 - 7. What is b in -1/4*b**4 + 0*b + 0 + 0*b**2 - 1/4*b**k = 0?
-1, 0
Factor 10*b**2 - 4*b**2 + 2*b**3 + 18*b - 14*b.
2*b*(b + 1)*(b + 2)
Solve -1/2*k**3 - 3/8*k**5 + 0 - k**2 + 0*k + 5/4*k**4 = 0.
-2/3, 0, 2
Determine h so that 0 + 0*h**2 - 4/5*h + 1/5*h**3 = 0.
-2, 0, 2
Let b(s) = -s**3 - s**2. Let p(t) = 5*t**3 + 12*t**2 - 5*t. Let g(u) = 6*b(u) + p(u). Factor g(y).
-y*(y - 5)*(y - 1)
Let w = 1 + 4. Let u(m) be the first derivative of 5*m**4 + 2*m + w*m**2 + 1/3*m**6 + 20/3*m**3 + 2 + 2*m**5. Factor u(g).
2*(g + 1)**5
Let l(g) be the third derivative of -g**7/70 + 7*g**6/120 - g**5/20 - g**4/8 + g**3/3 + 14*g**2. Factor l(a).
-(a - 1)**3*(3*a + 2)
Let h(u) = -u - 3. Let w be h(-4). Let z(x) = -4*x**3 + 10*x**2 - 14*x + 6. Let v(t) = -7 - t**3 - 2 + t + 8 + 0*t**3. Let c(j) = w*z(j) - 2*v(j). Factor c(y).
-2*(y - 2)**2*(y - 1)
Let p(f) = -13*f**3 - 12*f**2. Let z(d) = 25*d**3 + 25*d**2. Let x(q) = 5*p(q) + 2*z(q). Factor x(k).
-5*k**2*(3*k + 2)
Let b(q) = -q**4 + q**3 - q**2 + q. Let k(c) = -8*c**4 + 6*c**3 - 10*c**2 + 14*c - 2. Let l(j) = 10*b(j) - k(j). Factor l(w).
-2*(w - 1)**3*(w + 1)
Let s(b) be the first derivative of -1/3*b**4 - b**2 - 2/5*b**5 + 4/3*b**3 + 1/5*b**6 + 2 - b. Let p(u) be the first derivative of s(u). Solve p(m) = 0 for m.
-1, 1/3, 1
Let i(l) be the first derivative of 6*l**6/7 + 12*l**5/7 + 33*l**4/28 + 2*l**3/7 + 2. Suppose i(t) = 0. Calculate t.
-2/3, -1/2, 0
Determine v, given that -1/4*v - 1/4*v**3 + 1/2*v**2 + 0 = 0.
0, 1
Let f(m) be the second derivative of -m**4/30 + m**3/15 + 6*m**2/5 - 2*m - 33. Determine g, given that f(g) = 0.
-2, 3
Let h(m) be the first derivative of -m**3/9 - 5*m**2/6 - 18. Suppose h(p) = 0. Calculate p.
-5, 0
Let q(k) be the third derivative of 0*k**4 + 5*k**2 + 1/30*k**3 + 0 - 1/300*k**5 + 0*k. Factor q(c).
-(c - 1)*(c + 1)/5
Let x = -837 - -5865/7. Solve 2/7*a**3 - 2/7*a**4 + 4/7 + x*a**2 - 10/7*a = 0 for a.
-2, 1
Let o be 1 - 2*3/(-6). Let s(b) be the third derivative of 1/480*b**6 + 0*b**5 - o*b**2 + 0 + 0*b**3 + 0*b - 1/96*b**4. Factor s(t).
t*(t - 1)*(t + 1)/4
Let l(f) be the second derivative of 1/1080*f**6 - 1/2*f**3 + 0*f**4 + 1/360*f**5 + 3*f + 0 + 0*f**2. Let x(i) be the second derivative of l(i). Factor x(j).
j*(j + 1)/3
Let a(w) be the second derivative of w**6/6 - 2*w**5 + 15*w**4/2 - 135*w**2/2 + 14*w. Factor a(o).
5*(o - 3)**3*(o + 1)
Let k(o) be the third derivative of 1/300*o**5 + 2/15*o**3 + 1/30*o**4 + 0*o + 3*o**2 + 0. Let k(v) = 0. What is v?
-2
Determine r so that 7/4*r**5 + 9/4*r**2 - 1/2*r - 5/4*r**3 + 0 - 9/4*r**4 = 0.
-1, 0, 2/7, 1
Let b(h) = -10 - 8*h**2 - h**3 + 7 + 8*h - 4. Let i be b(-9). Determine p so that 5*p**i + 4/3 - 5/3*p**4 + 2/3*p**3 - 16/3*p = 0.
-2, 2/5, 1
Let y(q) be the first derivative of -27*q + 1/4*q**4 - 1 + 27/2*q**2 - 3*q**3. Factor y(f).
(f - 3)**3
Let b = 866/91 + -120/13. Let u(m) be the first derivative of -2/7*m**2 - 2 - 2/21*m**3 - b*m. What is r in u(r) = 0?
-1
Let m be 14/(-10)*(-544)/112. Factor m*t + 32/5*t**3 + 16*t**2 + 4/5.
2*(t + 2)*(4*t + 1)**2/5
Suppose 0 = 3*g + 3 - 12. Factor -k**2 - 2*k**2 + k**2 - g*k - k.
-2*k*(k + 2)
Let j = 103 + -100. Factor 0 + 4/3*z + 4/3*z**2 - z**j.
-z*(z - 2)*(3*z + 2)/3
Let 0*m**2 + 51*m**3 - 37*m**3 - 4*m**2 = 0. Calculate m.
0, 2/7
Let d be -1 + 4 - (39/15 + 0). Factor -4/5*b**2 + 2/5*b**4 + 2/5*b**5 + 2/5 - 4/5*b**3 + d*b.
2*(b - 1)**2*(b + 1)**3/5
Let c(l) be the second derivative of l**5/8 + 7*l**4/24 + l**3/6 - 4*l + 1. Determine t, given that c(t) = 0.
-1, -2/5, 0
Let j = 36 - 36. Suppose j*f - 1/3*f**2 + 1/3 = 0. What is f?
-1, 1
Let q(t) = t**3 + 3*t**2 - 7*t - 12. Let f be q(-4). Let -2/3*j**3 + 4/3 + f*j**2 + 2*j = 0. Calculate j.
-1, 2
Let x(l) be the third derivative of -l**8/112 + 2*l**7/105 + l**6/120 - l**5/30 - 9*l**2. Solve x(u) = 0 for u.
-2/3, 0, 1
Let r(i) be the second derivative of i**7/8820 - i**5/420 - i**4/6 - i. Let c(q) be the third derivative of r(q). Factor c(y).
2*(y - 1)*(y + 1)/7
Solve 0*n**2 + 2/3*n**3 + 0*n + 0 = 0.
0
Let s be ((-12)/(-63)*-3)/(2/(-7)). Factor -1/4*z + 1/2 - 1/4*z**s.
-(z - 1)*(z + 2)/4
Factor 4/3*i**3 - 4/3*i**2 + 0 + 0*i.
4*i**2*(i - 1)/3
Let g(u) be the second derivative of 1/135*u**6 + 1/54*u**4 + 1/45*u**5 + 0*u**3 + 0*u**2 - 3*u + 0. Factor g(d).
2*d**2*(d + 1)**2/9
Let t be 4/2 + (1 - 1). What is v in -t*v**2 - 3*v - 2*v - 2 + v = 0?
-1
Determine w so that -2/5*w + 2/5*w**2 - 2/5 + 2/5*w**3 = 0.
-1, 1
Determine f so that -2*f**2 + 8*f**4 - 5*f**2 - 4*f - f**2 + 4*f**5 = 0.
-1, 0, 1
Let o(u) be the first derivative of 0*u**2 + 0*u**3 + 3/5*u**5 + 7 + 3/4*u**4 + 0*u. Factor o(j).
3*j**3*(j + 1)
Let c(x) be the second derivative of -x**5/60 + x**4/36 + 5*x**3/18 + x**2/2 + 19*x. Factor c(k).
-(k - 3)*(k + 1)**2/3
Factor 12/11*v**2 - 14/11*v**3 + 0 - 6/11*v**4 + 0*v.
-2*v**2*(v + 3)*(3*v - 2)/11
Let u(p) = -p**2 - 5*p - 1. Let t be u(-4). Suppose 7*y - 8 = t*y. Determine r, given that 24*r - 2 - 18*r - 7 + 3*r**y = 0.
-3, 1
Let l be (-4)/(-2) + -1*5. Let k = 0 - l. Factor 4 - j - j**5 + 2*j**2 - 4*j**2 + j**4 - 3 + 2*j**k.
-(j - 1)**3*(j + 1)**2
Let p be 15/10*18/81. Find n such that 4/3 + p*n**2 + 4/3*n = 0.
-2
Let n be (7 + -1)*3/24*4. Let g be 1/(-4) - 2/(-8). Factor -5*d**3 - d**2 + g*d**2 - 2 + 3*d**2 - 2*d + 7*d**n.
2*(d - 1)*(d + 1)**2
Let 0 + 0*b - 27/5*b**3 - 12/5*b**2 - 18/5*b**4 - 3/5*b**5 = 0. Calculate b.
-4, -1, 0
Let w = 358 - 356. Find n, given that 0 + 0*n - 2/7*n**w = 0.
0
Let u(o) = o**4 - o**2 - o + 1. Let z(w) = -w**5 + 4*w**3 - 5*w + 2. Let k(i) = -6*u(i) + 3*z(i). Suppose k(s) = 0. Calculate s.
-3, -1, 0, 1
Let a(k) be the first derivative of k**7/840 - k**6/160 + k**5/240 + k**4/32 - k**3/12 + 7*k**2/2 + 7. Let m(z) be the second derivative of a(z). Factor m(c).
(c - 2)*(c - 1)**2*(c + 1)/4
Let y be (-1)/4 - (-125)/20. Let m(g) be the third derivative of g**2 - 1/6*g**4 + 0 + 5/96*g**y - 1/6*g**3 - 1/48*g**5 + 0*g. Factor m(f).
(f - 1)*(5*f + 2)**2/4
Let i(d) = 2*d**2 - 2*d - 4. Let b(a) = -9 - 2*a**2 - a**2 + 7*a**2 - 5*a. Let f(q) = -2*b(q) + 5*i(q). Let f(c) = 0. Calculate c.
-1, 1
Let b(w) be the third derivative of w**8/560 + w**7/56 + w**6/15 + w**5/10 + w**3/2 - 2*w**2. Let g(p) be the first derivative of b(p). Factor g(l).
3*l*(l + 1)*(l + 2)**2
Let z be 17/5 - (-30)/50. Let t(i) be the first derivative of 2/3*i**3 + 1/4*i**z + 1 - 2*i - 1/2*i**2. Factor t(k).
(k - 1)*(k + 1)*(k + 2)
Suppose 66 - 18 = 16*k. Let 4/5*a**2 - 4/5*a**4 + 2/5*a + 0 - 2/5*a**k = 0. Calculate a.
-1, -1/2, 0, 1
Solve 2 + 0 + 14*v**3 + 4*v**2 + 6*v**4 + 9*v + 12*v**2 + v**5 = 0.
-2, -1
Let d(p) be the first derivative of 2*p**3/15 + 4*p**2/5 + 14. Factor d(x).
2*x*(x + 4)/5
Suppose 4 = 2*c - 0*c. Find b, given that 1/4*b**c + 9/4 + 3/2*b = 0.
-3
Factor 2/9*t**3 + 0*t**2 - 2/3*t + 4/9.
2*(t - 1)**2*(t + 2)/9
Let p(s) be the third derivative of s**8/168 + s**7/35 + s**6/20 + s**5/30 - s**2. Let p(y) = 0. What is y?
-1, 0
Let t = 70 + -49. Suppose 0 = 2*h - 3*d - t, -2*h - 5*d - 31 = -4*h. Suppose -h*m**4 - 6*m**4 - m**3 + 4*m**3 + 6*m**2 = 0. What is m?
-2/3, 0, 1
Let v(s) be the third derivative of s**6/280 + s**5/140 - s**4/28 + 2*s**2. Factor v(h).
3*h*(h - 1)*(h + 2)/7
Let j(g) = 5*g**4 - 2*g**3 - 4*g**2 + 2*g - 1. Let f(x) = -x**2 + x**3 - x**4 + 2*x**4 - x + 0*x**4 + 0*x**3. Let v(w) = 2*f(w) - j(w). Factor v(s).
-(s - 1)**2*(s + 1)*(3*s - 1)
Let l(h) = -h**3 + 13*h**2 + 32*h - 22. Let p be l(15). Let r be ((-5)/(-3))/(2/6). Factor -r - u**2 + 1 + 0 - 2*u**2 + p*u.
-(u - 2)*(3*u - 2)
Let s(v) = -v**3 - 14*v**2 - 14*v - 11. Let l be s(-13). Let u(n) be the first derivative of 0*n**3 + 9/4*n**2 + 3*n - 3/8*n**4 - l. What is h in u(h) = 0?
-1, 2
Let n(r) = -r**3 - 6*r**2 - r - 4. Let l be n(-6). Let o(k) be the first derivative of -4/5*k**l - 2/5*k + 2/5*k**4 + 2 + 2/15*k**3. Factor o(f).
2*(f - 1)*(f + 1)*(4*f + 1)/5
Suppose 2*w - 2 = -0*w. Suppose -4 = -2*j + 2*k, -4 + w = -3*j + 4*k. Find c such that 6*c**2 + j*c - 2*c**4 + 5*c**5 + 1 - 10*c**3 - 2*c**2 - 3 = 0.
-1, 2/5, 1
Let t(h) be the second derivative of 0 + 0*h**3 + 1/10*h**2 - 2*h - 1/60*h**4. Factor t(v).
-(v - 1)*(v + 1)/5
Let a(k) = -11*k**4 - 17*k**3 + 5*k**2 + 12*k + 11. Let i(p) = 17*p**4 + 26*p**3 - 8*p**2 - 18*p - 17. Let b(r) = 8*a(r) + 5*i(r). Factor b(d).
-