s**j + 0*s**2 + s**4. Suppose r(p) = 0. Calculate p.
-1, 0
Let q(b) be the second derivative of b**4/36 + 26*b**3/9 - 18*b**2 - 9*b + 25. Find r such that q(r) = 0.
-54, 2
Let l = -49 - -53. Factor -125*h**3 + 20*h**l + 6*h**2 - 35 - 45*h + 35 + 204*h**2.
5*h*(h - 3)**2*(4*h - 1)
Solve -6/5*p**2 - 2*p**3 + 26/5*p + 2/5*p**4 + 4 = 0 for p.
-1, 2, 5
Let g(h) = h**2 + 10*h + 2. Let n be g(-12). Suppose -86 = -12*y - n. Solve y + 5/4*t**2 + 5*t = 0.
-2
Suppose -i + 3*y + 4 = -2*i, 4*y = 3*i - 14. What is l in 4*l**3 - 13*l**2 + 5*l**3 + 17*l**i = 0?
-4/9, 0
Let m = -4430/357 - -662/51. Factor 1/7*r**4 - 3/7*r**2 - m - 8/7*r + 2/7*r**3.
(r - 2)*(r + 1)**2*(r + 2)/7
Let n(m) = m**3 - 44*m**2 + 421*m - 11. Let b be n(14). Find q, given that 8/11*q**2 + 6/11*q + 0 - 14/11*q**b = 0.
-3/7, 0, 1
Let w(v) be the second derivative of -28*v + 0 + 1/20*v**5 + 0*v**2 - 1/3*v**3 - 1/10*v**6 + 1/4*v**4 + 1/42*v**7. Factor w(c).
c*(c - 2)*(c - 1)**2*(c + 1)
Let t(d) = d**3 + 4*d**2 + d - 8. Let i be t(2). Factor 128*c**3 + 308*c**4 + 16*c**5 + 180*c**5 - 2*c**2 + i*c**2.
4*c**2*(c + 1)*(7*c + 2)**2
Find t, given that -36*t**3 + 10*t**2 + 41*t**3 + 0*t**2 = 0.
-2, 0
Let h(u) be the second derivative of -189*u**5/20 - 185*u**4/4 + 8*u**3 + 18*u**2 + 63*u. What is q in h(q) = 0?
-3, -2/9, 2/7
Solve 2/9*b**3 + 2/3*b**2 - 2/9*b - 2/3 = 0.
-3, -1, 1
Let h(y) be the first derivative of -y**4/2 - 20*y**3/3 - 33*y**2 - 72*y + 198. Solve h(u) = 0.
-4, -3
Let y(j) be the first derivative of 2*j**2 - j**4 - 2/5*j**5 + 0*j**3 - 6 + 2*j. Let y(m) = 0. What is m?
-1, 1
Let h = -5 + 5. Let r(m) be the third derivative of -1/15*m**5 + h + 0*m - 1/3*m**4 - 3*m**2 - 2/3*m**3. Factor r(g).
-4*(g + 1)**2
Let q(n) be the first derivative of -1/6*n**6 + 0*n**2 + 1/5*n**5 + 0*n + 43 + n**4 - 4/3*n**3. Suppose q(k) = 0. What is k?
-2, 0, 1, 2
Let o(g) be the third derivative of g**7/35 - 2*g**6/15 - 17*g**5/30 + g**4/6 + 8*g**3/3 + 125*g**2. Factor o(d).
2*(d - 4)*(d + 1)**2*(3*d - 2)
Suppose 13 + 7 = 4*h. Suppose -5*z = 5*s, h*z + 2 + 4 = s. Factor -14*j**2 + 3 - 2*j**3 + 6*j + s - 4*j**3 + 2*j**4 + 8*j**4.
2*(j - 1)**2*(j + 1)*(5*j + 2)
Factor -189/2*t + 255/2 - 6*t**2.
-3*(t + 17)*(4*t - 5)/2
Let k(w) be the third derivative of -w**8/6720 + w**6/60 - 23*w**5/60 - 9*w**2. Let q(d) be the third derivative of k(d). Factor q(y).
-3*(y - 2)*(y + 2)
Let i(c) = -c**2 - c. Let y(t) be the second derivative of 2/3*t**3 + 0*t**2 + 6*t + 1/4*t**4 + 0. Let s(u) = -2*i(u) - y(u). Factor s(p).
-p*(p + 2)
Let q = -656 - -659. Let r(i) be the third derivative of 0*i - 1/1020*i**6 + 8/51*i**q + 1/85*i**5 - 1/17*i**4 + 5*i**2 + 0. Factor r(f).
-2*(f - 2)**3/17
Let -39*x + 19*x - 1 + 3*x**4 - x**5 - 2*x**3 - 2*x**2 + 23*x = 0. Calculate x.
-1, 1
Let m(b) = -b**3 - b**2 - 2*b. Let p be m(0). Let h be 1 - ((0 - 0 - 2) + p). Factor 0 + 0*t + 22/7*t**h + 2*t**5 - 32/7*t**4 - 4/7*t**2.
2*t**2*(t - 1)**2*(7*t - 2)/7
Suppose -65*n**2 + 320*n**3 - 256*n - 83 - 100*n**4 + 19 - 31*n**2 = 0. What is n?
-2/5, 2
Let p be ((-9)/(-6))/3*18. Factor -97*m**2 + 94*m**2 + 3*m**3 - p*m**3 - 3*m**4.
-3*m**2*(m + 1)**2
Let a(l) = l**3 - 19*l**2 - 70*l + 88. Let o be a(22). Factor -1/2*r**2 + 1/4*r**5 + o*r - r**4 + 0 + 5/4*r**3.
r**2*(r - 2)*(r - 1)**2/4
Let y(l) be the first derivative of 0*l + 14 - 2/3*l**6 - 3*l**4 + 8*l**2 - 16/5*l**5 + 16/3*l**3. Find c, given that y(c) = 0.
-2, -1, 0, 1
Let i(x) be the second derivative of -2*x**7/105 + x**6/30 + x**5/3 + x**4/2 - 11*x**2/2 - 23*x. Let v(a) be the first derivative of i(a). Factor v(o).
-4*o*(o - 3)*(o + 1)**2
Suppose -49/3*p**4 + 0 + 47*p**3 + 46/3*p + 1/3*p**5 - 139/3*p**2 = 0. What is p?
0, 1, 46
Let g(c) = -22*c**2 + 342*c + 340. Let a(d) = 25*d**2 - 343*d - 340. Let p(v) = -6*a(v) - 7*g(v). Let p(k) = 0. Calculate k.
-1, 85
Let t(r) = 2*r**2 - r - 1. Let m(x) = 5*x**2 + 10*x + 33. Let a(h) = -2*m(h) + 4*t(h). Factor a(c).
-2*(c + 5)*(c + 7)
Find g, given that -2/3*g**3 + 0*g**2 + 2/3*g + 0 = 0.
-1, 0, 1
Let i = 72/61 + 533/427. Factor 5/7*z**5 - i*z**4 + 3*z**3 - 11/7*z**2 + 2/7*z + 0.
z*(z - 1)**3*(5*z - 2)/7
Let i(r) be the second derivative of -r**6/20 - 3*r**5/8 - r**4/2 + 226*r. Factor i(x).
-3*x**2*(x + 1)*(x + 4)/2
Let a be 18 + 0 + (-5 - -7). Let j be 84/a - 2/10. Let f**2 - f**j + 4*f**4 - 6*f + 6*f**3 - 4*f**2 = 0. What is f?
-2, -1, 0, 1
Let w(d) be the second derivative of d**6/15 + 7*d**5/10 - 19*d**4/6 - 7*d**3/3 + 18*d**2 + 44*d. What is i in w(i) = 0?
-9, -1, 1, 2
Let h(l) be the third derivative of l**5/360 - l**4/16 + 30*l**2. Suppose h(a) = 0. Calculate a.
0, 9
Let x(s) be the third derivative of -s**7/1470 + s**5/420 + 18*s**2. Find h such that x(h) = 0.
-1, 0, 1
Let y(h) be the third derivative of 0*h - 1/84*h**4 - 1/735*h**7 + 0*h**3 + 0 - 1/70*h**5 - 1/140*h**6 - 26*h**2. Factor y(c).
-2*c*(c + 1)**3/7
Let h(v) = 3 - v**3 + 5*v + 3*v**4 + 2 + 2*v**2 + 3*v**2. Let b(n) = -3*n**4 - 6*n**2 - 6*n - 6. Let g(d) = -5*b(d) - 6*h(d). Factor g(z).
-3*z**3*(z - 2)
Suppose -45*t + 38*t = -21. Let j be 4/(((-4)/3)/((-2)/t)). Factor 1/3*n**j - 2/3 + 1/3*n**4 - n + n**3.
(n - 1)*(n + 1)**2*(n + 2)/3
Factor 0 - 3/5*x - 6/5*x**2.
-3*x*(2*x + 1)/5
Let v = 31 + -27. Factor -12*j**v - 5*j**3 + 0*j**3 - 3*j**3.
-4*j**3*(3*j + 2)
Let l = -77414/39 + 1985. Let n(i) be the first derivative of -7 + 2/65*i**5 + 0*i**4 + 0*i**2 + l*i**6 + 0*i**3 + 0*i. Factor n(u).
2*u**4*(u + 1)/13
Let t(u) be the second derivative of u**6/480 - u**5/160 - 3*u**4/16 + 5*u**3/2 + 4*u. Let z(g) be the second derivative of t(g). Factor z(c).
3*(c - 3)*(c + 2)/4
Let o be 34/(-255) + 1/(45/141). Let n be (-1 - 21/(-27))*-6. Factor 0*s + 1/3*s**5 + 0*s**2 + 0 + n*s**4 + 4/3*s**o.
s**3*(s + 2)**2/3
Factor -12*j**2 - 23*j**2 - 11*j**3 + 10*j - 73*j**2 + 18 - 89*j.
-(j + 1)*(j + 9)*(11*j - 2)
Let h = -19776 - -296644/15. Let l = 1033/7860 + 1/524. Factor 2/15*r + 0 + l*r**3 + h*r**2.
2*r*(r + 1)**2/15
Let m be 18/(42/(-7)) - (-1 + -4). Let v(c) be the third derivative of 1/3*c**3 + 0*c - 1/24*c**4 + 0 - 1/60*c**5 - 9*c**m. Factor v(z).
-(z - 1)*(z + 2)
Suppose 0 = -3*p - 173 - 331. Let g be (14/p)/((-2)/8)*3. Solve -4/3*s + 1/3*s**2 + g = 0 for s.
1, 3
Let o = 10 + -10. Let q(i) = -i + 3. Let v be q(o). Factor -5*x**v + 4*x**3 + 9*x**3 + 12*x**3 + 8 + 4*x - 32*x**2.
4*(x - 1)**2*(5*x + 2)
Let g(d) = 2*d**2 - 3*d + 1. Let f(q) = 2*q**2 + 33 - q**2 - 32. Let r(l) = 3*f(l) - g(l). Solve r(k) = 0 for k.
-2, -1
Let s(i) = -1. Let m(u) = -2. Let w(a) = -2*m(a) + 3*s(a). Let y(k) = -39*k**2 + 6*k + 5. Let j(h) = 5*w(h) - y(h). Factor j(g).
3*g*(13*g - 2)
Suppose -35 = n - 38. Factor 0*c**2 - 1/6*c**n + 1/3 + 1/2*c.
-(c - 2)*(c + 1)**2/6
Let c(u) be the third derivative of 0 + 0*u**3 - 1/210*u**7 - 1/60*u**6 + 29*u**2 + 0*u**4 + 0*u**5 + 0*u. Factor c(v).
-v**3*(v + 2)
Factor -26*t - 5*t**4 - 15*t - 120*t**2 + 22*t**3 + 25*t**2 - 77*t**3 - 4*t.
-5*t*(t + 1)**2*(t + 9)
Let r(w) be the third derivative of w**9/3024 - w**8/672 - 17*w**4/24 + 28*w**2. Let n(v) be the second derivative of r(v). Factor n(o).
5*o**3*(o - 2)
Suppose -4 = -0*v - v. Factor -21*f**v - f**3 - 2*f**3 + 18*f**4.
-3*f**3*(f + 1)
Factor 2*x**2 + 100 + 3*x**2 - 1410*x + 1470*x.
5*(x + 2)*(x + 10)
Suppose 0 = -g - 4*g. Suppose -2*u + a + 7 = 4*a, 0 = 2*u + 2*a - 6. Factor u*i**4 + 2 + 5*i + g*i**2 - 5*i - 4*i**2.
2*(i - 1)**2*(i + 1)**2
Let j(o) = -o**2 + o - 3. Let l(q) = -5*q**2 + 128*q - 1329. Let m(c) = -2*j(c) + l(c). Solve m(p) = 0 for p.
21
Let v be 60 + -6 + 6 + -1. Let s = -57 + v. Find x such that 1/3*x**4 - 20/3*x - 7/3*x**3 + 8/3 + 6*x**s = 0.
1, 2
Suppose 1/4*w**3 + 0 - 3*w + w**2 = 0. Calculate w.
-6, 0, 2
Let p be 2/6*(143/(-13) + 11). Let k(i) be the first derivative of -1/8*i**4 + 0*i + 3 + p*i**3 + 1/4*i**2. Determine v so that k(v) = 0.
-1, 0, 1
Let d(m) be the first derivative of -m**4/20 - 6*m**3/5 + 42*m**2/5 - 88*m/5 - 334. Let d(n) = 0. What is n?
-22, 2
Let u(a) = 10*a**2 - 625*a - 585. Let y(v) = v**2 - 78*v - 73. Let g(m) = -3*u(m) + 25*y(m). Let g(k) = 0. What is k?
-14, -1
Let t(f) = -5*f**3 + 85*f**2 - 75*f - 185. Let w(g) = 2*g**2 - g + 1. Let d(s) = t(s) + 5*w(s). Factor d(x).
-5*(x - 18)*(x - 2)*(x + 1)
Let q(x) be the third derivative of -x**7/525 + x**6/150 + x**5/150 - x**4/30 + 56*x**2. Facto