15. Let g(w) = 7*m(w) + 3*v(w). Solve g(b) = 0 for b.
-2, 1
Let o = 83/5 - 77/5. Let l = 37/130 + 3/26. Factor 4*t**4 + 12/5*t**2 + o*t**5 + 24/5*t**3 + l*t + 0.
2*t*(t + 1)**3*(3*t + 1)/5
Suppose 0*c + 2 = 2*c. Suppose -3/2*t + 1/2*t**3 - c + 0*t**2 = 0. What is t?
-1, 2
Let c(f) = 4*f - 10. Let k be c(7). Suppose -k = -3*j - 3*j. What is l in 2/7*l**5 + 0 - l**4 + 1/7*l - 5/7*l**2 + 9/7*l**j = 0?
0, 1/2, 1
Let m(c) = -7*c**5 + 2*c**4 + 6*c**3 - 2*c**2 + c - 6. Let i(y) = -y**5 + y**3 - 1. Let p(a) = 6*i(a) - m(a). Factor p(k).
k*(k - 1)**3*(k + 1)
Let u(r) be the first derivative of -1/5*r**5 - 1/3*r**4 + 0*r - 1/9*r**3 - 1 + 0*r**2. Let u(t) = 0. What is t?
-1, -1/3, 0
Suppose h + 15 + 11 = 5*k, -2*h - 5*k + 23 = 0. Let o be (-12)/(5 + h) - -3. Let -3/5*y**3 + 3/5*y**2 + o*y + 0 = 0. Calculate y.
0, 1
Let n be (9/(-6))/(1/(-9)). Let u = 14 - n. Solve 1/2*c**2 + u - c = 0.
1
Let y = 12 + -15. Let o be y/(-9) + 3/9. Factor -2/3*a**2 + 0 - 2/3*a + 2/3*a**4 + o*a**3.
2*a*(a - 1)*(a + 1)**2/3
Factor -8/7 + 8/7*d - 2/7*d**2.
-2*(d - 2)**2/7
Let j(g) be the second derivative of 2/5*g**3 + 0 + 5*g + 1/20*g**4 + 0*g**2. Factor j(q).
3*q*(q + 4)/5
Let d be (-2 + -3 + 1)/2 + 2. Let n(r) be the second derivative of 1/4*r**4 + d*r**2 + 0 - 1/30*r**6 + 0*r**5 + 4*r + 1/3*r**3. Factor n(v).
-v*(v - 2)*(v + 1)**2
Solve -2/5*f**3 - 50 - 30*f - 6*f**2 = 0.
-5
Suppose -5*x = -0*x + 275. Let s = 121/2 + x. Factor 3/4*f - 1/2 - 5/4*f**5 + 2*f**2 + 9/2*f**4 - s*f**3.
-(f - 1)**4*(5*f + 2)/4
Suppose 0 = 5*k - 5*x + 15, -x + 1 = -6*k + 4*k. Suppose -l - k*l = 0. Factor l*r + 0 + 0*r**2 - 1/5*r**3.
-r**3/5
Let o(p) = -19*p**3 + 12*p**2 - 7*p. Let w(r) = -13*r**3 + 8*r**2 - 5*r. Let x(q) = 5*o(q) - 7*w(q). Determine g, given that x(g) = 0.
0, 1
Let a(t) be the second derivative of -t**7/6300 + t**6/900 + t**4/12 - 2*t. Let y(j) be the third derivative of a(j). Suppose y(o) = 0. Calculate o.
0, 2
Let g be (-5)/(5/(-2)) - -1. Factor c**2 - 3*c**g - c**3 + 0*c**3 + c**2 + 2*c**4.
2*c**2*(c - 1)**2
Let j(l) be the first derivative of l**9/3024 + l**8/1680 - l**7/840 - l**6/360 - 5*l**3/3 - 3. Let f(s) be the third derivative of j(s). Factor f(a).
a**2*(a - 1)*(a + 1)**2
Let v(i) be the second derivative of -i**8/30240 + i**6/3240 - 5*i**4/12 + 6*i. Let g(f) be the third derivative of v(f). Solve g(n) = 0 for n.
-1, 0, 1
Let r(j) be the third derivative of 1/945*j**7 + 0*j**3 + 0*j**6 + 4*j**2 + 0*j + 0 - 1/90*j**5 - 1/54*j**4. Determine i so that r(i) = 0.
-1, 0, 2
Let i(w) be the first derivative of w**4/20 - w**3 + 15*w**2/2 - 25*w + 26. Factor i(q).
(q - 5)**3/5
What is d in -8/7*d**4 + 32/7*d**2 + 0 + 0*d**3 - 2/7*d**5 + 32/7*d = 0?
-2, 0, 2
Let s = -14 + 15. Let v be (s + -1)*9/9. Find o, given that -2/9*o**3 + v + 2/9*o + 0*o**2 = 0.
-1, 0, 1
Let w = 11 - 6. Let k(z) be the second derivative of -2*z + 0*z**2 + 0*z**3 + 1/24*z**4 + 0 + 7/80*z**w. Factor k(t).
t**2*(7*t + 2)/4
Factor -2/13 - 12/13*l**2 + 8/13*l**3 - 2/13*l**4 + 8/13*l.
-2*(l - 1)**4/13
Let x be (-3)/15 + 98/480. Let h(d) be the third derivative of 0 - 1/480*d**6 + 1/24*d**3 + 1/96*d**4 + 0*d - x*d**5 - 2*d**2. Factor h(a).
-(a - 1)*(a + 1)**2/4
Let u(a) = a**3 + 12*a**2 + a + 14. Let h be u(-12). Let n(x) be the first derivative of 0*x**2 - 1/4*x**4 - 3/5*x**5 + 0*x + 2/3*x**3 + h. Factor n(p).
-p**2*(p + 1)*(3*p - 2)
Let i = 12 + -12. Suppose 2*z - 2 = 2. Solve 0 + 1/2*l**3 + 1/2*l**z + i*l = 0 for l.
-1, 0
Factor 0 + 0*k + 1/4*k**2.
k**2/4
Let n(a) be the third derivative of -a**5/12 - 2*a**3/3 - 3*a**2. Let t(r) = 0*r + 9*r**2 - 2*r + r + 8. Let u(b) = 7*n(b) + 4*t(b). Factor u(p).
(p - 2)**2
Let v(f) be the second derivative of f**6/40 - 3*f**4/16 + f**3/4 + 5*f. Factor v(n).
3*n*(n - 1)**2*(n + 2)/4
Let 4/5 - 12/5*k**2 - 2/5*k**4 + 1/5*k - 11/5*k**3 = 0. Calculate k.
-4, -1, 1/2
Let f(s) = -4*s**3 + s**2 - 3*s + 3. Let i(r) be the second derivative of r**5/20 + r**3/6 - r**2/2 + 4*r. Let k(a) = -f(a) - 3*i(a). Factor k(v).
v**2*(v - 1)
Let t(o) = o**3 - 12*o**2 + 4. Let x be t(12). Let 2*j - 4*j**3 + 7*j**3 - 24*j**2 + 24*j**x - 14*j + 9*j**5 = 0. Calculate j.
-2, -1, -2/3, 0, 1
Let j(x) = -4*x**3 + 2*x**2 - 1. Let r be j(-1). Suppose -1 + 16 = q + 3*p, -p = -4*q - r. Factor -m**2 - 9*m - 1 + q*m + 7*m.
-(m + 1)**2
Factor 12*s**4 + 25*s + 44*s**3 + 4*s**2 - 57*s - 5*s**2 - 23*s**2.
4*s*(s - 1)*(s + 4)*(3*s + 2)
Let b(g) be the second derivative of -g**5/100 + g**4/30 - g**3/30 - 7*g. Suppose b(a) = 0. Calculate a.
0, 1
Let b(h) be the first derivative of 5 - 5/3*h**2 - 2/9*h**3 + 1/6*h**4 - 2*h. Factor b(g).
2*(g - 3)*(g + 1)**2/3
Let l(k) = 4*k**4 + 3*k**3 - k**2 - k. Let s(q) = q**4 - q**2 - q. Let j(m) = -l(m) + s(m). Let j(d) = 0. What is d?
-1, 0
Let y(r) = 2*r**3 + r - 1. Let i(c) = -12*c**3 + 5*c**2 + 3*c + 2. Let b(z) = i(z) + 4*y(z). What is q in b(q) = 0?
-1, 1/4, 2
Let n = -1076 - -1078. Factor -26/7*m - 8/7*m**n + 6/7*m**3 - 12/7.
2*(m - 3)*(m + 1)*(3*m + 2)/7
Let p(h) = -h**2 - h. Let v(o) = -o**2. Let q(b) = -2*p(b) + 3*v(b). Factor q(y).
-y*(y - 2)
Solve -2/5 - 3/5*y - 1/5*y**2 = 0 for y.
-2, -1
Let z(a) be the second derivative of a**4/7 + 3*a**3/14 - 3*a**2/14 - a. Factor z(o).
3*(o + 1)*(4*o - 1)/7
Let p(k) be the third derivative of -k**8/448 - 13*k**7/140 - 241*k**6/160 - 23*k**5/2 - 38*k**4 - 64*k**3 + 21*k**2. Determine m, given that p(m) = 0.
-8, -1
Factor 22/9*w + 14/9*w**3 + 4/9 + 32/9*w**2.
2*(w + 1)**2*(7*w + 2)/9
Let t(w) be the first derivative of w**3/12 + w**2/4 + 20. Factor t(p).
p*(p + 2)/4
Determine p so that -3*p**5 - 5*p**5 + 4*p**5 = 0.
0
Let m = 59/2 + -29. Solve -1/4*g**2 - 1/4*g**4 - m*g**3 + 0 + 0*g = 0 for g.
-1, 0
Suppose 4*z + 16 = 0, 4*w - 15 - 9 = 3*z. Factor n**w + 3*n**2 + 3*n**3 - 4 - 8 - 12*n - n**3.
3*(n - 2)*(n + 1)*(n + 2)
Let u(m) be the third derivative of -m**7/70 + m**6/40 + 3*m**5/10 - m**4/2 - 4*m**3 - 16*m**2. Suppose u(v) = 0. What is v?
-2, -1, 2
Factor 2/11*y**2 + 2/11 - 4/11*y.
2*(y - 1)**2/11
Let v(r) be the first derivative of -r**7/42 - r**6/30 + r**5/10 - 3*r + 1. Let b(t) be the first derivative of v(t). Factor b(i).
-i**3*(i - 1)*(i + 2)
Suppose 4*g - 9 + 1 = 0. Factor -2/5*f + 0 + 2/5*f**g.
2*f*(f - 1)/5
Let w(o) be the second derivative of -o**4/12 + o**3/2 - o**2 - o. Factor w(h).
-(h - 2)*(h - 1)
Let v = 63 - 60. Suppose -2/3*c + 4/3*c**v + 2/3 + 2/3*c**4 - 4/3*c**2 - 2/3*c**5 = 0. What is c?
-1, 1
Let c(x) be the second derivative of 0 - 1/5*x**5 + 7/6*x**3 + x**2 - 5/12*x**4 - x. Factor c(g).
-(g - 1)*(g + 2)*(4*g + 1)
Let l(w) be the third derivative of w**7/945 + w**6/135 + w**5/90 - w**4/27 - 4*w**3/27 - 17*w**2. Factor l(j).
2*(j - 1)*(j + 1)*(j + 2)**2/9
Let o(z) = 6*z**4 - 11*z**3 + 9*z - 4. Let s(h) = 35*h**4 - 65*h**3 + 55*h - 25. Let r(k) = -25*o(k) + 4*s(k). What is q in r(q) = 0?
-1/2, 0, 1
Factor 1/2*x - 1/2 + 1/2*x**2 - 1/2*x**3.
-(x - 1)**2*(x + 1)/2
Let u(r) = r**2 + 3*r - 4. Let j be u(-4). Factor -2/3*t**2 + j + 0*t.
-2*t**2/3
Let t(d) be the third derivative of d**5/150 - 9*d**2. Factor t(h).
2*h**2/5
Let b(u) be the second derivative of 4*u**7/35 - u**6/12 - u**5/15 - u**2 + u. Let c(j) be the first derivative of b(j). Solve c(a) = 0.
-1/4, 0, 2/3
Let w = -413/2 - -207. Factor 0*h**2 + 1/4*h**4 - w*h**3 + 1/2*h - 1/4.
(h - 1)**3*(h + 1)/4
Let g(k) be the first derivative of -k**4/22 - 2*k**3/33 + k**2/11 + 2*k/11 - 39. Find z such that g(z) = 0.
-1, 1
Factor -6*u + 2*u + 2*u + 0*u + 2*u**2.
2*u*(u - 1)
Let l be (2/72)/((-1)/(-3)). Let y(m) be the third derivative of 0 + 1/240*m**5 + l*m**3 + 7/96*m**4 - 1/48*m**6 + 0*m + 4*m**2. Suppose y(d) = 0. Calculate d.
-1/2, -2/5, 1
Let g(t) be the first derivative of -t**6/4 + 3*t**5/5 + 3*t**4/8 - t**3 - 6. Solve g(o) = 0 for o.
-1, 0, 1, 2
Solve -6/7*c**2 + 2/7*c**3 + 2/7*c**5 + 0 + 6/7*c**4 - 4/7*c = 0.
-2, -1, 0, 1
Let i = 1/100 + 49/100. What is z in -7/2*z**2 + 15/2*z - 9/2 + i*z**3 = 0?
1, 3
Suppose 3*q + l = -17, 0 = -q - 3*l + l - 9. Let g be (4/q)/(5/(-25)). Determine w so that -4*w**3 + w**2 + g*w**3 - 3 - w**3 + 2 + w = 0.
-1, 1
Suppose -2*z = -3*p - 1 - 15, 21 = 5*z + 2*p. Factor 0*d + d**2 - 2*d**4 - d + d**4 - 4*d**3 + z*d**3.
-d*(d - 1)**2*(d + 1)
Let i(z) be the first derivative of z**6/180 - z**5/60 - z**4/6 - z**3/3 - 3. Let p(h) be the