4 - 2/3*s**2 + 2*s + 0 - 2*s**3.
2*s*(s - 3)*(s - 1)*(s + 1)/3
Factor -2/9*f**2 + 8/9*f + 0.
-2*f*(f - 4)/9
Let g(f) = f**3 + f**2 + f - 1. Let y(p) be the third derivative of p**6/20 + p**5/30 + p**4/3 - p**3 + 3*p**2. Let u(o) = 5*g(o) - y(o). Factor u(w).
-(w - 1)**3
Let g = 116 - 579/5. Suppose 1/5*o - g*o**5 + 0 + 2/5*o**2 - 2/5*o**4 + 0*o**3 = 0. Calculate o.
-1, 0, 1
Suppose 3*n - 23*n = -40. Determine w so that -2/7*w - 2/7*w**n + 2/7 + 2/7*w**3 = 0.
-1, 1
Let m(d) = -d**3 - 3*d**2 - 6*d + 7. Let v(o) = 3*o**3 + 7*o**2 + 12*o - 