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question:Multiply and expand the polynomials p(x) = 4x^2 + 8x + 11 and q(x) = 14 - 6x.
answer:begin{align*} p(x)q(x) &= (4x^2 + 8x + 11)(14 - 6x) &= 4x^2(14 - 6x) + 8x(14 - 6x) + 11(14 - 6x) &= 56x^2 - 24x^3 + 112x - 48x^2 + 154 - 66x &= -24x^3 + 8x^2 + 46x + 154 end{align*} Therefore, the product of p(x) and q(x) is -24x^3 + 8x^2 + 46x + 154.
question:Find the sum p(x) + q(x) of the following two polynomials: p(x) = 9x^2 - x + 1 q(x) = -2(7x^2 + 5x - 7)
answer:To find the sum, we will add the corresponding terms of both polynomials: begin{align*} p(x) + q(x) &= (9x^2 - x + 1) + (-2 cdot 7x^2 - 2 cdot 5x + 2 cdot 7) &= 9x^2 - x + 1 - 14x^2 - 10x + 14 &= (9x^2 - 14x^2) + (-x - 10x) + (1 + 14) &= -5x^2 - 11x + 15 end{align*}
question:What is the equation of a line that is perpendicular to the line y = -2x + 5 and passes through the point (-1, 2)?
answer:The given equation of a line is: {eq}y=-2x+5 {/eq}. Comparing this with {eq}y=m_1x+b {/eq}, its slope is, {eq}m_1=-2 {/eq}. The slope of the line that is perpendicular to the given line is, {eq}m= dfrac{1}{2} {/eq}. Also, this line passes through a point {eq}(x_1, y_1)=(-1, 2) {/eq}. Its equation is found using: y-y_1=m(x-x_1) y-2=dfrac{1}{2} (x-(-1)) y-2= dfrac{1}{2}x + dfrac{1}{2} text{Adding 2 on both sides}, boxed{mathbf{y= dfrac{1}{2} x + dfrac{5}{2}}}
question:Convert 10 × 3 tens into its unit form and standard form.
answer:In unit form, 10 × 3 tens is 300 units. In standard form, it is written as 30.