he second derivative of -j**4/54 - j**3/9 - 2*j**2/9 - j. Factor w(b).
-2*(b + 1)*(b + 2)/9
Let y(b) be the first derivative of b**6/18 + b**5/15 - b**4/4 - 5*b**3/9 - b**2/3 + 1. Find n such that y(n) = 0.
-1, 0, 2
Let i be 2*3*(-2)/(-3). Let n be 5/(100/(-8)) - 27/(-5). Determine v so that -11/4*v + 1/2 + 6*v**2 - 13/2*v**3 + 7/2*v**i - 3/4*v**n = 0.
2/3, 1
Let a = 87/4 - 21. Factor -3/2*i + a*i**2 + 0 + 3/4*i**3.
3*i*(i - 1)*(i + 2)/4
Factor 9/4 - 3/8*m**2 + 15/8*m.
-3*(m - 6)*(m + 1)/8
Let b = 9 - 4. Suppose -14 - 11 = -b*o. Suppose 2*k**2 + o + 15 - 2 - 15*k + 3*k = 0. Calculate k.
3
Factor -4*s + 4 + 9*s**2 - s**3 - 4*s**2 + 0*s**3 - 4*s.
-(s - 2)**2*(s - 1)
Let p be (-5)/(-1) + (9 - 11). Factor -3*x**2 + p*x**2 - x**2 - 2*x - 1.
-(x + 1)**2
Find x, given that -45*x**2 + 45*x**2 + 4*x**5 = 0.
0
Determine l so that 1/9*l**2 + 5/3*l + 0 = 0.
-15, 0
Factor 31*j**2 - 14*j**2 - 19*j**2 - 4*j + 2*j.
-2*j*(j + 1)
Let m be (415/(-60) - -4) + 3. Let c(z) be the first derivative of -1/3*z**5 - 2/9*z**6 + 0*z**3 - 2 + 0*z**2 - m*z**4 + 0*z. Find a such that c(a) = 0.
-1, -1/4, 0
Let s(z) = -7*z**3 - 10*z**2 - 26*z - 26. Let m(c) = c**3 - c - 1. Let p(j) = 6*m(j) + s(j). Suppose p(u) = 0. What is u?
-4, -2
Let g(n) be the third derivative of -n**7/735 + n**6/210 - n**4/42 + n**3/21 + 9*n**2. Factor g(o).
-2*(o - 1)**3*(o + 1)/7
Let p be ((-749)/(-126) + -6)*(-4 + 0). Find y such that 4/9 - p*y**2 - 2/9*y = 0.
-2, 1
Suppose 0 = 3*f - f. Let g = 0 - f. Factor -2*h**3 + 4*h**2 - 2*h**2 - 6*h**2 + g*h**2.
-2*h**2*(h + 2)
What is w in -2/3 + 2*w**4 - 4/3*w**2 - 2*w + 4/3*w**3 + 2/3*w**5 = 0?
-1, 1
Suppose 11 = 4*a - 1. Let y = a + -1. Determine x, given that -9*x + x + 3*x**2 + 8 - x**y = 0.
2
Let t(n) be the third derivative of -5*n**8/3192 + 2*n**7/1995 + n**6/228 - n**5/285 + 12*n**2. Solve t(s) = 0 for s.
-1, 0, 2/5, 1
Let h(p) be the third derivative of 0*p**3 + 1/30*p**5 + 0*p - 1/168*p**8 + 1/60*p**6 + 0 - 1/105*p**7 - p**2 + 0*p**4. Determine m, given that h(m) = 0.
-1, 0, 1
Let w(a) = -3*a**2 + 8*a**2 - 3*a**3 - 6 - 2*a**3. Let t(y) = -3*y + 1. Let u be t(4). Let g(h) = 9*h**3 - 9*h**2 + 11. Let q(r) = u*w(r) - 6*g(r). Factor q(v).
v**2*(v - 1)
Determine s, given that -1/7*s**3 + 0 + 5/7*s**2 - 3/7*s - 1/7*s**4 = 0.
-3, 0, 1
Suppose -2*f + 27 = -63. Let j be -12*(-4 - f/(-12)). Factor 0*a**2 - 2/11*a**j + 6/11*a - 4/11.
-2*(a - 1)**2*(a + 2)/11
Let w(i) be the third derivative of -i**2 + 0 + 0*i + 1/3*i**3 - 1/30*i**5 + 1/12*i**4 + 1/180*i**6. Let q(s) be the first derivative of w(s). Factor q(x).
2*(x - 1)**2
Let p(a) be the third derivative of 0 + 1/10*a**5 + 0*a - 1/20*a**6 + 1/105*a**7 + 2*a**2 + 0*a**3 - 1/12*a**4. Find z, given that p(z) = 0.
0, 1
Let z(x) be the first derivative of -x**7/4200 + x**6/1800 + x**5/600 - x**4/120 + 2*x**3/3 - 1. Let h(i) be the third derivative of z(i). Solve h(f) = 0.
-1, 1
Let g be (-684)/(-48) + (-2)/8. Let a(v) = v**3 + 29*v**2 - 13*v - 7. Let k(z) = z**3 + 14*z**2 - 6*z - 3. Let m(d) = g*k(d) - 6*a(d). Solve m(s) = 0 for s.
-3, 0, 1/4
What is d in 7/2*d**3 + 1/2*d**5 + 0 + 5/2*d**4 + 3/2*d**2 + 0*d = 0?
-3, -1, 0
Let n(a) be the first derivative of 2*a**7/525 + a**6/150 - 2*a**5/75 + 7*a**2/2 + 1. Let c(t) be the second derivative of n(t). Factor c(r).
4*r**2*(r - 1)*(r + 2)/5
Let k = -1/124 + -485/1364. Let y = k - -23/33. Factor 0 + y*v**3 + 1/3*v**4 - 1/3*v**2 - 1/3*v.
v*(v - 1)*(v + 1)**2/3
Let b(q) be the first derivative of -2*q**5/35 - q**4/7 - 2*q**3/21 + 4. Factor b(m).
-2*m**2*(m + 1)**2/7
What is b in 98/11 + 34/11*b**4 + 2/11*b**5 + 380/11*b**2 + 188/11*b**3 + 322/11*b = 0?
-7, -1
Determine n, given that 0*n**3 + 0 + 0*n**2 + 2/5*n**4 + 0*n + 2/5*n**5 = 0.
-1, 0
Determine p, given that 5*p**2 + 20 + 25*p + 7*p**2 - 7*p**2 = 0.
-4, -1
Let d(r) = r + 21. Let o(b) = -b**3 - 6*b**2 + 11*b + 9. Let z be o(-7). Let c be d(z). Let -11/2*k - 4*k**3 - 9*k**2 - 1 + 3/2*k**5 + c*k**4 = 0. Calculate k.
-1, -1/3, 2
Let c(m) = m**3 + 19*m**2 + 16*m - 33. Let h be c(-18). Factor 0 + 0*f**h - 1/3*f**4 + 0*f + 1/3*f**2.
-f**2*(f - 1)*(f + 1)/3
Factor 3*z**4 - 2*z**3 - 22*z - 18*z**2 - 8 - z**4 + 0*z**4.
2*(z - 4)*(z + 1)**3
Factor -6*u**2 + 4 - 8*u**2 - 32*u + 22*u.
-2*(u + 1)*(7*u - 2)
Let q = 1355/1796 - 2/449. Suppose s - 3*m - 1 = -3*s, 10 = 5*s - 2*m. Factor 0 - q*t**s - 1/4*t**3 + t**5 + 0*t**2 + 0*t.
t**3*(t - 1)*(4*t + 1)/4
Let b(k) be the third derivative of -k**7/2268 + k**6/405 + k**5/135 - k**4/24 - 4*k**2. Let y(x) be the second derivative of b(x). Factor y(w).
-2*(w - 2)*(5*w + 2)/9
Suppose -20 = -2*j - j + h, -3*h = -2*j + 11. Factor -3*r**3 - 6*r**2 - 7*r + j*r.
-3*r**2*(r + 2)
Let l be (-9)/(-30)*2/9. Let a(n) be the third derivative of -n**2 + 1/30*n**4 + 1/150*n**5 + 0 + l*n**3 + 0*n. Factor a(k).
2*(k + 1)**2/5
Let q(p) be the second derivative of p**8/672 - p**6/240 - 3*p**2/2 + 3*p. Let o(m) be the first derivative of q(m). Find h such that o(h) = 0.
-1, 0, 1
Let x = 5 + -1. Let f(q) be the second derivative of -2*q + 0*q**3 - 3/40*q**5 - 1/20*q**6 - 1/84*q**7 + 0*q**2 + 0 - 1/24*q**x. Solve f(y) = 0 for y.
-1, 0
Suppose -4*v = -2*d, 20*d - 19*d - 5 = -3*v. What is r in 40/9*r**d + 2/3*r**3 - 140/9*r**4 + 0 - 98/9*r**5 - 8/9*r = 0?
-1, 0, 2/7
Let u = 3 - -2. Let q(i) be the third derivative of 2*i**2 + 0 + 1/600*i**6 + 1/120*i**4 - 1/150*i**u + 0*i + 0*i**3. Factor q(h).
h*(h - 1)**2/5
Let h(n) = -3*n - 3. Let r be h(-2). Suppose 2*z + r*z = 0. Factor q**3 + 8*q + q**3 - 8*q**2 + z*q**2.
2*q*(q - 2)**2
Let k be (-3)/((-5 + 23)*(-1)/4). Factor -k*i**3 + 2/3*i**2 + 2/9*i**4 - 2/9*i + 0.
2*i*(i - 1)**3/9
Let a be 80/(-32)*((-273)/75 - -3). Determine n so that -4/5*n + 1/5*n**5 + 1/5*n**3 - a + 2*n**2 - 4/5*n**4 = 0.
-1, 2
Let p be 2/((3/(-6))/(-1)). Find w, given that -4*w**3 - 2/5*w**5 - 2*w**p - 2/5 - 2*w - 4*w**2 = 0.
-1
Let l(c) = -c**3 - 10*c**2 - 9*c + 5. Let j be l(-9). Let o = 7 - j. What is u in -u + o + u + 2*u + u**2 - 5*u = 0?
1, 2
Let w = -60 + 64. Let p(h) be the second derivative of 3*h + 0*h**3 - 1/24*h**w + 0 + 7/80*h**5 - 1/24*h**6 + 0*h**2. Factor p(f).
-f**2*(f - 1)*(5*f - 2)/4
Let u(f) be the third derivative of -f**5/20 + 5*f**4/4 - 25*f**3/2 + f**2. Suppose u(d) = 0. What is d?
5
Let o(g) = -4*g**2 + 6*g - 5. Let h = -11 + 15. Let p(t) = 3*t**2 - 5*t + 4. Let r(z) = h*o(z) + 5*p(z). Factor r(k).
-k*(k + 1)
Suppose -3 = z + 2*h + 1, 2*z + h - 1 = 0. Let u = -3 - -12. Suppose 13*s**3 - 9*s**2 - 4*s**4 + u*s - 6*s**z - 2*s - 1 = 0. What is s?
1/4, 1
Suppose 3*p = 4*r + 26, -5*r - 12 = p + 11. Suppose 8/5*t**3 - 8/5*t**5 + 2/5*t**4 + 0 + 0*t - 2/5*t**p = 0. What is t?
-1, 0, 1/4, 1
Suppose 1/4*c**2 + 3/4 - c = 0. What is c?
1, 3
Let i(d) be the first derivative of d**6/36 - d**5/15 + d**3/9 - d**2/12 - 35. Solve i(l) = 0 for l.
-1, 0, 1
Determine g so that -7*g + 3*g + 581*g**2 - 577*g**2 - 24 = 0.
-2, 3
Suppose 72*t - 77*t + 15 = 0. Find i, given that 1/6*i**t + 0 - 1/6*i**2 + 0*i = 0.
0, 1
Let s = -878/9 - -98. What is k in 2/3*k - 4/9*k**3 + s - 2/3*k**2 = 0?
-2, -1/2, 1
Suppose 0 = 8*x - 10*x. Let j(z) be the third derivative of 2*z**2 + 1/30*z**5 + x + 1/3*z**3 - 1/6*z**4 + 0*z. Solve j(m) = 0 for m.
1
Let z = 1 - -1. Let i = 11702/8781 + 2/2927. Find p, given that -i*p**z - 16/9 + 2*p**3 - 40/9*p = 0.
-2/3, 2
Let b be (-26)/(-7) - (-6)/21. Factor 7*s**4 - 4*s - 9*s**b + 5*s**3 + 2 - s**3.
-2*(s - 1)**3*(s + 1)
Let -3/4*f**3 + 3/4*f + 0 + 0*f**2 = 0. What is f?
-1, 0, 1
Factor -4*b**2 - 43*b + 59*b + 0 - 12.
-4*(b - 3)*(b - 1)
Suppose -b + 6 = 1. Determine h so that 4 - 8*h**2 + 14*h + 20*h**5 + 4*h**4 - 28*h**3 - 6*h**b + 0 = 0.
-1, -2/7, 1
Factor 4/5*i + 0 + 0*i**3 - 2/5*i**4 + 6/5*i**2.
-2*i*(i - 2)*(i + 1)**2/5
Let l(d) be the third derivative of -d**7/231 + d**6/220 + 7*d**5/330 - d**4/44 - 2*d**3/33 + 11*d**2. Find k such that l(k) = 0.
-1, -2/5, 1
Let i(u) be the first derivative of 4/35*u**5 + 3/14*u**2 + 1/4*u**4 + 1 - 2/3*u**3 + 0*u. Factor i(d).
d*(d - 1)*(d + 3)*(4*d - 1)/7
Suppose 2*r + 11 + 1 = 0. Let i be (50/r)/((-14)/21). Suppose 15*o**4 + 2*o + 0 + i*o**5 - 6*o**2 - 11/2*o**3 = 0. Calculate o.
-1, 0, 2/5
Let k(i) = i + 1. Let c(s) = 2*s - 1 - 2*s**2 + 1 + 0*s**2 + 2. Let a(z) = c(z) - 2*k(z). Find u such that a(u) = 0.
0
Factor 3/4 + 1/4*k**2 +