 - 10. Determine a, given that b(a) = 0.
1, 3
Suppose 15*x - 12*x - 3 = 0. Let t(d) be the first derivative of x - 2*d - 2/3*d**3 + 2*d**2. Factor t(v).
-2*(v - 1)**2
Factor -2*n**4 - n**3 + 3*n**4 - 31*n**2 + 29*n**2.
n**2*(n - 2)*(n + 1)
Let h = -8 - -18. Suppose 0 = -5*q - 0*q + h. Suppose -1/3 + 1/6*m**q + 1/6*m = 0. What is m?
-2, 1
Let l be (4/12)/((-2)/(-18)). Solve -l*h**2 + 2*h + 0*h**2 + 2*h**4 - h**4 + 0*h**4 = 0 for h.
-2, 0, 1
Let l(v) be the first derivative of v**4/15 + 2*v**3/15 + v - 4. Let o(k) be the first derivative of l(k). Find b, given that o(b) = 0.
-1, 0
Let g be (-2 - -2)/(4/4). Suppose -d - 4*d + 20 = g. Factor 1/3*x**d - x**2 - 1/3*x + 1/3*x**3 + 2/3.
(x - 1)**2*(x + 1)*(x + 2)/3
Let d be 24/(-14) - (-2 - 0). Factor 0*p**2 + 2/7*p**3 + 0*p + d*p**4 + 0.
2*p**3*(p + 1)/7
Let h(x) be the first derivative of -1/9*x**3 + 3 + 0*x - 1/12*x**4 + 0*x**2. Factor h(s).
-s**2*(s + 1)/3
Suppose 12*f**3 - 38*f**3 - 35*f**2 - 50*f + 10*f**3 + 11*f**3 = 0. Calculate f.
-5, -2, 0
Suppose -15 = m - 5*b, 0 = -m + b - 3. Determine k so that m + 1/5*k**5 - 1/5*k**2 + 0*k + 3/5*k**3 - 3/5*k**4 = 0.
0, 1
Let c(z) be the second derivative of z**5/5 - 2*z**4 + 6*z**3 - 8*z**2 - 38*z. Suppose c(q) = 0. Calculate q.
1, 4
Let o(w) = w**5 - w**2 - w. Let v(h) = -10*h**5 + 39*h**4 - 45*h**3 + 19*h**2 - 5*h. Let g(b) = 2*o(b) - v(b). Solve g(r) = 0 for r.
0, 1/4, 1
Let p(o) be the third derivative of 0*o**3 + 0 + 0*o + 1/90*o**6 + 1/126*o**7 + 1/180*o**5 + 1/504*o**8 - o**2 + 0*o**4. Factor p(m).
m**2*(m + 1)**2*(2*m + 1)/3
Let c(i) be the first derivative of -i**5/150 - i**4/60 + 3*i**2/2 + 1. Let j(l) be the second derivative of c(l). Suppose j(w) = 0. What is w?
-1, 0
Let q be (-6)/(-9)*(-1)/(-3 - -1). Solve 2/3*r**2 - 1/3*r - q*r**3 + 0 = 0.
0, 1
Let b(w) be the third derivative of w**6/24 + 5*w**5/3 + 125*w**4/6 + 59*w**2. Determine p, given that b(p) = 0.
-10, 0
Factor 8*f**2 - 4*f**3 - 14*f**2 - 8 - 20*f - 10*f**2.
-4*(f + 1)**2*(f + 2)
Let v be (4 - (0 - -1)) + -1. Find s, given that 3*s**4 - 162*s**2 + 162*s**v = 0.
0
Suppose 0 - 3/2*p**2 + 9/2*p**3 - p + 5*p**4 = 0. Calculate p.
-1, -2/5, 0, 1/2
Suppose -3*s + 4 = -8. Let h(f) be the second derivative of 1/12*f**s + 1/20*f**5 - 1/6*f**3 + 0*f**2 - 2*f - 1/30*f**6 + 0. What is y in h(y) = 0?
-1, 0, 1
Suppose 15/2*k**3 + 11/2*k**4 + 3/2*k**5 + 9/2*k**2 + k + 0 = 0. Calculate k.
-1, -2/3, 0
Let k(o) be the first derivative of 2*o**2 + 4 + 2/3*o**3 + 0*o. Suppose k(u) = 0. What is u?
-2, 0
Factor u**2 - 2*u**4 - 5*u**2 - 3*u**4 + 14*u**2 - 5.
-5*(u - 1)**2*(u + 1)**2
Let j(z) = 13*z + 1. Let k be j(1). Suppose k = 11*o - 4*o. Factor -q - 1 - 1/4*q**o.
-(q + 2)**2/4
Let t(n) = -4*n**3 - 18*n**2 - 2*n. Let y(q) = -9*q**3 - 36*q**2 - 5*q. Let u(d) = 5*t(d) - 2*y(d). Suppose u(r) = 0. What is r?
-9, 0
Let o(i) be the second derivative of -2*i**6/15 + 4*i**4/3 + 26*i. Factor o(v).
-4*v**2*(v - 2)*(v + 2)
Let a(c) be the second derivative of -c**4/21 - 20*c**3/21 - 50*c**2/7 - 27*c. Factor a(t).
-4*(t + 5)**2/7
Let q = -19 + 23. Let 0*y + 0*y**3 - 1/3*y**q + 0*y**2 - 1/3*y**5 + 0 = 0. What is y?
-1, 0
Let j(u) be the first derivative of -u**3 - 9*u**2/2 - 6*u + 4. Find i such that j(i) = 0.
-2, -1
Let h be -1 + (-24)/((-4)/1). Let j be (-34)/(-85) + (-2)/h. Factor 2/7*p**4 + 0*p + j + 4/7*p**3 + 2/7*p**2.
2*p**2*(p + 1)**2/7
Let w(x) = -x**2 - x. Let h(d) = 5*d**2 + 7*d + 2. Let t(c) = h(c) + 4*w(c). Suppose t(z) = 0. What is z?
-2, -1
Factor 2/9*k**2 + 4/9*k + 0.
2*k*(k + 2)/9
Suppose -y - x + 107 = 0, 4*x - 8*x + 113 = y. Let g be (-7)/(y/4)*-10. Determine i, given that -2/3*i**2 - 8/3*i - g = 0.
-2
Let t be -3 + (-62)/(-10) + -3. Let n = 32/85 - -2/85. Factor 1/5*p + n*p**2 + t*p**3 + 0.
p*(p + 1)**2/5
Let j = 23 + -14. Suppose -j*s**2 - 6*s**3 + 6 + 8*s + 0*s + s = 0. What is s?
-2, -1/2, 1
Let r(y) be the first derivative of y**4/26 + 2*y**3/13 + 3*y**2/13 + 2*y/13 + 15. Factor r(z).
2*(z + 1)**3/13
Let i(s) be the third derivative of s**6/300 + s**5/75 + 2*s**2. Solve i(w) = 0.
-2, 0
Let r(w) be the first derivative of w**8/448 - w**7/140 + w**6/160 + w**2 - 4. Let h(y) be the second derivative of r(y). Factor h(a).
3*a**3*(a - 1)**2/4
Let u = -73/19 - -4. Let c = 53/95 - u. Determine z, given that 4/5*z**2 - 2/5*z + 0 - c*z**3 = 0.
0, 1
Let i(n) be the third derivative of n**8/3360 + n**7/840 + n**6/720 + 4*n**3/3 + 7*n**2. Let o(x) be the first derivative of i(x). Solve o(w) = 0.
-1, 0
Let x = 3 - 1. Suppose 0 = -5*n + x*n. Determine i, given that -i + 14*i + n*i**2 - 2 - 11*i**2 = 0.
2/11, 1
Determine c so that 144*c**3 + 6391*c + 2592*c**2 + 32596 + 29612 + 3*c**4 + 14345*c = 0.
-12
Let s(t) be the first derivative of -t**6/180 + t**4/12 - 7*t**3/3 - 3. Let i(m) be the third derivative of s(m). Factor i(q).
-2*(q - 1)*(q + 1)
Suppose -8 = -4*c + 8. Determine a so that 3*a**2 + 4*a**2 - a**4 - 6*a**2 - c*a**3 + 4*a**5 = 0.
-1, 0, 1/4, 1
Let m = -72 - -361/5. Let b(i) be the first derivative of -1/20*i**4 + 0*i**2 + 2 - 4/5*i + m*i**3. Suppose b(c) = 0. Calculate c.
-1, 2
Suppose -5*q + 3*k - 2 = 0, 4*q + 3*k - 28 = -2*k. Suppose 4*a = -4*h + 160, -3*a + 5*h + 95 = 3*h. Factor 6*l**2 + 20*l - a*l**3 - q + 5*l**2 + 6.
-(l - 1)*(5*l + 2)*(7*l + 2)
Let v = 41 + -36. Let z(l) be the first derivative of -5/8*l**4 + l - 7/4*l**2 + 1/10*l**v + 3/2*l**3 - 3. Let z(w) = 0. Calculate w.
1, 2
Let m = 16 - 24. Let b be (-21)/30 - 12/m. Determine n, given that 54/5*n**4 - 6/5*n - 56/5*n**5 + 62/5*n**3 - 58/5*n**2 + b = 0.
-1, -2/7, 1/4, 1
Let x(v) = -2*v + 21. Let w(f) = -f + 10. Let c(i) = -7*w(i) + 4*x(i). Let l be c(11). Solve -2/5*u**4 - 2/5*u**l + 0*u + 0 + 4/5*u**2 = 0 for u.
-2, 0, 1
Let k(i) be the second derivative of i**6/420 - i**5/105 + i**4/84 - 3*i**2/2 - 2*i. Let q(a) be the first derivative of k(a). Find p, given that q(p) = 0.
0, 1
Factor -3/5*k**3 + 3/5*k**5 + 3/5*k**2 + 0*k - 3/5*k**4 + 0.
3*k**2*(k - 1)**2*(k + 1)/5
Suppose -5*a = f - 3*f - 42, 4*a = 4*f + 24. Let j = a - 29/3. Factor -1/3*w**3 + 1/3*w + j*w**2 - 1/3*w**4 + 0.
-w*(w - 1)*(w + 1)**2/3
Let j be 3/6*6 - 0. Factor -3*k + 0 + j*k**2 + 1 - 4 - 3.
3*(k - 2)*(k + 1)
Find x such that -2*x**3 + 0 - 22/5*x**2 - 4/5*x = 0.
-2, -1/5, 0
Let f(s) be the second derivative of -3*s**5/20 - s**4/4 + s**3/2 + 3*s**2/2 - 15*s. Let f(j) = 0. Calculate j.
-1, 1
Let b be (-2)/(-11) - 168/(-44). Factor -o**5 - 59*o - 2*o**3 + 59*o - o**5 + 4*o**b.
-2*o**3*(o - 1)**2
Factor -k**2 - 1/2*k**5 - 2*k**3 + 2*k**4 - 1 + 5/2*k.
-(k - 2)*(k - 1)**3*(k + 1)/2
Determine g, given that 0*g + 0 - 1/3*g**3 - 2/3*g**2 = 0.
-2, 0
Let s(q) = 2*q - 28. Let c be s(15). Factor 0 - 1/2*u**4 - 3/2*u**c - 3/2*u**3 - 1/2*u.
-u*(u + 1)**3/2
Let g = 65 - 65. Suppose -2/3*t**4 + 0*t + 0*t**3 + g*t**2 + 0 = 0. What is t?
0
Let f(d) be the third derivative of -1/24*d**5 + 0*d - 1/80*d**6 + 0*d**3 - 1/48*d**4 + 1/168*d**8 - d**2 + 1/84*d**7 + 0. Find y such that f(y) = 0.
-1, -1/4, 0, 1
Suppose -6 = -3*f - 0*f. Let i(j) be the first derivative of -1/4*j**4 - 5/6*j**2 - 1/3*j - 7/9*j**3 - f. Factor i(s).
-(s + 1)**2*(3*s + 1)/3
Suppose -3*s = i - 8, 3*s = i - 3*i + 22. Factor -i*g**2 - 8*g - 4*g**3 + 6*g**3 - 2*g**2 + 8*g**3.
2*g*(g - 2)*(5*g + 2)
Let w = -27 + 27. Suppose n + 4*n = w. What is b in -2/5*b + 2/5*b**2 + n = 0?
0, 1
Let x(n) be the first derivative of n**7/1155 + n**6/165 + 2*n**5/165 + n**2/2 + 5. Let w(a) be the second derivative of x(a). Factor w(j).
2*j**2*(j + 2)**2/11
Let x(q) = -6*q**4 - 7*q**3 + 3*q**2 + 8*q - 1. Let f(g) = 5*g**4 + 6*g**3 - 3*g**2 - 8*g. Let m(j) = 5*f(j) + 4*x(j). Solve m(b) = 0 for b.
-2, -1, 2
Let v(r) be the first derivative of -1/13*r**2 + 1/26*r**4 - 4 - 4/39*r**3 + 4/13*r. Factor v(o).
2*(o - 2)*(o - 1)*(o + 1)/13
Let w be -8 - -9 - -1*(-4)/(-4). Factor h + 1/6*h**w + 3/2.
(h + 3)**2/6
Let b(v) be the third derivative of 0 + 0*v**4 + 0*v + 4/105*v**7 + 1/60*v**5 + 1/96*v**8 - v**2 + 11/240*v**6 + 0*v**3. Factor b(y).
y**2*(y + 1)**2*(7*y + 2)/2
Suppose 0 = 5*d + 5*g - 5, 0 - 5 = -5*g. Factor 0 + 2/7*u**4 + 3/7*u**3 - 1/7*u + d*u**2.
u*(u + 1)**2*(2*u - 1)/7
Let l be (-444)/220 + 2 + 4/20. Let -2/11*i**4 + 0 - l*i**2 + 0*i - 4/11*i**3 = 0. Calculate i.
-1, 0
Let c = 1/405 - -629/405. Determine s so that 0 + 4/9*s - 10/9